Core individual-based model simulation script and landscape data

Description

Notes

Methods

The model landscapes were generated by sampling Gaussian random fields with zero mean and a variance-covariance structure with specified parameters. 

Individual-based model:

On each simulated landscape, semelparous individuals mature during every non-overlapping generation and each produces a Poisson-distributed number of propagules, after which the sessile adult dies instantaneously. The propagules disperse according to a bivariate Gaussian kernel with mean zero and a variance-covariance matrix. Propagules that disperse into the matrix die immediately and do not influence local competition. Those that disperse into habitat experience density-dependent competition with other recruits, influencing their probability of becoming established as members of the next generation. We estimated the local propagule densities by convolving the distribution of propagules with a competition kernel. The code for simulating all individual-level processes is vectorized to improve runtimes.

To model regional stochasticity, we assumed that the fecundity rate varies over space and time. Variation was assumed to be independent among generations (no temporal autocorrelation). Fecundity was spatially correlated, such that it is multivariate log-normally distributed. We randomized the spatial distribution of habitat quality over time by resampling a Gaussian random field for fecundity rate at the start of each generation.

In our first simulation script (sim_persistence), we investigate how the classical relationships between metapopulation persistence time (i.e., mean-time to global extinction) and model parameters could be altered on fragmented landscapes. In this analysis, we sample square subregions of a given area from each pre-generated landscape 1, reset the periodic boundary condition, and simulate metapopulation dynamics until no individual remains or the generation limit is reached. This part of our analysis assumes globally synchronized environmental stochasticity, which we describe by randomizing a global value of fecundity rate per generation. In the case of mass-action mixing, propagules disperse uniformly, and offspring competitions are influenced by global rather than local density. We also test the effects of habitat aggregation and, by extension, fragmentation per se by collecting the habitat fragments in each previously sampled subregion into a square patch and rerunning the simulations.

In our second simulation script (sim_abundance), we explore how fragmentation mediates metapopulation abundance (i.e., global population density). Here, each simulation continues for a fixed number of generations long enough for metapopulation abundance to reach quasi-stationarity. Two values of mean fecundity rate are used to represent a contrast in reproductive output: on the habitat-poor landscapes, one gives rise to global persistence and the other to global extinction. We then compare our abundance predictions to results from the stochastic mean-field (Beverton-Holt) model.

In our third simulation script (sim_synchrony), we estimate metapopulation synchrony in the forms of spatial correlations in local occupancy and local abundance, conditional on persistence. Each landscape is divided into a grid of square sampling sites; neighboring sites are separated by one lattice spacing. To measure local occupancy, we determine the fraction of habitat cells that are occupied on sampling sites containing habitat. To measure local abundance, we calculate the number of occupants divided by the number of habitat cells on nonempty sites. Since any inherent spatial synchrony in the system can be confounded if, at the time of measurement, a vast majority of sampling sites is either vacant or fully occupied, we adjust the mean fecundity rates to keep mean global population size always within a standard, ecologically informative range.