Equivalence relationships between stage-structured population models.

Matrix population models are widely applied in conservation ecology to help predict future population trends and guide conservation effort. Researchers must decide upon an appropriate level of model complexity, yet there is little theoretical work to guide such decisions. In this paper we present an analysis of a stage-structured model, and prove that the model's structure can be simplified and parameterised in such a way that the long-term growth rate, the stable-stage distribution and the generation time are all invariant to the simplification. We further show that for certain structures of model the simplified models require less effort in data collection. We also discuss features of the models which are not invariant to the simplification and the implications of our results for the selection of an appropriate model. We illustrate the ideas using a population model for short-tailed shearwaters (Puffinus tenuirostris). In this example, model simplification can increase parameter elasticity, indicating that an intermediate level of complexity is likely to be preferred

Quantum Arrival Time Formula from Decoherent Histories

In the arrival time problem in quantum mechanics, a standard formula that frequently emerges as the probability for crossing the origin during a given time interval is the current integrated over that time interval. This is semiclassically correct but can be negative due to backflow. Here, we show that this formula naturally arises in a decoherent histories analysis of the arrival time problem. For a variety of initial states, we show that histories crossing during different time intervals are approximately decoherent. Probabilities may therefore be assigned and coincide with the standard formula (in a semiclassical approximation), which is therefore positive for these states. However, for initial states for which there is backflow, we show that there cannot be decoherence of histories, so probabilities may not be assigned.Comment: 11 page

Invasion and eradication of a competitively superior species in heterogeneous landscapes

The effect of heterogeneous environments upon the dynamics of invasion and the eradication or control of invasive species is poorly understood, although it is a major challenge for biodiversity conservation. Here, we first investigate how the probability and time for invasion are affected by spatial heterogeneity. Then, we study the effect of control program strategies (e.g. species specificity, spatial scale of action, detection and eradication efficiency) on the success and time of eradication. We find that heterogeneity increases both the invasion probability and the time to invasion. Heterogeneity also reduces the probability of eradication but does not change the time taken for successful eradication. We confirm that early detection of invasive species reduces the time until eradication, but we also demonstrate that this is true only if the local control action is sufficiently efficient. The criterion of removal efficiency is even more important for an eradication program than simply ensuring control effort when the invasive species is not abundant

Weak interactions, omnivory and emergent food-web properties

Empirical studies have shown that, in real ecosystems, species-interaction strengths are generally skewed in their distribution towards weak interactions. Some theoretical work also suggests that weak interactions, especially in omnivorous links, are important for the local stability of a community at equilibrium. However, the majority of theoretical studies use uniform distributions of interaction strengths to generate artificial communities for study. We investigate the effects of the underlying interaction-strength distribution upon the return time, permanence and feasibility of simple Lotka-Volterra equilibrium communities. We show that a skew towards weak interactions promotes local and global stability only when omnivory is present. It is found that skewed interaction strengths are an emergent property of stable omnivorous communities, and that this skew towards weak interactions creates a dynamic constraint maintaining omnivory. Omnivory is more likely to occur when omnivorous interactions are skewed towards weak interactions. However, a skew towards weak interactions increases the return time to equilibrium, delays the recovery of ecosystems and hence decreases the stability of a community. When no skew is imposed, the set of stable omnivorous communities shows an emergent distribution of skewed interaction strengths. Our results apply to both local and global concepts of stability and are robust to the definition of a feasible community. These results are discussed in the light of empirical data and other theoretical studies, in conjunction with their broader implications for community assembly

Delayed costs of growth and compensatory growth rates

1. Many studies recognize that growth carries with it a mortality risk that can influence an animal's growth rate.\ud \ud 2. Data suggest that these costs of growth act over a range of time-scales, from instantaneous to an animal's lifetime.\ud \ud 3. Models of adaptive growth rate have not addressed the issue of differing time-scales over which the costs of growth act. Here, we develop an adaptive growth model in which the costs of growth are delayed for a period of time, to assess optimal growth strategies in relation to delays in growth costs.\ud \ud 4. The optimal growth rates are calculated assuming one of two possible fitness measures: the reproductive rate, R-0 and the intrinsic population growth rate, r.\ud \ud 5. It is shown that if the costs of growth are felt only after maturity, then growth compensation can be an adaptive strategy, even in an unchanging environment.\ud \ud 6. Compensatory growth is predicted only when R-0 is the relevant fitness measure, implying that this mechanism of compensatory growth is sensitive to the processes of population regulation.\ud \ud 7. The effect of time-delayed costs for other life-history problems is discussed in light of these results

