Size-dependent life-history traits promote catastrophic collapses of top predators

Abstract

Catastrophic population collapses such as observed in many exploited fish populations have been argued to result from depensatory growth mechanisms (i.e., reduced reproductive success at low population densities, also known as Allee effect). Empirical support for depensation from population-level data is, however, hard to obtain and inconclusive. Using a size-structured, individualbased model we show that catastrophic population collapses may nonetheless be an intrinsic property of many communities, because of two general aspects of individual life history: size-and fooddependent individual growth and individual mortality decreasing with body size. Positive density dependence, characteristic for depensatory growth mechanisms and catastrophic behavior, results as a direct and robust consequence of the interplay between these individual life-history traits, which are commonly found in many species.R ecent studies on lakes, coral reefs, oceans, forests, and arid lands document drastic changes in the composition of the biological community and the functioning of the ecosystem (1, 2). One view is that these abrupt changes represent catastrophic shifts between contrasting states of the system that are both stable equilibria (1, 2). The collapse of several exploited fish stocks, which fail to recover after over-fishing and a closure of fisheries, could be interpreted as such a shift, if the community state without the exploited fish species represents a stable equilibrium (2-4). If the interpretation in terms of alternative stable equilibria is correct, our view of how these ecological systems function and how to manage them is heavily affected (5). Models of biological communities show that the extinct state may be stable if the exploited species exhibits a reduced population growth capacity at low densities (2, 6). Such depensatory growth (also known as Allee effect, positive or inverse densitydependence) will prevent rebound of the population after a crash. Population-level data do not unambiguously support or refute the presence of depensatory mechanisms in natural systems (6-9). Estimates of spawner abundance and the number of surviving progeny for 128 fish stocks indicated only 3 stocks with significant depensation (7). More advanced statistical testing of these stock-recruitment relations showed that the probability of depensation was nonetheless significant (8). Also, 15 years after a collapse of the population most of the exploited fish stocks have yet to recover. Assuming that management strategies have been implemented to reduce fishing mortality after a collapse, such a lack of recovery indicates a reduced capacity to rebound from low densities (9).Community models incorporating depensatory mechanisms do so as an assumption (7), which is justified by verbal arguments. For example, it is argued that depensatory growth may result from adult individuals negatively affecting competitors of their own juveniles (6), from reduced cooperative behavior at low densities (10), or predator swamping at high density (11)...

How cod shapes its world

“…Clearly identifying the consequences of this positive feedback allows for the development of management actions that at first sight seem counter-intuitive. For example, De Roos and Persson (2002) suggested that, if indeed the change in prey population size distribution after a predator collapse prohibits recovery of the predator, thinning the prey population might be an effective strategy to foster recovery. Modeling studies suggested that such a counter-intuitive approach might be more successful than release or stocking of predators (van Kooten et al, 2005).…”

“…This mechanism, referred to as an emergent Allee effect (De Roos and Persson, 2002;see Fig. 1 for a schematic representation), has been shown to occur in predatorprey-resource systems when predators forage exploitatively on selective size ranges of prey only.…”

Physiologically Structured Population Models: Towards a General Mathematical Theory

“…A more detailed analysis by de Roos, Persson and Thieme (2003) shows that the essence of the matter is that in the absence of predators the consumer population is regulated mainly by the rate at which individuals pass through a certain size range, with the predators specialising on a different size range. As noted by de Roos and Persson (2002), a mechanism of this sort may well explain the failure of the Northwest Atlantic cod to recover after its collapse from overfishing: After the cod collapsed, the abundance of their main food, capelin, increased, but capelin growth rates decreased and adults became significantly smaller. (See Scheffer et al (2001) for a general survey on catastrophic collapses.…”

Integrating ecological insight derived from individual-based simulations and physiologically structured population models

“…In this section, we describe work on a food chain model developed by de Roos and Persson (2002). The model recognizes three trophic levels: a resource, a size structured consumer population that feeds on the resource, and an unstructured predator population that feeds on the small consumers.…”

“…Thus, in section 2, we describe features that can be understood by comparison of representations of populations that do, and do not, contain discrete individuals. In section 3, we compare/contrast the properties of a three-trophiclevel model (resource-consumer-predator) for which previous analysis of a PSPM demonstrated the possibility of bistability, hysteresis and population cycles (De Roos and Persson, 2002) with an analogous IBM that demonstrates how different forms of stochasticity influence qualitative outcome including invasion, persistence or extinction of the predator. The case study also demonstrates the value of "dialog" between the two approaches.…”