On the Extinction Probability for Bisexual Branching Processes in Varying Environments

2000 Mathematics Subject Classification: 60J80

The collision branching process

We consider a branching model, which we call the collision branching process (CBP), that accounts for the effect of collisions, or interactions, between particles or individuals. We establish that there is a unique CBP, and derive necessary and sufficient conditions for it to be nonexplosive. We review results on extinction probabilities, and obtain explicit expressions for the probability of explosion and the expected hitting times. The upwardly skip-free case is studied in some detail.

Detecting environmental impacts on metapopulations of mound spring invertebrates - Assessing an incidence function model

We use a stochastic patch occupancy model of invertebrates in the Mound Springs ecosystem of South Australia to assess the ability of incidence function models to detect environmental impacts on metapopulations. We assume that the probability of colonisation decreases with increasing isolation and the probability of extinction is constant across spring vents. We run the models to quasi-equilibrium, and then impose an impact by increasing the local extinction probability. We sample the output at various times pre- and postimpact, and examine the probability of detecting a significant change in population parameters. The incidence function model approach turns out to have little power to detect environmental impacts on metapopulations with small numbers of patches. (C) 2001 Elsevier Science Ltd. All rights reserved.

The use of stochastic dynamic programming in optimal landscape reconstruction for metapopulations

A decision theory framework can be a powerful technique to derive optimal management decisions for endangered species. We built a spatially realistic stochastic metapopulation model for the Mount Lofty Ranges Southern Emu-wren (Stipiturus malachurus intermedius), a critically endangered Australian bird. Using diserete-time Markov,chains to describe the dynamics of a metapopulation and stochastic dynamic programming (SDP) to find optimal solutions, we evaluated the following different management decisions: enlarging existing patches, linking patches via corridors, and creating a new patch. This is the first application of SDP to optimal landscape reconstruction and one of the few times that landscape reconstruction dynamics have been integrated with population dynamics. SDP is a powerful tool that has advantages over standard Monte Carlo simulation methods because it can give the exact optimal strategy for every landscape configuration (combination of patch areas and presence of corridors) and pattern of metapopulation occupancy, as well as a trajectory of strategies. It is useful when a sequence of management actions can be performed over a given time horizon, as is the case for many endangered species recovery programs, where only fixed amounts of resources are available in each time step. However, it is generally limited by computational constraints to rather small networks of patches. The model shows that optimal metapopulation, management decisions depend greatly on the current state of the metapopulation,. and there is no strategy that is universally the best. The extinction probability over 30 yr for the optimal state-dependent management actions is 50-80% better than no management, whereas the best fixed state-independent sets of strategies are only 30% better than no management. This highlights the advantages of using a decision theory tool to investigate conservation strategies for metapopulations. It is clear from these results that the sequence of management actions is critical, and this can only be effectively derived from stochastic dynamic programming. The model illustrates the underlying difficulty in determining simple rules of thumb for the sequence of management actions for a metapopulation. This use of a decision theory framework extends the capacity of population viability analysis (PVA) to manage threatened species.

Mother-offspring competition promotes colonization success.

Colonization is the crucial process underlying range expansions, biological invasions, and metapopulation dynamics. Which individuals leave their natal population to colonize empty habitats is a crucial question and is presently unresolved. Dispersal is the first step in colonization. However, not all dispersing individuals are necessarily good colonizers. Indeed, in some species, the phenotype of dispersers differs depending on the selective pressures that induce dispersal. In particular, kin-based interactions, a factor driving social evolution, should induce different social response profiles in nondispersing and dispersing individuals. Kin competition (defined here as between the mother and offspring) has been proven to produce dispersers with a particular phenotype that may enhance their colonizing ability. By using the common lizard (Lacerta vivipara), we conducted a multipopulation experiment to study the effect of kin competition on dispersal and colonization success. We manipulated mother-offspring interactions, which are the most important component of kin competition in the studied species, at the family and population levels and measured the consequences on colonization success. We demonstrate that mother-offspring competition at the population level significantly influences colonization success. Increased competition at the population level enhanced the colonization rate of the largest juveniles as well as the growth and survival of the colonizers. Based on these results, we calculated that kin-induced colonization halves the extinction probability of a newly initiated population. Because interactions between relatives are likely to affect the ability of a species to track habitat modifications, kin-based dispersal should be considered in the study of invasion dynamics and metapopulation functioning.

