2.1. D-SPOM: coupling spatio-temporal dynamics wetland hydrology and metapopulation patch occupancy

LB L. E. Bertassello EB E. Bertuzzo GB G. Botter JJ J. W. Jawitz AA A. F. Aubeneau JH J. T. Hoverman AR A. Rinaldo PR P. S. C. Rao

This protocol is extracted from research article:

Dynamic spatio-temporal patterns of metapopulation occupancy in patchy habitats

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R Soc Open Sci**,
Jan 13, 2021;
DOI:
10.1098/rsos.201309

Dynamic spatio-temporal patterns of metapopulation occupancy in patchy habitats

DOI:
10.1098/rsos.201309

Procedure

We developed a dynamic version of the stochastic patch occupancy model, SPOM [6,39,40], to simulate the presence/absence of a given species in a time-varying wetlandscape. SPOM computes the distribution of occupied patches, in discrete time steps, by considering focal species traits (extinction, colonization and dispersal distance) and patch spatial organization (patch gap distances). A binary state variable, *p _{i}*(

Similarly, species in occupied patches can go extinct with a probability

A discrete time SPOM is a homogeneous first-order Markov chain in which the state of the metapopulation at time *t* + 1 depends only on the state (occupancy pattern) of the metapopulation at time *t* [39]. For each patch and each time step, the probabilities of colonization and extinction events depend on colonization and extinction rates with exponential survival probability [41]

and

where Δ*t* is the simulation time step and *C _{i}*(

The key difference between the static and dynamic SPOM is that while SPOM assumes static conditions for landscape patches, D-SPOM captures the time variability in habitat structure, embedded by the amount of suitable habitat, *S _{i}*(

where *d _{ij}*(

In classical metapopulation theory [9,42], the metapopulation capacity, *λ*_{max}, is derived for a static landscape (i.e. *S _{i}*(

The theoretical prediction of the classical metapopulation theory [6,9] is that a species can persist whenever *λ*_{max} > *e*/*c*. However, when simulating the stochastic discrete process using SPOM, a species with *λ*_{max} slightly above the threshold *e*/*c* could go extinct due to demographic stochasticity. The novelty we introduce here with the D-SPOM consists in calculating the metapopulation capacity *λ*_{max} at each discrete time step because of the different hydrological habitat conditions, *d*_{ij}(*t*), *S*_{i}(*t*) and *S*_{j}(*t*) that are manifested at time *t*. In a dynamic landscape, *λ*_{max}(*t*) represents the survival threshold for the hydrologic conditions at time *t*. Metapopulation dynamics are estimated in terms of wetlandscape occupancy, Ω(*t*), which identifies the temporal dynamics of the fraction of patches that are occupied by a focal species.

The advantage of the proposed D-SPOM approach is to explicitly account for patch dynamics influencing habitat availability and accessibility for a focal species. The model requires two fundamental variables of metapopulation dynamics: habitat suitability (e.g. patch areas) and connectivity (e.g. gap distances). The key novelty introduced here is to consider the two quantities as temporally variable, driven by external stochastic forcing. Following Bertassello *et al.* [26], we estimated temporal fluctuations in attributes (e.g. surface area) of each wetland resulting from the net of precipitation falling over each wetland contributing area, evapotranspiration losses and water exchanged with shallow groundwater (see electronic supplementary material for details). The choice of an appropriate proxy for habitat suitability, *S _{j}*(

In this work, *S _{j}*(

Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.

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