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.

Extinction times for a birth-death process with two phases

Many populations have a negative impact on their habitat or upon other species in the environment if their numbers become too large. For this reason they are often subjected to some form of control. One common control regime is the reduction regime: when the population reaches a certain threshold it is controlled (for example culled) until it falls below a lower predefined level. The natural model for such a controlled population is a birth-death process with two phases, the phase determining which of two distinct sets of birth and death rates governs the process. We present formulae for the probability of extinction and the expected time to extinction, and discuss several applications. (c) 2006 Elsevier Inc. All rights reserved.

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.

The use and abuse of population viability analysis

A recent study by Brook ef al. empirically tested the performance of population viability analysis (PVA) using data from 21 populations across a wide range of species. The study concluded that PVAs are good at predicting the future dynamics of populations. We suggest that this conclusion is a result of a bias in the studies that Brook et al, included in their analyses, We present arguments that PVAs can only be accurate at predicting extinction probabilities if data are extensive and reliable, and if the distribution of vital rates between individuals and years can be assumed stationary in the future, or if any changes can be accurately predicted. In particular, we note th at although catastrophes are likely to have precipitated many extinctions, estimates of the probability of catastrophes are unreliable.

Cenomanian (early Late Cretaceous) ammonoid faunas of Western Europe - Part II: Diversity patterns and the end-Cenomanian anoxic event

Diversity patterns of ammonoids are analyzed and compared with the timing of anoxic deposits around the Cenomanian/Turonian (C/T) boundary in the Vocontian, Anglo-Paris, and Monster basins of Western Europe. Differing from most previous studies, which concentrate on a narrow time span bracketing the C/T boundary, the present analysis covers the latest Albian to Early Turonian interval for which a high resolution, ammonoid-based biochronology, including 34 Unitary Associations zones, is now available. During the latest Albian-Middle Cenomanian interval, species richness of ammonoids reveals a dynamical equilibrium oscillating around an average of 20 species, whereas the Late Cenomanian-Early Turonian interval displays an equilibrium centered on an average value of 6 species. The abrupt transition between these two successive equilibria lasted no longer than two Unitary Associations. The onset of the decline of species richness thus largely predates the spread of oxygen-poor water masses onto the shelves, while minimal values of species richness coincide with the Cenomanian-Turonian boundary only. The decline of species richness during the entire Late Cenomanian seems to result from lower origination percentages rather than from higher extinction percentages. This result is also supported by the absence of statistically significant changes in the extinction probabilities of the poly-cohorts. Separate analyses of species richness for acanthoceratids and heteromorphs, the two essential components of the Cenomanian ammonoid community, reveal that heteromorphs declined sooner than acanthoceratids. Moreover, acanthoceratids showed a later decline at the genus level than at the species level. Such a decoupling is accompanied by a significant increase in morphological disparity of acanthoceratids, which is expressed by the appearance of new genera. Last, during the Late Cenomanian, paedomorphic processes, juvenile innovations and reductions of adult size dominated the evolutionary radiation of acanthoceratids. Hence, the decrease in ammonoid species richness and their major evolutionary changes significantly predates the spread of anoxic deposits. Other environmental constraints such as global flooding of platforms, warmer and more equable climate, as well as productivity changes better correlate with the timing of diversity changes and evolutionary patterns of ammonoids and therefore, provide more likely causative mechanisms than anoxia alone.

