Theoretical Ecology

Guttal, Vishwesha; Jayaprakash, C.

doi: 10.1007/s12080-008-0033-1pmid: N/A

Ecosystems can undergo large-scale changes in their states, known as catastrophic regime shifts, leading to substantial losses to services they provide to humans. These shifts occur rapidly and are difficult to predict. Several early warning signals of such transitions have recently been developed using simple models. These studies typically ignore spatial interactions, and the signal provided by these indicators may be ambiguous. We employ a simple model of collapse of vegetation in one and two spatial dimensions and show, using analytic and numerical studies, that increases in spatial variance and changes in spatial skewness occur as one approaches the threshold of vegetation collapse. We identify a novel feature, an increasing spatial variance in conjunction with a peaking of spatial skewness, as an unambiguous indicator of an impending regime shift. Once a signal has been detected, we show that a quick management action reducing the grazing activity is needed to prevent the collapse of vegetated state. Our results show that the difficulties in obtaining the accurate estimates of indicators arising due to lack of long temporal data can be alleviated when high-resolution spatially extended data are available. These results are shown to hold true independent of various details of model or different spatial dispersal kernels such as Gaussian or heavily fat tailed. This study suggests that spatial data and monitoring multiple indicators of regime shifts can play a key role in making reliable predictions on ecosystem stability and resilience.

Ricotta, Carlo

doi: 10.1007/s12080-008-0028-ypmid: N/A

Jost (Ecology, 88:2427–2439, 2007) recently showed that the Shannon diversity is the only standard diversity measure that can be partitioned into meaningful independent alpha and beta components when plot weights are unequal. This conclusion is very disappointing if one wants to calculate the beta diversity of unequal weighted plots using a parametric measure with varying sensitivities to the occurrence of rare and abundant species. To overcome this impasse, at least partially, in this paper, I propose a parametric measure of beta diversity that is based on the combination of Shannon’s entropy with Hurlbert’s ‘expected species diversity’. Unlike most parametric measures of diversity, the proposed index has a clear probabilistic interpretation, allowing at the same time a multiplicative partition of diversity into independent alpha and beta components for unequally weighted plots.

Hackett-Jones, E.; Cobbold, C.; White, A.

doi: 10.1007/s12080-008-0025-1pmid: N/A

There are many well-documented cases in which multiple parasitoids can coexist on a single host species. We examine a theoretical framework to assess whether parasitoid coexistence can be explained through differences in timing of parasitoid oviposition and parasitoid emergence. This study explicitly includes the phenology of host and parasitoid development and explores how this mechanism affects the population dynamics. Coexistence of the host with two parasitoids requires a balance between parasitoid fecundity and survival and occurs most readily if one parasitoid attacks earlier but emerges later than the other parasitoid. The host density can either be decreased or increased when a second coexisting parasitoid is introduced into the system. However, there always exists a single parasitoid type that is most effective at depressing the host density, although this type may not be successful due to parasitoid competition. The coexistence of multiple parasitoids also affects the population dynamics. For instance, population oscillations can be removed by the introduction of a second parasitoid. In general, subtle differences in parasitoid phenology can give rise to different outcomes in a host–multi-parasitoid system, and this may offer some insight into why establishing criteria for the ‘ideal’ biological control agent has been so challenging.

Mougi, Akihiko; Nishimura, Kinya

doi: 10.1007/s12080-008-0026-0pmid: N/A

We show that the paradox of enrichment can be theoretically resolved in a flexible predator–prey system in which the predator practices imperfect optimal foraging. A previous study showed that perfect optimal foraging can mitigate increases in the amplitude of population oscillations associated with enrichment, but it did not show a stabilization pattern. Our results show that imperfect optimal foraging can stabilize the system and resolve the paradox of enrichment under nonequilibrium dynamics. Furthermore, the degree of stabilization with enrichment was stronger when the imperfection of optimal foraging was larger.

Drury, Kevin; Lodge, David

doi: 10.1007/s12080-008-0027-zpmid: N/A

Regime shift inducibility depends on equilibrium resilience, which depends on species interactions. When species interactions include intraguild predation (IGP), integrated pest management may induce regime shifts because enhancing the abundance of intraguild predators simultaneously increases competition with, and predation on, invasive prey. To explore the dynamical consequences of such manipulations, we use a bistable, deterministic IGP model with stochastic removals that perturb invader density from the high-density equilibrium. We quantify the combined effects of IGP and such perturbations in terms of mean first passage times (MFPTs) to target invader densities such as thresholds between regimes. Analytical MFPTs compare favorably with those generated by Monte Carlo numerical solutions of the stochastically perturbed IGP model. MFPTs can therefore usefully quantify equilibrium resilience in terms of perturbation schedules.

Bell, Sally; White, Andrew; Sherratt, Jonathan; Boots, Mike

doi: 10.1007/s12080-008-0029-xpmid: N/A

Theory has been developed that examines the role of infectious disease in ecological invasions for particular natural systems. However, a general understanding of the role that shared disease may play in invasions is lacking. Here, we develop a strategic theoretical framework to determine the role of disease, in addition to competition, in ecological invasions and the expansion of species’ spatial range. We investigate the effect of different disease parameters on the replacement time of a native species by an alien invader. The outcome is critically dependent on the relative effects that the disease has on the two species and less dependent on the basic epidemiological characteristics of the interaction. This framework is also used to investigate the effect of disease on the spatial spread of the invader. Our results show an interesting phenomenon where a wave of disease spreads through the landscape ahead of the wave of replacement.