Sequences of patch disturbance in a spatial eco-evolutionary model

Perturbation responses in co‐evolved model meta‐communities

“…As with regular migration in the model, neighboring patches are considered to be the 2-4 (non-diagonally) adjacent patches. This set of experiments was previously tested for two ensembles with reduced species range resulting from different dispersal rules (Abernethy, 2021), and in a set of models that were compared with the observations of empirical experiments on white-footed mice (Burns & Grear, 2008).…”

“…Populations may only move between patches that are directly adjacent on the two‐dimensional spatial lattice, and are prohibited from moving diagonally, so $$$ {\delta}_{j,k,x,y}=1 $$$ if and only if either $$$ \mid j-x\mid =1 $$$ and $$$ k=y $$$ or $$$ j=x $$$ and $$$ \mid k-y\mid =1 $$$ (and $$$ {\delta}_{j,k,x,y}=0 $$$ otherwise). In order to generate emergent meta‐communities composed of species with a range of more than 1–2 patches, while preventing homogenization of the spatial network, we combine two dispersal mechanisms previously used (Abernethy, 2021), so that a small portion of each local population is constantly attempting to enter the neighboring patches, but much greater emigration will occur from patches where that population has declined since the previous ecological time step, with the fraction of the remaining population that emigrates proportional to the relative loss suffered. This is given by:…”

“…The spatial eco‐evolutionary model used to generate the trophic meta‐communities is a modification of that employed previously in Abernethy ( 2021 ) based on the original formulation by Drossel et al ( 2001 ). The model design was previously explained in (Abernethy, 2020 ), with the main distinction being the formulation of the rules governing the movement.…”

“…Previous studies have used population dynamics on food webs specified by hand (Eklöf & Ebenman, 2006 ) or constructed with assembly models (Berg et al, 2015 ). However, recent work has extended eco‐evolutionary community models with the explicit spatial structure to develop a class of eco‐evolutionary meta‐community models (Abernethy, 2021 ; Abernethy et al, 2019b ; Allhoff, Weiel, et al, 2015 ; Bolchoun et al, 2017 ; Hagen et al, 2021 ; Hamm & Drossel, 2021 ; Rogge et al, 2018 ). While not readily amenable to mathematical analysis, co‐evolved model ecosystems display more realistic structural patterns emerging from their evolutionary dynamics (Allhoff, Ritterskamp, et al, 2015 ; Loeuille & Loreau, 2005 , 2009 ) than can be achieved by models of community assembly via invasions from a pre‐defined pool (Romanuk et al, 2019 ).…”

“…In addition to the applied ecology and conservation literature, the response of model communities to perturbation is also a question that arises out of the stability-complexity debate (McCann, 2000) in the study of complex networks (ecological and otherwise), and this model has its heritage in the statistical physics literature. The response of its generated communities to species deletion (Quince et al, 2005) and patch disturbance (Abernethy, 2021) has been previously investigated, and this work will further generalize how such eco-evolutionary models respond to perturbation while also addressing the need described above for more developed modeling solutions to the questions of applied ecology. Here, we improve the species range by a modified dispersal function and investigate the role of species properties in invasion dynamics, how the distribution of species governs the relative impact of different types of patch-level disturbance, and the optimal placement and connectedness of nature reserves in the spatial metanetwork.…”