chemistry

Acid-base and electrochemical relations:
  pH                     -log[H+];  pOH = -log[OH-];  pH + pOH = 14 at 25 C
  weak acid              Ka = [H+][A-]/[HA];  pKa = -log Ka
  Henderson-Hasselbalch  pH = pKa + log([A-]/[HA])
  buffer capacity        maximal when pH = pKa;  effective within about +/- 1 unit
  titration equivalence  strong-strong at pH 7; weak acid-strong base above 7
  half-equivalence       pH = pKa;  the practical way to measure pKa
  oxidation              loss of electrons, increase in oxidation number
  reduction              gain of electrons, decrease in oxidation number
  cell potential         E_cell = E_cathode - E_anode;  positive means spontaneous
  Nernst equation        E = E0 - (RT/nF) ln Q
  Faraday relation       moles of electrons = It / F;  F = 96485 C/mol
  free energy link       dG = -nFE


chemistry

Equilibrium, Acids, and Electrochemistry

Buffers resist pH change and are the reason biological systems function, since enzymes
operate over narrow pH ranges. A buffer is a weak acid with its conjugate base in
comparable amounts; added acid is consumed by the base component and added base by the
acid component. The Henderson-Hasselbalch equation shows that pH depends on the ratio
rather than the absolute concentrations, which is why dilution barely changes buffer pH
while it does reduce capacity. Blood is buffered principally by the bicarbonate system,
coupled to respiration — which allows the body to adjust pH by changing breathing rate,
an unusually direct link between a physiological control and a chemical equilibrium.


chemistry

Electrochemistry connects chemical and electrical energy. In a galvanic cell a
spontaneous redox reaction drives current, with oxidation at the anode and reduction at
the cathode. In electrolysis an applied potential drives a non-spontaneous reaction. The
standard reduction potential table ranks species by their tendency to be reduced, and the
cell potential is the difference between the two half-reactions. Because potentials are
intensive, they are not multiplied by stoichiometric coefficients when combining half
reactions — a frequent error — though the free energy, being extensive, does scale with
the electron count through dG = -nFE.


chemistry

## Organic Chemistry

Organic chemistry is the chemistry of carbon, and carbon's dominance follows from its
four valence electrons, its ability to form stable bonds to itself in chains and rings of
unlimited length, and the comparable strength of its bonds to hydrogen, oxygen, nitrogen,
and the halogens. Silicon, directly below carbon, forms far weaker bonds to itself and
cannot support the same structural diversity, which is the chemical basis for expecting
carbon-based rather than silicon-based life.


chemistry

Functional groups organize the field. A functional group is a specific arrangement of
atoms conferring characteristic reactivity, and the value of the concept is that a given
group behaves similarly regardless of the rest of the molecule. Learning perhaps a dozen
groups and their characteristic transformations covers most of introductory organic
chemistry, and the systematic naming conventions follow from identifying the parent
chain, the principal functional group, and the substituents.


chemistry

Functional groups by increasing oxidation state of carbon:
  alkane        C-C, C-H only; unreactive, combustion and radical halogenation
  alkene        C=C; addition reactions, Markovnikov orientation
  alkyne        C-C triple bond; addition, acidic terminal hydrogen
  alcohol       C-OH; hydrogen bonding, oxidation to carbonyl
  ether         C-O-C; unreactive, common solvent
  amine         C-N; basic, nucleophilic
  aldehyde      CHO at chain end; readily oxidized
  ketone        C=O within chain; resistant to further oxidation
  carboxylic acid  COOH; acidic, pKa ~4-5
  ester         COOR; from acid plus alcohol, hydrolyzable
  amide         CONR2; the peptide bond, unusually stable
  aromatic      delocalized ring; substitution rather than addition


chemistry

Isomerism is where organic structure becomes subtle. Constitutional isomers differ in
connectivity. Stereoisomers share connectivity and differ in spatial arrangement:
geometric isomers (cis and trans across a double bond or ring) and optical isomers
(enantiomers, non-superimposable mirror images arising from a carbon with four different
substituents). Enantiomers have identical physical properties except for the direction
they rotate polarized light, and identical chemical properties except toward other chiral
molecules — which is the entire issue in pharmacology, since biological receptors are
chiral and typically bind one enantiomer while the other is inactive or harmful.


chemistry

Reaction mechanisms explain transformations in terms of electron movement, conventionally
drawn with curved arrows from electron source to electron sink. The major mechanistic
families are nucleophilic substitution (SN1 through a carbocation intermediate with
racemization, SN2 in one concerted step with inversion of configuration), elimination
(E1 and E2, competing with substitution and favoured by heat and strong bulky bases),
addition to multiple bonds, and radical chains. Predicting which pathway dominates
requires weighing substrate structure, nucleophile strength, leaving group ability, and
solvent — tertiary substrates with weak nucleophiles in polar protic solvents favour SN1,
primary substrates with strong nucleophiles in polar aprotic solvents favour SN2, and
recognizing that pattern converts a great deal of apparent memorization into reasoning.


climate_science

## The Planetary Energy Balance

Earth's climate is fundamentally an energy balance problem. Solar radiation arrives,
some is reflected, the rest is absorbed and eventually re-emitted as infrared. When
incoming and outgoing energy balance, temperature is steady; when they do not, the system
gains or loses heat until a new balance is reached.


climate_science

The arithmetic is straightforward. The solar constant at Earth's distance is about 1361
watts per square metre, intercepted over a disc of the planet's cross-sectional area and
distributed over the whole sphere, giving 340 watts per square metre averaged globally.
About 30 percent is reflected by clouds, aerosols, ice, and the surface — the planetary
albedo — leaving roughly 240 watts per square metre absorbed. Setting that equal to
blackbody emission gives an effective temperature of about 255 kelvin, or minus 18 degrees
Celsius.


climate_science

The observed global mean surface temperature is about 15 degrees Celsius, some 33 degrees
warmer. That difference is the greenhouse effect, and its existence is not in dispute by
anyone: without it the planet would be frozen. The scientific questions concern its
magnitude under changed composition, the feedbacks that amplify or damp the response, and
the regional and temporal distribution of the consequences.


climate_science

Energy balance quantities:
  solar constant           ~1361 W/m^2 at the top of the atmosphere
  global mean insolation   ~340 W/m^2 (divided by 4 for sphere vs disc)
  planetary albedo         ~0.30
  absorbed shortwave       ~240 W/m^2
  effective temperature    255 K from Stefan-Boltzmann
  observed surface mean    ~288 K
  greenhouse warming       ~33 K
  current imbalance        ~+0.9 W/m^2 measured; energy accumulating
  ocean heat uptake        >90% of the excess energy goes into the ocean
  CO2 doubling forcing     ~3.7 W/m^2


climate_science

The measured top-of-atmosphere energy imbalance is the single most direct evidence that
the system is out of equilibrium. Satellite radiometry combined with ocean heat content
measurements from autonomous floats shows the planet absorbing roughly 0.9 watts per square
metre more than it emits. That is a small number relative to 340, and integrated over the
Earth's surface and over years it is an enormous amount of energy — the equivalent of
several Hiroshima-scale detonations per second, more than 90 percent of which is going into
the ocean rather than the atmosphere. This is why ocean heat content is a better metric of
the energy imbalance than surface air temperature, which is noisy and reflects a small
fraction of the total.


climate_science

Q: Earth's effective radiating temperature is 255 K while its surface averages 288 K.
This difference is because:
A. The Sun's output has increased
B. Greenhouse gases absorb outgoing infrared and re-emit, raising the altitude of effective
   emission to space and warming everything below
C. The atmosphere generates heat
D. Albedo has decreased
Reasoning: The effective temperature is the temperature at which the planet radiates to
space. Greenhouse gases are largely transparent to incoming visible light and opaque to
outgoing infrared, so radiation to space occurs from high, cold layers rather than the
surface. Since the atmosphere cools with altitude and the emission level must be at 255 K to
balance, the surface below is correspondingly warmer. Answer: B.


climate_science

## Greenhouse Physics and Radiative Forcing

A greenhouse gas is one that absorbs and emits infrared radiation, which requires a
molecule with a dipole moment that changes during vibration. Diatomic molecules of
identical atoms — nitrogen and oxygen, which together are 99 percent of the atmosphere —
have no such mode and are therefore transparent to infrared. Water vapour, carbon dioxide,
methane, nitrous oxide, and ozone all do absorb, which is why trace gases can dominate the
planet's radiative properties.


climate_science

The mechanism is often described loosely as heat being trapped, and the more accurate
framing is about emission altitude. Adding greenhouse gas makes the atmosphere more opaque
in the relevant infrared bands, so photons escaping to space are emitted from higher in the
atmosphere. Because temperature decreases with altitude in the troposphere, that higher
emission level is colder and radiates less, creating an imbalance. The surface and
troposphere then warm until the emission level, still at higher altitude, has warmed enough
to restore balance.


climate_science

Radiative forcing quantifies the imbalance a perturbation causes before the climate
responds, measured in watts per square metre. Doubling carbon dioxide produces about 3.7
watts per square metre. The relationship is logarithmic rather than linear — each doubling
adds roughly the same forcing — because the strongest absorption bands become saturated at
the centre and additional absorption occurs in the band wings. This logarithmic dependence
means the forcing does not run away with concentration, and it also means that reducing
concentration from a high level buys back less than adding it cost.


