Density-Dependent Dispersal and Predator-Prey Population Dynamics

Project Overview

Dispersal can have major consequences for individual fitness, population dynamics, and species’ distributions. In light of the important need to predict how populations will respond to invasion and spread of alien species, habitat fragmentation, and climate change, understanding the causes and consequences of dispersal at both the patch and landscape levels is vital for population management and conservation. As the impact of dispersal on population dynamics is becoming increasingly recognized, the consequences and causes of dispersal have become a focus of much current research. Theoretical studies play an extremely important role in predicting the population level effects of dispersal. However, the assumptions of most theoretical models regarding the dispersal process often lack a great deal of realism, typically treating dispersal as a constant or a positive density-dependent (+DDD) response. Models have largely ignored alternative and nonlinear responses to density and the conditional dependency of dispersal (e.g., presence of interspecific competitors or predators).

Graph of Hypothetical DDD
Fig. 1. Forms of Density-dependent dispersal. A fixed dispersal rate or +DDD are almost universally used in population dynamics models. However, there are logical reasons for the occurrence of –DDD and UDDD.

In the literature, the dispersal process is usually considered to consist of three stages: 1) emigration, 2) inter-patch movement, and 3) immigration. Regarding the first stage of dispersal, empirical investigations have revealed several important factors influencing these stages of dispersal, particularly conspecific density. The paradigmatic view is that dispersal increases with density; i.e. positive density-dependent dispersal (Fig. 1). However, alternate forms of density dependent dispersal have been reported in the literature (e.g. Enfjall and Leimar 2005). Negative (-DDD) or U-shaped (UDDD) relationships between conspecific density and dispersal have been observed in a wide range of taxa. Thus, there are empirical observations indicating that individuals emigrate at higher rates from patches with low conspecific densities, corresponding to negative DDD (see Lawrence et al. 1973, Kuussaari et al. 1996, 1998). The U-shape in the relationship can arise if, at higher densities, emigration increases. Almost nothing is known regarding the influence of an interspecific competitor’s density on an organism’s dispersal patterns.

It has been suggested that -DDD could result from mate scarcity, conspecific attraction, which predicts lower emigration rates from high density populations, and habitat selection in which presence of conspecifics might be used as an indicator of suitable habitat. On the other hand, +DDD has been suggested to be a consequence of social interactions among the members of a local population. It has also been suggested that since a high density of conspecifics could indicate that vital resources are becoming scarce, organisms would suffer reduced habitat quality and thus exhibit emigration rates that increase with density.

Seemingly contradictory evidence for both +DDD and -DDD has simultaneously been observed in the same organism for both the Glanville fritillary butterfly, Melitaea cinxia (see Kuussaari et al 1996, 1998 for -DDD and Enjfarr and Leimar 2005 for +DDD) and the Blue-footed Booby, Sula nebouxii, (Kim et al. 2009). Kim et al. and Enfjall et al. both independently proposed a hypothesis to reconcile these contradictory patterns of DDD by integrating the conspecific hypothesis with the traditional competition hypothesis. They suggested that the relationship between density and dispersal is not linear but U-shaped (UDDD; Figure 1). U-shaped DDD can be brought about by the same factors that promote an Allee effect, a phenomenon in which the population growth rate is initially positively related to population density. For example, a gregarious herbivore at low density may not be able to effectively extract nutrients from its host or overwhelm plant defenses. Under these circumstances, Allee effects can be mitigated by dispersal. DDD and Allee effects have rarely been considered but their interactions can have profound effects on population dynamics. In the context of metapopulations or landscapes, interactions between Allee effects and DDD have not been explored.

With funding from NSF Mathematical Biology Program, we are in the process of examining different forms of DDD, habitat fragmentation, competition and predation and their effects of the population dynamics of natural and model systems. Experimental studies are being led by my graduate student, Rachel Harman, and me, and mathematical models are being developed by Jerome Goddard (Dept. of Mathematics & Computer Science, Auburn University, Montgomery) and Ratnasingham Shivaji (Department of Mathematics & Statistics, The University of North Carolina at Greensboro) (see photo).

group picture of field trip
Workshop and field trip to Cameron Jetties (Louisiana), February, 2016. PIs on the project include Ratnasingham Shivaji (left), Jim Cronin (5th from left), and Jerome Goddard (back right). Visiting Rachel Harman’s (bottom, right) field sites for this project.