PS 53-93 - The importance of negative and nonlinear density-emigration relationships

Thursday, August 10, 2017
Exhibit Hall, Oregon Convention Center
Rachel R. Harman1, Jerome Goddard II2, Ratnasingham Shivaji3 and James T. Cronin1, (1)Biological Sciences, Louisiana State University, Baton Rouge, LA, (2)Mathematics, Auburn University Montgomery, (3)Mathematics and Statistics, University of North Carolina Greensboro

A key process affecting metapopulation and metacommunity dynamics is dispersal. Published models suggest that qualitative differences in the relationship between emigration rate and density can profoundly influence population persistence. For example, compared to a positive-linear density-emigration rate, an accelerating or decelerating nonlinear rate can increase or decrease extinction risk respectively. In addition, different life history traits (e.g., gregariousness and macroptery) may be important indicators of a particular density-emigration relationship.

We performed a literature review to synthesize what is known about the relationship between emigration, density, and specie’s life history. We hypothesized that linear-positive density-emigration relationships would show in the majority of papers, but we predicted that nonlinearity is common, when rigorously tested, and that there is overlooked diversity in the relationship forms (e.g., U-shaped and negative).

To address some of our perceived weaknesses in characterizing the density-emigration relationship, we supplemented the review with two additional cases. We conducted emigration experiments using a solitary planthopper, Prokelisia marginata, and a gregarious bug, Ischnodemus falicus, which occur on the same host plant in a coastal marsh system. We hypothesize that the solitary and gregarious insects would show nonlinear-positive and nonlinear-negative relationships respectively.


Of the 1,556 publications meeting our search criteria, 98 articles included data on density-emigration relationships. Overall, emigration was density independent in 40%, positive density dependent in 33%, and negative density dependent in 22% of the studies. In 27% of the studies there was clear evidence of nonlinearity.

P. marginata exhibited a nonlinear-positive relationship and I. falicus showed a nonlinear-negative curve, matching our hypothesis. Cursory results of our literature survey show no evidence that life history is correlated with the density-emigration relationship. Our survey indicates that the likelihood of detecting a nonlinear relationship increases with the number of densities included in the study (t108=1.88, p=0.03). Given that the average number of density levels included in published studies is small, especially for experimental studies, the occurrence of nonlinear density dependent emigration may be much more common in nature than our literature review would suggest.

Research investigating the density-emigration relationship should look at a wide range of densities with many treatments. This may allow nonlinear or overlooked relationships to be more ubiquitous in future literature. Qualitative differences in the relationship may influence metapopulation and metacommunity dynamics, such as population persistence, and should be given more consideration.