climate_science

Greenhouse gases and their properties:
  water vapour     the strongest greenhouse gas; a feedback, not a forcing, since
                   its concentration is set by temperature and its residence time
                   is days
  carbon dioxide   the dominant anthropogenic forcing; extremely long-lived, with
                   a substantial fraction persisting for millennia
  methane          ~80x CO2 potency over 20 years, ~28x over 100; ~12 year
                   lifetime, so cuts act fast
  nitrous oxide    ~270x CO2 over 100 years; ~115 year lifetime; mainly
                   agricultural
  halocarbons      thousands of times more potent per molecule; regulated under
                   the Montreal Protocol, which also proved a large climate benefit
  ozone            tropospheric ozone warms; stratospheric ozone loss cools
  aerosols         mostly cooling, by scattering sunlight and seeding clouds;
                   short-lived, regionally concentrated, and the largest source of
                   uncertainty in the total forcing
  forcing of 2xCO2 ~3.7 W/m^2
  logarithmic law  forcing ≈ 5.35 ln(C/C0) W/m^2


climate_science

The distinction between a forcing and a feedback is essential and is where a common
argument goes wrong. Water vapour is indeed the largest contributor to the natural
greenhouse effect, and it is not a driver of change, because its atmospheric concentration
is controlled by temperature through the Clausius-Clapeyron relation and its residence time
is about nine days. Adding water vapour to the atmosphere does nothing lasting; it rains
out. Adding carbon dioxide raises temperature, which raises the equilibrium water vapour
content, which amplifies the warming — water vapour acts as a feedback multiplying whatever
forcing is applied rather than as an independent cause.


climate_science

## The Carbon Cycle

Carbon moves between reservoirs — atmosphere, ocean, land biosphere, soils, rocks — on
timescales spanning years to millions of years. The fast cycle exchanges enormous fluxes:
photosynthesis and respiration each move roughly 120 gigatonnes of carbon per year, and
ocean-atmosphere exchange moves about 80, against an atmospheric stock of around 875
gigatonnes. Human emissions of roughly 10 gigatonnes per year are small against those
gross fluxes and are not balanced by an offsetting return flux, which is why they
accumulate.


climate_science

About half of anthropogenic emissions remain in the atmosphere; the ocean absorbs roughly a
quarter and the land biosphere roughly a quarter. These sinks are services performed at a
cost: ocean uptake acidifies seawater, with surface pH having fallen about 0.1 units since
preindustrial times, a 30 percent increase in hydrogen ion concentration, with direct
consequences for organisms building calcium carbonate structures. Land uptake depends on
ecosystems whose future behaviour under warming and drought is uncertain, and there is
evidence that sink efficiency is declining.


climate_science

Carbon dioxide's atmospheric lifetime is frequently misstated because it is not a simple
exponential. An individual molecule exchanges out of the atmosphere within a few years, but
the perturbation to atmospheric concentration decays much more slowly, because the removed
carbon largely enters the ocean surface which then re-equilibrates. Roughly half of an
emission pulse is gone within a few decades, a quarter persists for centuries, and something
like ten to twenty percent remains for tens of thousands of years until silicate weathering
removes it. This long tail is why cumulative emissions rather than emission rate determine
peak warming.


climate_science

Carbon cycle numbers:
  preindustrial CO2      ~278 ppm
  current CO2            >420 ppm and rising ~2.5 ppm/yr
  atmospheric stock      ~875 GtC (2.13 GtC per ppm)
  annual emissions       ~10 GtC (~37 Gt CO2) from fossil fuels and land use
  airborne fraction      ~45%
  ocean sink             ~25%; causes acidification
  land sink              ~30%; uncertain and possibly weakening
  ocean pH change        -0.1 units since preindustrial (~30% more H+)
  permafrost carbon      ~1400 GtC, roughly twice the atmospheric stock
  transient response     ~1.65 C per 1000 GtC cumulative emissions


climate_science

The near-linear relationship between cumulative emissions and warming is one of the more
useful results in the field. Because carbon dioxide's long residence time and the ocean's
thermal inertia happen to offset each other, peak warming is approximately proportional to
total carbon emitted regardless of the emission pathway. This produces the carbon budget
framing: a given temperature target corresponds to a total quantity of carbon that can be
emitted, and once it is spent, the target requires net zero emissions. It also means that
stabilizing temperature requires net zero rather than merely reduced emissions, which is a
frequently misunderstood point — cutting emissions in half slows the accumulation without
stopping the warming.


climate_science

## Feedbacks and Climate Sensitivity

Climate sensitivity is the equilibrium warming resulting from a doubling of carbon
dioxide, and it is the single most consequential number in the field. The direct radiative
effect alone would produce about 1.2 degrees; feedbacks amplify this substantially. Current
assessment places the likely range at 2.5 to 4 degrees with a best estimate around 3, a
range that has narrowed only modestly over decades because the dominant uncertainty is
clouds.


climate_science

The feedbacks are individually well characterized in sign if not in magnitude. Water vapour
is strongly positive: warmer air holds more moisture at about 7 percent per degree, and
water vapour is a greenhouse gas. The lapse rate feedback is negative, because warming aloft
exceeds surface warming in the tropics, increasing emission to space. Surface albedo is
positive: melting ice and snow expose darker ocean and land, absorbing more sunlight, and
this is amplified at high latitudes, producing Arctic warming at roughly three times the
global rate. Clouds are the problem: they both reflect sunlight (cooling) and trap infrared
(warming), and which dominates depends on altitude, thickness, and phase, so the net cloud
feedback has been the largest uncertainty since the beginning.


climate_science

Feedback inventory:
  water vapour       strongly positive; roughly doubles the direct forcing
  lapse rate         negative; partially offsets the water vapour feedback
  combined WV+LR     positive, and better constrained together than separately
  surface albedo     positive; ice-albedo, strongest in the Arctic
  cloud              net positive by current assessment, largest uncertainty;
                     low clouds cool, high thin clouds warm
  Planck response    the fundamental negative feedback; a warmer planet radiates
                     more, which is what makes the system stable at all
  carbon cycle       positive; warming reduces sink efficiency
  permafrost         positive; thaw releases CO2 and methane
  ocean circulation  uncertain sign; changes to overturning redistribute heat


climate_science

Tipping elements are components of the system that may pass thresholds beyond which change
becomes self-sustaining and effectively irreversible on human timescales. The candidates
include the Greenland and West Antarctic ice sheets, whose loss would raise sea level by
metres over centuries; Atlantic overturning circulation, whose slowdown would substantially
alter European and tropical climate; Amazon forest dieback converting a sink into a source;
and widespread permafrost thaw. Confidence in specific thresholds is low, and their
existence is well established in paleoclimate records — the system has undergone abrupt
reorganizations before, which is the principal reason for concern about them.


climate_science

## Observations, Paleoclimate, and Models

The observational record rests on multiple independent lines that agree. Surface
thermometers extend back to the mid-nineteenth century, with careful treatment of station
moves, instrument changes, and urban heat effects; several groups process the raw data
independently with different methods and obtain closely matching results. Satellite
measurements provide global coverage since 1979. Ocean heat content from floats gives the
best measure of the energy imbalance. Sea level rise is measured by tide gauges and
altimetry. Ice sheet mass loss is measured by satellite gravimetry. Glacier retreat, sea
ice decline, and shifts in the timing of biological events all corroborate.


climate_science

Paleoclimate reconstruction extends the record using proxies. Ice cores from Antarctica and
Greenland trap air bubbles giving direct measurements of past atmospheric composition back
800,000 years, alongside isotopic temperature proxies. Ocean sediment cores give
temperature and ice volume over millions of years. Tree rings, corals, speleothems, and
pollen assemblages fill in regional detail. These records establish that the current carbon
dioxide concentration is higher than at any point in at least the last 800,000 years and
probably several million, and that the current rate of increase is roughly a hundred times
faster than the fastest natural change in the ice core record.


climate_science

Attribution — determining what caused observed change — uses fingerprinting. Different
forcings produce distinct spatial and temporal patterns, and the observed pattern matches
greenhouse forcing rather than the alternatives. Greenhouse warming warms the troposphere
while cooling the stratosphere; increased solar output would warm both. Greenhouse warming
produces more warming at night than during the day, and more in winter than summer. Solar
output has been flat or slightly declining since the 1980s while temperature has risen.
Each of these is an independent discriminating test.


climate_science

Model types and their roles:
  energy balance models      simple, transparent, useful for understanding the
                             basic physics
  general circulation models fluid dynamics on a rotating sphere with radiation,
                             convection, and surface processes
  Earth system models        GCMs plus interactive carbon cycle, chemistry,
                             vegetation, ice sheets
  parameterization           sub-grid processes — clouds, convection, turbulence —
                             represented statistically; the main source of
                             inter-model spread
  ensembles                  many models and many initial conditions; the spread
                             is an uncertainty estimate, not a range of opinion
  hindcast validation        models are tested against past climate they were not
                             tuned on, including volcanic eruption responses
  emergent constraints       observable present-day quantities that correlate with
                             model sensitivity, used to narrow projections


climate_science

Model evaluation deserves comment because model skill is often questioned in general terms
rather than assessed. Projections made in the 1970s through 1990s can now be compared
against what happened, and when adjusted for the actual emissions that occurred rather than
the scenarios assumed, most were skillful. Models reproduce the observed response to
volcanic eruptions, which are natural experiments applying a known forcing over a known
period. They reproduce the vertical structure of warming, the seasonal cycle, and
paleoclimate states with different configurations. They remain weak at regional detail,
precipitation extremes, and clouds — which is precisely where their published uncertainty is
largest, indicating that the uncertainties are being reported honestly rather than
concealed.


climate_science

[user] How much of recent warming is human-caused versus natural? What's the actual
evidence?
[assistant] tool_call climate.attribution({"period": "1850-2020",
"observed_warming_c": 1.1, "forcings": ["ghg", "aerosol", "solar", "volcanic",
"internal_variability"]})
[tool] {"ghg_contribution_c": [1.0, 2.0], "aerosol_contribution_c": [-0.8, 0.0],
"solar_contribution_c": [-0.1, 0.1], "volcanic_contribution_c": [-0.1, 0.1],
"internal_variability_c": [-0.2, 0.2], "net_anthropogenic_c": [0.8, 1.3],
"observed_c": 1.1, "best_estimate_human_share": 1.0}
[assistant] The best estimate is that essentially all of it is human-caused — the central
estimate for the human contribution equals the observed 1.1 degrees, and natural factors
net to approximately zero.


