Statistical Assessment of Climate Change Effects on Biodiversity Using Generalized Linear Models

INTRODUCTION

The accelerating loss of global biodiversity is increasingly linked to climate change through warming, precipitation shifts, drought intensification, and extreme weather events. Projected exposure to warming indicates that insects, vertebrates, and plants face substantially different levels of risk under 1.5°C and 2°C warming pathways, while observed biodiversity redistribution is already altering ecosystem structure and human well-being (Pecl et al., 2017; Warren et al., 2018). Large-scale biodiversity time series further show that community composition is changing across marine and terrestrial systems, although the direction and magnitude of local change vary by region and taxonomic group (Blowes et al., 2019; Antão et al., 2020). These patterns require statistical approaches that distinguish climate signals from background ecological variability, land-use pressure, and imperfect observation.

Quantifying climate-biodiversity relationships is challenging because many response variables are counts, proportions, or binary outcomes rather than continuous normally distributed measurements (Carpio-Vargas et al., 2023; Huata-Panca et al., 2025). Species richness and abundance are non-negative integers, occupancy is often recorded as presence or absence, and community change may be summarized through indices with bounded or skewed distributions (Hudson et al., 2017; Dornelas et al., 2018). Citizen-science and monitoring data also contain uneven spatial coverage, variable sampling intensity, and repeated observations through time, all of which complicate direct comparison among sites (Johnston et al., 2020; Torres-Cruz et al., 2025). As a result, ordinary least squares regression may produce inefficient, biased, or biologically impossible predictions when applied to biodiversity responses without distributional adjustment.

Generalized linear models offer a flexible statistical framework for ecological data because they connect the expected value of a response to predictors through a link function while allowing non-normal error distributions. Poisson, binomial, and negative binomial models can represent count, binary, and overdispersed count responses, respectively, making them suitable for richness, abundance, and occurrence analyses (Brooks et al., 2017; Warton, 2018). Species distribution modeling standards emphasize transparent model specification, evaluation, and reporting because inference about climate effects depends strongly on the response distribution, predictor selection, and validation strategy (Araújo et al., 2019; Zurell et al., 2020; Carita et al., 2025). For ecological count data, negative binomial models are especially important when variance exceeds the mean and transformation-based approaches fail to solve the underlying distributional problem (Warton, 2018).

This article argues that a rigorous GLM framework can produce interpretable and statistically defensible estimates of climate effects on biodiversity when it correctly specifies error structure, tests overdispersion, includes effort offsets, and evaluates nonlinear climate responses. Model comparison using information criteria, cross-validation, and structured residual diagnostics is necessary because biodiversity data often include spatial, temporal, and hierarchical dependence (Roberts et al., 2017; Valavi et al., 2018; Norberg et al., 2019). Mixed-effects extensions and diagnostic tools improve robustness when site-level heterogeneity, repeated observations, or excess zeros violate simple independence assumptions (Brooks et al., 2017; Harrison et al., 2018; Lüdecke et al., 2021). The resulting effect estimates can be translated into incidence rate ratios, odds ratios, and marginal predictions that directly inform conservation planning under climate change.

Figure 1 presents the hierarchical analytical workflow linking biodiversity monitoring data, climate covariates, GLM family selection, diagnostic evaluation, and conservation interpretation

Background

Climate change impacts on biodiversity

Climate change affects biodiversity through phenological shifts, range contractions, local extinctions, altered abundance, and restructuring of ecological communities. Empirical and projected studies indicate that species responses differ among taxa, biomes, and climate zones, with tropical and temperate systems often showing different capacities for tracking suitable climates (Román-Palacios & Wiens, 2020; Freeman et al., 2021). Abrupt ecological disruption is expected when climate exposure exceeds species-specific tolerances across assemblages, and extinction risk increases when climatic change interacts with dispersal limitation and habitat degradation (Trisos et al., 2020; Wiens & Zelinka, 2024). These processes justify statistical models that can estimate both linear and nonlinear climate effects across repeated biodiversity observations.