Loss of functionally unique species may gradually undermine ecosystems

Functionally unique species contribute to the functional diversity of natural systems, often enhancing ecosystem functioning. An abundance of weakly interacting species increases stability in natural systems, suggesting that loss of weakly linked species may reduce stability. Any link between the functional uniqueness of a species and the strength of its interactions in a food web could therefore have simultaneous effects on ecosystem functioning and stability. Here, we analyse patterns in 213 real food webs and show that highly unique species consistently tend to have the weakest mean interaction strength per unit biomass in the system. This relationship is not a simple consequence of the interdependence of both measures on body size and appears to be driven by the empirical pattern of size structuring in aquatic systems and the trophic position of each species in the web. Food web resolution also has an important effect, with aggregation of species into higher taxonomic groups producing a much weaker relationship. Food webs with fewer unique and less weakly interacting species also show significantly greater variability in their levels of primary production. Thus, the loss of highly unique, weakly interacting species may eventually lead to dramatic state changes and unpredictable levels of ecosystem functioning

Having it all: historical energy intakes do not generate the anticipated trade-offs in fecundity

An axiom of life-history theory, and fundamental to our understanding of ageing, is that animals must trade-off their allocation of resources since energy and nutrients are limited. Therefore, animals cannot ‘have it all’—combine high rates of fecundity with extended lifespans. The idea of life-history trade-offs was recently challenged by the discovery that ageing may be governed by a small subset of molecular processes independent of fitness. We tested the ‘trade-off’ and ‘having it all’ theories by examining the fecundities of C57BL/6J mice placed onto four different dietary treatments that generated caloric intakes from −21 to +8.6% of controls. We predicted body fat would be deposited in relation to caloric intake. Excessive body fat is known to cause co-morbidities that shorten lifespan, while caloric restriction enhances somatic protection and increases longevity. The trade-off model predicts that increased fat would be tolerated because reproductive gain offsets shortened longevity, while animals on a restricted intake would sacrifice reproduction for lifespan extension. The responses of body fat to treatments followed our expectations, however, there was a negative relationship between reproductive performance (fecundity, litter mass) and historical intake/body fat. Our dietary restricted animals had lower protein oxidative damage and appeared able to combine life-history traits in a manner contrary to traditional expectations by having increased fecundity with the potential to have extended lifespans

High connectivity in a long-lived High-Arctic seabird, the ivory gull Pagophila eburnea

Species may cope with rapid habitat changes by distribution shifts or adaptation to new conditions. A common feature of these responses is that they depend on how the process of dispersal connects populations, both demographically and genetically. We analyzed the genetic structure of a near-threatened high-Arctic seabird, the ivory gull (Pagophila eburnea) in order to infer the connectivity among gull colonies. We analyzed 343 individuals sampled from 16 localities across the circumpolar breeding range of ivory gulls, from northern Russia to the Canadian Arctic. To explore the roles of natal and breeding dispersal, we developed a population genetic model to relate dispersal behavior to the observed genetic structure of worldwide ivory gull populations. Our key finding is the striking genetic homogeneity of ivory gulls across their entire distribution range. The lack of population genetic structure found among colonies, in tandem with independent evidence of movement among colonies, suggests that ongoing effective dispersal is occurring across the Arctic Region. Our results contradict the dispersal patterns generally observed in seabirds where species movement capabilities are often not indicative of dispersal patterns. Model predictions show how natal and breeding dispersal may combine to shape the genetic homogeneity among ivory gull colonies separated by up to 2800 km. Although field data will be key to determine the role of dispersal for the demography of local colonies and refine the respective impacts of natal versus breeding dispersal, conservation planning needs to consider ivory gulls as a genetically homogeneous, Arctic-wide metapopulation effectively connected through dispersal