pmf-dark 0.1.1

Modelling species dark diversity using bayesian Probabilistic Matrix Factorisation

PMF-dark: Using matrix factorisation for dark diversity estimation

Overview

This repository implements a PMF-dark using Bayesian Probabilistic Matrix Factorisation to estimate dark diversity - the set of species absent from a site despite having suitable environmental conditions. The method uses counterfactual predictions to reconstruct the potential species pool by separating environmental effects from unmeasured drivers of absence (e.g., land-use degradation, dispersal limitation, biotic interactions).

The Problem: What is Dark Diversity?

Traditional biodiversity assessments only count observed species (alpha diversity). However, many species are absent from sites where they could thrive based on environmental conditions. This "dark diversity" represents:

• Species lost due to historical or ongoing land-use degradation
• Species unable to reach suitable sites due to dispersal limitation
• Species suppressed by biotic interactions

Quantifying dark diversity is crucial for:

• Conservation planning and restoration potential assessment
• Understanding true biodiversity patterns
• Identifying areas with highest restoration value

Methodology

Core Model

The framework decomposes species occurrence probabilities into three additive components:

$$\text{logit}(p_{ij}) = \underbrace{\alpha_j}_{\text{Intercept}} + \underbrace{f_j(\mathbf{x}i)}{\text{Environmental Effects}} + \underbrace{\mathbf{w}_i^\top \mathbf{z}j}{\text{Latent Factors}}$$

Where:

• $\alpha_j$: Species-specific baseline prevalence
• $f_j(\mathbf{x}_i)$: Environmental response function to measured abiotic variables (temperature, pH, elevation, etc.), which can be modelled as linear, Gaussian niche, or non-linear (e.g. Bayesian neural network)
• $\mathbf{w}_i^\top \mathbf{z}_j$: Latent factors capturing unmeasured drivers of absence

Key Innovation: Counterfactual Predictions

1. Full Predictions: Include all components (environment + latent factors)

   • Represents observed diversity with all drivers active

2. Environment-Only Predictions: Exclude latent factors

   • Represents potential diversity (setting $\mathbf{w}_i^\top \mathbf{z}_j = 0$)

3. Dark Diversity Proxy: Difference between full and environment-only predictions

   • Quantifies species lost to unmeasured stressors

Inference: Stochastic Variational Inference (SVI)

The model is fit using Pyro-based SVI, which:

• Handles high-dimensional ecological matrices efficiently
• Treats inference as an optimisation problem (ELBO maximisation)
• Scales to thousands of sites and species
• Requires minimal computational resources

Repository Structure

PMF_dark/
├── README.md                                    # This file
├── mat_fact_dark_div.ipynb                     # Main analysis notebook
├── data/
│   ├── survey.csv                              # Species presence/absence matrix (sites × species)
│   ├── env.csv                                 # Environmental predictors (sites × covariates)
│   └── truth.csv                               # Ground truth data (if available)
└── output/
    ├── mat_fact_predicted_probabilities_full.csv           # Full model predictions
    ├── mat_fact_predicted_probabilities_env_only.csv       # Environment-only predictions
    └── mat_fact_dark_diversity_proxy.csv                   # Dark diversity estimates

Installation

Requirements

• Python 3.13 or 3.14
• PyTorch (with CUDA support if using GPU)
• Pyro (pyro-ppl)
• Pandas
• NumPy
• scikit-learn
• scipy

Setup

To ensure PyTorch is installed with the correct CUDA version for your system, it is recommended to install PyTorch manually first before installing the package or its other dependencies.

1. Setup Virtual Environment

# Clone the repository
git clone https://github.com/davidyshen/PMF_dark.git
cd PMF_dark

# Create virtual environment (optional but recommended)
python -m venv .venv
source .venv/bin/activate  # On Windows: .venv\Scripts\activate

2. Install PyTorch with CUDA

Visit the PyTorch Getting Started guide to select the correct command for your CUDA version and OS. For example, to install PyTorch with CUDA 12.4 support on Windows/Linux:

pip install torch --index-url https://download.pytorch.org/whl/cu124

If not using CUDA, simply install the CPU version:

pip install torch

3. Install remaining dependencies

If installing via pip:

pip install pyro-ppl pandas numpy scikit-learn scipy jupyter

If using Poetry:

# This will install the package and its remaining dependencies into your environment
poetry install

Usage

pmf_dark provides a flexible Python API to fit models, generate predictions, and estimate dark diversity.

