The concerted emergence of well-known spatial and temporal ecological patterns in an evolutionary food web model in space

Abstract

Ecological systems show a variety of characteristic patterns of biodiversity in space and time. It is a challenge for theory to find models that can reproduce and explain the observed patterns. Since the advent of island biogeography these models revolve around speciation, dispersal, and extinction, but they usually neglect trophic structure. Here, we propose and study a spatially extended evolutionary food web model that allows us to study large spatial systems with several trophic layers. Our computer simulations show that the model gives rise simultaneously to several biodiversity patterns in space and time, from species abundance distributions to the waxing and waning of geographic ranges. We find that trophic position in the network plays a crucial role when it comes to the time evolution of range sizes, because the trophic context restricts the occurrence and survival of species especially on higher trophic levels.

Figure 1

Illustration of the food web construction. Species are determined by their body mass and Gaussian feeding kernels. Any species inside this feeding kernel is possible prey for a species. The inset shows the resulting food web.

Figure 2

(a) Time series for one habitat out of a grid of 10 $\times$ 10 habitats. At each time point the body masses of all species present at this habitat are plotted. The blue curve denotes species number in this habitat. (b) Food web structure and rank abundance curves for the three time points indicated in (a) by dashed vertical lines. Rank is determined by sorting species for their abundance. This results in the most abundant species having the smallest rank. Colors indicate trophic level (blue = basal, yellow = intermediate, red = top).

Figure 3

Patterns emerging in a square lattice of 1600 habitats for different dispersal rates d, note the logarithmic scaling of the axes. (a) Lifetime distributions are broad and close to a power law with exponent $-2.4$ (black, dashed), considerably steeper than the slope of $-1.67$ reported by (grey dotted). (b) SAR reach empirically reasonable values (black dashed, slope of 0.36) for intermediate areas. For large areas curves bend toward a slope of 1 (grey, dotted). Dispersal rate decreases the slope of the SAR. (c) Average area (number of occupied habitats over the lifetime of a species) increases with lifetime. Larger dispersal rate shifts the curve to larger areas. Dashed line has a slope of 1.

Figure 4

Range distribution and similarity decay with distance in a system with 400 habitats and a dispersal rate of 10. (a) Distribution of maximum and average range for the basal layer (TL1) and all other species (> TL1). Average range refers to the average number of habitats a species occupied during its lifetime. Dashed line has a slope of − 3, so most species have small ranges. (b) Food web similarity, measured by the Jaccard index for the same simulation as in (a), error bars denote standard deviation from the mean (for calculation see “Model and methods”). Similarity decreases with distance. The decrease is small for the basal layer, but steep for the higher trophic levels.

Figure 5

Collection of time evolution examples for range (black) and abundance-based rank (blue) of exemplary species from different trophic levels. Simulation set up was 400 habitats and a dispersal rate of 10. (a–c) Trophic level $\ge$ 3, (d–f) trophic level 2, (g–i) trophic level 1. Range evolution shows a triangular shape in some cases, especially often in the basal layer, whilst other species have large fluctuations in their range and rank over time.

Figure 6

Extinction causes for species on different trophic levels, again for a system of 400 habitats and a dispersal rate of 10. Blue shades refer to local processes, i.e., to speciation events, red shades refer to processes triggered by immigrants from neighbouring habitats. We sort events into classes depending on whether the change occurs in the same trophic level (competition) or in the trophic level below or above. ‘Sec’ denotes secondary extinctions, which occur as the result of a preceding extinction in the same simulation step. Basal species are mostly affected by incoming competitors, whilst higher trophic species are more sensitive to all kind of changes in the network, e.g. a rearrangement in the lower trophic level.