Key climate predictors in ecological studies

Key climate predictors include annual mean temperature, seasonal temperature variability, total precipitation, precipitation anomalies, drought indices, growing degree days, heatwave frequency, and extreme weather events. High-resolution products such as WorldClim, CHELSA, CRU TS, and ERA5-Land provide gridded climate variables that can be matched to ecological monitoring locations at annual or seasonal resolutions (Fick & Hijmans, 2017; Karger et al., 2017; Harris et al., 2020; Muñoz-Sabater et al., 2021). Temperature-related biodiversity change has been detected across temperate marine and terrestrial systems, while precipitation and drought are especially important where water availability constrains productivity, occupancy, and population growth (Antão et al., 2020; Outhwaite et al., 2022). Including both central-tendency variables and climate extremes is therefore necessary to avoid underestimating climate stress.

Biodiversity response metrics

Biodiversity responses can be expressed as species richness counts, abundance indices, occupancy states, community composition, or diversity indices such as Shannon and Simpson measures. Global time-series resources and human-impact databases show that richness and abundance data often arise from repeated monitoring, transects, plots, or opportunistic occurrence records, each with distinct sampling properties (Hudson et al., 2017; Dornelas et al., 2018). Count responses are discrete and frequently overdispersed, while occupancy responses are binary and require a probability model rather than a Gaussian mean model (Araújo et al., 2019). These statistical properties determine whether the appropriate GLM family is Poisson, negative binomial, binomial, or an extension such as a zero-inflated or mixed-effects model.

Limitations of linear models for count and binary data

Linear models are limited for ecological count and binary data because they assume constant variance, normally distributed residuals, and unbounded continuous outcomes. For species counts, this can generate negative fitted values and misleading standard errors, particularly when the count variance increases with the mean or contains many zeros (Warton, 2018). For presence/absence responses, linear probability models can predict probabilities below zero or above one, whereas binomial GLMs constrain predictions to the valid probability range through the logit link (Araújo et al., 2019). These limitations are amplified in climate-biodiversity applications because climate gradients often create nonlinear responses and heterogeneous uncertainty across sites.

Generalized linear models as a solution

Generalized linear models address these limitations by modeling the conditional mean of the response through a link function and an exponential-family or related distribution. For richness counts, the log link ensures positive fitted means, while for occurrence data, the logit link maps linear predictors to probabilities between zero and one (Brooks et al., 2017; Warton, 2018). Maximum likelihood estimation allows direct comparison among candidate models through AIC, likelihood ratio tests, and information-theoretic evidence, provided the model family reflects the observed mean-variance relationship (Harrison et al., 2018; Norberg et al., 2019). This makes GLMs a practical foundation for climate ecology because effect sizes can be interpreted as multiplicative changes in counts or odds under specified climate increments.

Data sources and study design

Biodiversity response data

The study design uses a hypothetical longitudinal dataset from 50 monitoring sites surveyed annually over 10 years, producing 500 site-year observations. The primary response is species richness count for vascular plants or breeding birds, with supplementary abundance indices and presence/absence outcomes available for sensitivity analysis. Sampling effort is recorded as person-hours, transect length, checklist duration, trap nights, or number of survey visits, allowing effort to be incorporated as an offset rather than treated as an ordinary covariate. This design is consistent with long-term biodiversity time-series databases and monitoring schemes that compile repeated ecological observations across sites and years (Dornelas et al., 2018; Johnston et al., 2020).

Climate covariates

Climate covariates are assigned to each site-year using gridded climate products at matched spatial and temporal resolution. Annual mean temperature, represented by Bio1, and annual precipitation, represented by Bio12, can be extracted from WorldClim v2.1 at approximately 1-km resolution, while CHELSA, CRU TS, and ERA5-Land provide complementary climate surfaces and time-varying meteorological estimates (Fick & Hijmans, 2017; Karger et al., 2017; Harris et al., 2020; Muñoz-Sabater et al., 2021). Growing-season temperature from April to September and summer drought intensity, summarized as SPEI-3 or an analogous drought index, are included to capture biologically relevant seasonal stress. This covariate structure allows the GLM to test whether biodiversity responds more strongly to annual climate means, seasonal constraints, or short-term drought exposure.