climate_science

The reason that sounds surprising is that the greenhouse contribution alone is assessed at
1.0 to 2.0 degrees, more than the observed warming. Aerosols, mostly from the same fossil
fuel combustion, have masked part of it by reflecting sunlight, contributing between minus
0.8 and zero. The net anthropogenic effect is 0.8 to 1.3 degrees, and the observed 1.1 sits
squarely in that range. This is also why air quality improvements produce a warming
commitment that was previously being offset.


climate_science

Natural factors cannot account for it. Solar output has been flat to slightly declining
since the 1980s while temperature rose sharply, so the sign is wrong. Volcanic activity
produces brief cooling episodes, not sustained warming. Internal variability — ocean
oscillations such as ENSO — redistributes heat between ocean and atmosphere and does not
add energy to the system, so it produces year-to-year noise around a trend rather than a
trend, and its contribution over 170 years is bounded at a couple of tenths.


climate_science

The discriminating evidence that makes this more than a process of elimination is the
pattern. Greenhouse warming makes a specific prediction: the troposphere warms while the
stratosphere cools, because more infrared is absorbed below and less reaches the layers
above. Increased solar input would warm both. The stratosphere has cooled, measured by
satellite since 1979. Additional independent fingerprints all match: nights warm faster than
days, winters faster than summers, the Arctic faster than the tropics, and the isotopic
signature of atmospheric carbon shows the added carbon is depleted in carbon-13 and
carbon-14 exactly as fossil carbon is.


climate_science

Each of those is a test that could have come out otherwise and did not.


climate_science

## Impacts and Response

Warming is not the impact; it is the driver of impacts, which are distributed unevenly and
are largely nonlinear. Heat extremes increase disproportionately with mean temperature
because they occur in the tail of a distribution — a modest shift in the mean produces a
large multiplication in the frequency of what were rare extremes. A warmer atmosphere holds
more moisture, intensifying heavy precipitation while also increasing evaporative demand and
therefore drought severity in dry periods. Sea level rises from thermal expansion and ice
loss, with the commitment extending centuries beyond stabilization because ice sheets
respond slowly.


climate_science

Ecosystem impacts include range shifts toward poles and higher elevations, mismatches
between interdependent species whose seasonal timing responds differently, coral bleaching
from marine heatwaves compounded by acidification, and elevated extinction risk for species
unable to move or adapt fast enough. Agricultural effects are regionally mixed but net
negative at higher warming levels, with carbon dioxide fertilization providing some benefit
offset by heat stress, water limitation, and reduced nutritional content.


climate_science

Response divides into mitigation, reducing emissions, and adaptation, reducing vulnerability
to what occurs. Both are necessary: some warming is already committed by past emissions and
requires adaptation, and unmitigated warming would eventually exceed any plausible adaptive
capacity.


climate_science

Mitigation approaches by sector and maturity:
  electricity        the most advanced; solar and wind are now the cheapest new
                     generation in most markets, with storage and grid flexibility
                     the remaining challenge
  transport          electrification is proven for light vehicles; aviation and
                     shipping need fuels rather than batteries
  buildings          heat pumps, efficiency, electrification; a large near-term
                     opportunity with a favourable cost profile
  industry           the hardest sector; cement and steel emit chemically, not just
                     from energy, requiring process change or capture
  agriculture        methane from livestock and rice, nitrous oxide from
                     fertilizer; diffuse and hard to regulate
  land use           halting deforestation and restoring ecosystems; large,
                     cheap, and difficult to make permanent and verifiable
  carbon removal     necessary for residual emissions and overshoot; currently
                     expensive and at negligible scale
  geoengineering     solar radiation management is fast and cheap and addresses
                     none of the causes, carries poorly understood risks, and
                     raises acute governance problems


climate_science

The economics have shifted substantially and unevenly. Solar photovoltaic costs fell by
roughly ninety percent over a decade and batteries similarly, making decarbonized
electricity the low-cost option rather than a premium one across most of the world. That
does not extend to the harder sectors, and the remaining difficulty is concentrated in
industrial heat, chemical process emissions, aviation, shipping, and agriculture. The
framing that the problem is either solved or hopeless misrepresents a situation in which
some parts have become straightforward and others have not, and where the binding
constraints are increasingly institutional — permitting, transmission, capital allocation,
and coordination — rather than technological.


ecology

## Population Ecology

Population ecology studies how numbers of organisms change, and the two baseline models
frame everything that follows. Exponential growth occurs when per-capita birth and death rates
are constant, producing growth proportional to current size and therefore unbounded increase.
It describes real populations only briefly — during colonization of new habitat, or recovery
from a crash — because resources are finite.


ecology

Logistic growth introduces a carrying capacity at which growth stops, with the per-capita
rate declining linearly as the population approaches it. This produces the sigmoid curve
familiar from textbooks and is a substantial idealization: carrying capacity is not a fixed
property of an environment but varies with conditions, resource availability, and the
population's own effects on its habitat. Its value is as a null model against which real
dynamics are compared, not as a description.


ecology

Real populations exhibit dynamics the simple models do not predict. Time lags between
population size and its regulatory effect produce oscillations and overshoot, because the
population continues growing past carrying capacity before the feedback takes effect. Discrete
generations with strong density dependence produce cycles and, at high growth rates, chaos —
the logistic map's period-doubling route to chaos was discovered in exactly this ecological
context. Stochasticity matters disproportionately at small population size, where random
variation in births and deaths can drive extinction regardless of average conditions, which
is the demographic basis for minimum viable population sizes.


ecology

Population concepts:
  exponential growth     dN/dt = rN;  unbounded, brief in practice
  logistic growth        dN/dt = rN(1 - N/K);  sigmoid, carrying capacity K
  intrinsic rate r       maximum per-capita growth under ideal conditions
  carrying capacity K    variable, not a fixed environmental constant
  density dependence     regulation through competition, disease, predation
  density independence   weather, disturbance; affects rate regardless of density
  r-selected             high fecundity, low survival, early reproduction; favoured
                         in variable or disturbed environments
  K-selected             low fecundity, high investment, late reproduction;
                         favoured in stable saturated environments
  life table             age-specific survival and fecundity; the demographic core
  metapopulation         subpopulations linked by dispersal; local extinction and
                         recolonization
  source-sink            productive patches exporting individuals to patches where
                         mortality exceeds reproduction
  Allee effect           reduced per-capita growth at low density; mate-finding,
                         group defence, cooperative foraging
  minimum viable pop.    the size below which stochastic extinction becomes likely


ecology

The Allee effect deserves emphasis because it inverts the usual expectation and has direct
conservation consequences. Standard density dependence means small populations grow fastest,
which would make recovery from low numbers easy. Where individuals depend on each other — for
finding mates, for cooperative hunting, for predator dilution, for maintaining a modified
habitat — per-capita growth falls at low density instead, creating a threshold below which the
population declines to extinction regardless of protection. The passenger pigeon's collapse
from billions to zero is the standard example, and it explains why some species fail to
recover after harvesting stops.


ecology

Q: A conservation programme protects a species whose population has fallen to a few dozen
individuals, and the population continues to decline despite complete protection from its
former threat. The most likely ecological explanation is:
A. The carrying capacity fell
B. An Allee effect, in which per-capita growth is reduced at very low density
C. Exponential decay
D. Density dependence
Reasoning: Removing the original threat should permit growth under ordinary density
dependence, since small populations face least competition. Continued decline suggests
per-capita growth is negative at low density, which is the Allee effect — from difficulty
finding mates, loss of cooperative behaviours, or inbreeding depression. Answer: B.


ecology

## Species Interactions

Interactions between species are classified by their effect on each participant, and the
classification is useful because the dynamics differ systematically. Competition harms both.
Predation, parasitism, and herbivory benefit one at the other's expense. Mutualism benefits
both. Commensalism benefits one and is neutral for the other, and genuine examples are rarer
than casual classification suggests, since most apparently neutral relationships turn out to
have small costs or benefits when measured.


ecology

The competitive exclusion principle states that two species competing for exactly the same
limiting resource cannot coexist indefinitely — the better competitor excludes the other. Its
apparent contradiction by the enormous diversity of coexisting species is resolved by niche
differentiation: species partition resources by type, by space, by time, or by size, so they
are not in fact competing for an identical resource. Character displacement, where
coexisting species diverge in traits more than allopatric populations do, is the evolutionary
signature of this partitioning.


ecology

Predator-prey dynamics generate cycles under simple assumptions, with the predator population
lagging the prey by a quarter cycle. The classic lynx and hare data from fur trading records
show this pattern, though the interpretation is complicated by the fact that the hare cycle
appears in areas without lynx, indicating that vegetation and other factors contribute. This
is a general caution about the field: the mechanism that a simple model attributes a pattern
to is frequently one among several, and demonstrating which operates requires manipulation
rather than correlation.


ecology

Interaction types and dynamics:
  competition            -/-;  interference or exploitation
  competitive exclusion  identical niches cannot coexist stably
  niche partitioning     resource, spatial, temporal differentiation
  character displacement evolutionary divergence where species co-occur
  predation              +/-;  can generate cycles with a lag
  functional response    predation rate versus prey density; saturating, and the
                         sigmoid type can stabilize prey at low density
  parasitism             +/-;  the parasite generally does not kill the host
  parasitoid             kills the host; important in biological control
  mutualism              +/+;  pollination, mycorrhizae, gut microbiota
  obligate vs facultative  whether the partner is required
  cheating               mutualisms are exploitable and require enforcement or
                         partner choice to persist
  keystone species       an effect on the community disproportionate to abundance
  ecosystem engineer     modifies the physical habitat; beavers, corals, trees
  trophic cascade        predator effects propagating down through multiple levels


ecology

Keystone species and trophic cascades are the ideas with the widest reach outside ecology.
Removing a top predator releases its prey, which then over-exploits the next level down,
altering the community structure far beyond the direct interaction. Sea otter removal allowed
sea urchin populations to explode and eliminate kelp forests; wolf reintroduction in
Yellowstone altered elk browsing behaviour and, through that, riparian vegetation and stream
morphology. The size of these effects has sometimes been overstated in popular accounts,
which attribute to a single reintroduction changes that had multiple causes, and the general
phenomenon of top-down regulation is nonetheless well established.


