Probability of Mitochondrial Lineage Extinction in Female Offspring,Modern and Paleolithic: Branching Process Analysis

We evaluate the probability of extinction of the female offspring of two populations of women: the one Paleolithic, the other that of Italy today. In both cases it is assumed that possible extinction arises exclusively on account of limitations in the degree of fertility and/or an imbalance in the sex-ratio of the population. The value is obtained as the probability that a Branching Process describing the evolution of the offspring by a progenitor degenerates to a “Blank Generation,” that is, a generation without women. Mathematically, it derives from a solution between 0 and 1 of a linear equation whose coefficients are the probabilities that a single progenitor breeds various integer numbers of daughters. We evaluated such probabilities by consulting literature. The probability of branch extinction is also the probability of extinction of progenitor’s mitochondrial lineage.     

Rules of thumb for conservation of metapopulations based on a stochastic winking-patch model

From a theoretical viewpoint, nature management basically has two options to prolong metapopulation persistence: decreasing local extinction probabilities and increasing colonization probabilities. This article focuses on those options with a stochastic, single-species metapopulation model. We found that for most combinations of local extinction probabilities and colonization probabilities, decreasing the former increases metapopulation extinction time more than does increasing the latter by the same amount. Only for relatively low colonization probabilities is an effort to increase these probabilities more beneficial, but even then, decreasing extinction probabilities does not seem much less effective. Furthermore, we found the following rules of thumb. First, if one focuses on extinction, one should preferably decrease the lowest local extinction probability. Only if the extinction probabilities are (almost) equal should one prioritize decreases in the local extinction probability of the patch with the best direct connections to and from other patches. Second, if one focuses on colonization, one should preferably increase the colonization probability between the patches with the lowest local extinction probability. Only if the local extinction probabilities are (almost) equal should one instead prioritize increases in the highest colonization probability (unless extinction probabilities and colonization probabilities are very low). The rules of thumb have an important common denominator: the local extinction process has a greater bearing on metapopulation extinction time than colonization.     

Extinct or still out there? Disentangling influences on extinction and rediscovery helps to clarify the fate of species on the edge

Each year, two or three species that had been considered to be extinct are rediscovered. Uncertainty about whether or not a species is extinct is common, because rare and highly threatened species are difficult to detect. Biological traits such as body size and range size are expected to be associated with extinction. However, these traits, together with the intensity of search effort, might influence the probability of detection and extinction differently. This makes statistical analysis of extinction and rediscovery challenging. Here, we use a variant of survival analysis known as cure rate modelling to differentiate factors that influence rediscovery from those that influence extinction. We analyse a global data set of 99 mammals that have been categorized as extinct or possibly extinct. We estimate the probability that each of these mammals is still extant and thus estimate the proportion of missing (presumed extinct) mammals that are incorrectly assigned extinction. We find that body mass and population density are predictors of extinction, and body mass and search effort predict rediscovery. In mammals, extinction rate increases with body mass and population density, and these traits act synergistically to greatly elevate extinction rate in large species that also occurred in formerly dense populations. However, when they remain extant, larger‐bodied missing species are rediscovered sooner than smaller species. Greater search effort increases the probability of rediscovery in larger species of missing mammals, but has a minimal effect on small species, which take longer to be rediscovered, if extant. By separating the effects of species characteristics on extinction and detection, and using models with the assumption that a proportion of missing species will never be rediscovered, our new approach provides estimates of extinction probability in species with few observation records and scant ecological information.     

Autocorrelated environmental variation and the establishment of invasive species

Environmental parameters such as temperature and rainfall have a positively autocorrelated variance structure which makes it likely that runs of good or bad conditions will occur. It has previously been demonstrated that such autocorrelated environmental variance can increase the probability of extinction in small populations, in much the same way that increased variance without autocorrelation can increase extinction risk. As a result, it has also been suggested that positive autocorrelation will decrease the probability that a species will establish in a novel location. We suggest that describing the probability of invasion success as the probability of indefinite persistence may be an inappropriate definition of risk. Economic or ecological damage may be associated with a population that initially reaches high densities before going extinct in the new location. In addition, such populations may spread to new locations before extirpation. We use a modeling approach to examine the effect of positively autocorrelated conditions on the probability that small populations will reach large size before extinction. We find that where variance is high and the geometric mean of the population growth rate is low, autocorrelation increases the risk that a population will pass a an upper threshold density, even when extinction probability is unaffected. Therefore species classified as having low probability of invasion risk on the basis of population growth rates measured in low variance environments may actually have quite a substantial probability of establishing a large population for a period of time. The mechanism behind the effect is the disproportionate influence of short runs of good conditions initially following introduction.     

