Modeling Allee Effect from Beta(p, 2) Densities

In this work we develop and investigate generalized populational growth models, adjusted from Beta(p, 2) densities, with Allee effect. The use of a positive parameter leads the presented generalization, which yields some more flexible models with variable extinction rates. An Allee limit is incorporated so that the models under study have strong Allee effect

Modelling temperature-dependent larval development and\ud subsequent demographic Allee effects in adult populations of the alpine butterfly Parnassius smintheus

Climate change has been attributed as a driver of changes to ecological systems worldwide and understanding the effects of climate change at individual, population, community, and ecosystem levels has become a primary concern of ecology. One avenue toward understanding the impacts of climate change on an ecosystem is through the study of environmentally sensitive species. Butterflies are sensitive to climatic changes due to their reliance on environmental cues such as temperature and photoperiod, which regulate the completion of life history stages. As such, the population dynamics of butterflies may offer insight into the impacts of climate change on the health of an ecosystem. In this paper we study the effects of rearing temperature on the alpine butterfly Parnassius smintheus (Rocky Mountain Apollo), both directly through individual phenological changes and indirectly through adult reproductive success at the population level. Our approach is to formulate a mathematical model of individual development parameterized by experimental data and link larval development to adult reproductive success. A Bernoulli process model describes temperature-dependent larval phenology, and a system of ordinary differential equations is used to study impacts on reproductive success. The phenological model takes field temperature data as its input and predicts a temporal distribution of adult emergence, which in turn controls the dynamics of the reproductive success model. We find that warmer spring and summer temperatures increase reproductive success, while cooler temperatures exacerbate a demographic Allee effect, suggesting that observed yearly fluctuations in P. smintheus population size may be driven by inter-annual temperature variability. Model predictions are validated against mark-recapture field data from 2001 and 2003 − 2009

Implications of complex connectivity patterns, disturbance, Allee effects, and fisheries in the dynamics of marine metapopulations

textNearshore populations have been depleted and some have not yet recovered. Therefore, theoretical studies focus on improving fisheries management and designing marine protected areas (MPAs). Depleted populations may be undergoing an Allee effect, i.e. a decrease in fitness at low densities. Here, I constructed a marine metapopulation model that included pre- and post-dispersal Allee effects using a network theory approach. Networks represent metapopulations as groups of nodes connected by dispersal paths. With this model I answered four questions: What is the role of Allee effects on habitat occupancy? Are MPAs effective in recovering exploited populations? What is the importance of larval dispersal patterns in preventing local extinctions due to exploitation and Allee effects? Can exploitation fragment nearshore metapopulations? When weak Allee effects are included, habitat occupancy drops as larval retention decreases because more larvae are lost to unsuitable habitat. With strong Allee effects habitat occupancy also drops at high larval retention because more larvae are needed to overcome the Allee effect. Post-dispersal Allee effects seem more detrimental for nearshore metapopulations. MPA effectiveness seems also lower in a post-dispersal Allee effect scenario. In overexploited systems, local populations that go extinct are also less likely to recover even after protecting the whole coastline. In exploited nearshore metapopulations with Allee effects, local occupancy or the recovery of local populations depends not only on larval inflow from neighbor populations, but also on larval inflow for these neighbors. Nearshore metapopulations with intense fishing mortality and Allee effects may also suffer a decrease in dispersal strength and fragmentation. Population fragmentation occurs when large populations are split into smaller groups. A tool for detecting partitioning in a network is modularity. The modularity analysis performed for red abalone in the Southern California Bight showed that exploitation increases partitioning through time before the entire metapopulation collapses. These findings call for research effort in estimating the strength of potential Allee effects to prevent stock collapse and assess MPA effectiveness, evaluating the predictability of local occupancy by centrality metrics to help identify important sites for conservation, and using modularity analysis to quantify the health of exploited metapopulations to prevent their collapse.Ecology, Evolution and Behavio

Allee effects introduced by density dependent phenology.

We consider both the nonspatial model and spatial model of a species that gives birth to eggs at the end of the year. It is assumed that the timing of emergence from eggs is controled by phenology, which is density dependent. In general, the solution maps for our models are implicit; When the solution map is explicit, it is extremely complex and it is easier to work with the implicit map. We derive integral conditions for which the nonspatial model exhibits strong Allee effect. We also provide a necessary condition and a sufficient condition for the existence of positive equilibrium solutions. We also numerically explore the complex dynamics of both models. It is shown that varying a parameter can cause an Allee threshold to appear/disappear. We also show that the spatial model can have a growth function with overcompensation, wave solutions, oscillating waves, and nonspreading solutions. It is also shown that the wave solutions can have constant, oscillating, or chaotic spreading speeds. We also provide an example where the solutions to the spatial model are persistent, even though the underlying dynamics of the nonspatial model is essential extinction

Effects of climate and density on the survival of whiteooted mice (Peromyscus leucopus)