Objectives for multiple-species conservation planning

The first step in conservation planning is to identify objectives. Most stated objectives for conservation, such as to maximize biodiversity outcomes, are too vague to be useful within a decision-making framework. One way to clarify the issue is to define objectives in terms of the risk of extinction for multiple species. Although the assessment of extinction risk for single species is common, few researchers have formulated an objective function that combines the extinction risks of multiple species. We sought to translate the broad goal of maximizing the viability of species into explicit objectives for use in a decision-theoretic approach to conservation planning. We formulated several objective functions based on extinction risk across many species and illustrated the differences between these objectives with simple examples. Each objective function was the mathematical representation of an approach to conservation and emphasized different levels of threat Our objectives included minimizing the joint probability of one or more extinctions, minimizing the expected number of extinctions, and minimizing the increase in risk of extinction from the best-case scenario. With objective functions based on joint probabilities of extinction across species, any correlations in extinction probabilities bad to be known or the resultant decisions were potentially misleading. Additive objectives, such as the expected number of extinctions, did not produce the same anomalies. We demonstrated that the choice of objective function is central to the decision-making process because alternative objective functions can lead to a different ranking of management options. Therefore, decision makers need to think carefully in selecting and defining their conservation goals.

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.

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.

Kinematic parameters and membership probabilities of open clusters in the Bordeaux PM2000 catalogue

Aims. We derive lists of proper-motions and kinematic membership probabilities for 49 open clusters and possible open clusters in the zone of the Bordeaux PM2000 proper motion catalogue (+ 11 degrees <= delta <= + 18 degrees). We test different parametrisations of the proper motion and position distribution functions and select the most successful one. In the light of those results, we analyse some objects individually. Methods. We differenciate between cluster and field member stars, and assign membership probabilities, by applying a new and fully automated method based on both parametrisations of the proper motion and position distribution functions, and genetic algorithm optimization heuristics associated with a derivative-based hill climbing algorithm for the likelihood optimization. Results. We present a catalogue comprising kinematic parameters and associated membership probability lists for 49 open clusters and possible open clusters in the Bordeaux PM2000 catalogue region. We note that this is the first determination of proper motions for five open clusters. We confirm the non-existence of two kinematic populations in the region of 15 previously suspected non-existent objects.

Jensen inequalities for tunneling probabilities in complex systems

The Jensen theorem is used to derive inequalities for semiclassical tunneling probabilities for systems involving several degrees of freedom. These Jensen inequalities are used to discuss several aspects of sub-barrier heavy-ion fusion reactions. The inequality hinges on general convexity properties of the tunneling coefficient calculated with the classical action in the classically forbidden region.

Collision probabilities in the rarefaction fan of asymmetric exclusion processes

We consider the one-dimensional asymmetric simple exclusion process (ASEP) in which particles jump to the right at rate p is an element of (1/2, 1.] and to the left at rate 1 - p, interacting by exclusion. In the initial state there is a finite region such that to the left of this region all sites are occupied and to the right of it all sites are empty. Under this initial state, the hydrodynamical limit of the process converges to the rarefaction fan of the associated Burgers equation. In particular suppose that the initial state has first-class particles to the left of the origin, second-class particles at sites 0 and I, and holes to the right of site I. We show that the probability that the two second-class particles eventually collide is (1 + p)/(3p), where a collision occurs when one of the particles attempts to jump over the other. This also corresponds to the probability that two ASEP processes. started from appropriate initial states and coupled using the so-called ""basic coupling,"" eventually reach the same state. We give various other results about the behaviour of second-class particles in the ASEP. In the totally asymmetric case (p = 1) we explain a further representation in terms of a multi-type particle system, and also use the collision result to derive the probability of coexistence of both clusters in a two-type version of the corner growth model.

Colonization and extinction of land planarians (Platyhelminthes, Tricladida) in a Brazilian Atlantic Forest regrowth remnant