Optimization and Phenotype Allocation

We study the phenotype allocation problem for the stochastic evolution of a multitype population in a random environment. Our underlying model is a multitype Galton–Watson branching process in a random environment. In the multitype branching model, different types denote different phenotypes of offspring, and offspring distributions denote the allocation strategies. Two possible optimization targets are considered: the long-term growth rate of the population conditioned on nonextinction, and the extinction probability of the lineage. In a simple and biologically motivated case, we derive an explicit formula for the long-term growth rate using the random Perron–Frobenius theorem, and we give an approximation to the extinction probability by a method similar to that developed by Wilkinson. Then we obtain the optimal strategies that maximize the long-term growth rate or minimize the approximate extinction probability, respectively, in a numerical example. It turns out that different optimality criteria can lead to different strategies.     

Extinction probabilities and times to extinction for populations of tsetse flies Glossina spp. (Diptera: Glossinidae) subjected to various control measures

A stochastic branching process was used to derive equations for the mean and variance of the probability of, and time to, extinction in tsetse populations. If the remnant population is a single inseminated female, the extinction probability increases linearly with adult mortality and is always certain if this mortality >3.5% per day even for zero pupal mortality. If the latter mortality is 4% per day, certain extinction is only avoided if adult mortality <1.5% per day. For remnant female populations >1, the extinction probability increases in a non-linear manner with adult mortality. Extinction is still certain for adult mortality >3.5% per day but, when the remnant population is >16, extinction is highly unlikely for adult mortality <2.5% per day if all females are inseminated. Extinction probability increases with increasing probability of sterile mating in much the same way as it does with increasing adult mortality. Extinction is assured if the probability of insemination can be reduced to 0.1. The required reduction decreases with increasing adult mortality. For adult mortality = 6-8% per day, the time to extinction increases only by one generation per order of magnitude increase in the starting population. Time to extinction is less sensitive to changes in the pupal than in the adult mortality. Reductions in the probability of insemination only become important when adult mortality is small; if the adult mortality is 8% per day, reducing the insemination probability from 1 to 0.1 only reduces the expected time to extinction by two generations. Conversely, increases in adult mortality produce important reductions in the required time even when the probability of insemination is 0.1. The practical, economic implication for the sterile insect technique is that the low-tech methods used to suppress tsetse populations should not be halted when the release of sterile males is initiated. The sterile insect technique should only be contemplated when it has been demonstrated that the low-tech methods have failed to effect eradication. The theory is shown to be in good accord with the observed results of tsetse control campaigns involving the use of odour-baited targets in Zimbabwe and the sterile insect technique on Unguja Island, Zanzibar.     

Genetic sex determination and extinction

Genetic factors can affect the probability of extinction either by increasing the effect of detrimental variants or by decreasing the potential for future adaptive responses. In a recent paper, Zayed and Packer demonstrate that low variation at a specific locus, the complementary sex determination (csd) locus in Hymenoptera (ants, bees and wasps), can result in a sharply increased probability of extinction. Their findings illustrate situations in which there is a feedback process between decreased genetic variation at the csd locus owing to genetic drift and decreased population growth, resulting in an extreme type of extinction vortex for these ecologically important organisms.     

Extinction and descent

The probability of lineal extinction is sensitive to all the moments of the reproductive success probability distribution. In particular, high variance in reproductive success is associated with high probability of lineal extinction. Where male variance in reproductive success exceeds female variance, strictly patrilineal lines of descent will become extinct more rapidly than strictly matrilineal lines of descent. Patrilineal genealogies will be expected to be shallower and broader than matrilineal genealogies under such conditions. Potential implications of this genealogical asymmetry for human descent systems include the greater information content of patrilineal kinship reckoning compared with any other unilineal system and the greater effectiveness of patrilineal kinship as a vehicle for corporate action.     

Minimisation of extinction probabilities in reproducing populations

In an attempt to explain variability in clutch size among laying birds of the same species, models are considered in which birds have to choose a randomised strategy for clutch size in the face of random environments in order to minimise a probability of extinction. Three models emerge, depending upon whether this is the probability of extinction of the whole species or that of an individual line of descent, and whether change of strategy from one generation to the next is allowed. In two of these models an asymptotically optimal strategy, which typically is randomised, is predicted for large populations.     

