Extinction Rate Estimates for Plant Populations in Revisitation Studies: Importance of Detectability

Abstract:  Many researchers have obtained extinction-rate estimates for plant populations by comparing historical and current records of occurrence. A population that is no longer found is assumed to have gone extinct. Extinction can then be related to characteristics of these populations, such as habitat type, size, or species, to test ideas about what factors may affect extinction. Such studies neglect the fact that a population may be overlooked, however, which may bias estimates of extinction rates upward. In addition, if populations are unequally detectable across groups to be compared, such as habitat type or population size, comparisons become distorted to an unknown degree. To illustrate the problem, I simulated two data sets, assuming a constant extinction rate, in which populations occurred in different habitats or habitats of different size and these factors affected their detectability. The conventional analysis implicitly assumed that detectability equalled 1 and used logistic regression to estimate extinction rates. It wrongly identified habitat and population size as factors affecting extinction risk. In contrast, with capture-recapture methods, unbiased estimates of extinction rates were recovered. I argue that capture-recapture methods should be considered more often in estimations of demographic parameters in plant populations and communities.     

A further contribution to the study of fish populations by capture-recapture experiments

In capture-recapture experiments, fish populations can be studied by two different sampling procedures. In both procedures, tagged fish are released on capture, but untagged fish are in one procedure released after tagging, in the second procedure they are retained. Using the two sampling techniques, Rafail (1971a,b) gave expressions for the estimation of an assumed constant (C) of proportionality between probabilities of capture of tagged to untagged fish which are simplified here to forms easier for calculation. The estimation of this constant (C) aids in estimation of abundance and mortality rates of untagged fish which are assumed to differ from those of tagged fish.     

Estimating Population Size in a Continuous-time Removal Experiment with a Known Sub-population Size Ratio

We study a continuous-time removal model for estimating the population size for a population in which a sub-population size ratio is known. The maximum likelihood estimate and the optimal martingale estimate of the population size are obtained; these are shown to be equivalent. A comparison between the proposed estimator and the maximum likelihood estimate which ignores the information on the known size ratio is made, using a simulation study. The asymptotic variances of these two estimators are also obtained, and a comparison between them is made. The sensitivity of mis-specification of the known size ratio is examined. We also apply the corresponding discrete-time model to the proposed continuous-time setting, and study the efficiency of the corresponding discrete-time type estimator relative to the proposed estimator.     

Population respiration: A theoretical approach

It is shown that the error in an estimate of the population respiration should generally not exceed 10% if the mean body weight is used instead of the full weight distribution. A convenient mathematical formulation of the Krogh-curve is given such that the commonly used exponential temperature dependence (Q₁₀ law) of the respiration rate is only a special case. A formula is derived which expresses the effect of a cyclic temperature relative to a constant temperature on the respiration of an animal, the respiration rate of which follows a Krogh-curve. This formula is shown to provide good estimates of annual population respiration both for cases where the population biomass can be considered as constant over the year and when its variation can be approximated with a sinusfunction. Our methods of estimating population respiration are shown to compare favourably with earlier shortcut methods.     

A generalized estimating equations approach for capture–recapture closed population models

The estimation of population density animal population parameters, such as capture probability, population size, or population density, is an important issue in many ecological applications. Capture–recapture data may be considered as repeated observations that are often correlated over time. If these correlations are not taken into account then parameter estimates may be biased, possibly producing misleading results. We propose a generalized estimating equations (GEE) approach to account for correlation over time instead of assuming independence as in the traditional closed population capture–recapture studies. We also account for heterogeneity among observed individuals and over-dispersion, modelling capture probabilities as a function of covariates. The GEE versions of all closed population capture–recapture models and their corresponding estimating equations are proposed. We evaluate the effect of accounting for correlation structures on capture–recapture model selection based on the quasi-likelihood information criterion (QIC). An example is used for an illustrative application and for comparison to currently used methodology. A Horvitz–Thompson-like estimator is used to obtain estimates of population size based on conditional arguments. A simulation study is conducted to evaluate the performance of the GEE approach in capture-recapture studies. The GEE approach performs well for estimating population parameters, particularly when capture probabilities are high. The simulation results also reveal that estimated population size varies on the nature of the existing correlation among capture occasions.     