ecology

## Communities and Ecosystems

A community is the set of interacting species in an area, and its structure is described by
species richness — the count — and evenness — how equally abundance is distributed. Diversity
indices combine both, and the choice among them matters because they weight rarity
differently: richness counts every species equally regardless of abundance, Shannon diversity
weights by log abundance, and Simpson diversity is dominated by the common species.
Conclusions about whether diversity increased or decreased can depend on which index is used.


ecology

Species-area relationships hold with remarkable generality: the number of species increases
with area following a power law with an exponent typically between 0.15 and 0.35. The
practical consequence is the basis of much conservation planning — reducing habitat area to
ten percent of its original extent is expected to retain roughly half of the species, not ten
percent. Island biogeography theory explains the pattern as a balance between immigration,
which decreases with isolation, and extinction, which decreases with area, and the theory
applies to habitat fragments as well as literal islands.


ecology

Ecosystems add the abiotic environment and focus on energy flow and material cycling. The
foundational asymmetry is that energy flows through while matter cycles: energy enters as
sunlight, is captured by primary producers, passes up trophic levels with large losses, and
leaves as heat, never to be reused. Matter, by contrast, is repeatedly recycled through
organisms, soil, water, and atmosphere.


ecology

Community and ecosystem structure:
  species richness       the count of species
  evenness               how equally abundance is distributed
  Shannon / Simpson      diversity indices weighting rarity differently
  species-area curve     S = cA^z, z typically 0.15-0.35
  island biogeography    immigration versus extinction; area and isolation
  trophic level          producer, primary consumer, secondary, tertiary
  ecological efficiency  ~10% of energy transferred per level, with wide variation
  food chain length      limited by energy loss; rarely exceeds four or five levels
  food web               the realistic network; most consumers feed at several levels
  primary production     GPP is total photosynthesis, NPP is GPP minus plant
                         respiration; NPP is what supports everything above
  biomass pyramid        can be inverted in aquatic systems, where fast-turnover
                         phytoplankton support a larger standing crop of consumers
  decomposers            return nutrients; without them, nutrients would be locked
                         in dead biomass and productivity would cease


ecology

The roughly ten percent transfer efficiency between trophic levels is the quantity with the
broadest consequences. Most energy at each level is lost to respiration, to unconsumed
biomass, and to indigestible material, so the energy available to support each successive
level falls by an order of magnitude. This limits food chain length, explains why top
predators are rare and require large territories, and underlies the arithmetic of human diet:
producing a given quantity of animal protein requires roughly an order of magnitude more
primary production than producing the equivalent plant protein, which is why land use and
agricultural emissions depend so strongly on dietary composition.


ecology

## Biogeochemical Cycles

Nutrients cycle between organisms and the environment, and the cycles differ in whether they
have a substantial atmospheric phase, which determines how quickly they equilibrate globally
and how susceptible they are to human perturbation.


ecology

The carbon cycle exchanges enormous fluxes between atmosphere, ocean, land biosphere, and
soils on annual timescales, and much smaller fluxes with rocks and fossil deposits over
geological time. Human extraction and combustion of fossil carbon transfers material from the
slow reservoir into the fast one at a rate the fast cycle cannot absorb, which is why
atmospheric concentration rises despite the ocean and land taking up roughly half the
emissions.


ecology

The nitrogen cycle is limited by a chemical barrier: atmospheric nitrogen is abundant and
inert, held by a triple bond that most organisms cannot break. Nitrogen fixation by bacteria,
some free-living and some symbiotic with legumes, converts it to biologically usable forms,
and this was the rate-limiting step for terrestrial productivity through most of Earth's
history. Industrial fixation by the Haber-Bosch process now roughly doubles the natural rate,
which supports a large fraction of the human population and produces the excess nitrogen that
causes eutrophication and nitrous oxide emissions.


ecology

Cycle characteristics:
  carbon           fast biological exchange, slow geological; fossil combustion
                   moves the slow reservoir into the fast one
  nitrogen         atmospheric N2 is inert; fixation is the bottleneck
  Haber-Bosch      industrial fixation roughly doubles the natural rate
  nitrification    ammonia to nitrite to nitrate, by bacteria
  denitrification  nitrate back to N2; returns nitrogen to the atmosphere
  phosphorus       no atmospheric phase; weathering to soil to organism to
                   sediment; effectively one-way on human timescales
  eutrophication   nutrient enrichment causing algal blooms, then decomposition
                   consuming oxygen, then hypoxic dead zones
  limiting nutrient  usually phosphorus in freshwater, nitrogen in marine systems
  water cycle      evaporation, transpiration, precipitation, runoff
  sulfur           volcanic and biological; acid deposition when combined with
                   fossil combustion
  residence time   how long an atom stays in a reservoir; determines how fast a
                   perturbation propagates


ecology

Phosphorus deserves particular attention because its cycle has no atmospheric phase, which
makes it fundamentally different from carbon and nitrogen. It enters ecosystems only by rock
weathering, cycles through organisms, and is eventually lost to ocean sediments where it is
unavailable until tectonic uplift returns it over millions of years. There is no biological or
industrial process that returns phosphorus from the ocean to land at scale. Phosphate rock is
therefore a genuinely finite resource on human timescales, and the fraction of mined phosphorus
that reaches the ocean through agricultural runoff is permanently lost — a resource question
distinct from the pollution question that the same runoff creates.


ecology

## Disturbance, Succession, and Conservation

Disturbance is any event that removes biomass and creates opportunity, from fire and flood to
windthrow and grazing. Succession is the sequence of community change that follows. Primary
succession begins on newly exposed substrate with no soil and proceeds slowly, since soil
formation is the rate-limiting step. Secondary succession follows a disturbance that left soil
intact and proceeds much faster, which is why an abandoned field reforests in decades while a
new lava flow takes centuries.


ecology

The intermediate disturbance hypothesis proposes that diversity peaks at intermediate
frequency and intensity of disturbance: too little allows competitive dominants to exclude
others, and too much permits only rapid colonizers. The hypothesis is intuitive, has empirical
support in some systems, and has been substantially criticized as not general — a useful case
study in the difference between a memorable idea and an established one.


ecology

The recognition that disturbance is a normal component of ecosystems rather than a departure
from a stable state changed management practice fundamentally. Fire suppression in
fire-adapted systems allows fuel accumulation that eventually produces catastrophic fires
far outside the historical range, and it eliminates the species that depend on periodic
burning. Managing for a fixed target state is generally less successful than managing for the
processes that maintain the system.


ecology

Disturbance, threats, and response:
  primary succession     on new substrate; soil formation limits the rate
  secondary succession   after disturbance with soil intact; much faster
  pioneer species        fast-colonizing, short-lived, high dispersal
  climax community       the historical framing; now understood as one of several
                         possible states rather than a fixed endpoint
  alternative stable states  a system can occupy more than one configuration under
                         identical conditions; shifts can be abrupt and hard to
                         reverse
  hysteresis             reversing the driver does not reverse the state
  resilience             capacity to absorb disturbance and retain function
  habitat loss           the leading cause of extinction, by a wide margin
  fragmentation          reduces effective area, increases edge, blocks dispersal
  invasive species       released from natural enemies; the second leading cause
  overexploitation       harvesting exceeding replacement
  climate change         range shifts, phenological mismatch, ocean acidification
  extinction debt        species committed to extinction by past habitat loss but
                         not yet gone; current diversity overstates future


ecology

Extinction debt is the concept most likely to mislead assessment of conservation status.
After habitat is reduced, the species that the remaining area cannot support do not disappear
immediately — long-lived individuals persist, populations decline gradually, and the new
equilibrium is reached over decades to centuries. A fragmented landscape therefore contains
species that are functionally already lost, and a survey showing they are present overstates
the conservation outcome. The corresponding hopeful case is that intervention during that
window can prevent the debt from being paid, which is a stronger argument for acting early
than the current species list would suggest.


ecology

Ecosystem services frame the practical case for conservation in terms that decision-makers
weigh: provisioning services such as food and timber, regulating services such as pollination,
water purification, flood control, and carbon storage, and cultural services. The framing is
useful for making otherwise invisible values explicit and it carries a genuine risk, which is
that it implies anything without a quantified service value is expendable. Both the
instrumental argument and the case that species have value independent of use are available,
and treating the economic framing as the only legitimate one concedes more than the evidence
requires.


environmental_science

## Biogeochemical Cycles and System Framing

Environmental science studies the interaction between human activity and natural systems, and its
characteristic analytical move is to follow a substance through its reservoirs and fluxes. Carbon,
nitrogen, phosphorus, sulfur, and water each cycle between the atmosphere, oceans, land, and
biosphere at rates that human activity has altered substantially, and the alteration is quantifiable
by comparing anthropogenic fluxes against natural ones.


environmental_science

The nitrogen cycle is the clearest case of human dominance. Industrial fixation of atmospheric
nitrogen into fertilizer now rivals or exceeds all natural fixation combined, which has roughly
doubled the reactive nitrogen circulating through the biosphere. The consequences follow the
nitrogen downstream: it leaches into groundwater, runs off into rivers, drives algal blooms whose
decay depletes oxygen and creates hypoxic zones, and volatilizes as a potent greenhouse gas. A
single intervention at one point in the cycle propagates through all of them.