Long-term assessments of species assemblages are valuable tools for detecting species ecological preferences and their dispersal tracks, as well as for assessing the possible effects of alien species on native communities. Here we report a 50-year-long study on population dynamics of the four species of land flatworms (Platyhelminthes, Tricladida, Terricola) that have colonized or become extinct in a 70-year-old Atlantic Forest regrowth remnant through the period 1955-2006. On the one hand, the two initially most abundant species, which are native to the study site, Notogynaphallia ernesti and Geoplana multicolor have declined over decades and at present do not exist in the forest remnant. The extinction of these species is most likely related with their preference for open vegetation areas, which presently do not exist in the forest remnant. On the other hand, the neotropical Geoplaninae 1 and the exotic Endeavouria septemlineata were detected in the forest only very recently. The long-term study allowed us to conclude that Geoplaninae 1 was introduced into the study area, although it is only known from the study site. Endeavouria septemlineata, an active predator of the exotic giant African snail, is originally known from Hawaii. This land flatworm species was observed repeatedly in Brazilian anthropogenic areas, and this is the first report of the species in relatively well preserved native forest, which may be evidence of an ongoing adaptive process. Monitoring of its geographic spread and its ecological role would be a good practice for preventing potential damaging effects, since it also feeds on native mollusk fauna, as we observed in lab conditions.

Extrinsic versus intrinsic factors in the decline and extinction of Australian marsupials

Recent attempts to explain the susceptibility of vertebrates to declines worldwide have largely focused on intrinsic factors such as body size, reproductive potential, ecological specialization, geographical range and phylogenetic longevity. Here, we use a database of 145 Australian marsupial species to test the effects of both intrinsic and extrinsic factors in a multivariate comparative approach. We model five intrinsic (body size, habitat specialization, diet, reproductive rate and range size) and four extrinsic (climate and range overlap with introduced foxes, sheep and rabbits) factors. We use quantitative measures of geographical range contraction as indices of decline. We also develop a new modelling approach of phylogenetically independent contrasts combined with imputation of missing values to deal simultaneously with phylogenetic structuring and missing data. One extrinsic variable-geographical range overlap with sheep-was the only consistent predictor of declines. Habitat specialization was independently but less consistently associated with declines. This suggests that extrinsic factors largely determine interspecific variation in extinction risk among Australian marsupials, and that the intrinsic factors that are consistently associated with extinction risk in other vertebrates are less important in this group. We conclude that recent anthropogenic changes have been profound enough to affect species on a continent-wide scale, regardless of their intrinsic biology.

Is affective learning really resistant to extinction? Stimulus ratings and affective priming give different answers

Affective learning, the learning of likes and dislikes, is proposed to differ from signal learning, the learning of relationships between events. However, affective learning research varies in the methodology used, and in addition, researchers concerned primarily with affective learning tend to use different paradigms from those concerned with signal learning. The current research used an affective priming task in addition to verbal ratings to assess changes in the valence of neutral geometric shapes in an aversive differential conditioning procedure. After acquisition, affective learning was present as indexed by ratings and affective priming, whereas after extinction, affective learning remained significant only in the ratings. This study suggests that different measures of affective learning may be differentially sensitive to valence, which has implications for studies that employ verbal ratings as the sole measure of affective learning. Moreover, there is no evidence from the current study that affective learning differs from signal learning.

Aquisition and extinction of two characteristics consistent with fear relevance

Fear relevance, the potential of a stimulus to become quickly associated with fear, is a characteristic assumed to have an evolutionary basis and to result in preferential processing. Previous research has shown that fear relevant stimuli share a number of characteristics, negative valence and preferential identification in a visual search task, for instance. The present research examined whether these two characteristics can be acquired by non-fear relevant stimuli (geometric shapes) as a result of Pavlovian fear conditioning. Two experiments employed an aversive learning paradigm with geometric shape CSs and a shock US, with stimulus ratings, affective priming and visual search performance assessed before and after acquisition and after extinction. Differential electrodermal responses, larger during CS1 than CS, were present during acquisition but not during extinction. Affective priming results suggest that the CS1 acquired negative valence during acquisition, which was lost during extinction. However, negative valence as indexed by more negative ratings for CS1 than for CS shapes seemed to survive extinction. Preferential attentional processing as indexed by faster detection of CS1 among CS shapes than vice versa on the visual search task also remained. The current research confirmed that characteristics of fear relevant stimuli can be acquired in an aversive learning episode and that they may be extinguished. This supports the proposal that fear relevance may be malleable through learning.