Some Definitions: Inverse Density-Dependence Occurs When

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Some definitions: Inverse density‐dependence occurs when the per capita rate of population growth increases as population sizes become larger. An Allee effec t refers to inverse ditdensity‐dddependence at low population densities. It can, but does not have to, lead to a negative population growth rate below a critical population size. Some mechanisms that lead to Allee effects: • Demographic stochasticity (particularly w.r.t. sex ratios) • Loss of genetic diversity • => mutational meltdown • => exposure of deleterious recessives through ibinbree ding • Loss of cooperative benefits • => defense (for prey, or pathogens) • => foraging success (for predators) • => inability to attract pollinators • => loss of ‘environmental conditioning’ (plants) • => many others Genetic drift is less effective at eliminating mildly deleterious mutations in small populations N=20 N=50 N=200 The extinction vortex (a term coined by Gilpin & Soulé, 1986) suggests that “as populations decline, an insidious mutual reinforcement can occur among biotic and abiotic processes such as environmental stochasticity, demographic stochasticity, inbreeding, and behavioural failures, driving population size downward to extinction” (text from Fagan & Holmes, 2006) . A major prediction of the extinction vortex is that “declines beget further declines”, thus accelerating a population’ s collapse as species near extinction. Fagan & Holmes (Ecology Letters 2006): evidence for an extinction vortex in local extinctions of vertebrates? Population ecology (led by Sir Robert May) played a major role in the mathematical discovery of chaos in the early 1970s. Chaos is found in systems with strong non‐linearities. Discrete‐time population growth models with strong density‐dependence provide such a setting. One of the signatures of chaos is a sensitive dependence on initial conditions. This sensitive dependence implies that chaotic systems are fundamentally unpredictable over long time scales, even in the absence of stochasticity. The 1980s witnesses an enthusiastic hunt for chaotic dynamics in ecological systems. Ultimately, the pursuit fizz le d withou t any satis fac tory resolltiution. Chaos: sensitive dependence on initial conditions Red begins with N0=0.5. Blue begins with N0=0.5001..

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Modeling Techniques
Appendix A Modeling Techniques A.1 Population Growth Models Using Differential Equations Our main goal here is to introduce a few modeling techniques we use throughout this book. We do not intend however to provide here the fundamentals on modeling, a tutorial or a review. For these, we refer to other sources (DeAngelis et al. 1992; Ford 2009; Grimm et al. 2006; Kuang 1993). This Appendix is rather a refresher as well as an example of why using different modeling techniques for one and the same problem can be beneficial to understand biological processes better. We start with the simple exponential population growth to make modeling accessible even to complete beginners. Biologists generally define a population as a collection of individuals that belong to the same species and can potentially breed with each other. One of the best-known early models on population growth was outlined by Malthus (1798). He famously maintained that the human population is predicted to grow in an exponential manner, but the crucial products needed to sustain the population grow in but a linear manner. He argued that these different types of growths will trigger disasters when the population’s needs are not satisfied. The basic exponential growth model consists of a single positive feedback loop that arises from the fact that every individual (N) is predicted to have a fixed number of offspring (r), regardless of the size of the population, and thus also regardless of the remaining resources in the habitat: dN = rN dt (A.1.1) This exponential growth model had a profound effect on biology such as developing the theory of natural selection (Darwin 1859).
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Density dependence in demography and dispersal generates fluctuating invasion speeds Lauren L. Sullivana,1, Bingtuan Lib, Tom E. X. Millerc, Michael G. Neubertd, and Allison K. Shawa aDepartment of Ecology, Evolution and Behavior, University of Minnesota, Saint Paul, MN 55108; bDepartment of Mathematics, University of Louisville, Louisville, KY 40292; cDepartment of BioSciences, Program in Ecology and Evolutionary Biology, Rice University, Houston, TX 77005; and dBiology Department, Woods Hole Oceanographic Institution, Woods Hole, MA 02543 Edited by Alan Hastings, University of California, Davis, CA, and approved March 30, 2017 (received for review November 23, 2016) Density dependence plays an important role in population regu- is driven by reproduction and dispersal from high-density pop- lation and is known to generate temporal fluctuations in popu- ulations behind the invasion front (13–15)]. The conventional lation density. However, the ways in which density dependence wisdom of a long-term constant invasion speed is widely applied affects spatial population processes, such as species invasions, (16, 17). are less understood. Although classical ecological theory suggests In contrast to classic approaches that emphasize a long-term that invasions should advance at a constant speed, empirical work constant speed, there is growing empirical recognition that inva- is illuminating the highly variable nature of biological invasions, sion dynamics can be highly variable and idiosyncratic (18–25). which often exhibit nonconstant spreading speeds, even in sim- There are several theoretical explanations for fluctuations in ple, controlled settings. Here, we explore endogenous density invasion speed (which we define here as any persistent tem- dependence as a mechanism for inducing variability in biologi- poral variability in spreading speed), including stochasticity in cal invasions with a set of population models that incorporate either demography or dispersal (24–28) and temporal or spatial density dependence in demographic and dispersal parameters.
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CORE Metadata, citation and similar papers at core.ac.uk Provided by Digital Repository @ Iowa State University Ecology, Evolution and Organismal Biology Ecology, Evolution and Organismal Biology Publications 12-2006 Counterintuitive density-dependent growth in a long-lived vertebrate after removal of nest predators Ricky-John Spencer Iowa State University Fredric J. Janzen Iowa State University, [email protected] Michael B. Thompson University of Sydney Follow this and additional works at: http://lib.dr.iastate.edu/eeob_ag_pubs Part of the Evolution Commons, and the Population Biology Commons The ompc lete bibliographic information for this item can be found at http://lib.dr.iastate.edu/ eeob_ag_pubs/151. For information on how to cite this item, please visit http://lib.dr.iastate.edu/ howtocite.html. This Article is brought to you for free and open access by the Ecology, Evolution and Organismal Biology at Iowa State University Digital Repository. It has been accepted for inclusion in Ecology, Evolution and Organismal Biology Publications by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Counterintuitive density-dependent growth in a long-lived vertebrate after removal of nest predators Abstract Examining the phenotypic and genetic underpinnings of life-history variation in long-lived organisms is central to the study of life-history evolution. Juvenile growth and survival are often density dependent in reptiles, and theory predicts the evolution of slow growth in response to low resources (resource-limiting hypothesis), such as under densely populated conditions. However, rapid growth is predicted when exceeding some critical body size reduces the risk of mortality (mortality hypothesis).
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Arxiv:2009.11357V3 [Physics.Bio-Ph] 18 Apr 2021 H Rbblt Itiuino H Otrcn Common Recent Most 15]
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