environmental_science

Phosphorus differs in an important way: it has no significant atmospheric phase and comes from
mined rock, so it is genuinely finite on a human timescale and it does not disperse the way nitrogen
does. The same runoff that carries nitrogen carries phosphorus, and in freshwater systems phosphorus
is usually the limiting nutrient, which means that controlling it is the more effective lever for
freshwater eutrophication while nitrogen matters more in coastal waters.


environmental_science

Cycles and framing:
  reservoirs and fluxes  the basic accounting; where a substance sits and how
                       fast it moves
  residence time       reservoir size divided by flux; determines response
                       timescale
  carbon cycle         atmosphere, ocean, land, and geological reservoirs
  the ocean sink       absorbs a large share of emitted carbon, at the cost of
                       acidification
  nitrogen fixation    industrial production rivalling all natural fixation
  reactive nitrogen    roughly doubled in circulation
  the cascade          one nitrogen atom causing effects in sequence across
                       multiple systems
  eutrophication       nutrient enrichment driving blooms and oxygen depletion
  hypoxic zones        oxygen-depleted water; seasonal and expanding
  phosphorus           mined, finite, no atmospheric phase
  the limiting nutrient  phosphorus in freshwater, nitrogen in coastal water
  the intervention implication  control the limiting nutrient for the system you
                       care about
  planetary boundaries  a framework identifying which system-level changes are
                       furthest outside their historical range; nitrogen and
                       biodiversity score worse than climate on this accounting


environmental_science

Q: A lake suffers algal blooms despite reduced nitrogen inputs. The most likely explanation is:
A. The measurements are wrong
B. Phosphorus is the limiting nutrient in most freshwater systems, so reducing nitrogen alone does
   not constrain growth; phosphorus loading must be addressed
C. Algae do not need nutrients
D. The lake is too warm
Reasoning: In freshwater, phosphorus typically limits primary production, partly because some
cyanobacteria fix atmospheric nitrogen and are therefore not nitrogen-limited at all. Reducing
nitrogen can even shift community composition toward those species. Answer: B.


environmental_science

## Pollution, Exposure, and Toxicology

Toxicology's foundational principle is that the dose makes the poison, and its practical corollary
is that a hazard statement without an exposure estimate carries no information about risk. Risk is
the product of hazard — the substance's intrinsic capacity to cause harm — and exposure, the amount
actually reaching the organism by a route that matters. A highly toxic substance sealed in a
container poses less risk than a mildly toxic one being inhaled daily.


environmental_science

Dose-response relationships are characterized experimentally and extrapolated, and the extrapolation
is where most of the uncertainty lives. Effects are measured at high doses in animals and
extrapolated to low doses in humans, across a species difference and a dose range of several orders
of magnitude. Threshold models assume a level below which no effect occurs, which is defensible for
many mechanisms; non-threshold models assume proportional risk to zero, which is the conservative
default for genotoxic carcinogens.


environmental_science

Persistence and bioaccumulation determine whether a small release becomes a large problem.
Substances that resist degradation stay in the environment; those that partition into fat
accumulate in organisms; those with both properties concentrate up the food chain, so a
concentration that is negligible in water becomes substantial in a predator. This combination is
what made the organochlorine pesticides and several industrial compounds so consequential, and it is
why persistence and bioaccumulation potential are screened for directly in modern chemical
assessment.


environmental_science

Pollution and toxicology:
  the dose makes the poison  the founding principle
  risk equals hazard times exposure  a hazard statement alone says nothing about
                       risk
  route of exposure    inhalation, ingestion, dermal; the same substance differs
                       greatly by route
  dose-response        characterized at high doses, extrapolated to low
  the extrapolation gap  species and dose range; where the uncertainty is
  threshold model      a level below which no effect occurs
  non-threshold model  proportional to zero; conservative for genotoxic
                       carcinogens
  acute versus chronic  different mechanisms and different relevant doses
  persistence          resistance to degradation
  bioaccumulation      partitioning into organisms, usually into fat
  biomagnification     concentration increasing up the food chain
  the combination      persistent plus bioaccumulative is what makes trace
                       releases matter
  endocrine disruption  effects at low doses through hormonal pathways;
                       non-monotonic responses complicate standard testing
  mixtures             substances assessed individually and encountered together;
                       a recognized gap in most regulatory frameworks
  body burden          what is actually measured in people; the most direct
                       exposure evidence and it lags emissions by years


environmental_science

## Water, Air, and Environmental Quality

Water quality is characterized by a set of measurements that each indicate something specific.
Dissolved oxygen indicates whether aquatic life can survive and is depleted by decomposition of
organic matter. Biological and chemical oxygen demand quantify how much oxygen the water's
contaminants will consume. Turbidity indicates suspended solids and interferes with disinfection.
Nutrient concentrations predict eutrophication. Bacterial indicators signal faecal contamination and
therefore the possible presence of pathogens that are impractical to test for individually.


environmental_science

Water treatment applies barriers in sequence, and the multiple barrier principle is the design
philosophy: no single step is relied upon, since each has failure modes the others cover.
Coagulation and flocculation aggregate fine particles; sedimentation removes them; filtration
removes what remains; disinfection inactivates pathogens. Wastewater treatment reverses the emphasis,
with biological treatment consuming organic matter and increasingly with nutrient removal steps
added because discharge standards now target eutrophication.


environmental_science

Air quality is dominated by a handful of pollutants with well-characterized health effects. Fine
particulate matter is the most consequential globally, penetrating deep into the lungs and
associated with cardiovascular as well as respiratory outcomes. Ground-level ozone forms
photochemically from precursors rather than being emitted directly, which is why its control
requires reducing those precursors and why its concentrations peak on hot sunny afternoons downwind
of sources rather than at the sources themselves.


environmental_science

Water and air:
  dissolved oxygen     whether aquatic life survives
  oxygen demand        how much the contaminants will consume
  turbidity            suspended solids; interferes with disinfection
  indicator bacteria   a proxy for faecal contamination and pathogen risk
  multiple barriers    no single step relied upon
  coagulation and flocculation  aggregating fine particles
  filtration           physical removal
  disinfection         chemical or ultraviolet inactivation
  disinfection byproducts  formed from organic matter and disinfectant; a
                       tradeoff against pathogen risk that favours disinfection
  wastewater treatment  organic matter first, nutrients increasingly
  non-point source     diffuse runoff; harder to control than any pipe and the
                       dominant remaining problem in many watersheds
  fine particulate matter  the most consequential air pollutant globally
  ground-level ozone   formed photochemically from precursors, not emitted
  the downwind pattern  ozone peaks away from its sources
  nitrogen oxides and sulfur dioxide  combustion products; acid deposition and
                       particulate precursors
  indoor air           where people spend most of their time and where
                       measurement is sparsest; combustion for cooking and
                       heating is a major global health burden


environmental_science

## Land Use, Biodiversity, and Materials

Land use change is the largest driver of biodiversity loss, exceeding climate change in current
impact though not in projected future impact. Habitat conversion removes species directly;
fragmentation of what remains has effects beyond the area lost, because small isolated patches
support fewer species than the same total area connected, and edge conditions differ from interior
conditions in microclimate, predation, and invasion.


environmental_science

The species-area relationship gives this quantitative form: species richness scales with area raised
to a fractional power, so reducing habitat area by ninety percent typically loses roughly half the
species. It is a robust empirical regularity and it underlies reserve design, which favours larger
and connected areas over the same area divided into fragments, with corridors where connection
cannot be maintained directly.


environmental_science

Materials and waste close the loop back to extraction. Linear material flows — extract, manufacture,
use, discard — impose costs at both ends, and the alternative framings emphasize keeping materials
in use. Recycling recovers material at some quality loss and energy cost; reuse avoids the
reprocessing entirely; reduction avoids the flow. The hierarchy is ordered by effectiveness and
inverted in practice, since recycling receives the most attention while reduction delivers the most
benefit.


environmental_science

Land, biodiversity, and materials:
  land use change      the largest current driver of biodiversity loss
  habitat fragmentation  effects beyond the area lost
  edge effects         microclimate, predation, and invasion at boundaries
  species-area relationship  richness scaling with a fractional power of area
  the practical figure  ninety percent area loss costs roughly half the species
  reserve design       larger and connected over fragmented
  corridors            connection where contiguity is impossible
  invasive species     a major driver, and the introduction rate tracks trade
                       volume
  ecosystem services   provisioning, regulating, supporting, cultural; a framing
                       that makes some values visible in decisions and that
                       cannot capture all of them
  extraction impacts   mining, water use, land disturbance at the source end
  linear flows         extract, manufacture, use, discard
  the waste hierarchy  reduce, reuse, recycle, recover, dispose
  the inversion in practice  recycling gets the attention, reduction delivers the
                       benefit
  material recovery    quality loss on each cycle for most materials
  extended producer responsibility  the manufacturer bearing end-of-life cost;
                       aligns design incentives with recoverability


environmental_science

## Assessment, Measurement, and the Policy Interface

Life cycle assessment quantifies environmental impacts across a product's full chain from extraction
to disposal, and its value is in exposing burden shifting — an improvement at one stage that creates
a larger cost at another. Its results depend heavily on the system boundary, the functional unit,
and the allocation of shared burdens among co-products, which means two studies of the same product
can reach opposite conclusions legitimately. Reading the methodology section is not optional.


environmental_science

Environmental monitoring faces the general problem that natural systems are variable and effects
are often small relative to that variability. Detecting a trend requires a baseline, adequate
statistical power, and control for confounding drivers, and monitoring programmes that were not
designed with a specific detectable effect in mind frequently cannot answer the question they were
established for. Before-after-control-impact designs and long time series are the approaches that
work.