A perda de grupos funcionais em comunidades virtuais: efeito das interações entre espécies e grupos funcionais

High levels of local, regional, and global extinctions has progressively simplified communities in terms of both species and ecosystem functioning. Theoretical models demonstrated that the degree of functional redundancy determines the rates of functional group loss in response to species extinctions. Here, we improve the theoretical predictions by incorporating in the model interactions between species and between functional groups. In this study, we tested the effect of different scenarios of interspecific interactions and effects between functional groups on the resistance to loss of community functional groups. Virtual communities have been built with different distribution patterns of species in functional groups, both with high and low evenness. A matrix A was created to represent the net effect of interspecific interactions among all species, representing nesting patterns, modularity, sensitive species, and dominant species. Moreover, a second matrix B was created to represent the interactions between functional groups, also exhibiting different patterns. The extinction probability of each species was calculated based on community species richness and by the intensity of the interspecific interactions that act upon it and group to which it belongs. In the model, successive extinctions decrease the community species richness, the degree of functional redundancy and, consequently, the number of functional groups that remain in the system. For each scenario of functional redundancy, A, and B, we ran 1000 simulations to generate an average functional extinction curve. Different model assumptions were able to generate remarkable variation on functional extinction curves. More extreme variations occurred when the matrix A and B caused a higher heterogeneity in the species extinction probability. Scenarios with sensitive species, positive or negative, showed a greater variation than the scenarios with dominant species. Nested interactions showed greater variation than scenarios where the interactions were in modules. Communities with maximal functional evenness can only be destabilized by the interactions between species and functional groups. In contrast, communities with low functional evenness can have its resistance either increased or decreased by the interactions. The concentration of positive interactions in low redundancy groups or negative interactions in high redundancy groups was able to decrease the functional extinction rates. In contrast, the concentration of negative interactions in low redundancy groups or positive interactions in high redundancy groups was able to increase the functional extinction rates. This model shows results that are relevant for species priorization in ecosystem conservation and restoration

Some Contributions to the Class of Two-Sex Branching Processes Depending on the Number of Couples in the Population

2000 Mathematics Subject Classification: 60J80

Branching Processes in Autoregressive Random Environment

2000 Mathematics Subject Classification: 60J80, 60K05.

Population viability analyses of Chamaecrista keyensis (Leguminosae: Caesalpinioideae), a narrowly endemic herb of the lower Florida Keys: Effects of seasonal timing of fires and the urban -wildland interface

This research first evaluated the effects of urban wildland interface on reproductive biology of the Big Pine Partridge Pea, Chamaecrista keyensis, an understory herb that is endemic to Big Pine Key, Florida. I found that C. keyensis was self-compatible, but depended on bees for seed set. Furthermore, individuals of C. keyensis in urban habitats suffered higher seed predation and therefore set fewer seeds than forest interior plants. ^ I then focused on the effects of fire at different times of the year, summer (wet) and winter (dry), on the population dynamics and population viability of C. keyensis. I found that C. keyensis population recovered faster after winter burns and early summer burns (May–June) than after late summer burns (July–September) due to better survival and seedling recruitment following former fires. Fire intensity had positive effects on reproduction of C. keyensis. In contrast, no significant fire intensity effects were found on survival, growth, and seedling recruitment. This indicated that better survival and seedling recruitment following winter and early summer burns (compared with late summer burns) were due to the reproductive phenology of the plant in relation to fires rather than differences in fire intensity. Deterministic population modeling showed that time since fire significantly affected the finite population growth rates (λ). Particularly, recently burned plots had the largest λ. In addition, effects of timing of fires on λ were most pronounced the year of burn, but not the subsequent years. The elasticity analyses suggested that maximizing survival is an effective way to minimize the reduction in finite population growth rate the year of burn. Early summer fires or dry-season fires may achieve this objective. Finally, stochastic simulations indicated that the C. keyensis population had lower extinction risk and population decline probability if burned in the winter than in the late summer. A fire frequency of approximately 7 years would create the lowest extinction probability for C. keyensis. A fire management regime including a wide range of burning seasons may be essential for the continued existence of C. keyensis and other endemic species of pine rockland on Big Pine Key. ^

