Are ecological systems chaotic — And if not, why not?

Berryman, Alan A.; Millstein, Jeffrey A.

doi:10.1016/0169-5347(89)90014-1

Cited by 202 publications

(95 citation statements)

References 5 publications

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“…This stability is surprising at first sight; in general, the more complex a n ecosystem model becomes, the greater is the likelihood of one or more non-decaying modes (May 1974). However, Berryman & Millstein (1989) have pointed out that when steady-state analyses are performed on mathematical models based on real data, almost invariably stable steady-state behaviour of the modelled systems is observed, suggesting that In real ecosystems there is a preponderance of negative rather than positive feedback processes. The present model would seem to support this.…”

Section: Discussionmentioning

confidence: 99%

A steady-state analysis of the 'microbial loop' in stratified systems

Taylor¹,

Joint²

1990

Mar. Ecol. Prog. Ser.

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ABSTRACT. Steady state solutions are presented for a simple model of the surface mixed layer, which contains the components of the 'microbial loop', namely phytoplankton, picophytoplankton, bacterioplankton, microzooplankton, dissolved organic carbon, detritus, nitrate and ammonia. This system is assumed to be in equilibrium with the larger grazers present at any time, which are represented as an external mortality function. The model also allows for dissolved organic nitrogen consumption by bacteria, and self-grazing and mixotrophy of the microzooplankton. The model steady states are always stable. The solution shows a number of general properties; for example, biomass of each individual component depends only on total nitrogen concentration below the mixed layer, not whether the nitrogen is in the form of nitrate or ammonia. Standing stocks and production rates from the model are compared with summer observations from the Celtic Sea and Porcupine Sea Bight. The agreement is good and suggests that the system is often not far from equilibrium. A sensitivity analysis of the model is included. The effect of varying the mixing across the pycnocline is investigated; more intense mixing results in the large phytoplankton population increasing at the expense of picophytoplankton, microzooplankton and DOC. The change from phytoplankton to picophytoplankton dominance at low mixing occurs even though the same physiological parameters are used for both size fractions. The F-ratio falls abruptly at low mixing rates. Estimates of microbial food web efficiency made with this model show that bacteria are not important, a result confirmed by excluding bacteria from the system. The model therefore does not support the 'microbial loop' hypothesis. The model solutions and parameter values are presented in full in 3 appendices.

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Section: Discussionmentioning

confidence: 99%

A steady-state analysis of the 'microbial loop' in stratified systems

Taylor¹,

Joint²

1990

Mar. Ecol. Prog. Ser.

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“…R max is the net reproductive rate for a population in the absence of densitydependent feedbacks and thus represents a maximum potential generational growth rate for that population. May & Oster (1976) and others (Berryman & Millstein 1989;Thomas et al 1980) suggested that the likelihood of population extinction is elevated when a population's R max is high enough to lead to instability, and, in particular, chaos. Thus, there may be a practical upper limit to the rate at which populations can grow.…”

Section: Introduction Robertmentioning

confidence: 99%

The May threshold and life-history allometry

2010

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One of Robert May's classic results was finding that population dynamics become chaotic when the average lifetime rate of reproduction exceeds a certain value. Populations whose reproductive rates exceed this May threshold probably become extinct. The May threshold in each case depends upon the shape of the density-dependence curve, which differs among models of population growth. However, species of different sizes and generation times that share a roughly similar density-dependence curve will also share a similar May threshold. Here, we argue that this fact predicts a striking allometric regularity among animal taxa: lifetime reproductive rate should be roughly independent of body size. Such independence has been observed in diverse taxa, but has usually been ascribed to a fortuitous combination of physiologically based life-history allometries. We suggest, instead, that the ecological elimination of unstable populations within groups that share a value of the May threshold is a likely cause of this allometry.

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“…Evolutionary explanations are often based upon group selectionist arguments resting on the premise that populations with demographic properties resulting in severe #uctuations in numbers would tend to go extinct, and that, therefore, extant populations would be precisely those that happened to have relatively stable dynamics (Thomas et al, 1980;Berryman & Millstein, 1989). On the other hand, many workers have also argued that, under a variety of biologically meaningful scenarios, selection at the individual level may be expected to give rise to the evolution of enhanced stability (Mueller & Ayala, 1981;Hansen, 1992;Mueller & Huynh, 1994;Doebeli & Koella, 1995;Ebenman et al, 1996), although this notion is supported by very meager empirical evidence (Stokes et al, 1988; but see also .…”

Section: Introductionmentioning

confidence: 99%