Fitting individual-based models of spatial population dynamics to long-term monitoring data

Anne-Kathleen Malchow, Guillermo Fandos, Urs G. Kormann, Martin U. Grüebler, Marc Kéry, Florian Hartig & Damaris Zurell

Abstract

Generating spatial predictions of species distribution is a central task for research and policy. Currently, correlative species distribution models (cSDMs) are among the most widely used tools for this purpose. However, a fundamental assumption of cSDMs, that species distributions are in equilibrium with their environment, is rarely fulfilled in real data and limits the applicability of cSDMs for dynamic projections. Process‐based, dynamic SDMs (dSDMs) promise to overcome these limitations as they explicitly represent transient dynamics and enhance spatiotemporal transferability. Software tools for implementing dSDMs are becoming increasingly available, but their parameter estimation can be complex. Here, we test the feasibility of calibrating and validating a dSDM using long‐term monitoring data of Swiss red kites (Milvus milvus). This population has shown strong increases in abundance and a progressive range expansion over the last decades, indicating a nonequilibrium situation. We construct an individual‐based model using the RangeShiftR modeling platform and use Bayesian inference for model calibration. This allows the integration of heterogeneous data sources, such as parameter estimates from published literature and observational data from monitoring schemes, with a coherent assessment of parameter uncertainty. Our monitoring data encompass counts of breeding pairs at 267 sites across Switzerland over 22 years. We validate our model using a spatial‐block cross‐validation scheme and assess predictive performance with a rank‐correlation coefficient. Our model showed very good predictive accuracy of spatial projections and represented well the observed population dynamics over the last two decades. Results suggest that reproductive success was a key factor driving the observed range expansion. According to our model, the Swiss red kite population fills large parts of its current range but has potential for further increases in density. We demonstrate the practicality of data integration and validation for dSDMs using RangeShiftR. This approach can improve predictive performance compared to cSDMs. The workflow presented here can be adopted for any population for which some prior knowledge on demographic and dispersal parameters as well as spatiotemporal observations of abundance or presence/absence are available. The fitted model provides improved quantitative insights into the ecology of a species, which can greatly aid conservation and management efforts.

What the paper shows and why it matters

(AI-generated)

Correlative species distribution models (cSDMs) are among the most used tools for predicting where species occur. They relate known occurrences to environmental conditions, which makes them flexible and easy to fit. They also assume that a distribution is in equilibrium with its environment, an assumption often violated for expanding or recovering populations. Process-based dynamic models (dSDMs), which simulate demography and dispersal, promise to avoid that assumption but are used less, because their parameters are hard to estimate and their predictions hard to validate. The study asks whether these obstacles can be overcome with existing tools.

The study shows that an individual-based model of a species’ spatial population dynamics can be fitted to long-term monitoring data with Bayesian inference and validated by cross-validation, and that it then predicts a range-expanding bird population very well overall. The test case is the Swiss red kite (Milvus milvus). The model simulates the reproduction, survival and dispersal of individual birds. Priors for its parameters come from the literature; Bayesian inference then updates them with counts of breeding pairs at 267 monitoring sites. To test predictions for unseen regions, each spatial block of sites is held out in turn and the fit repeated. The study suggests a gain over correlative models, but only by comparison with an earlier study of the same survey data (Briscoe et al. 2021), not in a direct test. The data informed only some parameters clearly, and the fitted model suggests that reproductive success was a key driver of the range expansion.

**Figure 5.** Mean posterior predicted population densities for years 1999 and 2019, and after 20 additional years under constant conditions (left column) as well as the differences between those years (right column). From Malchow et al. (2024), *Ecological Applications*, licensed under CC BY 4.0. Click the image to enlarge.

The study presents the workflow as a practical route to process-based models that represent transient dynamics rather than assuming equilibrium, transferable to any population with some prior knowledge of demographic and dispersal parameters and records of abundance or presence and absence. Because fitted parameters have ecological meaning, fitting can itself yield insight: for the red kite, the model suggests that the population fills large parts of its current range but has room for further increases in density. Only some parameters can be estimated, and which ones depends on the available data, so well-founded priors remain important. Jeltsch et al. (2025) cite the study in support of their expectation that advances in integrating individual-based modelling with big-data approaches will facilitate wider use of complex model–data fusion.

References

Briscoe et al. (2021). Can dynamic occupancy models improve predictions of species' range dynamics? A test using Swiss birds. Global Change Biology 27, 4269–4282. doi:10.1111/gcb.15723
Jeltsch et al. (2025). The need for an individual-based global change ecology. Individual-based Ecology 1, 1–18. doi:10.3897/ibe.1.148200