Metapopulation extinction thresholds in rain forest remnants

Although habitat fragmentation is a major threat to global biodiversity, the demographic mechanisms underlying species loss from tropical forest remnants remain largely unexplored. In particular, no studies at the landscape scale have quantified fragmentation's impacts on colonization, extinction, and local population growth simultaneously. In central Amazonia, we conducted a multiyear demographic census of 292 populations of two leaf-inhabiting (i.e., epiphyllous) bryophyte species transplanted from continuous forest into a network of 10 study sites ranging from 1, 10, and 100 to > 10,000 ha in size. All populations experienced significantly positive local growth (lambda > 1) and a nearly constant per-generational extinction probability (15%). However, experimental leaf patches in reserves of > or = 100 ha experienced nearly double (48%) the colonization probability observed in small reserves (27%), suggesting that the proximate cause of epiphyll species loss in small fragments (< or = 10 ha) is reduced colonization. Nonetheless, populations of small fragments exhibit rates of colonization above patch extinction, positive local growth, and low temporal variation, which are features that should theoretically reduce the probability of extinction. This result suggests that for habitat-tracking metapopulations subject to frequent and stochastic turnover events, including epiphylls, colonization/extinction ratios must be maintained well above unity to ensure metapopulation persistence.     

Invasibility and stochastic boundedness in monotonic competition models

We give necessary and sufficient conditions for stochastically bounded coexistence in a class of models for two species competing in a randomly varying environment. Coexistence is implied by mutual invasibility, as conjectured by Turelli. In the absence of invasibility, a species converges to extinction with large probability if its initial population is small, and extinction of one species must occur with probability one regardless of the initial population sizes. These results are applied to a general symmetric competition model to find conditions under which environmental fluctuations imply coexistence or competitive exclusion.     

Estimation of local extinction rates when species detectability covaries with extinction probability: is it a problem?

Estimating the rate of change of the composition of communities is of direct interest to address many fundamental and applied questions in ecology. One methodological problem is that it is hard to detect all the species present in a community. Nichols et al. presented an estimator of the local extinction rate that takes into account species probability of detection, but little information is available on its performance. However, they predicted that if a covariance between species detection probability and local extinction rate exists in a community, the estimator of local extinction rate complement would be positively biased.
Here, we show, using simulations over a wide range of parameters that the estimator performs reasonably well. The bias induced by biological factors appears relatively weak. The most important factor enhancing the performance (bias and precision) of the local extinction rate complement estimator is sampling effort. Interestingly, a potentially important biological bias, such as the covariance effect, improves the estimation for small sampling efforts, without inducing a supplementary overestimation when these sampling efforts are high. In the field, all species are rarely detectable so we recommend the use of such estimators that take into account heterogeneity in species detection probability when estimating vital rates responsible for community changes.     

Extinction risk assessment of declining wild populations: The case of the southern Bluefin Tuna

We estimate the extinction probability of a large and decreasing population, the southern bluefin tuna. This tuna was listed as critically endangered by the World Conservation Union (IUCN) in 1996. However, the absolute population size is still large and the extinction probability within the next half century is negligible if the recent population decline rate does not increase in the future. IUCN’s criterion with respect to the population decline rate should be linked to the absolute population size, if this is estimated. Several methods estimating the probability of extinction conclude that the southern bluefin tuna population will be below 500 mature individuals within the next 100 years and may be listed as vulnerable. These analyses suggest that extinction risk assessment is useful for management action for taxa that still have large population and are rapidly decreasing.     

Extinction Times of Epidemic Outbreaks in Networks

In the Susceptible–Infectious–Recovered (SIR) model of disease spreading, the time to extinction of the epidemics happens at an intermediate value of the per-contact transmission probability. Too contagious infections burn out fast in the population. Infections that are not contagious enough die out before they spread to a large fraction of people. We characterize how the maximal extinction time in SIR simulations on networks depend on the network structure. For example we find that the average distances in isolated components, weighted by the component size, is a good predictor of the maximal time to extinction. Furthermore, the transmission probability giving the longest outbreaks is larger than, but otherwise seemingly independent of, the epidemic threshold.     

Establishment Probability in Fluctuating Environments: A Branching Process Model

We study the establishment probability of invaders in stochastically fluctuating environments and the related issue of extinction probability of small populations in such environments, by means of an inhomogeneous branching process model. In the model it is assumed that individuals reproduce asexually during discrete reproduction periods. Within each period, individuals have (independent) Poisson distributed numbers of offspring. The expected numbers of offspring per individual are independently identically distributed over the periods. It is shown that the establishment probability of an invader varies over the reproduction periods according to a stable distribution. We give a method for simulating the establishment probabilities and approximations for the expected establishment probability. Furthermore, we show that, due to the stochasticity of the establishment success over different periods, the expected success of sequential invasions is larger then that of simultaneous invasions and we study the effects of environmental fluctuations on the extinction probability of small populations and metapopulations. The results can easily be generalized to other offspring distributions than the Poisson.     