Short-lived rodents are sensitive to changes in environmental conditions and exhibit annual fluctuations under seasonal environments in northern temperate regions. I analyzed 34 years of monthly live-trapping data on whiteooted mice (Peromyscus leucopus) collected in Carter Woods, Ohio. I used a theoretic-information approach to select the best approximating models and analysis of deviance to infer effects of climate and density on survival of mice. I tested for a cost of reproduction to females and found no difference in survival between reproductive states. Directions and magnitudes of effects of climate and density varied over time. Increased variability in temperature reduced effects of density on survival. I detected an Allee effect and density dependent effects on survival. Long-term trapping data are needed to study temporal effects of climate and density on the demography of rodents. Recruitment had a greater impact on population growth rate than surviva

Generalized beta models and population growth: so many routes to chaos

Logistic and Gompertz growth equations are the usual choice to model sustainable growth and immoderate growth causing depletion of resources, respectively. Observing that the logistic distribution is geo-max-stable and the Gompertz function is proportional to the Gumbel max-stable distribution, we investigate other models proportional to either geo-max-stable distributions (log-logistic and backward log-logistic) or to other max-stable distributions (Fréchet or max-Weibull). We show that the former arise when in the hyper-logistic Blumberg equation, connected to the Beta (Formula presented.) function, we use fractional exponents (Formula presented.) and (Formula presented.), and the latter when in the hyper-Gompertz-Turner equation, the exponents of the logarithmic factor are real and eventually fractional. The use of a BetaBoop function establishes interesting connections to Probability Theory, Riemann–Liouville’s fractional integrals, higher-order monotonicity and convexity and generalized unimodality, and the logistic map paradigm inspires the investigation of the dynamics of the hyper-logistic and hyper-Gompertz maps.info:eu-repo/semantics/publishedVersio

No Allee effect detected during the natural recolonization by a large carnivore despite low growth rate

Eurasian lynx (Lynx lynx) have recently naturally recolonized southern Sweden. The first documented reproduction of lynx in recent times occurred in 2003, and the population increased from 2 to 48 family groups (the unit of measurement in Swedish monitoring) during its first 18 years (2003/2004-2020/2021). We did not detect any Allee effect, that is, lower growth rate at low population density, during the recolonization of southern Sweden, although our population simulations revealed a non-negligible (30%) chance that population observed development could include an Allee effect. The probable absence of an Allee effect was likely because colonizing females did not lack mating partners, as a larger number of wide-ranging males were established in the area before documented reproduction took place. Despite the absence of an Allee effect, the growth rate during recolonization was lower in southern Sweden (lambda = 1.20) than in central Sweden (lambda = 1.29). We have no evidence of higher mortality, including that from poaching, or lower reproduction in southern Sweden could explain the lower growth rate. Instead, we suggest that the lower growth rate during the recolonization of southern Sweden was explained by fewer immigrants arriving from central Sweden due to areas of less suitable habitat between central and southern Sweden, partially preventing immigration southward. From a conservation point of view, it is positive that this small population could recover without being negatively influenced by an Allee effect, as small populations with an Allee effect experience lower viability than those without

The influence of isolation on the dynamics of populations and communities

Isolation is defined as the separation in time or space of individuals, populations, or of species within a community. Though isolation can be the result of many ecological processes, its role in affecting the structure and dynamics of populations and communities is not often acknowledged directly. For example, spatial heterogeneity is a frequently recognized as a significant ecological factor, but the effects of spatial heterogeneity are manifested through the isolation that heterogeneity imposes on the focal populations or communities. Isolation is an important, but hidden, component of many other ecological theories and frameworks as well. In this dissertation, I explore the role of isolation per se as an organizing theme in ecology by studying the effects of isolation in time and in space on both populations and communities. Chapter 1 explores how isolation in time among individuals in a population may affect the population's dynamics and risk of extinction. Through a combination of modeling and meta-analysis, Chapter 1 demonstrates that reproductive asynchrony, a form of temporal isolation, can have profound negative effects at the population level in species that feature annual lifecycles. Chapter 2 reviews and synthesizes the literature on habitat connectivity, the inverse of spatial isolation, and lays out a novel framework for organizing and understanding the different metrics used to measure the connectivity. Chapter 3 examines the role of spatial isolation among species in an assemblage of Costa Rican bark beetles in mediating species interactions. The chapter uses a combination of modeling and field-collected observational data to test the hypothesis that isolation among species in this bark beetle assemblage results in a community that behaves neutrally. The studies presented in this dissertation represent a broad sweep of the ways in which the concept of isolation may be applied to better understand the dynamics of populations and communities. Individually, each chapter is an original contribution to the ecology literature. Taken together, these papers demonstrate the power of isolation as an organizing theme in ecology and will hopefully stimulate increased research effort and theoretical development around the concept of isolation

Multi-scale processes in metapopulations : Contributions of stage structure, rescue effect, and correlated extinctions

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