Quick Start: Basic API Usage

import pandas as pd
from pmf_dark import compute_dark_diversity

# 1. Load data
y = pd.read_csv("data/survey.csv", index_col=0)
x = pd.read_csv("data/env.csv", index_col=0)

# Drop non-species/non-environmental metadata
coords = y[["x", "y"]]
y = y.drop(columns=["x", "y", "ID"])
x = x.drop(columns=["ID"])

# 2. Run Dark Diversity Estimation using a Gaussian Niche Model with SVI
predictions = compute_dark_diversity(
    y=y,
    x=x,
    model_type="gaussian",   # Ecological response model
    method="svi",            # Stochastic Variational Inference
    num_factors=2,           # Latent factors
    num_iterations=2500,     # SVI parameters
    categorical_cols=["landuse"] # Explicitly treat landuse as categorical
)

---

compute_dark_diversity() Function Arguments

compute_dark_diversity(
    y,                      # Species presence-absence/count matrix (n_sites, n_species)
    x,                      # Environmental predictor matrix (n_sites, n_env)
    model_type="gaussian",  # "linear" | "gaussian" | "bnn"
    num_factors=1,          # Number of latent factors for residual covariance
    method="svi",           # "svi" | "mcmc"
    cuda=False,             # GPU computation (SVI only)
    include_latent=True,    # Include latent factors in predictions
    return_means=True,      # Return means or full posterior samples
    batch_size=None,        # Mini-batch size for SVI training (default: None)
    pred_batch_size=None,   # Site-chunk size for prediction output (default: None)
    categorical_cols=None,  # Explicit list of columns to treat as categorical variables
    **kwargs,               # Extra model/method specific arguments
)

Parameter Details

Parameter	Type	Default	Description
y	array-like	—	Species matrix (presence/absence or counts) with shape (n_sites, n_species).
x	array-like	—	Environmental predictor matrix with shape (n_sites, n_env).
model_type	str	"gaussian"	Ecological response model: "linear", "gaussian" (quadratic niche), or "bnn" (Bayesian Neural Network).
num_factors	int	1	Number of latent factors used to model residual species covariance.
method	str	"svi"	Inference method: "svi" (Stochastic Variational Inference) or "mcmc" (Hamiltonian NUTS).
cuda	bool	False	Use GPU computation (SVI only, requires CUDA-enabled PyTorch build).
include_latent	bool	True	Include latent factors when computing predictions (Full predictions). Set False for counterfactual (environment-only) predictions.
return_means	bool	True	Return posterior means (True) or full posterior samples (False).
batch_size	int	None	Mini-batch size for SVI training (None fits all data in one step).
pred_batch_size	int	None	Site-chunk size for prediction output (None uses full-batch prediction).
categorical_cols	list	None	Explicit list of column names in x to treat as categorical variables (e.g. label-encoded integers).

Method-Specific Arguments (**kwargs)

• SVI (method="svi"):
  • num_iterations=2500: Number of training steps.
  • lr=0.01: Adam optimizer learning rate.
  • num_samples=1000: Number of posterior samples to draw for predictions.
• MCMC (method="mcmc"):
  • num_samples=1000: Number of posterior samples.
  • warmup_steps=500: Warmup (burn-in) steps for NUTS.

---

Ecological Response Models

1. Linear Model (model_type="linear")

Models species responses linearly (on the logit scale). Good baseline model.

p_linear = compute_dark_diversity(
    y, x,
    model_type="linear",
    method="svi",
    num_iterations=2000
)

2. Gaussian Niche Model (model_type="gaussian")

Models symmetric, bell-shaped (quadratic niche) responses relative to predictors. Suitable for continuous gradients (e.g. temperature, elevation).

p_gaussian = compute_dark_diversity(
    y, x,
    model_type="gaussian",
    method="svi"
)

3. Bayesian Neural Network Model (model_type="bnn")

Models highly complex, non-linear interactions using a single hidden-layer BNN. Best for complex datasets and mixed continuous/one-hot inputs.

p_bnn = compute_dark_diversity(
    y, x,
    model_type="bnn",
    method="svi",
    hidden_size=10  # size of BNN hidden layer
)

---

Handling Categorical & Label-Encoded Data

Columns with dtypes of category, object, bool, or string are automatically auto-detected and one-hot encoded, while continuous variables are standardized.

