models/declining_increment/README.md

# Declining Increment Model

This folder documents the **Declining Increment** growth model used in the Mangrove ER Dashboard.

- **Growth Model:** Declining Increment (annual increment declines linearly to zero; total size is the sum of non-negative increments)
- **Parameters:** See `configs/declining_increment.yaml`
- **Purpose:** For comparison with other models; may be appropriate for species or sites where growth slows with age.
- **Usage:** Available as a tab in the dashboard for side-by-side comparison, or as a standalone dashboard.

## Model Details

### Discrete Version (Default)
- **Logic:** Growth is calculated by summing annual increments for each year of age. The increment for year \(i\) is \( r_0 \cdot \max(0, 1 - \frac{i-1}{T_m}) \).
- **No Negative Growth:** Increments decline to zero but never go negative, so DBH and height never decrease.
- **Fractional Years:** If the age is not an integer, a proportional part of the next increment is added.
- **Mortality:** Annual mortality is compounded each year according to the schedule in the config.

### Continuous Version (Optional)
- **Logic:** Uses the analytical formula:  
  \( \text{size}(t) = \text{initial} + r_0 \cdot (t - \frac{t^2}{2T_m}) \)
- **How to Enable:** Set `continuous_growth: true` in `configs/declining_increment.yaml`.
- **Implications:** This version is smoother and may yield slightly different results than the discrete sum, especially for short time periods or small Tm.

### Display Names
- Species are now displayed as "Rhizophora spp." and "Avicennia germinans" throughout the dashboard for clarity.

**Note:**
This model is flexible and can be toggled between discrete and continuous modes via the config. Small differences in ERs compared to other implementations (e.g., Jupyter notebooks) may arise from differences in how increments, mortality, or fractional years are handled.