Theoretical Ecology

Caswell, Hal; Neubert, Michael; Hunter, Christine

doi: 10.1007/s12080-010-0091-zpmid: N/A

Invasion speeds can be calculated from matrix integrodifference equation models that incorporate stage-specific demography and dispersal. These models also permit the calculation of the sensitivity and elasticity of invasion speed to changes in demographic and dispersal parameters. Such calculations have been used to understand the factors determining invasion speed and to explore possible tactics to manage invasive species. In this paper, we extend these calculations to temporally varying environments. We present formulas for the invasion speed and its sensitivity and elasticity in both periodic and stochastic environments. Periodic models can describe seasonal variation within a year, or can be used to study the frequency of occurrence of events (e.g., floods, fires) on interannual time scales. Stochastic models can incorporate variances, covariances, and temporal autocorrelation of parameters. We show that the invasion speed is calculated from a growth rate which is in turn calculated from a periodic or stochastic product of moment-generating function matrices. We present a new formulation of sensitivity analysis, using matrix calculus, that applies equally to constant, periodic, and stochastic environments.

Schreiber, Sebastian; Ryan, Maureen

doi: 10.1007/s12080-010-0098-5pmid: N/A

We live in a time where climate models predict future increases in environmental variability and biological invasions are becoming increasingly frequent. A key to developing effective responses to biological invasions in increasingly variable environments will be estimates of their rates of spatial spread and the associated uncertainty of these estimates. Using stochastic, stage-structured, integrodifference equation models, we show analytically that invasion speeds are asymptotically normally distributed with a variance that decreases in time. We apply our methods to a simple juvenile–adult model with stochastic variation in reproduction and an illustrative example with published data for the perennial herb, Calathea ovandensis. These examples buttressed by additional analysis reveal that increased variability in vital rates simultaneously slow down invasions yet generate greater uncertainty about rates of spatial spread. Moreover, while temporal autocorrelations in vital rates inflate variability in invasion speeds, the effect of these autocorrelations on the average invasion speed can be positive or negative depending on life history traits and how well vital rates “remember” the past.

Jones, Edward; Webb, Steven; Ruiz-Fons, Francisco; Albon, Steven; Gilbert, Lucy

doi: 10.1007/s12080-010-0087-8pmid: N/A

Landscape heterogeneity can be instrumental in determining local disease risk, pathogen persistence and spread. This is because different landscape features such as habitat type determine the abundance and spatial distributions of hosts and pathogen vectors. Therefore, disease prevalence and distribution are intrinsically linked to the hosts and vectors that utilise the different habitats. Here, we develop a simplified reaction diffusion model of the louping-ill virus and red grouse (Lagopus lagopus scoticus) system to investigate the occurrence of a tick-borne pathogen and the effect of host movement and landscape structure. Ticks (Ixodes ricinus), the virus-vector, are dispersed by a virally incompetent tick host, red deer (Cervus elephus), between different habitats, whilst the virus infects only red grouse. We investigated how deer movement between different habitats (forest and moorland) affected tick distribution and hence prevalence of infected ticks and grouse and hence, the effect of habitat size ratio and fragmentation on infection. When habitat type has a role in the survival of the pathogen vector, we demonstrated that habitat fragmentation can have a considerable effect on infection. These results highlight the importance of landscape heterogeneity and the proximity and size of adjacent habitats when predicting disease risk in a particular location. In addition, this model could be useful for other pathogen systems with generalist vectors and may inform policy on possible disease management strategies that incorporate host movements.

Rossberg, Axel; Farnsworth, Keith

doi: 10.1007/s12080-010-0088-7pmid: N/A

Goldstone’s idea of slow dynamics resulting from spontaneously broken symmetries is applied to Hubbell’s neutral hypothesis of community dynamics, to efficiently simplify stage-structured multi-species models—introducing the quasi-neutral approximation (QNA). Rather than assuming population-dynamical neutrality in the QNA, deviations from ideal neutrality, thought to be small, drive dynamics. The QNA is systematically derived to first and second order in a two-scale singular perturbation expansion. The total reproductive value of species, as computed from the effective life-history parameters resulting from the non-linear interactions with the surrounding community, emerges as the new dynamic variables in this aggregated description. Using a simple stage-structured community-assembly model, the QNA is demonstrated to accurately reproduce population dynamics in large, complex communities. Further, the utility of the QNA in building intuition for management problems is illustrated by estimating the responses of a fish stock to harvesting and variations in fecundity.