If your categorical data is label-encoded as integers (e.g. landuse represented by 0, 1, 2), specify them explicitly using categorical_cols to prevent the model from treating them as continuous:

predictions = compute_dark_diversity(
    y, x,
    model_type="linear",
    categorical_cols=["landuse"]
)

---

Counterfactual Prediction Flow

To calculate dark diversity, run predictions both with and without latent factors:

# 1. Full prediction (environment + latent factors)
p_full = compute_dark_diversity(
    y, x, model_type="gaussian", include_latent=True
)

# 2. Counterfactual prediction (environment only)
p_env = compute_dark_diversity(
    y, x, model_type="gaussian", include_latent=False
)

# 3. Dark Diversity Proxy (Species pool index)
dark_diversity = p_full - p_env

---

Working with Count Data

If your species matrix y contains counts (integers $\ge 0$) instead of binary presence/absence, the package automatically infers the data type and fits a Poisson likelihood instead of Bernoulli:

# y contains count values (e.g., abundance)
abundance_predictions = compute_dark_diversity(
    y_abundance, x,
    model_type="gaussian"
)

---

Extra Evaluation & Plotting Utilities

The package includes utility modules under extras/ to evaluate model performance and plot predictions:

from extras.evaluation import compute_overall_error_metrics
from extras.plots import plot_environmental_response, plot_spatial_predictions

# 1. Evaluate performance (returns AUC, Brier Score, F1, etc.)
metrics = compute_overall_error_metrics(
    true_probabilities=true_values,
    predicted_probabilities=p_gaussian,
    observed_y=y
)
print("Model Performance:", metrics)

# 2. Plot spatial probability distribution maps
plot_spatial_predictions(
    probabilities=p_gaussian,
    coords=coords,
    species_name="species_1",
    y=y
)

Output Files

• mat_fact_predicted_probabilities_full.csv: Predicted species occurrence probabilities including all effects
• mat_fact_predicted_probabilities_env_only.csv: Predicted probabilities using only environmental effects
• mat_fact_dark_diversity_proxy.csv: Dark diversity estimates (full - env_only)

Data Format

survey.csv

site_id,species_1,species_2,...,species_n,ID,x,y
site_1,0,1,0,...,1,id_1,100.5,200.3
site_2,1,0,1,...,0,id_2,101.2,201.5
...

• Rows: Sites/locations
• Columns: Species (0/1 presence/absence) + ID + spatial coordinates
• Note: ID and spatial coordinates are automatically extracted/dropped

env.csv

site_id,temp,pH,elevation,...,ID,landuse
site_1,15.2,7.1,500,...,id_1,degraded
site_2,14.8,6.9,520,...,id_2,pristine
...

• Rows: Sites matching survey.csv
• Columns: Environmental predictors + ID + land-use
• Note: ID and land-use columns are dropped; only abiotic predictors are used

Interpretation of Results

Dark Diversity Proxy Values

• High values (close to 1): Species should be present based on environment but are absent—candidate for restoration
• Low values (close to 0): Species absence explained by environmental conditions
• Negative values: Model predicts species should be absent (rare, indicates environmental unsuitability)

Key Metrics

• AUC (Area Under ROC Curve): Overall model discrimination (0.5 = random, 1.0 = perfect)
• Brier Score: Prediction calibration error (lower is better)
• F1 Score: Balance between precision and recall

Advantages of This Approach

✓ No subjective benchmarking: Automated separation of environmental vs. unmeasured effects
✓ Mathematically principled: Latent factors naturally absorb degradation signals
✓ Scalable: SVI handles thousands of species and sites
✓ Species-specific: Each species can have unique environmental responses
✓ Reproducible: Fully probabilistic framework with clear assumptions

Limitations

• Assumes species responses are log-linear (logit link)
• Requires sufficient environmental variation to estimate effects reliably
• May overestimate dark diversity if detection is imperfect
• Computational cost increases with number of species and sites
• Requires careful tuning of number of latent factors

References & Theoretical Background

Key Concepts

• Joint Species Distribution Models (JSDMs): Latent variable models for multivariate species data
• Matrix Factorisation: Low-rank decomposition of high-dimensional species matrices
• Stochastic Variational Inference: Scalable Bayesian inference for probabilistic models
• Counterfactual Predictions: Causal inference approach to estimate potential outcomes