Confounding and contextual variables

Confounding variables include land use type, elevation, year, habitat fragmentation, and spatial coordinates, all of which can influence biodiversity independently of climate. Land-use change and agricultural intensification are known to interact with climate pressure, particularly for insects and other taxa sensitive to both habitat conversion and thermal stress (Hudson et al., 2017; Outhwaite et al., 2022). Elevation is included because it structures local temperature, precipitation, dispersal barriers, and species pools, while year captures unmeasured temporal trends such as policy shifts, disease outbreaks, or observer protocol changes. Spatial coordinates are retained for residual autocorrelation checks and for possible transition to clustered standard errors or mixed models if independence assumptions are not supported (Roberts et al., 2017; Valavi et al., 2018).

Exploratory data analysis and dispersion assessment

Distribution of biodiversity responses

Exploratory analysis begins with histograms, frequency tables, and mean-variance plots for species richness and abundance counts. Under a Poisson GLM, the theoretical variance equals the mean, so an empirical variance-mean ratio greater than one indicates overdispersion and motivates a negative binomial specification (Warton, 2018). Biodiversity time-series data commonly display heterogeneity among sites, years, and taxa, making overdispersion plausible before formal modeling (Dornelas et al., 2018; Blowes et al., 2019). The count distribution should also be inspected for excess zeros, high-leverage observations, and unusually rich sites that may dominate the fitted climate response.

Pairwise relationships with climate variables

Pairwise relationships between biodiversity responses and climate predictors are examined using scatterplots, binned summaries, and loess smoothing. These visual checks are important because temperature effects may be unimodal, with richness increasing under moderate warming but declining beyond physiological or ecological thresholds (Antão et al., 2020; Freeman et al., 2021). Boxplots across temperature and precipitation quantiles help reveal whether extreme heat, drought, or precipitation anomalies are associated with compressed richness distributions or elevated absence probabilities (Trisos et al., 2020; Outhwaite et al., 2022). Such exploratory evidence guides whether the GLM should include quadratic temperature terms, interaction terms, or later sensitivity analysis with generalized additive models.

Preliminary dispersion testing

Preliminary dispersion testing is conducted by fitting a Poisson GLM and calculating the Pearson chi-square statistic divided by the residual degrees of freedom. A value near one supports the Poisson mean-variance assumption, whereas values above 1.5 indicate overdispersion that can inflate type I error if ignored (Warton, 2018; Lüdecke et al., 2021). Simulated residual diagnostics can supplement this calculation by evaluating whether residuals are uniform, whether zeros are more frequent than expected, and whether dispersion remains after covariate adjustment (Lüdecke et al., 2021). If overdispersion persists, the negative binomial GLM becomes the primary count model rather than a secondary robustness check.

Generalized linear model specification

Table 1 provides a decision matrix for matching biodiversity response variables to GLM families, link functions, diagnostic risks, and interpretable climate effect measures.

Table 1. Decision matrix for selecting GLM-family models in climate-biodiversity analysis

Base model for count data

The base count model is a negative binomial generalized linear model with a log link because species richness is non-negative, discrete, and expected to be overdispersed. The model is specified as , where  represents survey duration, transect length, or another measure of sampling intensity. The negative binomial dispersion parameter θ is estimated separately, with smaller θ values indicating stronger overdispersion relative to a Poisson model (Brooks et al., 2017; Warton, 2018). Coefficients are interpreted after exponentiation as incidence rate ratios, giving the multiplicative change in expected richness for a one-unit change in each climate predictor.

