Estimation of survival rate and extinction probability for stage-structured populations with overlapping life stages

The development of methods providing reliable estimates of demographic parameters (e. g., survival rates, fecundity) for wild populations is essential to better understand the ecology and conservation requirements of individual species. A number of methods exist for estimating the demographics of stage-structured populations, but inherent mathematical complexity often limits their uptake by conservation practitioners. Estimating survival rates for pond-breeding amphibians is further complicated by their complex migratory and reproductive behaviours, often resulting in nonobservable states and successive cohorts of eggs and tadpoles. Here we used comprehensive data on 11 distinct breeding toad populations (Bufo calamita) to clarify and assess the suitability of a relatively simple method [the Kiritani-Nakasuji-Manly (KNM) method] to estimate the survival rates of stage-structured populations with overlapping life stages. The study shows that the KNM method is robust and provides realistic estimates of amphibian egg and larval survival rates for species in which breeding can occur as a single pulse or over a period of several weeks. The study also provides estimates of fecundity for seven distinct toad populations and indicates that it is essential to use reliable estimates of fecundity to limit the risk of under- or overestimating the survival rates when using the KNM method. Survival and fecundity rates for B. calamita populations were then used to define population matrices and make a limited exploration of their growth and viability. The findings of the study recently led to the implementation of practical conservation measures at the sites where populations were most vulnerable to extinction. © 2010 The Society of Population Ecology and Springer.

On the Extinction Probability for Bisexual Branching Processes in Varying Environments

2000 Mathematics Subject Classification: 60J80

Extinction risk in cloud forest fragments under climate change and habitat loss

Aim: To quantify the consequences of major threats to biodiversity, such as climate and land-use change, it is important to use explicit measures of species persistence, such as extinction risk. The extinction risk of metapopulations can be approximated through simple models, providing a regional snapshot of the extinction probability of a species. We evaluated the extinction risk of three species under different climate change scenarios in three different regions of the Mexican cloud forest, a highly fragmented habitat that is particularly vulnerable to climate change. Location: Cloud forests in Mexico. Methods: Using Maxent, we estimated the potential distribution of cloud forest for three different time horizons (2030, 2050 and 2080) and their overlap with protected areas. Then, we calculated the extinction risk of three contrasting vertebrate species for two scenarios: (1) climate change only (all suitable areas of cloud forest through time) and (2) climate and land-use change (only suitable areas within a currently protected area), using an explicit patch-occupancy approximation model and calculating the joint probability of all populations becoming extinct when the number of remaining patches was less than five. Results: Our results show that the extent of environmentally suitable areas for cloud forest in Mexico will sharply decline in the next 70 years. We discovered that if all habitat outside protected areas is transformed, then only species with small area requirements are likely to persist. With habitat loss through climate change only, high dispersal rates are sufficient for persistence, but this requires protection of all remaining cloud forest areas. Main conclusions: Even if high dispersal rates mitigate the extinction risk of species due to climate change, the synergistic impacts of changing climate and land use further threaten the persistence of species with higher area requirements. Our approach for assessing the impacts of threats on biodiversity is particularly useful when there is little time or data for detailed population viability analyses. © 2013 John Wiley & Sons Ltd.

Uniqueness and extinction properties of generalised Markov branching processes

This paper focuses on the basic problems regarding uniqueness and extinction properties for generalised Markov branching processes. The uniqueness criterion is firstly established and a differential–integral equation satisfied by the transition functions of such processes is derived. The extinction probability is then obtained. A closed form is presented for both the mean extinction time and the conditional mean extinction time. It turns out that these important quantities are closely related to the elementary gamma function.

Optimal allocation of conservation effort among subpopulations of a threatened species: How important is patch quality?

