Impact of colonization history on the composition of ecological systems

Observational studies of ecological systems have shown that different species compositions can arise from distinct species arrival orders during community assembly—also known as colonization history. The presence of multiple interior equilibria in the positive orthant of the state space of the population dynamics will naturally lead to history dependency of the final state. However, it is still unclear whether and under which conditions colonization history will dominate community composition in the absence of multiple interior equilibria. Here, by considering that only one species can invade at a time and there are no recurrent invasions, we show clear evidence that the colonization history can have a big impact on the composition of ecological systems even in the absence of multiple interior equilibria. In particular, we first derive two simple rules to determine whether the composition of a community will depend on its colonization history in the absence of multiple interior equilibria and recurrent invasions. Then we apply them to communities governed by generalized Lotka-Volterra (gLV) dynamics and propose a numerical scheme to measure the probability of colonization history dependence. Finally, we show, via numerical simulations, that for gLV dynamics with a single interior equilibrium, the probability that community composition is dominated by colonization history increases monotonically with community size, network connectivity, and the variation of intrinsic growth rates across species. These results reveal that in the absence of multiple interior equilibria and recurrent invasions, community composition is a probabilistic process mediated by ecological dynamics via the interspecific variation and the size of regional pools.

Figure 1

Ecological communities can display different dependencies on colonization history. For illustration purposes, we show the assembly of a three-species community $\{1,2,3\}$ by the invasion or colonization of one species at a time, following the gLV dynamics. There are in total $3!=6$ different colonization trajectories. (a) The ecological network depicts the pairwise interactions among the three species (which are also encoded in the interaction matrix $\mathbf{A}$). The feasible intrinsic growth rate vector $\mathbf{r}$ is set to be ${\left(\frac{1}{3},\frac{1}{3},\frac{1}{3}\right)}^{\top }$. (b) Starting from an empty ecological community $⌀$ (top node), the three species are added successively into the community via different orders. Since species 2 and 3 cannot coexist (gray node), the community composition will be dependent on colonization history. That is, the final state of the three species together cannot be assembled if we follow the trajectory $⌀\to 3\to 2\to 1$ or $⌀\to 2\to 3\to 1$, while the other four trajectories will lead to the desired final state. (c) As an example, we show two different trajectories and their final community compositions. Panels (d)–(f) show a similar case as the previous example but with different interaction matrix $\mathbf{A}$. In this case, the community composition is independent on colonization history.

Figure 2

The probability $P$ that community composition depends on colonization history as a function of community properties. $P$ is calculated as a function of community properties: community size $S$, connectance $C$, and interaction types, using the gLV model (line plots with error bars) or the null model (lines). (Top) $P$ as a function of connectance $C$, with fixed community size $S=10$. Bottom: $P$ as a function of community size $S$, with fixed connectance $C=0.5$. Each column corresponds to a particular interaction type: random interactions, predator-prey, and mixture of competition and mutualism.

Figure 3

The probability $P$ that community composition depends on colonization history as a function of intrinsic properties of species. The probability is calculated for different levels of interspecific variation $\xi$ (intrinsic growth rate) and interaction types, using the gLV model (line plots with error bars) or the null model (lines). We fix community size $S=8$ and network connectance $C=0.4$. Each column corresponds to a particular interaction type: random interactions, predator-prey, and mixture of competition and mutualism.