Development And Characterization Of Microsatellite Loci For Ocotea Species (lauraceae) Threatened With Extinction.

The Atlantic rainforest species Ocotea catharinensis, Ocotea odorifera, and Ocotea porosa have been extensively harvested in the past for timber and oil extraction and are currently listed as threatened due to overexploitation. To investigate the genetic diversity and population structure of these species, we developed 8 polymorphic microsatellite markers for O. odorifera from an enriched microsatellite library by using 2 dinucleotide repeats. The microsatellite markers were tested for cross-amplification in O. catharinensis and O. porosa. The average number of alleles per locus was 10.2, considering all loci over 2 populations of O. odorifera. Observed and expected heterozygosities for O. odorifera ranged from 0.39 to 0.93 and 0.41 to 0.92 across populations, respectively. Cross-amplification of all loci was successfully observed in O. catharinensis and O. porosa except 1 locus that was found to lack polymorphism in O. porosa. Combined probabilities of identity in the studied Ocotea species were very low ranging from 1.0 x 10-24 to 7.7 x 10-24. The probability of exclusion over all loci estimated for O. odorifera indicated a 99.9% chance of correctly excluding a random nonparent individual. The microsatellite markers described in this study have high information content and will be useful for further investigations on genetic diversity within these species and for subsequent conservation purposes.

Comparing predictions of extinction risk using models and subjective judgement

Models of population dynamics are commonly used to predict risks in ecology, particularly risks of population decline. There is often considerable uncertainty associated with these predictions. However, alternatives to predictions based on population models have not been assessed. We used simulation models of hypothetical species to generate the kinds of data that might typically be available to ecologists and then invited other researchers to predict risks of population declines using these data. The accuracy of the predictions was assessed by comparison with the forecasts of the original model. The researchers used either population models or subjective judgement to make their predictions. Predictions made using models were only slightly more accurate than subjective judgements of risk. However, predictions using models tended to be unbiased, while subjective judgements were biased towards over-estimation. Psychology literature suggests that the bias of subjective judgements is likely to vary somewhat unpredictably among people, depending on their stake in the outcome. This will make subjective predictions more uncertain and less transparent than those based on models. (C) 2004 Elsevier SAS. All rights reserved.

Bayesian estimation of speciation and extinction from incomplete fossil occurrence data.

The temporal dynamics of species diversity are shaped by variations in the rates of speciation and extinction, and there is a long history of inferring these rates using first and last appearances of taxa in the fossil record. Understanding diversity dynamics critically depends on unbiased estimates of the unobserved times of speciation and extinction for all lineages, but the inference of these parameters is challenging due to the complex nature of the available data. Here, we present a new probabilistic framework to jointly estimate species-specific times of speciation and extinction and the rates of the underlying birth-death process based on the fossil record. The rates are allowed to vary through time independently of each other, and the probability of preservation and sampling is explicitly incorporated in the model to estimate the true lifespan of each lineage. We implement a Bayesian algorithm to assess the presence of rate shifts by exploring alternative diversification models. Tests on a range of simulated data sets reveal the accuracy and robustness of our approach against violations of the underlying assumptions and various degrees of data incompleteness. Finally, we demonstrate the application of our method with the diversification of the mammal family Rhinocerotidae and reveal a complex history of repeated and independent temporal shifts of both speciation and extinction rates, leading to the expansion and subsequent decline of the group. The estimated parameters of the birth-death process implemented here are directly comparable with those obtained from dated molecular phylogenies. Thus, our model represents a step towards integrating phylogenetic and fossil information to infer macroevolutionary processes.

