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Making sense of transient dynamics Ecological systems can switch between alternative dynamic states. For example, the species composition of the community can change or nutrient dynamics can shift, even if there is little or no change in underlying environmental conditions. Such switches can be abrupt or more gradual, and a growing number of studies examine the transient dynamics between one state and another—particularly in the context of anthropogenic global change. Hastings et al. review current knowledge of transient dynamics, showing that hitherto idiosyncratic and individual patterns can be classified into a coherent framework, with important general lessons and directions for future study. Science , this issue p. eaat6412

Conservation vs. eradication What's an ecologist to do when an endangered bird lives in an invasive grass? Ecosystems are complicated networks, with one species relying on another, and managing one species in isolation may damage other members of a community. Lampert et al. (see the Perspective by Buckley and Han) looked at the conflict between eradicating a damaging invasive grass species and protecting an endangered bird species that uses the grass as its home. The most effective management and restoration approach focused not on eradicating the invasive grass as quickly as possible but on making changes slowly enough that the birds could adapt. This approach may prove useful in other situations in which active restoration conflicts with other conservation goals. Science , this issue p. 1028 ; see also p. 975

Limits to Invasion Predictions Using mathematical models linked to experiments on laboratory insect populations, Melbourne and Hastings (p. 1536 ) show that current models seriously underestimate variability in spatial spread. Genetic founder effects resulting from small population sizes are probably responsible for the surprising increase in variability and for increased uncertainty of ecological forecasts. Thus, even without exogenous sources of variability such as weather, fundamental uncertainties arise biologically from inherent differences among individuals and small population sizes.

Ecologists have fiercely debated for many decades whether populations are self-regulated by density-dependent biological mechanisms or are controlled by exogenous environmental forces. Here, a stochastic mechanistic model is used to show that the interaction of these two forces can explain observed large fluctuations in Dungeness crab ( Cancer magister ) numbers. Relatively small environmental perturbations interact with realistic nonlinear (density dependent) biological mechanisms, to produce dynamics that are similar to observations. This finding has implications throughout population biology, suggesting both that the study of deterministic density-dependent models is highly problematic and that stochastic models must include biologically relevant nonlinear mechanisms.

Simple discrete-time ecological models for a species with alternating reproduction and dispersal are shown to have complex transient dynamics. If the density dependence (nonlinearity) is strong enough, then the time required to reach the final dynamics is usually very long, approaching thousands of generations, and there are typically very sudden changes in the form of the dynamics. Apparent chaos can change to cycles or vice versa. These results are consistent with observed sudden changes in the form of the dynamics of a single species and imply that transient dynamics of ecological models may be more relevant than long-term behavior.

Simple metapopulation models with random disturbances are used in species conservation or management, relying on the condition for persistence that the per-patch colonization rate be greater than the per-patch extinction rate. For a general model incorporating the role of succession or patch age–dependent extinction, I show that persistence requires the per-patch colonization rate to be greater than the inverse of mean patch age, where age is the time since the patch became available for colonization. Because mean patch age can be arbitrarily large relative to the extinction rate, currently persisting metapopulations may be persisting despite small colonization rates, and management approaches that do not consider the role of mean patch age may unnecessarily doom populations to extinction.

How can mathematicians help to solve questions about biology? In a Perspective, Hastings and Palmer report the results of a recent series of workshops that set out to address this question.

Interactions between enemies and their victims are found in all ecological communities. But what has puzzled ecologists is how victims and enemies coexist together for long periods of time without all of the victims being killed off. In a Perspective, [Hastings][1] explains a new model ([ Keeling et al .][2]), which shows that variation in the distribution of victim and enemy species acts as a stabilizing factor in interactions between them. [1]: http://www.sciencemag.org/cgi/content/full/290/5497/1712 [2]: http://www.sciencemag.org/cgi/content/short/290/5497/1758

Marine reserves have been proposed as a remedy for overfishing and declining marine biodiversity, but concern that reserves would inherently reduce yields has impeded their implementation. It was found that management of fisheries through reserves and management through effort control produce identical yields under a reasonable set of simplifying assumptions corresponding to a broad range of biological conditions. Indeed, for populations with sedentary adults (invertebrates and reef fishes), reserves have important advantages for sustainability, making marine reserves the preferred management approach.

The comment by Dushoff ([ 1 ][1]) elaborates on the probabilistic arguments in ([ 2 ][2]) and provides a succinct explanation of the connection between patch age and the process of disturbance. The further expansion of the analogy to the Feller ([ 3 ][3]) example of buses cited in ([ 2 ][2]) also provides a heuristic explanation of Dushoff's results. The underlying view that colonizing species are most likely to be found in the patches that survive the longest just due to chance is worth further emphasis and consideration. Choosing the most valuable sites for conservation in a matrix of habitat needs to be done with caution, so that mere chance is not the only reason that some sites appear more valuable. Despite the importance of the formulas in ([ 1 ][1]), it is also important to be cautious in applying these insights directly, or even indirectly, to field systems. The relationship among patch age, disturbance process, and metapopulation persistence will also depend critically on the temporal autocorrelation of the disturbance process, which was ignored in ([ 1 ][1], [ 2 ][2]). The incorporation of further details into metapopulation models that remove other underlying, often implicit and underappreciated assumptions, is a very promising avenue for further research. 1. [↵][4] J. Dushoff, Science 304 , 684 (2004); [www.sciencemag.org/cgi/content/full/304/5671/684c][5]. 2. [↵][6] A. Hastings, Science 301, 1525 (2003). [OpenUrl][7][Abstract/FREE Full Text][8] 3. [↵][9] W. Feller, An Introduction to Probability Theory and Its Applications (Wiley, New York, 1971), vol. 2. [1]: #ref-1 [2]: #ref-2 [3]: #ref-3 [4]: #xref-ref-1-1 "View reference 1 in text" [5]: http://www.sciencemag.org/cgi/content/full/304/5671/684c [6]: #xref-ref-2-1 "View reference 2 in text" [7]: {openurl}?query=rft.jtitle%253DScience%26rft.stitle%253DScience%26rft.issn%253D0036-8075%26rft.aulast%253DHastings%26rft.auinit1%253DA.%26rft.volume%253D301%26rft.issue%253D5639%26rft.spage%253D1525%26rft.epage%253D1526%26rft.atitle%253DMetapopulation%2BPersistence%2Bwith%2BAge-Dependent%2BDisturbance%2Bor%2BSuccession%26rft_id%253Dinfo%253Adoi%252F10.1126%252Fscience.1087570%26rft_id%253Dinfo%253Apmid%252F12970563%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [8]: /lookup/ijlink/YTozOntzOjQ6InBhdGgiO3M6MTQ6Ii9sb29rdXAvaWpsaW5rIjtzOjU6InF1ZXJ5IjthOjQ6e3M6ODoibGlua1R5cGUiO3M6NDoiQUJTVCI7czoxMToiam91cm5hbENvZGUiO3M6Mzoic2NpIjtzOjU6InJlc2lkIjtzOjEzOiIzMDEvNTYzOS8xNTI1IjtzOjQ6ImF0b20iO3M6MjQ6Ii9zY2kvMzA0LzU2NzEvNjg0LjQuYXRvbSI7fXM6ODoiZnJhZ21lbnQiO3M6MDoiIjt9 [9]: #xref-ref-3-1 "View reference 3 in text"