Emerging predictable features of replicated biological invasion fronts

Abstract

Biological dispersal shapes species' distribution and affects their coexistence. The spread of organisms governs the dynamics of invasive species, the spread of pathogens, and the shifts in species ranges due to climate or environmental change. Despite its relevance for fundamental ecological processes, however, replicated experimentation on biological dispersal is lacking, and current assessments point at inherent limitations to predictability, even in the simplest ecological settings. In contrast, we show, by replicated experimentation on the spread of the ciliate Tetrahymena sp. in linear landscapes, that information on local unconstrained movement and reproduction allows us to predict reliably the existence and speed of traveling waves of invasion at the macroscopic scale. Furthermore, a theoretical approach introducing demographic stochasticity in the Fisher-Kolmogorov framework of reaction-diffusion processes captures the observed fluctuations in range expansions. Therefore, predictability of the key features of biological dispersal overcomes the inherent biological stochasticity. Our results establish a causal link from the short-term individual level to the long-term, broad-scale population patterns and may be generalized, possibly providing a general predictive framework for biological invasions in natural environments.

Keywords: Fisher wave; colonization; frontiers; microcosm; spatial.

Fig. 1.

Schematic representation of the experiment. (A) Linear landscape. (B) Individuals of the ciliate Tetrahymena sp. move and reproduce within the landscape. (C) Examples of reconstructed trajectories of individuals (Movie S1). (D) Individuals are introduced at one end of a linear landscape and are observed to reproduce and disperse within the landscape (not to scale). (E) Illustrative representation of density profiles along the landscape at subsequent times. A wavefront is argued to propagate undeformed at a constant speed v according to the Fisher–Kolmogorov equation.

Fig. 2.

Density profiles in the dispersal experiment and in the stochastic model. (A–F) Density profiles of six replicated experimentally measured dispersal events, at different times. Legends link each color to the corresponding measuring time. Black dots are the estimates of the front position at each time point. Organisms were introduced at the origin and subsequently colonized the whole landscape in 4 d ( generations). (G and H) Two dispersal events simulated according to the generalized model equation, with initial conditions as at the second experimental time point. Data are binned in 5-cm intervals, typical length scale of the process.

Fig. 3.

Range expansion in the dispersal experiment and in the stochastic model. (A) Front position of the expanding population in six replicated dispersal events; colors identify replicas as in Fig. 2. The dark and light gray shadings are, respectively, the and confidence intervals computed by numerically integrating the generalized model equation, with initial conditions as at the second experimental time point, in 1,020 iterations. The black curve is the mean front position in the stochastic integrations. (B) The increase in range variability between replicates in the dispersal experiment (blue diamonds) is well described by the stochastic model (red line). (C) Mean front speed for different choices of the reference density value at which we estimated the front position in the experiment; error bars are smaller than symbols.