The effects of connectivity on metapopulation persistence: network symmetry and degree correlations

Abstract

A spatial metapopulation is a mosaic of interconnected patch populations. The complex routes of colonization between the patches are governed by the metapopulation's dispersal network. Over the past two decades, there has been considerable interest in uncovering the effects of dispersal network topology and its symmetry on metapopulation persistence. While most studies find that the level of symmetry in dispersal pattern enhances persistence, some have reached the conclusion that symmetry has at most a minor effect. In this work, we present a new perspective on the debate. We study properties of the in-and out-degree distribution of patches in the metapopulation which define the number of dispersal routes into and out of a particular patch, respectively. By analysing the spectral radius of the dispersal matrices, we confirm that a higher level of symmetry has only a marginal impact on persistence. We continue to analyse different properties of the in-out degree distribution, namely the 'in-out degree correlation' (IODC) and degree heterogeneity, and find their relationship to metapopulation persistence. Our analysis shows that, in contrast to symmetry, the in-out degree distribution and particularly, the IODC are dominant factors controlling persistence.

Classical metapopulation dynamics and eco‐evolutionary feedbacks in dendritic networks

“…In this sense, our results are in good accordance with evidence from population genetics (Morrissey andde Kerckhove 2009, Paz-Vinas andBlanchet 2015), metapopulation (Bascompte and Solé 1996, Fagan 2002, Vuilleumier and Possingham 2006, Labonne et al 2008, Gilarranz and Bascompte 2012, Shtilerman and Stone 2015 and metacommunity ecology (Holland and Hastings 2008, Salomon et al 2010, Carrara et al 2012, Seymour et al 2015 as well as the geographic mosaic of coevolution (Nuismer 2006, Nuismer et al 1999, 2000, Gibert et al 2013, for example. In this sense, our results are in good accordance with evidence from population genetics (Morrissey andde Kerckhove 2009, Paz-Vinas andBlanchet 2015), metapopulation (Bascompte and Solé 1996, Fagan 2002, Vuilleumier and Possingham 2006, Labonne et al 2008, Gilarranz and Bascompte 2012, Shtilerman and Stone 2015 and metacommunity ecology (Holland and Hastings 2008, Salomon et al 2010, Carrara et al 2012, Seymour et al 2015 as well as the geographic mosaic of coevolution (Nuismer 2006, Nuismer et al 1999, 2000, Gibert et al 2013, for example.…”

“…More generally, we highlight the relevance of taking the spatial structure of populations explicitly into account in order to understand and predict ecological and evolutionary dynamics. In this sense, our results are in good accordance with evidence from population genetics (Morrissey andde Kerckhove 2009, Paz-Vinas andBlanchet 2015), metapopulation (Bascompte and Solé 1996, Fagan 2002, Vuilleumier and Possingham 2006, Labonne et al 2008, Gilarranz and Bascompte 2012, Shtilerman and Stone 2015 and metacommunity ecology (Holland and Hastings 2008, Salomon et al 2010, Carrara et al 2012, Seymour et al 2015 as well as the geographic mosaic of coevolution (Nuismer 2006, Nuismer et al 1999, 2000, Gibert et al 2013, for example.…”

Spatial variation in branch size promotes metapopulation persistence in dendritic river networks

“…Here we develop a modelling framework for metapopulation dynamics in size-structured, bifurcating riverine networks based on the traditional metapopulation model (Hanski, 1998;Levins, 1969), which has become increasingly prevalent in the modern ecological literature as it has already proven extremely useful for understanding the interactive effects of variation in patch size, network topology, and dispersal asymmetry on metapopulation patterns (Shtilerman & Stone, 2015;Vuilleumier & Possingham, 2006). In our model, we further consider species dispersal directionality to reflect the reality that different species often display distinct dispersal behaviours, such as upstream only-dispersal, downstream-only dispersal, or two-way upstream and downstream dispersal (Schick & Lindley, 2007).…”

Network theory and metapopulation persistence: incorporating node self‐connections

“…; Grilli et al . ; Shtilerman & Stone ), raising questions about the causal inferences that can be drawn from such studies. In other cases, some network metrics have been hypothesised to be linked to persistence (e.g.…”

“…Some studies use idealised network topologies and isolate, from the effect other metrics could have, one or a few network metrics, such as asymmetry, to evaluate how metapopulation persistence responds to the network metric of interest (Kleinhans & Jonsson 2011). Others, however, do not completely isolate the focal metric's effect on persistence from the effect that other, potentially correlated, metrics could have (Vuilleumier & Possingham 2006;Bode et al 2008;Artzy-Randrup & Stone 2010;Kininmonth et al 2010;Vuilleumier et al 2010;Gilarranz & Bascompte 2012;Barbillon et al 2015;Grilli et al 2015;Shtilerman & Stone 2015), raising questions about the causal inferences that can be drawn from such studies. In other cases, some network metrics have been hypothesised to be linked to persistence (e.g.…”