Alternative model for presence/absence

The alternative presence/absence model uses a logistic GLM with binomial error and a logit link. The model is specified as , with optional adjustment for land cover, elevation, and year when occurrence records are drawn from heterogeneous monitoring contexts. This formulation is appropriate for occupancy-style responses because it estimates the probability that a species or taxonomic group is recorded at a site-year rather than treating presence as a continuous outcome (Araújo et al., 2019; Johnston et al., 2020). Exponentiated coefficients are interpreted as odds ratios, which provide a direct measure of how climatic conditions alter the odds of observed presence.

Inclusion of nonlinear and interaction terms

Nonlinear and interaction terms are included to reflect the ecological expectation that climate effects are not always monotonic. A quadratic temperature term is specified as , allowing estimation of a temperature optimum when β3 is negative. A Temp×Precip interaction tests whether warming effects differ under wet and dry conditions, which is important when thermal stress is intensified by aridity or reduced by water availability (Antão et al., 2020; Trisos et al., 2020; Outhwaite et al., 2022). Candidate models are compared using AIC, cross-validation, and ecological interpretability rather than relying only on statistical significance (Roberts et al., 2017; Valavi et al., 2018; Norberg et al., 2019).

Handling overdispersion, zero inflation, and offsets

Comparing poisson vs. negative binomial

The Poisson and negative binomial count models are compared by examining the dispersion statistic, likelihood-based evidence, and AIC. A likelihood ratio test can be used when models are nested or comparable, while an AIC difference greater than two provides practical evidence favoring the negative binomial model if it improves fit without excessive complexity (Harrison et al., 2018; Norberg et al., 2019). The dispersion parameter θ is reported because smaller θ indicates stronger extra-Poisson variation, which is common in biodiversity monitoring where unobserved habitat quality, observer differences, and local population aggregation inflate count variance (Brooks et al., 2017; Warton, 2018). In the present GLM framework, negative binomial superiority over Poisson would support the conclusion that richness responses to temperature and precipitation cannot be modeled reliably under an equidispersion assumption.

Zero-inflated models as sensitivity test

Zero-inflated models are used as a sensitivity test when observed zeros exceed the number expected under the fitted Poisson or negative binomial model. In climate-biodiversity data, excess zeros may arise from unsuitable habitat, local extinction, dispersal limitation, imperfect detection, or stochastic absence during extreme weather years (Román-Palacios & Wiens, 2020; Trisos et al., 2020). A zero-inflated negative binomial model separates the ecological process generating structural zeros from the count process generating observed abundance or richness, and packages such as glmmTMB allow this structure to be estimated flexibly (Brooks et al., 2017). Comparing standard and zero-inflated specifications helps determine whether apparent climate effects reflect changes in expected richness, changes in occupancy suitability, or both.

Inclusion of offsets for sampling effort

An offset for sampling effort is included when the number of species or individuals observed depends partly on survey duration, transect length, checklist number, trap nights, or observer time. The offset term offset(log(Effort_i)) fixes the effort coefficient at one, so the model estimates biodiversity rates rather than raw counts that are confounded by unequal sampling intensity (Johnston et al., 2020). This is essential for citizen-science and long-term monitoring data because spatial and temporal variation in recorder effort can mimic ecological change if not explicitly modeled (Hudson et al., 2017; Dornelas et al., 2018). In practical terms, the fitted model estimates how expected richness changes with temperature and precipitation after standardizing observations to a common effort scale.

Interpreting climate effect sizes and uncertainty

Incidence rate ratios for count models

In the negative binomial GLM, exponentiated coefficients are interpreted as incidence rate ratios. If β1 represents annual mean temperature, then e^(β1) gives the multiplicative change in expected species richness associated with a 1°C increase, holding precipitation, effort, land cover, elevation, and year constant (Brooks et al., 2017; Warton, 2018). Confidence intervals can be estimated using profile likelihood or robust standard errors, and their interpretation should emphasize effect magnitude as well as statistical uncertainty. This approach is more informative for conservation planning than reporting coefficients only on the log scale because it translates climate effects into proportional gains or losses in biodiversity (Belfiore et al., 2024; Figueroa-Valverde et al., 2024; Karatas, 2024; Lee & Ferreira, 2024; Negreiros & Ory, 2024).

