Can inverse density dependence at small spatial scales produce dynamic instability in animal populations?

Abstract

All else being equal, inversely density-dependent (IDD) mortality destabilizes population dynamics. However, stability has not been investigated for cases in which multiple types of density dependence act simultaneously.To determine whether IDD mortality can destabilize populations that are otherwise regulated by directly density-dependent (DDD) mortality, I used scale transition approximations to model populations with IDD mortality at smaller "aggregation" scales and DDD mortality at larger "landscape" scales, a pattern observed in some reef fish and insect populations. I evaluated dynamic stability for a range of demographic parameter values, including the degree of compensation in DDD mortality and the degree of spatial aggregation, which together determine the relative importance of DDD and IDD processes. When aggregation-scale survival was a monotonically increasing function of density (a "dilution" effect), dynamics were stable except for extremely high levels of aggregation combined with either undercompensatory landscape-scale density dependence or certain values of adult fecundity. When aggregation-scale survival was a unimodal function of density (representing both "dilution" and predator "detection" effects), instability occurred with lower levels of aggregation and also depended on the values of fecundity, survivorship, detection effect, and DDD compensation parameters. These results suggest that only in extreme circumstances will IDD mortality destabilize dynamics when DDD mortality is also present, so IDD processes may not affect the stability of many populations in which they are observed. Model results were evaluated in the context of reef fish, but a similar framework may be appropriate for a diverse range of species that experience opposing patterns of density dependence across spatial scales.

Meiobenthic communities in permanently open estuaries and open/closed coastal lagoons of Uruguay (Atlantic coast of South America)

“…The zero-inflated component of the models accounts for the potential problems of heterogeneity in dispersion due to excessive zeros in the samples. In addition, the choice of the negative binomial distribution account for aggregation, that is common in soft sediment benthic organisms Gim enez and Yannicelli, 2000;Barbone and Basset, 2010;White, 2011;G omez and Defeo, 2012). Other solutions to these problems may consist in modelling presence/absence with logistic regression (e.g.…”

Density‐dependent prey behaviours and mutable predator foraging modes induce Allee effects and over‐prediction of prey mortality rates

“…For example, Sandin and Pacala (2005) found predation on aggregating blue chromis (Chromis cyanea) to decrease as a function of group size and Stier et al (2013) found a similar pattern in shoaling bluntnose wrasse (Thalassoma amblycephalum). The degree to which inverse density dependence (Allee, 1941), leads to population instability depends on the strength of the Allee effect (Kramer et al, 2009) as well as co-occurring compensation (White, 2011). Kramer and Drake (2010) showed an increase in the probability of extinction as prey density declined from a predator-driven Allee effect in Daphnia magnus populations.…”

“…Redistribution of prey and predators across the landscape would probably occur in response to the local decline of prey density as prey seek to reduce predation risk through aggregation (Sutherland, 1983) and predators seek to reduce mutual interference (Kacelnik, Krebs, & Bernstein, 1992). White et al (2010) and White (2011) proposed that the patch defined by predators may exceed the size of the prey aggregation resulting in little effect on predator foraging behaviour and stabilisation of the effects of inverse density-dependent mortality. This phenomenon may explain the inverse density dependence observed as the predators' patch could have exceeded the size of our experimental system and prey were subjugated to concentrated predation pressure that would have otherwise been distributed over other local aggregations.…”

“…Despite this, experiments in this vein are important for the development and refinement of predator-prey theory but also continuing the search for mechanisms of population regulation when inversely density-dependent mortality is detected (White, 2011).…”

Functional responses and scaling in predator-prey interactions of marine fishes: contemporary issues and emerging concepts

“…In general, the degree of bias involved in scaling up (or down) will depend on the degree of nonlinearity in the functional response and the magnitude of spatial variation in prey abundance. White (2011) used a coral reef fish example to illustrate how one can model variation in those two factors analytically and compare the results to field data to determine the degree to which large-scale dynamics are affected by the scale transition.…”