Extinction debt in source-sink metacommunities

Abstract

In an increasingly modified world, understanding and predicting the consequences of landscape alteration on biodiversity is a challenge for ecologists. To this end, metacommunity theory has developed to better understand the complexity of local and regional interactions that occur across larger landscapes. While metacommunity ecology has now provided several alternative models of species coexistence at different spatial scales, predictions regarding the consequences of landscape alteration have been done exclusively for the competition-colonization trade off model (CC). In this paper we investigate the effects of landscape perturbation on source-sink metacommunities. We show that habitat destruction perturbs the equilibria among species competitive effects within the metacommunity, driving both direct extinctions and an indirect extinction debt. As in CC models, we found a time lag for extinction following habitat destruction that varied in length depending upon the relative importance of direct and indirect effects. However, in contrast to CC models, we found that the less competitive species are more affected by habitat destruction. The best competitors can sometimes even be positively affected by habitat destruction, which corresponds well with the results of field studies. Our results are complementary to those results found in CC models of metacommunity dynamics. From a conservation perspective, our results illustrate that landscape alteration jeopardizes species coexistence in patchy landscapes through complex indirect effects and delayed extinctions patterns.

Figure 1. Mean local species richness in the metacommunity for 20 species and 20 communities, with increasing proportion of dispersal among communities and different values of regional similarity ω (from 0 to 1 with 0.05 increments).

Other parameters are given in the text. We present means of 2000 simulations with different random matrices (Rand as defined in the methods). For clarity, we have omitted the standards deviation (however, they were always <15% of the means).

Figure 2. Direct and indirect consequences of habitat destruction.

(a) Example of the consequence of habitat destruction on species dynamics within one community included in a metacommunity. For clarity we have simulated a metacommunity with only 10 species and 10 communities. Parameters are as described in the methods with ω = 1 and a = 0.7 (these values of ω and a were chosen to clearly illustrate extinction patterns). The simulation was run for 5000 iterations with a delta of 0.1 for the Euler approximation. We present species abundances (proportion of occupied sites) as a function of time (log scale). The destruction of two communities was simulated when equilibrium was reached (here after 200 iterations). The dashed lines represent the species lost through the direct effect and the dotted line the species lost through the indirect effect (see text). (b) A simple example of how the destruction of some communities from the metacommunity will alter the complimentarity in species' competitive ability and decrease the level of regional similarity. The figure gives a hypothetical distribution of competitive abilities in a metacommunity consisting of three species (A, B and C) that occur across three communities (1, 2 and 3). Averaging species competitive abilities at the scale of the region (line below the matrix) is the simplest definition of regional competitive ability. The left matrix illustrates the extreme case of strict regional similarity between competing species as defined in the text: each species is the best competitor in one community, but the species have equal (similar) competitive abilities at the scale of the region. In the right matrix we destroy one community from the metacommunity (community 2) and show how it leads to less similarity at the scale of the region. One species (species A) will be lost through the direct effect but another species (species C) can also be excluded from the metacommunity by the species (species B) that is now the best competitor at the scale of the region.

Figure 3. Effect of habitat destruction fro difference values of dispersal and regional similarity.

Consequences of destroying 4 communities in a metacommunity of 20 communities and 20 competing species for different values of dispersal and regional similarity. We present means of 2000 simulations as described in the methods and the Fig. 1. (a) Total number of species lost (both through direct and indirect effects). (b) Net indirect effect (proportion of species lost because of the indirect vs. direct effects). Note that the z axis of the panel (a) has been limited to 8 species but the values go up to 15 species for high levels of dispersal and similarity. Note also that on the panel b, for clarity, we have not represented the values obtained for dispersal = 0 and 1. When dispersal = 0 there is no source sink dynamics and thus no indirect effect is possible (direct effect is always maximal when extinction happens, except at very low regional similarity when the distinction between sources and sink is less trivial). When dispersal = 1 the metacommunity is homogenized, local diversity is equal to one and there is no extinction after habitat destruction.

Figure 4. Regional Competitive abilities.

Distribution of regional competitive abilities of the species extinct through the indirect effect (left axis, grey distribution) and the species remaining into the metacommunity at the end of each simulation (right axis, white distribution). Light grey indicates where the two distributions overlap. The results have been obtained by combining results found for the simulations presented in Figure 1 and 3 with fixed regional similarity ω = 0.8 and all dispersal values (between 0 and 1). Note that similar tendencies are found for other values of regional similarity (Fig. S1).

Figure 5. Relaxation time.

(a) Distribution of the direct (left axes, grey distribution) and indirect (right axis, white distribution) values of relaxation time. We have combined all the values found obtained for all simulations (for all values of regional similarity and dispersal). Light grey has been used when the two distributions overlap.(b) Direct relaxation time with increasing dispersal and different values of regional similarity (ω = 0 white circles, ω = 0.5 light grey circles, ω = 0.7 dark grey circles, ω = 0.9 black circles). We present means calculated for 2000 simulations; parameters are given in methods. We do not present data where we found fewer than 30 simulations with regional extinctions (low values of dispersal). Standards deviations are omitted for clarity and are presented in Figure S2.