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“Frequency of occurrence and population-dynamic consequences of different forms of density-dependent emigration”

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Rachel R. Harman, Jerome Goddard II, Ratnasingham Shivaji, and James T. Cronin (May 2020)

Density-dependent emigration (DDE) is more diverse than we thought! Review & population persistence of 5 forms of DDE

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Changing emigration patterns can have dynamic population consequences!

Individuals will emigrate from a patch for several reasons including to escape competition, avoid predators, find resources, or form a group. These emigrants in turn affect colonization and local densities of patches around the landscape, which can lead to changes in population persistence. The proportion of the population emigrating based on density (density-dependent emigration; DDE), has been widely accepted to be density-independent or positive density-dependent (DIE and +DDE respectively; see figure). However, other forms of DDE (see figure) are biologically possible.

But do these other forms of DDE even exist in nature? To answer this, Harman and associates reviewed 145 empirical studies of DDE to examine the range and frequency of each DDE relationship. As expected, the majority of these studies represented DIE and +DDE results; however, they regularly found the other forms of DDE (negative, u-shaped, and hump-shaped; see figure).

So, do these rare forms of DDE matter to population stability? Harman and associates claim that they do, particularly in small patches commonly found in fragmented landscapes. Using models incorporating patch size and landscape quality, the authors show that population persistence changes with the form of DDE. Negative and u-shape DDE forms allow for populations to survive in smaller patches, but at the risk of sudden extinction. Additionally, negative and hump-shaped DDE forms allow for different sized populations to persist in same-sized patches.

Harman and associates suggest that to limit bias against detecting non-linear DDE forms in nature, future research should utilize methods that include wider ranges of density treatments and statistics that test for all forms of DDE. With further investigation of these forms of DDE, better predictions for species conservation (such as metapopulation extinction and invasive species movement) are possible as the form of emigration can change if a population will persist.


Emigration is a fundamental process affecting species local, regional, and large-scale dynamics. 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. We reviewed the empirical literature to assess the frequency of different forms of density-dependent emigration and whether the form depended on methodology. We also developed a reaction-diffusion model to illustrate how different forms of DDE can affect patch-level population persistence. We found 145 studies, the majority representing DIE (30%) and +DDE (36%). However, we also regularly found −DDE (25%) and evidence for nonlinear DDE (9%), including one case of uDDE and two cases of hDDE. Nonlinear DDE detection is likely hindered by the use of few density levels and small density ranges. Based on our models, DIE and +DDE promoted stable and persistent populations. uDDE and −DDE generated an Allee effect that decreases minimum patch size. Lastly, −DDE and hDDE models yielded bistability that allows the 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.