environmental_science

The interface with policy introduces considerations that are not scientific. Environmental problems
are typically externalities — costs imposed on parties who did not consent and are not compensated —
and the instruments for addressing them each have distinct properties. Regulation specifies
behaviour and is predictable and inflexible. Pricing sets a cost and lets actors find the cheapest
reduction. Information disclosure changes behaviour through reputation and consumer choice. The
choice among them is a political decision informed by, and not determined by, the science.


environmental_science

Assessment and policy:
  life cycle assessment  impacts across the full chain
  burden shifting      an improvement at one stage costing more at another
  system boundary      what is included; determines the answer
  functional unit      the basis of comparison; must be equivalent service
  allocation           dividing shared burdens among co-products; a methodological
                       choice with large consequences
  the reading discipline  two legitimate studies can disagree; the methodology
                       explains why
  monitoring design    a baseline, power, and confounder control
  before-after-control-impact  the design that supports causal attribution
  long time series     often the only way to detect slow change against high
                       variability
  detection limits     a non-detect is not an absence; it is a bound
  externality          costs imposed without consent or compensation
  regulation           specifies behaviour; predictable, inflexible
  pricing instruments  set a cost, let actors find cheap reductions
  information disclosure  changes behaviour through reputation and choice
  precautionary principle  acting under uncertainty when consequences are severe
                       and irreversible; its application is contested precisely
                       because it shifts the burden of proof, and being explicit
                       about which direction the burden should fall is more
                       productive than arguing about the principle in the abstract


evolutionary_biology

## Selection, Drift, and the Mechanisms of Change

Evolution is change in the heritable characteristics of populations across generations, and it
requires only three conditions: variation among individuals, heritability of that variation, and
differential reproduction associated with it. Where those three hold, the composition of the
population changes, and the argument is close to a logical necessity rather than an empirical
claim about biology specifically.


evolutionary_biology

Natural selection is the process arising when the differential reproduction is caused by the
variation. It is not the only mechanism of evolutionary change and it is frequently not the
dominant one. Genetic drift — the random sampling of which individuals happen to reproduce — changes
allele frequencies in any finite population, and its magnitude is inversely proportional to
population size. In a small population drift overwhelms weak selection entirely, which means that a
mildly advantageous variant can be lost and a mildly deleterious one can fix, purely by chance.


evolutionary_biology

The relationship between the two is quantified by comparing the selection coefficient with the
reciprocal of the effective population size. When selection is much stronger, the outcome is
deterministic; when it is much weaker, the variant behaves as though neutral. This threshold is why
effective population size is one of the most consequential quantities in evolutionary biology, and
why species with small populations accumulate slightly deleterious mutations that large populations
purge.


evolutionary_biology

Mechanisms of evolutionary change:
  the three conditions  variation, heritability, differential reproduction
  natural selection    differential reproduction caused by the variation
  genetic drift        random sampling; magnitude scales inversely with
                       population size
  the threshold        selection dominates when its coefficient exceeds one over
                       the effective population size
  effective population size  the size of an idealized population with the same
                       drift; usually far smaller than the census count
  mutation             the ultimate source of variation; mostly neutral or
                       deleterious
  recombination        reshuffles combinations; decouples linked sites
  gene flow            migration between populations; homogenizes them
  directional selection  shifts the mean
  stabilizing selection  reduces the variance; the most common form
  disruptive selection  favours extremes; can initiate divergence
  balancing selection  maintains polymorphism through heterozygote advantage,
                       frequency dependence, or spatial variation
  sexual selection     differential mating success; can oppose survival
                       advantage, which is why extravagant traits persist


evolutionary_biology

Q: A slightly deleterious mutation becomes fixed in a population. The most likely explanation is:
A. The mutation was actually beneficial
B. The population was small enough that drift dominated weak selection, so the allele's fate was
   effectively random despite its mild disadvantage
C. Selection does not act on mutations
D. The measurement is wrong
Reasoning: Selection is effective only when its strength exceeds the magnitude of drift, which
scales inversely with effective population size. In a small population, mutations with small
fitness effects behave as though neutral and can fix by chance. This is a routine outcome, not an
anomaly. Answer: B.


evolutionary_biology

## Population Genetics

Population genetics is the quantitative core of evolutionary theory, and it began by establishing
what happens in the absence of evolution. The Hardy-Weinberg principle states that under random
mating, no selection, no drift, no mutation, and no migration, allele and genotype frequencies
remain constant. Its value is as a null model: a population departing from Hardy-Weinberg
proportions is telling you that one of those assumptions fails, and which direction the departure
runs narrows down which.


evolutionary_biology

The dynamics of a single locus under selection are tractable and instructive. A beneficial dominant
allele rises quickly at first and then slowly, because when it is common the recessive homozygotes
that selection acts against are rare. A beneficial recessive allele does the opposite, lingering at
low frequency for a long time because it is almost always masked in heterozygotes. This asymmetry
means that the rate of adaptation depends on dominance as much as on the strength of selection.


evolutionary_biology

Linkage complicates the single-locus picture in ways that matter for interpretation. Sites near a
selected variant are dragged along with it, a process called genetic hitchhiking, which reduces
diversity in the surrounding region and produces a signature called a selective sweep. Detecting
these signatures in genome data is how selection is inferred in species that cannot be
experimented on, and distinguishing them from the diversity reductions produced by demographic
history — a bottleneck reduces diversity genome-wide — is the central inferential difficulty.


evolutionary_biology

Population genetics:
  Hardy-Weinberg       the null model; frequencies constant absent evolution
  the diagnostic use   departures indicate which assumption fails
  allele frequency     the fundamental state variable
  fitness              expected relative reproductive contribution
  selection coefficient  the fitness difference per generation
  dominance            determines the shape of the frequency trajectory
  the recessive lag    beneficial recessives rise slowly while rare
  heterozygote advantage  maintains both alleles; sickle-cell and malaria the
                       textbook case
  linkage disequilibrium  non-random association between sites
  genetic hitchhiking  neutral sites carried by a selected neighbour
  selective sweep      the diversity reduction signature around a swept variant
  background selection  diversity reduction from purging deleterious mutations;
                       mimics a sweep
  the confound         demographic history reduces diversity genome-wide;
                       distinguishing it from selection requires comparing
                       regions rather than looking at one
  coalescent theory    tracing lineages backward to common ancestors; the modern
                       inferential framework


evolutionary_biology

## Speciation and Phylogenetics

A species is a population or set of populations that is reproductively isolated from others, under
the most widely used definition, and speciation is the process by which that isolation arises. The
definition has well-known difficulties — it does not apply to asexual organisms, it is untestable
for fossils, and hybridization between recognized species is common — which is why several
alternative species concepts coexist and why the boundary is often genuinely fuzzy rather than
merely uncertain.


evolutionary_biology

Geographic separation is the most straightforward route. Populations divided by a barrier accumulate
differences independently through drift and divergent selection, and if they remain separated long
enough, reproductive incompatibilities arise as a byproduct. When secondary contact occurs,
selection against unfit hybrids can then strengthen prezygotic isolation directly, a process called
reinforcement. Speciation without geographic separation is harder because gene flow opposes
divergence, but it occurs — through host shifts, polyploidy in plants, and strong disruptive
selection with assortative mating.


evolutionary_biology

Phylogenetics reconstructs the branching history relating organisms. Characters shared through
common ancestry are informative; characters shared through convergent evolution are misleading, and
distinguishing them is the core methodological problem. Molecular data made the field quantitative
because sequences supply many independent characters and because models of substitution allow
likelihood-based inference rather than counting.


evolutionary_biology

Speciation and phylogeny:
  biological species   reproductive isolation; the standard concept and an
                       imperfect one
  alternative concepts  morphological, ecological, phylogenetic; each fails
                       differently
  allopatric           geographic separation; the common route
  sympatric            divergence without separation; requires strong selection
                       and assortative mating
  polyploidy           instantaneous speciation, common in plants
  reinforcement        selection strengthening isolation after secondary contact
  hybrid zones         stable regions of interbreeding; informative about
                       the strength of isolation
  homology             similarity through common ancestry; the informative signal
  homoplasy            similarity through convergence or reversal; the noise
  parsimony            fewest character changes; simple, biased under unequal
                       rates
  maximum likelihood   a substitution model plus optimization; the standard
  Bayesian inference   posterior distributions over trees; gives uncertainty
                       directly
  long branch attraction  rapidly evolving lineages grouping spuriously; a
                       specific and diagnosable artifact
  molecular clock      substitutions accumulating roughly linearly; calibrated by
                       fossils, and rate variation across lineages is the main
                       source of error
  incomplete lineage sorting  gene trees disagreeing with the species tree; a
                       real biological phenomenon, not an analytical failure


evolutionary_biology

## Molecular Evolution and Evolutionary Development

The neutral theory of molecular evolution asserts that most substitutions between species are
neither advantageous nor deleterious but effectively neutral, fixed by drift. It was controversial
when proposed and is now the standard null model, which is a substantial shift: the question asked
of any observed sequence difference is no longer whether it is adaptive but whether it departs
detectably from neutral expectation.


evolutionary_biology

The tests for that departure are elegant. Comparing the rate of substitutions that change an amino
acid with the rate of those that do not gives a ratio whose expected value under neutrality is one;
values below indicate purifying selection removing changes, and values above indicate positive
selection driving them. Comparing polymorphism within a species with divergence between species
gives an independent test, because selection affects the two differently. Both are applied
routinely to genome data and both are sensitive to demography in ways that require care.


evolutionary_biology

Evolutionary developmental biology addresses how genetic change produces morphological change, and
its central finding is that the same small set of regulatory genes patterns the body plans of
animals as different as flies and vertebrates. Morphological diversity arises far more from changes
in when and where those genes are expressed than from changes in the genes themselves. This
resolves an old puzzle — how such varied forms arise from such conserved genomes — and it relocates
the action from protein-coding sequence to regulatory sequence.