Money is often a limiting factor in conservation, and attempting to conserve endangered species can be costly. Consequently, a framework for optimizing fiscally constrained conservation decisions for a single species is needed. In this paper we find the optimal budget allocation among isolated subpopulations of a threatened species to minimize local extinction probability. We solve the problem using stochastic dynamic programming, derive a useful and simple alternative guideline for allocating funds, and test its performance using forward simulation. The model considers subpopulations that persist in habitat patches of differing quality, which in our model is reflected in different relationships between money invested and extinction risk. We discover that, in most cases, subpopulations that are less efficient to manage should receive more money than those that are more efficient to manage, due to higher investment needed to reduce extinction risk. Our simple investment guideline performs almost as well as the exact optimal strategy. We illustrate our approach with a case study of the management of the Sumatran tiger, Panthera tigris sumatrae, in Kerinci Seblat National Park (KSNP), Indonesia. We find that different budgets should be allocated to the separate tiger subpopulations in KSNP. The subpopulation that is not at risk of extinction does not require any management investment. Based on the combination of risks of extinction and habitat quality, the optimal allocation for these particular tiger subpopulations is an unusual case: subpopulations that occur in higher-quality habitat (more efficient to manage) should receive more funds than the remaining subpopulation that is in lower-quality habitat. Because the yearly budget allocated to the KSNP for tiger conservation is small, to guarantee the persistence of all the subpopulations that are currently under threat we need to prioritize those that are easier to save. When allocating resources among subpopulations of a threatened species, the combined effects of differences in habitat quality, cost of action, and current subpopulation probability of extinction need to be integrated. We provide a useful guideline for allocating resources among isolated subpopulations of any threatened species. © 2010 by the Ecological Society of America.

Modeling the effect of striped bass (Morone saxatilis) on the population viability of Sacramento River winter-run chinook salmon (Onchorhynchus tshawytscha)

We estimated the impact of striped bass (Morone saxatilis) predation on winter-run chinook salmon (Oncorhynchus tshawytscha) with a Bayesian population dynamics model using striped bass and winter-run chinook salmon population abundance data. Winter-run chinook salmon extinction and recovery probabilities under different future striped bass abundance levels were estimated by simulating from the posterior distribution of model parameters. The model predicts that if the striped bass population declines to 512,000 adults as expected in the absence of stocking, winter-run chinook salmon will have about a 28% chance of quasi-extinction (defined as three consecutive spawning runs of fewer than 200 adults) within 50 years. If stocking stabilizes the striped bass population at 700,000 adults, the predicted quasi-extinction probability is 30%. A more ambitious stocking program that maintains a population of 3 million adult striped bass would increase the predicted quasi-extinction probability to 55%. Extinction probability, but not recovery probability, was fairly insensitive to assumptions about density dependence. We conclude that winter-run chinook salmon face a serious extinction risk without augmentation of the striped bass population and that substantial increases in striped bass abundance could significantly increase the threat to winter-run chi-nook salmon if not mitigated by increasing winter chinook salmon survival in some other way.

A metapopulation model of species boundaries

The majority, if not all, species have a limited geographic range bounded by a distribution edge. Violent ecotones such as sea coasts clearly produce edges for many species; however such ecotones, while sufficient for the formation of an edge, are not always necessary. We demonstrate this by simulation in discrete time of a spatially structured finite size metapopulation subjected to a spatial gradient in per-unit-time population extinction probability together with spatially structured dispersal and recolonisation. We find that relatively sharp edges separating a homeland or main geographical range from an outland or zone of relatively sparse and ephemeral colonisation can form in gradual environmental gradients. The form and placing of the edge is an emergent property of the metapopulation dynamics. The sharpness of the edge declines with increasing dispersal distance, and is dependent on the relative scales of dispersal distance and gradient length. The space over which the edge develops is short relative to the potential species range. The edge is robust against changes in both the shape of the environmental gradient and to a lesser extent to alterations in the kind of dispersal operating. Persistence times in the absence of environmental gradients are virtually independent of the shape of the dispersal function describing migration. The common finding of bell shaped population density distributions across geographic ranges may occur without the strict necessity of a niche mediated response to a spatially autocorrelated environment.

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. ^

Extinction risk from climate change

Climate change over the past ,30 years has produced numerous shifts in the distributions and abundances of species1,2 and has been implicated in one species-level extinction3. Using projections of species’ distributions for future climate scenarios, we assess extinction risks for sample regions that cover some 20% of the Earth’s terrestrial surface. Exploring three approaches in which the estimated probability of extinction shows a powerlaw relationship with geographical range size, we predict, on the basis of mid-range climate-warming scenarios for 2050, that 15–37% of species in our sample of regions and taxa will be ‘committed to extinction’. When the average of the three methods and two dispersal scenarios is taken, minimal climate-warming scenarios produce lower projections of species committed to extinction (,18%) than mid-range (,24%) and maximum change (,35%) scenarios. These estimates show the importance of rapid implementation of technologies to decrease greenhouse

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.