Brännström, Åke; Loeuille, Nicolas; Loreau, Michel; Dieckmann, Ulf

doi: 10.1007/s12080-010-0089-6pmid: N/A

Ecological communities emerge as a consequence of gradual evolution, speciation, and immigration. In this study, we explore how these processes and the structure of the evolved food webs are affected by species-level properties. Using a model of biodiversity formation that is based on body size as the evolving trait and incorporates gradual evolution and adaptive radiation, we investigate how conditions for initial diversification relate to the eventual diversity of a food web. We also study how trophic interactions, interference competition, and energy availability affect a food web’s maximum trophic level and contrast this with conditions for high diversity. We find that there is not always a positive relationship between conditions that promote initial diversification and eventual diversity, and that the most diverse food webs often do not have the highest trophic levels.

Nakazawa, Takefumi

doi: 10.1007/s12080-010-0090-0pmid: N/A

Several recent studies have shown that food web coupling by ontogenetic niche shifts can generate alternative stable states (ASS). However, these studies mainly considered cases where juvenile and adult stages are the top level consumers. The conditions under which ASS occur in more structurally diverse food web configurations have not been explored. In this study, I examine the influence of food-chain length and the trophic positions of juveniles and adults on the existence of ASS. Comprehensive model analysis showed that if both juveniles and adults are top predators, ASS are possible irrespective of their trophic level, because of overcompensation in reproduction and maturation due to strong density dependence, as previously predicted. However, the following potential food-web effects were found: ASS potential (1) disappears if either or both the juveniles and adults have a predator and (2) is once again observed if another predator is added on the stage-specific predator. These mechanisms involve (1) top–down control that relaxes intrastage food competition and (2) top–down cascade that intensifies the intrastage competition, respectively. Furthermore, it was illustrated that the environmental conditions under which ASS occurred varied in complex ways with the coupled food-web configurations. My results provide a novel concept that anthropogenic changes in local community structure (e.g., species extinction and invasion) propagate through space and may cause or prevent regime shifts in broad-scale community structure by altering the resilience to environmental perturbations.

Esther, Alexandra; Groeneveld, Jürgen; Enright, Neal; Miller, Ben; Lamont, Byron; Perry, George; Tietjen, Britta; Jeltsch, Florian

doi: 10.1007/s12080-010-0092-ypmid: N/A

Mathematical models and ecological theory suggest that low-dimensional life history trade-offs (i.e. negative correlation between two life history traits such as competition vs. colonisation) may potentially explain the maintenance of species diversity and community structure. In the absence of trade-offs, we would expect communities to be dominated by ‘super-types’ characterised by mainly positive trait expressions. However, it has proven difficult to find strong empirical evidence for such trade-offs in species-rich communities. We developed a spatially explicit, rule-based and individual-based stochastic model to explore the importance of low-dimensional trade-offs. This model simulates the community dynamics of 288 virtual plant functional types (PFTs), each of which is described by seven life history traits. We consider trait combinations that fit into the trade-off concept, as well as super-types with little or no energy constraints or resource limitations, and weak PFTs, which do not exploit resources efficiently. The model is parameterised using data from a fire-prone, species-rich Mediterranean-type shrubland in southwestern Australia. We performed an exclusion experiment, where we sequentially removed the strongest PFT in the simulation and studied the remaining communities. We analysed the impact of traits on performance of PFTs in the exclusion experiment with standard and boosted regression trees. Regression tree analysis of the simulation results showed that the trade-off concept is necessary for PFT viability in the case of weak trait expression combinations such as low seed production or small seeds. However, species richness and diversity can be high despite the presence of super-types. Furthermore, the exclusion of super-types does not necessarily lead to a large increase in PFT richness and diversity. We conclude that low-dimensional trade-offs do not provide explanations for multi-species co-existence contrary to the prediction of many conceptual models.

Armsworth, Paul; Block, Barbara; Eagle, Josh; Roughgarden, Joan

doi: 10.1007/s12080-010-0093-xpmid: N/A

Time-area closures are commonly used to manage fisheries bycatch and involve temporarily closing an area of the ocean to particular fishing gears. We examine conditions in which implementing a time-area closure would increase the economic value of fisheries, focusing on a case study application in the Gulf of Mexico. Pelagic longline fishermen catch the highly valued Atlantic bluefin tuna (Thunnus thynnus, Scombridae) on their Gulf of Mexico spawning grounds while fishing for Atlantic yellowfin tuna (Thunnus albacares). We analyze a multispecies, multifishery bioeconomic model that includes information on migratory patterns from electronic tagged bluefin tuna. We use dynamic optimization to identify management strategies that would maximize the net present value of tuna fisheries, allowing for discounting of future benefits and costs relative to the present. If past fishing mortality rates continue in Atlantic bluefin tuna fisheries, implementing a time-area closure in the Gulf of Mexico incurs economic costs. However, the net present value of the fisheries is increased by implementing a time-area closure as part of a broader commitment to rebuild the heavily depleted bluefin population, provided the discount rate and the costs of such a closure in forgone fishing opportunities are not too large. The increase in economic value offered by a time-area closure is small relative to the overall economic value of rebuilding itself and it may be economically optimal only to implement a closure once sufficient rebuilding has already taken place.