evolutionary_biology

Molecular and developmental evolution:
  neutral theory       most substitutions are effectively neutral
  the shift            neutrality is the null; adaptation must be demonstrated
  synonymous vs nonsynonymous  the ratio test for selection
  purifying selection  the dominant mode; removes deleterious changes
  positive selection   drives change; detectable but far less common
  the McDonald-Kreitman test  polymorphism versus divergence
  demography as confound  population size change mimics selection signals
  gene duplication     the raw material for new function; one copy free to
                       diverge
  neofunctionalization  a duplicate acquiring a new role
  subfunctionalization  duplicates partitioning the ancestral role
  horizontal gene transfer  transfer between lineages; pervasive in prokaryotes
                       and it makes a strictly branching tree the wrong model
                       there
  Hox genes            conserved patterning genes across animal phyla
  regulatory evolution  changes in expression, not protein sequence, as the main
                       source of morphological difference
  constraint           developmental pathways limiting what variation is possible;
                       evolution explores a restricted space
  exaptation           a structure co-opted for a function it did not evolve for


evolutionary_biology

## Evidence and Inference

The evidence for common descent is convergent from independent lines, and the convergence is what
makes it robust rather than any single line being conclusive. The fossil record documents forms
intermediate between major groups. Comparative anatomy shows shared structures repurposed across
lineages, including structures that are functionally poor and make sense only as inherited
constraints. Biogeography shows distributions that track geological history. Molecular sequences
produce a phylogeny that matches the one derived from morphology, from entirely independent data.


evolutionary_biology

Vestigial structures and molecular pseudogenes are particularly informative because they are
evidence of history rather than of function. A non-functional copy of a gene that works in related
species, disabled by an identifiable mutation shared with the nearest relatives, records both the
ancestry and the loss. The shared inactivating mutation is the key detail — an independently
disabled gene would carry a different lesion.


evolutionary_biology

Evolution is observable on human timescales where generation times are short and selection is
strong. Antibiotic resistance, pesticide resistance, herbicide resistance, and viral immune escape
are all evolution occurring in real time under selection pressures we apply, and they are also
the practical reason the theory matters outside biology: resistance management is applied
evolutionary biology, and strategies that ignore it fail predictably.


evolutionary_biology

Evidence and application:
  independent convergence  fossils, anatomy, biogeography, molecules agreeing
  transitional fossils  documented for the major transitions
  homologous structures  the same underlying plan in different functions
  vestigial structures  reduced and functionally poor; evidence of history
  pseudogenes          disabled copies; the shared inactivating mutation dates
                       the loss
  endogenous retroviruses  insertions at identical genomic positions across
                       species; essentially unambiguous shared ancestry
  biogeography         distributions tracking continental history
  observed evolution   resistance evolution on human timescales
  antibiotic resistance  the most consequential applied case
  resistance management  rotation, combination, refugia; strategies designed
                       against the evolutionary response
  directed evolution   selection applied deliberately in the laboratory to
                       produce enzymes and binders; the theory used as an
                       engineering method
  the general lesson   any replicating system with variation and differential
                       success evolves, which is why the same reasoning applies
                       to tumours, to viruses within a host, and to populations
                       of algorithms under a selection criterion


geology

## Earth Structure and Interior

Earth's internal structure is known almost entirely from seismology, because no borehole has
penetrated even the full thickness of the crust. Earthquake waves refract and reflect at
boundaries where physical properties change, and mapping those boundaries from arrival times
at stations worldwide produced the layered model.


geology

Two classification schemes describe the same planet and are often confused. The compositional
division — crust, mantle, core — is based on chemistry. The mechanical division —
lithosphere, asthenosphere, mesosphere, outer core, inner core — is based on how the material
behaves. The lithosphere comprises the crust plus the uppermost rigid mantle and is what
breaks into tectonic plates; the asthenosphere beneath it is mantle rock close enough to
melting to flow slowly. The distinction matters because plate tectonics operates on the
mechanical layering, not the compositional one.


geology

Seismic waves come in two types with different diagnostic value. Primary waves are
compressional, travel fastest, and pass through both solids and liquids. Secondary waves are
shear, travel slower, and cannot propagate through liquid because a fluid has no shear
strength. The existence of a shadow zone where secondary waves do not arrive is the direct
evidence that the outer core is liquid, and the refraction pattern of primary waves revealed
the solid inner core within it. This is a good example of a global structural conclusion drawn
from a simple physical property of wave propagation.


geology

Earth's layers:
  crust               oceanic 5-10 km, basaltic, dense, young (< 200 Myr);
                      continental 30-70 km, granitic, less dense, up to 4 Gyr old
  Moho                the crust-mantle boundary, marked by a velocity jump
  upper mantle        peridotite; the asthenosphere lies within it
  transition zone     410 and 660 km discontinuities from mineral phase changes
  lower mantle        to 2890 km; high pressure phases
  outer core          liquid iron-nickel; generates the magnetic field by dynamo
  inner core          solid iron despite higher temperature, because pressure
                      raises the melting point
  geothermal gradient ~25 C/km in the crust, far lower in the mantle
  heat sources        radioactive decay of U, Th, K plus primordial heat
  magnetic field      requires a liquid conducting layer in convective motion


geology

The geodynamo deserves note because it links the deep interior to the surface environment.
Convection in the liquid outer core, organized by Earth's rotation, sustains a self-exciting
magnetic field that deflects the solar wind and protects the atmosphere from stripping. The
field reverses polarity at irregular intervals averaging a few hundred thousand years, and the
record of those reversals frozen into cooling oceanic crust produced the symmetric magnetic
stripes on either side of mid-ocean ridges — which was the decisive evidence for seafloor
spreading and hence for plate tectonics.


geology

Q: Secondary seismic waves do not arrive in a shadow zone on the far side of Earth from an
earthquake. This establishes that:
A. The core is denser than the mantle
B. Some layer is liquid, since shear waves cannot propagate through fluid
C. The Earth is layered
D. The inner core is solid
Reasoning: Shear waves require a medium with shear strength, which liquids lack. Their
complete absence beyond a certain angular distance indicates a liquid layer blocking them —
the outer core. The solidity of the inner core was inferred separately from refracted primary
wave arrivals. Answer: B.


geology

## Plate Tectonics

Plate tectonics is the unifying theory of geology, explaining the distribution of
earthquakes, volcanoes, mountain ranges, and the shapes and geological correspondences of
continents. The lithosphere is divided into rigid plates that move relative to one another at
rates of centimetres per year, driven primarily by the negative buoyancy of cold subducting
slabs pulling the trailing plate — slab pull — with ridge push from the elevated
mid-ocean ridge contributing less, and mantle convection providing the underlying circulation.


geology

Continental drift was proposed by Wegener in 1912 on the basis of fitting coastlines, matching
fossil assemblages across oceans, and correlated rock formations, and it was rejected for
decades because no plausible mechanism existed for moving continents through oceanic crust.
The resolution came from seafloor spreading: the continents do not plough through the ocean
floor, they ride on plates that include it, and new oceanic crust is created at ridges and
destroyed at trenches. The history of the idea is a useful case of correct observation with an
unacceptable mechanism, resolved only when the mechanism was found.


geology

Boundary types determine the geology:
  divergent           plates separate; mid-ocean ridges and continental rifts;
                      shallow earthquakes, basaltic volcanism, new crust created
  convergent, ocean-continent  oceanic subducts beneath continental; deep trench,
                      volcanic arc, deep earthquakes along the Benioff zone
  convergent, ocean-ocean      island arc; the older, denser plate subducts
  convergent, continent-continent  neither subducts easily; crustal thickening
                      and mountain building, as in the Himalaya
  transform           plates slide past; shallow earthquakes, little volcanism,
                      as along the San Andreas
  hotspot             a mantle plume independent of plate boundaries; produces
                      island chains as the plate moves over it
  triple junction     where three plates meet; complex and often unstable


geology

Subduction zones are where the most consequential geology happens. The descending slab
carries water in hydrated minerals; as it heats, that water is released into the overlying
mantle wedge, lowering the melting point and generating magma that rises to form volcanic
arcs. The magma interacts with continental crust on its way up, differentiating toward more
silica-rich compositions, which is why arc volcanoes erupt explosively — silica-rich magma is
viscous and traps gas — while ridge and hotspot basalts flow effusively. The largest
earthquakes on record are all subduction megathrust events, because the fault plane is
shallow-dipping, enormous in area, and locked over long intervals.


geology

## Minerals, Rocks, and the Rock Cycle

A mineral is a naturally occurring inorganic solid with a definite chemical composition and
an ordered internal crystal structure. Rocks are aggregates of minerals. The silicate minerals
dominate the crust because silicon and oxygen are the most abundant elements available, and
their structural family is organized by how the silica tetrahedra link — isolated,
in chains, in sheets, or in three-dimensional frameworks — which determines cleavage,
hardness, and weathering behaviour.


geology

Igneous rocks crystallize from melt. Their texture records cooling rate: slow cooling at
depth allows large crystals to grow, giving coarse-grained intrusive rocks such as granite,
while rapid cooling at the surface gives fine-grained extrusive rocks such as basalt, and
quenching gives volcanic glass. Their composition records the source and the degree of
differentiation, running from mafic, iron and magnesium rich and silica poor, to felsic,
silica and alkali rich. Bowen's reaction series describes the order in which minerals
crystallize from a cooling melt and explains why fractional crystallization drives residual
melts toward felsic compositions.


geology

Sedimentary rocks form from accumulated particles or precipitates and are the ones that
record surface history. Clastic rocks are made of fragments, classified by grain size from
conglomerate through sandstone to shale, with the grain size and sorting recording the
transport energy and distance. Chemical and biochemical rocks precipitate from solution or
accumulate from organisms, limestone being by far the most important. Sedimentary rocks cover
most of the continental surface, contain nearly all fossils, and host most fossil fuel and
groundwater resources.


