Persistence probability of a random polynomial arising from evolutionary game theory

We obtain an asymptotic formula for the persistence probability in the positive real line of a random polynomial arising from evolutionary game theory. It corresponds to the probability that a multi-player two-strategy random evolutionary game has no internal equilibria. The key ingredient is to approximate the sequence of random polynomials indexed by their degrees by an appropriate centered stationary Gaussian process.

The geometry of habitat fragmentation: effects of distribution patterns on short-term species persistence

Land-use changes cause habitat loss and fragmentation and are thus important drivers of anthropogenic biodiversity change. However, there is an ongoing debate about how fragmentationper seaffects biodiversity in a given amount of habitat. We illustrate why it is important to distinguish two different aspects of fragmentation to resolve this debate: (i) geometric fragmentation effects, which exclusively arise from the spatial distributions of species and habitat fragments, and (ii) demographic fragmentation effects due to reduced fragment size, increased isolation, or edge effects. While most empirical studies are primarily interested in quantifying demographic fragmentation effects, geometric effects are typically invoked only as post-hoc explanations of biodiversity responses to fragmentationper se. Here, we present an approach to quantify geometric fragmentation effects on species persistence probability. We illustrate this approach using spatial simulations where we systematically varied the initial abundances and distribution patterns (i.e. random, aggregated, and regular) of species as well as habitat amount and fragmentationper se.As expected, we found no geometric fragmentation effects when species were randomly distributed. However, when species were aggregated, we found positive effects of fragmentationper seon persistence probability for a large range of scenarios. For regular species distributions, we found weakly negative geometric effects. These findings are independent of the ecological mechanisms which generate non-random species distributions. Our study helps to reconcile seemingly contradictory results of previous fragmentation studies. Since intraspecific aggregation is a ubiquitous pattern in nature, our findings imply widespread positive geometric fragmentation effects. This expectation is supported by many studies that find positive effects of fragmentationper seon species occurrences and diversity after controlling for habitat amount. We outline how to disentangle geometric and demographic effects of fragmentation, which is critical for predicting the response of biodiversity to landscape change.

Persistence-Based Area Prioritization for Conservation: Applying Occupancy and Habitat Threats and Risks Analyses

Effective habitat conservation is predicated on maintaining high levels or increasing local persistence probability of the species it purports to protect. Thus, methodological approaches that improve the inferential value of local persistence are of utmost value to guide conservation planning as they inform area selection processes. Herein we used the painted bunting Passerina ciris, a species of conservation interest in North Carolina, as an illustrative case that combined single-season, single-species occupancy analyses and a threats and risk decision support tool to rank five areas of conservation interest in terms of local persistence probability. We used survey data from two seasons (2008–2009) grouped into 21 natal dispersal sampling units and land-cover data from 12 habitat classes to establish the relationship between local occupancy probability and habitat. Occupancy increased most strongly with increasing amount of maritime forest. Projections to year 2050, relative to year 2000, indicated that a potential loss of maritime forest of 200–1,300 ha, depending on the area of interest. Projected loss was lowest at Bald Head Island–Wilmington (2%) and highest at Camp Lejune (27%). Bald Head Island–Wilmington ranked highest in projected local persistence probability (0.91; 95% confidence interval [CI] = 0.53–0.99), whereas Top Sail–Hammocks Beach Park ranked lowest (0.28; 95% CI = 0.03–0.82). Estimates of local persistence offer decision-makers another criterion to prioritize areas for conservation and help guide efforts aimed at maintaining or enhancing local persistence. These include in situ habitat management, expanding or connecting existing areas of interest. In the future, we recommend the use of multiseason occupancy models, coupled with measures of uncertainty of land-cover projections, to strengthen inferences about local persistence, particularly useful in nonstationary landscapes driven by human activities.

Weather Window Analysis in Connection With Operation and Maintenance of Ocean Renewable Energy Devices

There is an increasing need for utilization of ocean renewable energy (ORE) around Japanese coast because Japan is surrounded by ocean. Because technologies for harnessing ORE have not been mature enough, Japanese government selects some demonstration sites for ORE devices and some demonstration projects are going. As these projects are progressed, the operation and maintenance (O&M) activities will increase and become essential factors for the success of demonstration projects. Hence, weather window analysis is required to quantify the levels of access for ORE devices in the demonstration projects, and commercial projects in the future. In this paper, two new parameters are proposed in order to evaluate accessibility to ORE devices. One is the operational probability, and the other is the forecasted waiting time. The operational probability assesses weather duration with considering variability of wave condition. The forecasted waiting time is an expectation value of waiting time before O&M planners get next chance to arrange the O&M activities. In order to check the effectivity of the proposed 2 parameters, accessibility is evaluated for significant wave height in terms of the 2 proposed parameters, these are • Operational probability • Forecasted waiting time and 3 conventional parameters, these are • Excess probability • Persistence probability • Waiting time between windows The accessibility is evaluated at two locations along the Japanese coast. This study reveals that large differences are caused between persistence probability and operational probability when operational wave height limit occurs intermittently and required window length is long. The forecasted waiting time has the same variation tendency as the waiting time between windows.

Persistence Probability for a Class of Gaussian Processes Related to Random Interface Models

We consider a class of Gaussian processes which are obtained as height processes of some (d + 1)-dimensional dynamic random interface model on ℤd. We give an estimate of persistence probability, namely, large T asymptotics of the probability that the process does not exceed a fixed level up to time T. The interaction of the model affects the persistence probability and its asymptotics changes depending on the dimension d.

Persistence Probability for a Class of Gaussian Processes Related to Random Interface Models

We consider a class of Gaussian processes which are obtained as height processes of some (d+ 1)-dimensional dynamic random interface model on ℤd. We give an estimate of persistence probability, namely, largeTasymptotics of the probability that the process does not exceed a fixed level up to timeT. The interaction of the model affects the persistence probability and its asymptotics changes depending on the dimensiond.