A dynamic theory of the area of distribution

Abstract

Aims The aim of this study is to propose and analyse a general, dynamic, process‐oriented theory of the area of distribution. Location Mexico, Southern United States and the Caribbean. Taxon Pierid butterflies. Methods The area of distribution is modelled by combining (by multiplication) three matrices: one matrix represents movements, another niche tolerances and a third, biotic interactions. Results are derived from general properties of this product and from simulation of a cellular automaton defined in terms of the matrix operations. Everything is implemented practically in an R package. Results Results are obtained by simulation and mathematical analysis. We show that the mid‐domain effect is a direct consequence of dispersal; that to include movements to Ecological Niche Modelling significantly affect results, but cannot be done without choosing an ancestral area of distribution. We discuss ways of estimating such ancestral areas. We show that, in our approach, movements and niche effects are mixed in ways almost impossible to disentangle, and show this is a consequence of the singularity of a matrix. We introduce a tool (the Connectivity‐Suitability‐Dispersal plot) to extend the results of simple niche modelling to understand the effects of dispersal. Main conclusions The conceptually straightforward scheme we present for the area of distribution integrates, in a mathematically sound and computationally feasible way, several key ideas in biogeography: the geographic and environmental matrix, the Grinnellian niche, dispersal capacity and the ancestral area of origin of groups of species. We show that although full simulations are indispensable to obtain the dynamics of an area of distribution, interesting results can be derived simply by analysing the matrices representing the dynamics.

Predicting the dispersal and invasion dynamics of ambrosia beetles through demographic reconstruction and process-explicit modeling

“…Despite illustrating its use in invasive species, its application can be extended to the study of other kinds of organisms and species assemblages at multiple scales in space and time 53 . The key advantage of process-explicit models lies in the capability of explicitly incorporating ecological mechanisms to better understand the determinants of species distributions 53 , 164 . However, the development of a process-explicit model depends primarily on the biological assumptions that are being explored and the mathematical form of the model.…”

“…Therefore, while the Allee effect may not be as relevant in the specific case of Xyleborus species due to their capacity for sib-mating or arrhenotokous inbreeding 67 , it is crucial to recognize its potential impact on other taxonomic groups that rely on it whenever this methodology and simulations are employed. Given the challenges associated with parameterizing demography-dependent process-explicit models, an alternative could be cellular automata models, where system states are presence/absence and a binarized niche model along with a first-neighbor dispersal kernel would suffice to estimate invasion paths 164 . However, these models cannot capture the level of complexity that process-explicit models like ours do, which incorporate demography and other key factors in many ecological and evolutionary processes.…”

The dispersal patterns of a migratory insect are driven by biotic interactions

“…All the simulations were performed in R, using the ‘bamm’ package (Soberón & Osorio‐Olvera, 2023). The R code needed to replicate these analyses is available at https://github.com/claununez/Dispersal_Urania (https://doi.org/10.5281/zenodo.7926299), and all data needed are available at https://doi.org/10.6084/m9.figshare.19217592 (Nuñez‐Penichet et al, 2022).…”

Calibration areas in ecological niche and species distribution modelling: Unravelling approaches and concepts

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