geology

Metamorphic rocks form when existing rock is altered by heat, pressure, or chemically active
fluids without melting. Regional metamorphism at convergent boundaries produces foliated
rocks whose platy minerals align perpendicular to the maximum stress, giving the sequence
slate, phyllite, schist, gneiss with increasing grade. Contact metamorphism near an intrusion
produces non-foliated rocks because the stress is not directional. Metamorphic mineral
assemblages are used as geothermobarometers, recording the pressure and temperature the rock
experienced, which is how the burial and exhumation history of a mountain belt is
reconstructed.


geology

Rock classification essentials:
  igneous, intrusive     granite, diorite, gabbro; coarse grained, slow cooling
  igneous, extrusive     rhyolite, andesite, basalt; fine grained, fast cooling
  composition series     felsic (granite/rhyolite) to mafic (gabbro/basalt)
  Bowen's series         olivine crystallizes first, quartz last
  clastic sedimentary    conglomerate, sandstone, siltstone, shale by grain size
  chemical sedimentary   limestone, rock salt, chert
  foliated metamorphic   slate, phyllite, schist, gneiss with increasing grade
  non-foliated           marble from limestone, quartzite from sandstone
  index minerals         indicate metamorphic grade
  rock cycle             any rock type can become any other through the
                         appropriate process; there is no fixed sequence


geology

## Deformation, Earthquakes, and Volcanoes

Rock deforms elastically under small stress and permanently under larger stress, and whether
that permanent deformation is brittle or ductile depends on temperature, pressure, strain
rate, and rock type. Cold, shallow, rapidly stressed rock fractures; hot, deep, slowly
stressed rock flows. This is why folds and faults often occur in the same rock unit — the
folding happened at depth and the faulting after uplift, or the strain rate differed.


geology

Faults are classified by relative motion, and each type corresponds to a stress regime and a
tectonic setting. Normal faults accommodate extension, with the hanging wall moving down, and
characterize rifts and mid-ocean ridges. Reverse and thrust faults accommodate compression
and characterize convergent margins. Strike-slip faults accommodate horizontal shear and
characterize transform boundaries. Reading the fault type from field evidence directly
constrains the stress field that produced it.


geology

Earthquakes result from the sudden release of accumulated elastic strain when friction on a
fault is overcome. Elastic rebound theory describes the cycle: stress accumulates as plates
move while the fault remains locked, the rock deforms elastically, and when the shear stress
exceeds the frictional strength, slip occurs and the rock springs back. This explains why
large earthquakes recur at intervals on a given fault segment and why the accumulated slip
deficit is a meaningful measure of hazard.


geology

Magnitude and intensity are distinct and routinely conflated. Magnitude is a single number
describing the energy released, computed from seismogram amplitudes, and it is logarithmic —
each unit corresponds to about 32 times more energy and ten times more ground motion
amplitude. Intensity describes shaking and damage at a particular location and varies across
the affected area with distance, depth, and local ground conditions. A moderate earthquake on
soft sediment can produce more damage than a larger one on bedrock, which is why site
response matters so much for building codes.


geology

Earthquake and volcano quantities:
  moment magnitude      based on fault area, slip, and rock rigidity; the modern
                        standard, valid for the largest events where the older
                        Richter scale saturates
  energy scaling        ~32x per magnitude unit; ~1000x per two units
  intensity             Modified Mercalli; location-specific shaking and damage
  focus / epicentre     the rupture point at depth / the point above it
  P, S, surface waves   P arrives first, S second, surface waves cause most damage
  liquefaction          saturated loose sediment loses strength during shaking
  site amplification    soft sediment amplifies ground motion substantially
  volcanic explosivity  VEI, logarithmic in erupted volume
  magma viscosity       rises with silica content; controls eruption style
  effusive vs explosive basaltic flows versus silicic explosive eruptions
  pyroclastic flow      the deadliest volcanic hazard; fast, hot, unsurvivable
  lahar                 volcanic mudflow; often the most damaging distal hazard


geology

Earthquake prediction — specifying time, place, and magnitude in advance — has not been
achieved and there is reasonable doubt it is possible, since the process appears to be
critically sensitive to conditions that cannot be measured. Forecasting, in the sense of
probabilistic hazard over years to decades, is well established and is what building codes
rest on. Early warning systems occupy a different niche entirely: they detect the fast P wave
at stations near the epicentre and transmit an alert electronically, which outruns the
slower and more damaging S and surface waves, providing seconds to tens of seconds — enough
to stop trains, close valves, and take cover.


geology

## Surface Processes, Stratigraphy, and Deep Time

Weathering breaks rock down in place, and erosion transports the products. Mechanical
weathering — frost wedging, thermal expansion, root growth, abrasion — increases surface area
without changing composition. Chemical weathering — dissolution, hydrolysis, oxidation —
changes composition and is greatly accelerated by the increased surface area, which is why the
two processes reinforce each other and why weathering is fastest in warm humid climates.


geology

The silicate weathering reaction is worth knowing outside geology because it is Earth's
long-term climate thermostat. Weathering of silicate rock consumes atmospheric carbon
dioxide, producing dissolved bicarbonate that is eventually deposited as carbonate in the
ocean. The reaction rate increases with temperature and rainfall, so a warmer world weathers
faster and draws down more carbon dioxide, cooling it; a colder world weathers slower and
allows volcanic carbon to accumulate, warming it. This negative feedback has kept Earth's
climate within habitable bounds for billions of years, and it operates over hundreds of
thousands of years — far too slowly to counteract the current rate of emission.


geology

Stratigraphy reads Earth history from layered rock, and its principles are simple and
powerful. Original horizontality holds that sediments deposit in near-horizontal layers, so
tilted strata have been deformed. Superposition holds that in an undisturbed sequence, lower
layers are older. Cross-cutting relationships hold that a feature cutting across another is
younger. Faunal succession holds that fossil assemblages change through time in a consistent
order, which allows correlation between distant sequences and is the basis of the geological
timescale. Unconformities are surfaces representing missing time — erosion or non-deposition
— and reading them is how gaps in the record are identified rather than overlooked.


geology

Deep time and dating:
  relative dating        superposition, cross-cutting, faunal succession,
                         unconformities
  radiometric dating     decay of unstable isotopes at a constant rate
  carbon-14              half-life 5,730 yr; organic material to ~50,000 yr
  potassium-argon        half-life 1.25 Gyr; volcanic rocks
  uranium-lead           half-life 4.47 Gyr; zircon; the most precise deep-time
                         method, and zircon resists alteration
  Earth's age            4.54 Gyr, from meteorites and the oldest terrestrial
                         minerals
  oldest rocks           ~4.0 Gyr;  oldest minerals (zircon) ~4.4 Gyr
  Precambrian            ~88% of Earth history
  Great Oxidation        ~2.4 Gyr; photosynthetic oxygen transforms the atmosphere
  Cambrian explosion     ~540 Myr; rapid diversification of animal body plans
  mass extinctions       five major events; the end-Permian removed ~80% of marine
                         species, the end-Cretaceous ended non-avian dinosaurs


geology

Radiometric dating works because radioactive decay proceeds at a rate independent of
temperature, pressure, and chemistry, so the ratio of parent to daughter isotope in a closed
system measures elapsed time. The assumptions that must be checked are that the system
remained closed, that the initial daughter abundance is known or can be determined, and that
the appropriate isotope system is used for the timescale — carbon-14 is useless beyond about
ten half-lives, and uranium-lead is useless for anything recent. Isochron methods determine
the initial daughter abundance from the data itself rather than assuming it, which is why they
are preferred where applicable.


geology

Economic geology connects all of this to resources. Ore deposits form where geological
processes concentrate an element far above its crustal abundance — hydrothermal circulation
depositing metals from solution, magmatic segregation concentrating dense sulfides, placer
deposits sorting heavy minerals by flowing water, and supergene enrichment concentrating
metals by weathering. Fossil fuels require organic matter accumulating under anoxic
conditions, burial to appropriate temperature, a porous reservoir rock, and an impermeable
seal, and the conjunction of all four is what makes petroleum systems localized. Groundwater
occupies pore space in aquifers, and its sustainable yield is set by recharge rate rather
than by stored volume — which is why aquifers that took millennia to fill can be depleted in
decades and why extraction exceeding recharge causes land subsidence that permanently
destroys the aquifer's storage capacity.


hydrology_and_water

## The Water Cycle and Water Budgets

Hydrology follows water through its reservoirs and pathways, and the organizing tool is the water
balance: over any defined area and period, inflow equals outflow plus the change in storage. Applied
to a catchment, the inflows are precipitation and any imports, the outflows are evapotranspiration,
streamflow, and groundwater exiting the boundary, and the storage terms are soil moisture,
groundwater, snowpack, and surface water bodies.


hydrology_and_water

The balance is simple to state and difficult to close in practice, because the terms are measured
with very different accuracy. Precipitation is measured at points and interpolated over areas with
substantial error, particularly for snow and in complex terrain. Streamflow is measured relatively
well at gauges through a stage-discharge relationship that must be recalibrated as the channel
changes. Evapotranspiration is rarely measured directly and is usually estimated from meteorological
variables. Groundwater exchange is the least constrained term and frequently absorbs the residual
error of everything else.


hydrology_and_water

Evapotranspiration deserves particular attention because it is the largest outflow in most
catchments and the least intuitive. It combines evaporation from surfaces and transpiration through
plants, and it is limited either by available energy or by available water depending on conditions.
In humid regions energy is limiting, so it tracks radiation; in arid regions water is limiting, so
it tracks supply. Vegetation change therefore alters catchment yield substantially, which is why
afforestation reduces streamflow and why land use change is a hydrological intervention whether or
not it is intended as one.