Spatial network structure and metapopulation persistence

Abstract

We explore the relationship between network structure and dynamics by relating the topology of spatial networks with its underlying metapopulation abundance. Metapopulation abundance is largely affected by the architecture of the spatial network, although this effect depends on demographic parameters here represented by the extinction-to-colonization ratio (e/c). Thus, for moderate to large e/c-values, regional abundance grows with the heterogeneity of the network, with uniform or random networks having the lowest regional abundances, and scale-free networks having the largest abundance. However, the ranking is reversed for low extinction probabilities, with heterogeneous networks showing the lowest relative abundance. We further explore the mechanisms underlying such results by relating a node's incidence (average number of time steps the node is occupied) with its degree, and with the average degree of the nodes it interacts with. These results demonstrate the importance of spatial network structure to understanding metapopulation abundance, and serve to determine under what circumstances information on network structure should be complemented with information on the species life-history traits to understand persistence in heterogeneous environments.

On the evolution of dispersal via heterogeneity in spatial connectivity

“…The landscape structure of our IBM was modelled as four different types of networks (figure 1) of increasing heterogeneity: regular, random, exponential and scale-free [35] (note that landscape and network are used interchangeably). To understand the effects of network heterogeneity, all networks were set with the same number of nodes (n p ¼ 1024 patches), edges (n c ¼ 4096 connections) and average degree (eight connections per patch).…”

Survivability of a metapopulation under local extinctions

“…Thus a patch will benefit more if it is connected to a higher degree patch, and the effect may be larger than the patch's own degree. Therefore, if we target to inactivate the hubs, the metapopulation persistence decreases [17]. In all the cases, the abundance of the metapopulation is very high until the inactivation ratio p reaches a critical value p c , but in the case of random inactivation the chances of metapopulation persistence are higher compared to targeted inactivations.…”

“…Like physicists, ecologists are also placing more importance on the study of networks of coupled oscillators. The rationale behind studying complex networks lies in the fact that the network topology highly affects its dynamics and some recent papers have explicitly investigated the dynamical consequences of network patterns [16][17][18].…”

Extinction cascades partially estimate herbivore losses in a complete Lepidoptera–plant food web

“…In the future, it will be important to independently assess the realism of these different extinction scenarios, as each of these scenarios result in different subsequent extinctions (Srinivasan et al 2007). Moreover, the network models used here were conservative in that they only took into account the topological structure of the herbivore-plant network, and these types of analysis may underestimate extinction risks, as they fail to account for interaction strengths between species and the resulting changes to population dynamics (Gilarranz and Bascompte 2012). Moreover, in a previous study, we showed that there is a relationship between the specificity of host plants by the larval and adult stages of these Lepidopterans, but that the strongest specificity is in the larval stage (Altermatt and Pearse 2011).…”