Variability of biological spread rates in uniform and heterogeneous landscapes: microcosm experiments and mathematical models
Dispersal is a key ecological process, fundamental to the understanding of invasive species dynamics, range shifts due to climate change and species distribution and coexistence. Biological invasions can pose threats to endangered species and may have detrimental economic impact.
Traditionally, biological invasions have been modeled via deterministic reaction-diffusion processes, in particular the Fisher-Kolmogorov equation. Most theoretical investigations of reaction-diffusion models considered invasions in uniform landscapes. Despite the widespread application of these models to describe field data, however, replicated experimentation is very limited to date. Furthermore, deterministic models cannot provide information on the stochasticity of invasions and current assessments point at inherent limitations to predictability owing to large variability even in simple ecological settings.
Here, we answer the following questions: Can we predict the speed of invasions by measuring species traits locally? How do demographic and environmental stochasticity affect invasion dynamics?
We performed laboratory experiments with Tetrahymena sp. (in uniform linear landscapes) and Euglena gracilis (in heterogeneous linear landscapes) measuring the invasion speed over ecological timescales. The reproduction (growth rate and demographic stochasticity) and movement (diffusion coefficient) of Tetrahymena sp. were measured locally in independent experiments. Heterogeneous landscapes were created by manipulating light, the resource for the photosynthetic protist E. gracilis.
We found excellent agreement between the Fisher-Kolmogorov prediction for the invasion speed in uniform landscapes and the experimental propagation speed. We generalized the Fisher-Kolmogorov equation to include demographic stochasticity and found quantitative agreement between the variability of spread rates across replicates in the model and in the experiments. Results are published in Giometto, A. et al (2014), PNAS 111(1).
In a second experiment, two treatments were performed to study the effect of spatial autocorrelation of resources on invasion speed. Treatment 1(2) had large(small) resource autocorrelation length. The total amount of resources was identical in all replicates. We further generalized the Fisher-Kolmogorov equation to account for heterogeneous resource distributions and directed movement towards resources (E. gracilis performs phototaxis). We verified experimentally the model prediction that the invasion speed decreases with increasing resource autocorrelation length. The model predicts that demographic stochasticity is necessary to cause such slowing-down.
The implications for ecology are manifold. We suggest that demographic stochasticity strongly affects invasion dynamics. We provide a general mathematical framework and a flexible experimental system to study variability in biological invasions. Our findings suggest new hypotheses to test in the field, such as the slowing-down of invasions according to the degree of resource heterogeneity.