Evaluating the legacy of landscape history: extinction debt and species credit in bird and small mammal assemblages in the Brazilian Atlantic Forest

There is now an extensive literature on extinction debt following deforestation. However, the potential for species credit in landscapes that have experienced a change from decreasing to expanding forest cover has received little attention. Both delayed responses should depend on current landscape forest cover and on species life-history traits, such as longevity, as short-lived species are likely to respond faster than long-lived species. We evaluated the effects of historical and present-day local forest cover on two vertebrate groups with different longevities understorey birds and non-flying small mammals - in forest patches at three Atlantic Forest landscapes. Our work investigated how the probability of extinction debt and species credit varies (i) amongst landscapes with different proportions of forest cover and distinct trajectories of forest cover change, and (ii) between taxa with different life spans. Our results suggest that the existence of extinction debt and species credit, as well as the potential for their future payment and/or receipt, is not only related to forest cover trajectory but also to the amount of remaining forest cover at the landscape scale. Moreover, differences in bird and small mammal life spans seem to be insufficient to affect differently their probability of showing time-delayed responses to landscape change. Synthesis and applications. Our work highlights the need for considering not only the trajectory of deforestation/regeneration but also the amount of forest cover at landscape scale when investigating time-delayed responses to landscape change. As many landscapes are experiencing a change from decreasing to expanding forest cover, understanding the association of extinction and immigration processes, as well as their interactions with the landscape dynamic, is a key factor to plan conservation and restoration actions in human-altered landscapes.

Extinction times for a general birth, death and catastrophe process

The birth, death and catastrophe process is an extension of the birth-death process that incorporates the possibility of reductions in population of arbitrary size. We will consider a general form of this model in which the transition rates are allowed to depend on the current population size in an arbitrary manner. The linear case, where the transition rates are proportional to current population size, has been studied extensively. In particular, extinction probabilities, the expected time to extinction, and the distribution of the population size conditional on nonextinction (the quasi-stationary distribution) have all been evaluated explicitly. However, whilst these characteristics are of interest in the modelling and management of populations, processes with linear rate coefficients represent only a very limited class of models. We address this limitation by allowing for a wider range of catastrophic events. Despite this generalisation, explicit expressions can still be found for the expected extinction times.

Exposing extinction risk analysis to pathogens: Is disease just another form of density dependence?

In the United States and several other countries., the development of population viability analyses (PVA) is a legal requirement of any species survival plan developed for threatened and endangered species. Despite the importance of pathogens in natural populations, little attention has been given to host-pathogen dynamics in PVA. To study the effect of infectious pathogens on extinction risk estimates generated from PVA, we review and synthesize the relevance of host-pathogen dynamics in analyses of extinction risk. We then develop a stochastic, density-dependent host-parasite model to investigate the effects of disease on the persistence of endangered populations. We show that this model converges on a Ricker model of density dependence under a suite of limiting assumptions, including. a high probability that epidemics will arrive and occur. Using this modeling framework, we then quantify: (1) dynamic differences between time series generated by disease and Ricker processes with the same parameters; (2) observed probabilities of quasi-extinction for populations exposed to disease or self-limitation; and (3) bias in probabilities of quasi-extinction estimated by density-independent PVAs when populations experience either form of density dependence. Our results suggest two generalities about the relationships among disease, PVA, and the management of endangered species. First, disease more strongly increases variability in host abundance and, thus, the probability of quasi-extinction, than does self-limitation. This result stems from the fact that the effects and the probability of occurrence of disease are both density dependent. Second, estimates of quasi-extinction are more often overly optimistic for populations experiencing disease than for those subject to self-limitation. Thus, although the results of density-independent PVAs may be relatively robust to some particular assumptions about density dependence, they are less robust when endangered populations are known to be susceptible to disease. If potential management actions involve manipulating pathogens, then it may be useful to. model disease explicitly.