Density-Dependent Emigration 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. The paradigmatic view in ecology is that emigration is density independent (DIE) or positive density dependent (+DDE).

However, alternative forms are biologically plausible, including negative (-DDE), u-shaped (uDDE), and hump-shaped (hDDE) forms (Fig 1).

Graph of Hypothetical DDE
Fig. 1. Forms of Density-dependent dispersal. DIE or +DDE are almost universally used in population dynamics models. However, there are biologically plausible reasons for the occurrence of –DDE, uDDE and hDDE.

We reviewed the empirical literature to assess the frequency of different forms of DDE and whether the likelihood of each form depended on taxonomic group or methodology (Harman et al. in review). We also developed a reaction-diffusion model to illustrate how different forms of DDE can affect patch-level population persistence. We found that the majority of studies exhibited DIE (30%) and +DDE (35%) but all other forms were evident in the literature: –DDE (25%), uDDE (6%) and hDDE (4%). There was no taxon bias in the detection of different forms of DDE. Based on our models, DIE and +DDE promoted stable and persistent populations. –DDE and uDDE generated an Allee effect that decreases minimum patch size. Lastly, -DDE and hDDE models yielded bi-stability that allows establishment of populations at lower densities. We conclude that the emigration process can be a diverse function of density in nature and that alternative DDE forms can have important consequences for population dynamics.

With funding from NSF Mathematical Biology Program in 2015 and a renewal of our grant in 2019, we have been examining how different forms of DDE, habitat fragmentation, competition (intra- and interspecific) and predation can affect the population dynamics of natural and model systems. Experimental studies are being led by my graduate student, Rachel Harman, and me, using Tribolium flour beetles as a model system. 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.

In a paper recently accepted for publication in the Bulletin of Mathematical Biology (Cronin et al. 2019), we developed a framework to facilitate the connection between small-scale movement and patch-level predictions of persistence through a mechanistic model based on reaction-diffusion equations. The model is flexible and can incorporate information about patch preference, movement behavior, and matrix-induced mortality. We mathematically analyzed the model’s predictions of persistence based on assumptions on the patch/matrix interface. Finally, we illustrated the utility of this framework with a well-studied planthopper species (Prokelisia crocea) living in a highly fragmented landscape. Qualitatively, the model results are in accord with experimental predictions regarding minimum patch size of P. crocea.

Current objectives of the project are three-fold:

(1) investigate the effects of conspecific and interspecific density, patch size and matrix hostility on species dispersal behavior, patch-level population dynamics and coexistence

(2) extend this work to the landscape-scale by exploring the effects of competition and conditional dispersal on population dynamics and coexistence in multi-patch systems

(3) parameterize models with data from dispersal experiments using two Tribolium flour beetle species and compare model predictions about coexistence and stability with results from long-term experiments.