Small population instability and island settlement patterns

A model of extinction probability, based on the general theory of island biogeography [MacArthur and Wilson, 1967], is proposed for humans on oceanic islands; extinction probability is determined by island carrying capacity, frequency and amplitude of fluctuations in resources determining carrying capacity, and the net costs of contact and exchange between population units. The model predicts that extinction probability will determine island settlement patterns within an island group resulting in nonsettlement of islands with low carrying capacities and settlement of all islands with high carrying capacities. Data examined from the Marshall Islands tend to support the model. The model is extended to initial atoll colonization patterns. Possible requirements for initial settlement are suggested.Deceased.     

Does inbreeding affect the extinction risk of small populations?: predictions from Drosophila

A fundamental assumption underlying the importance of genetic risks within conservation biology is that inbreeding increases the extinction probability of populations. Although inbreeding has been shown to have a detrimental impact on individual fitness, its contribution to extinction is still poorly understood. We have studied the consequences of different levels of prior inbreeding for the persistence of small populations using Drosophila melanogaster as a model organism. To this end, we determined the extinction rate of small vial populations differing in the level of inbreeding under both optimal and stress conditions, i.e. high temperature stress and ethanol stress. We show that inbred populations have a significantly higher short‐term probability of extinction than non‐inbred populations, even for low levels of inbreeding, and that the extinction probability increases with increasing inbreeding levels. In addition, we observed that the effects of inbreeding become greatly enhanced under stressful environmental conditions. More importantly, our results show that the impact of environmental stress becomes significantly greater for higher inbreeding levels, demonstrating explicitly that inbreeding and environmental stress are not independent but can act synergistically. These effects seem long lasting as the impact of prior inbreeding was still qualitatively the same after the inbred populations had been expanded to appreciable numbers and maintained as such for approximately 50 generations. Our observations have significant consequences for conservation biology.     

Chaotic dynamics may determine the effect of inter-patch migration on metapopulation survival

A simple, strategic model of a system of habitat fragments connected by conservation corridors is presented. The intrinsic dynamics of the population on each fragment are stochastic. In addition, at each generation there is a probability of a catastrophic event occurring which affects all the habitat fragments by greatly reducing the size of the population on each. Global extinction is considered to occur when all the populations simultaneously fall below a threshold value. If the intrinsic dynamics on each fragment are simple cycles or a stable equilibrium, then the addition of conservation corridors does not reduce the frequency of global extinction. This is because migration between fragments induces their populations to have values which are similar to each other. However, if the intrinsic population dynamics are chaotic then the probability of global extinction is greatly reduced by the introduction of conservation corridors. Although local extinction is likely, the chaos acts to oppose the synchronising effect of migration. Often a subset of the populations survive a catastrophe and can recolonize the other patches.     

The return of the Red Queen, or the law of the growth in the mean duration of the existence of genera during evolution

Phanerozoic marine genera apparently do not become less extinction-prone with age. Higher extinction probability in "young" cohorts of genera is better explained by initially different levels of extinction-tolerance of genera in the cohort. This fact agrees with one of the two basic statements of the "Red Queen" hypothesis (Van Valen, 1973). In the second statement (the idea that the increase in fitness lowers extinction probability) the term "fitness" should be changed to "adaptability". The increase of extinction-tolerance, that can be interpreted as the increase of adaptability to unpredictable changes of environment, is found in succession of "generations" of genera that replace one another through time. This increase reveals itself, firstly, in the growth of mean duration of genera, as well as in the decrease of extinction/origination rates, gradual accumulation of long-lived genera and origination of genera with higher duration. The increase of adaptability may be caused by selective extinction of stenotopic, ecologically specialized forms; Cope's law; evolution of ecosystems that involves development of more effective mechanisms of sustaining homeostasis which may stimulate the recovery of a genus after partial extinction.     

Investigating age‐dependency of species extinction rates using dynamic survivorship analysis

Survivorship curves with taxon lifespans normalised to variations in the real‐time extinction rate (the ‘Corrected Survivorship Score’ technique) are plotted for various fossil groups. Of five groups tested at the ‘species level’ (strictly speaking, Linnean morphospecies), only the calcareous nannoplankton are found to have had a constant extinction probability with respect to morphospecies age. The planktonic foraminifer, trilobite, conodont and graptolite data all show a significant age‐dependent effect (convexity of survivorship curves), which reveals in each case a progressively increasing extinction probability as morphospecies became older. This effect is found to be much reduced for trilobite genera and absent for ammonoid families, suggesting that age‐dependency of extinction probability is primarily a characteristic of the species level in some, but not all groups. However, the pattern may be partly an artefact of taxonomic methodology. Morphospecies range data, which are gathered primarily for biostratigraphic purposes, are far from ideal for the purpose of survivorship analysis. Therefore, survivorship curves for a specially‐developed lineage phylogeny of Palaeogene planktonic foraminifera are also presented. These do not indicate a similar age‐dependency to the extinction probability with respect to either the terminal or non‐terminal lineages.