Turbulent dispersal promotes species coexistence

Abstract

Several recent advances in coexistence theory emphasize the importance of space and dispersal, but focus on average dispersal rates and require spatial heterogeneity, spatio-temporal variability or dispersal-competition tradeoffs to allow coexistence. We analyse a model with stochastic juvenile dispersal (driven by turbulent flow in the coastal ocean) and show that a low-productivity species can coexist with a high-productivity species by having dispersal patterns sufficiently uncorrelated from those of its competitor, even though, on average, dispersal statistics are identical and subsequent demography and competition is spatially homogeneous. This produces a spatial storage effect, with an ephemeral partitioning of a 'spatial niche', and is the first demonstration of a physical mechanism for a pure spatiotemporal environmental response. 'Turbulent coexistence' is widely applicable to marine species with pelagic larval dispersal and relatively sessile adult life stages (and perhaps some wind-dispersed species) and complements other spatial and temporal storage effects previously documented for such species.

Figure 1

Simulations of realized dispersal in the ROMS model (a–c) and the packet model (d–f). Each of the three panels in each row represents a different year and the color scale represents the number of larvae dispersing from a given source to a given destination. (g) Correlation in connectivity patterns between the two species as a function of the overlap in their spawning windows; packet model results are means of 12 000 realizations and the ROMS results are means of 28 realizations. Parameter values for the dispersal models (used here and in rest of figures) are: T_sp = 30 days; T_L = 14 days; r=50 km; C=500 km. The resulting number of successful ‘packets’ per year (P ; eqn 4) is 21. The spatial variance in the packet model connectivity matrix is 0.5332, compared with 0.5362 for the ROMS model.

Figure 2

Left: Mean population size of both species through time using diffusive dispersal (a) and packet model dispersal with no overlap in spawning (b). For diffusive dispersal σ_d = 81 km. Right: Spatio-temporal patterns in population size using packet model dispersal for species A (c) and species B (d) for a 100 year time span and over the centre 300 km of the domain. Demographic parameter values (for this and other figures) are: a=1; b=0.045; m=0.1; f_A = 0.1818; f_B = 0.1727.

Figure 3

Mean percentage of the total population size for each species after 1000 years (mean of 50 simulations) over a range of overlap in spawning from none to complete.

Figure 4

Coexistence thresholds from the spatially implicit model, relating correlation in settlement and the fecundity ratio of species B to species A. Coexistence occurs to the right of the lines. Panel (a) varies the intensity of density dependence by changing the fecundity of Species A. Panel (b) varies the variance in settlement.

Figure 5

Coexistence thresholds estimated from the spatially explicit and spatially implicit models. (a) All parameters as in Figure 2. (b) f_A = 0.1290. (c) f_A = 1. The white line indicates the coexistence threshold from the spatially implicit model; coexistence is predicted to the right of the line. Grey indicates the proportion of species B in the population after 1000 years in the spatially explicit model (averaged over five simulations at each parameter combination). Black indicates that species B is ‘extinct’ (the simulation model does not allow absolute extinction, so we define competitive exclusion to have occurred if species B is below 1% of the total population after 1000 years).

Figure 6

The per-capita recruitment rate of species A (solid symbols and curve) and species B (open symbols and dashed curve), as a function of species A settler density, when species B is rare. This is a snapshot in time, with the variation being across space. The circles represent each patch in a simulation of the spatially explicit model, and the curves are the predicted values of actual (species A) and expected (species B) recruitment rates in the spatially implicit model (see Appendix S1). The squares mark the mean settler density and recruitment rates in the spatially explicit model, revealing that the nonlinearities in the recruitment curves cause settlement variability to reduce the mean recruitment rate of species A and increase the mean recruitment rate of species B. All parameters as in Fig. 2.