Marginal effects and predicted biodiversity surfaces

Marginal effects plots are used to show predicted richness or occurrence across climate gradients while holding other covariates at representative values. For the quadratic temperature model, the temperature optimum is identified where the derivative of the linear predictor with respect to temperature equals zero, giving Temp_optimum = -β1/(2*β3) when β3 is negative (Antão et al., 2020; Freeman et al., 2021). Predicted biodiversity surfaces over temperature and precipitation gradients can reveal whether richness declines most strongly under hot-dry conditions, moderate warming, or precipitation deficits (Trisos et al., 2020; Outhwaite et al., 2022). These visual summaries support interpretation of nonlinear GLM results without requiring readers to infer ecological thresholds from coefficient tables alone (Abdullah et al., 2025; Jagsi et al., 2025; Kęska & Suchy, 2024; Kounatidis et al., 2024; Lee & Ferreira, 2024; Noor et al., 2024; Petronis et al., 2025; Schneider & Krüger, 2025; Wong et al., 2025; Yu et al., 2025).

Contribution of climate vs. land use

The relative contribution of climate and land use is assessed by comparing nested models: a full model containing climate, land use, elevation, effort, and year against reduced models that remove climate terms or remove land-use terms. Changes in AIC, likelihood, and pseudo-R² indicate whether climate predictors explain variation beyond habitat conversion, agricultural intensity, and other human pressures (Hudson et al., 2017; Outhwaite et al., 2022). Because agriculture and climate change can jointly reshape biodiversity, the interpretation should avoid treating climate coefficients as purely causal unless confounders and spatial structure are adequately addressed (Outhwaite et al., 2022). Measures such as marginal and conditional R² are particularly useful when the GLM is extended to a mixed-effects model with site or year random effects (Nakagawa et al., 2017).

Practical implications for conservation planning

Identifying climate-sensitive biodiversity hotspots

Fitted GLMs can be used to predict biodiversity under alternative future climate scenarios, including moderate and high-emissions pathways, by applying estimated climate coefficients to projected temperature and precipitation surfaces. Areas where predicted richness or occurrence declines sharply can be classified as climate-sensitive biodiversity hotspots and prioritized for protection, restoration, or assisted connectivity (Trisos et al., 2020; Warren et al., 2018). This is especially important because projected ecological disruption may occur abruptly when multiple species cross climatic thresholds within a short period (Trisos et al., 2020). The same modeling framework can also identify potential climate refugia where predicted biodiversity remains relatively stable despite regional warming.

Designing climate-adapted monitoring

GLM outputs can guide climate-adapted monitoring by estimating the number of sites, years, or repeated surveys needed to detect a specified biodiversity trend with acceptable uncertainty. Standard errors from negative binomial and logistic models can be incorporated into simulation-based power analysis, allowing monitoring designs to account for overdispersion, baseline richness, and expected climate variability (Roberts et al., 2017; Johnston et al., 2020). Long-term biodiversity databases show that repeated observation is essential because climate signals are often embedded within substantial spatial, temporal, and taxonomic variation (Dornelas et al., 2018; Blowes et al., 2019). A model-based monitoring design is therefore more efficient than uniform sampling when climate risk is spatially structured and sampling resources are limited.

Model evaluation and validation strategy

Table 2 consolidates the diagnostic and validation checkpoints required to distinguish robust climate-biodiversity inference from model artifacts caused by dispersion, sampling effort, dependence, or extreme years (Carpio-Vargas et al., 2023; Belfiore et al., 2024; Figueroa-Valverde et al., 2024; Karatas, 2024; Lee & Ferreira, 2024; Negreiros & Ory, 2024; Wolderslund et al., 2024; Carita et al., 2025; Huata-Panca et al., 2025; Torres-Cruz et al., 2025).

Table 2. Analytical checkpoints for strengthening inference from climate-biodiversity GLMs