Spread dynamics of invasive species

Abstract

Species invasions are a principal component of global change, causing large losses in biodiversity as well as economic damage. Invasion theory attempts to understand and predict invasion success and patterns of spread. However, there is no consensus regarding which species or community attributes enhance invader success or explain spread dynamics. Experimental and theoretical studies suggest that regulation of spread dynamics is possible; however, the conditions for its existence have not yet been empirically demonstrated. If invasion spread is a regulated process, the structure that accounts for this regulation will be a main determinant of invasion dynamics. Here we explore the existence of regulation underlying changes in the rate of new site colonization. We employ concepts and analytical tools from the study of abundance dynamics and show that spread dynamics are, in fact, regulated processes and that the regulation structure is notably consistent among invasions occurring in widely different contexts. We base our conclusions on the analysis of the spread dynamics of 30 species invasions, including birds, amphibians, fish, invertebrates, plants, and a virus, all of which exhibited similar regulation structures. In contrast to current beliefs that species invasions are idiosyncratic phenomena, here we provide evidence that general patterns do indeed exist.

Fig. 1.

Schematic representation of different dynamic processes (Left) and their associated feedback structures (i.e., R-functions) (Right). Unregulated processes such as exponential growth (A) and random walk (B) do not present a negative feedback structure that stabilizes the system at some equilibrium value, as is observed in a regulated process (C). Dynamics were generated from the following processes: exponential, log(N_t+1) = R + log(N_t), where R is constant; random walk, log(N_t+1) = log(N_t) + R_t, where R is a set of random numbers taken from a normal distribution; and a regulated process, N_t+1 = N_t + R_t, where R_t = a - b N_t + e_t, where e_t is a set of random numbers taken from a normal distribution.

Fig. 2.

Observed R-functions for the 30 taxonomically distinct organisms analyzed in this study. In all plots, the y axis is the rate of change in S (i.e., R_t), and the x axis is S, as in Fig. 1. Estimated parameters, their statistical significance, and explained variance from the complete model are indicated within each plot. All cases indicate strong regulation of spread. Only two cases were best described by nonlinear R-functions (far right column, rows four and five).

Fig. 3.

Schematic of the proposed mechanism for spread regulation. The shaded area represents sites within the dispersal kernel. The semishaded area represents sites that are outside of the invasion front, because no empty sites are available within the dispersal kernel of these sites. The dispersal kernel depends on the age of invaded sites, because newly invaded sites do not produce propagules and, thus, do not contribute to the kernel. At t = 1 only those sites that are within the invader's dispersal kernel are truly available for colonization. If a large proportion of available sites are colonized (i.e., there is a large number of newly colonized sites at t = 2, and, thus, S_t is high), few empty sites can be colonized in the next time step (i.e., there are few newly colonized sites at t = 3), and so spread is reduced at t = 2. This dynamic is observed in the value of R_t, which is negative at t = 1, indicating a deceleration in spread. At t = 3 a large number of empty sites are again available for colonization, and a large number of new invasions are observed at t = 4, resulting in a high value of S_t+2. Consequently, R_t+1 is now positive, indicating acceleration in spread. This sequence is repeated throughout the invasion process, producing “sawtooth” dynamics in invasion spread, which are also called linear first-order dynamics. This dynamic is detected in the R-function as a negative slope that is 0 for some value of spread, indicating the existence of regulated dynamics. Regulation occurs as a result of two mechanisms: (i) “competition” for empty sites, reinforced by (ii) the time lag between invasion and propagule production.