Inbreeding in a lek-mating ant species, Pogonomyrmex occidentalis

In this paper we have two goals. First, we examine the effects of sample size on the statistical power to detect a given amount of inbreeding in social insect populations. The statistical power to detect a given level of inbreeding is largely a function of the number of colonies sampled. We explore two sampling schemes, one in which a single individual per colony is sampled for different sample sizes and a second sampling scheme in which constant sampling effort is maintained (the product of the number of colonies and the number of workers per colony is constant). We find that adding additional workers to a sample from a colony makes it easier to detect inbreeding in samples from given number of colonies; however, adding more colonies rather than more workers per colony always gives greater power to detect inbreeding. Because even relatively large amounts of sib-mating generate relatively small inbreeding coefficients, detection of even substantial deviations from random mating will require very large samples. Second, we look at the amount of inbreeding in a large population of the western harvest ant, Pogonomyrmex occidentalis. We find deviations from Hardy-Weinberg equilibrium equivalent to approximately 27% sib-mating in our population ( f = 0.09). Review of past studies on the population structure of other Pogonomyrmex species suggests that inbreeding may be a regular feature of the mating system of these ants. Although P. occidentalisis a swarm-mating species, there are a number of features of its population biology which suggest that the effective population size may be small. These include topographical variation that potentially breaks the population into demes, variation in the reproductive output of colonies, and variation in the size of reproductives produced by colonies. Received: 6 May 1996 / Accepted after revision: 6 October 1996     

A population viability analysis for the Island Fox on Santa Catalina Island,California

The island fox (Urocyon littoralis) on Santa Catalina Island is among the most imperiled species on the Channel Islands due to a recent outbreak of canine distemper virus (CDV). The western subpopulation, which was not exposed to CDV, is a crucial element in the recovery of foxes by providing a source of animals for translocation and captive breeding. Using the program VORTEX, we developed a population viability analysis for the Santa Catalina Island fox to (1) address the likelihood of population persistence, (2) estimate the current susceptibility of the population to catastrophic events, and (3) evaluate the efficacy of current restoration strategies of releasing captive bred foxes and transplanting wild animals. Overall, we found the population to be susceptible to catastrophic events; a 50% increase in mortality every 20 years was sufficient to elevate the extinction risk above 5%. Current management activities entail the transplanting of 12 juvenile foxes annually, which may reduce the viability of the western subpopulation. A minimum population size of at least 150 foxes should be maintained in each subpopulation to reduce the risk of extinction due to demographic stochasticity. Releases of translocated and captive bred animals affect the speed of recovery on the eastern half of Catalina Island, but not the probability of extinction, which is near zero under current conditions. We conducted a sensitivity analysis for demographic parameters by incrementally varying survival, fecundity and density-dependence parameters, while holding all other parameters constant. Sensitivity analyses identified mortality and mean litter size as the most sensitive parameters, while the implementation of density-dependence and environmental variation of model parameters did not seem to affect population performance. We conclude that the population of island foxes on Santa Catalina is currently at a critically low population level, but recovery of the species appears possible.     

Optimum size limit for a fishery with a limited fishing season

In the management of a fishery with many year-classes, a standard objective is to maximize the biomass yield. If the fishing effort is fixed, this objective can be attained by prescribing an optimum size limit. This implies that only fish which are larger than the optimum size limit should be caught. The theory for computing the optimum size limit when fishing is carried out continuously is well established. In contrast the theory for computing the optimum size limit when the fishing season is limited to the same period in each year has not been developed in spite of the fact that many fisheries are exploited in this manner. A fishing season may be limited because the weather or the migration patterns of the fish population permits fishing only during a certain period in the year. A fishing season may also be limited because it is necessary to reduce the fishing mortality in order to conserve the fish population.A theory for computing the optimum size limit when the fishing season is limited is developed in this paper. It is applied to a hypothetical fishery. The data for this example comes from the North Sea plaice fishery. It is found that for a given fishing effort the optimum size limit is 44.5 cm if fishing is carried out continuously, 41.3 cm if fishing is limited to 6 months in a year and 28.7 cm if fishing is limited to a period of one tenth of a year in each year.     

Genetic and Demographic Threats to the Black Rhinoceros Population in the Ngorongoro Crater

A resident population of 13 black rhinoceros ( Diceros bicornis ) persist in Ngorongoro Crater, Tanzania. The effective population size ( N _e ) may be as few as 5 animals. Projected growth for this population suggests that the effective population size will remain small for the near future, threatening this Iocal population with extinction due to the stochastic factors associated with small population size. A summary of historic and recent demographic data for this population reveals a population crash during the period of heavy poaching that affected this species throughout its range. Although poaching of this species has been brought under control the population remains small. These data and models of projected population growth argue for consideration of more-intensive management within the framework of the small population paradigm. This case is an example of applied conservation resulting from this paradigm used in conjunction with rather than competing with the declining population paradigm. We identify additional monitoring, particularly of density-dependent behaviors, that will be necessary for designing a successful management program. Finally, the use of molecular markers for developing an accurate pedigree for this population is suggested in order to maintain a genetically healthy population. These strategies have broad applicability to black rhinoceros conservation throughout Africa.     

Removal process estimation of population size for a population with a known sex ratio

A removal model for estimating population size which uses the known population sex ratio is studied. A maximum likelihood estimate and an optimal martingale estimate of the population size are proposed. Their standard errors and large sample properties are obtained. Simulation studies are reported, and the performance of the proposed estimators are compared with the standard maximum likelihood estimator which ignores the sex ratio information. An example on a capture study of deer mice is given.     

Cost-Effective Suppression and Eradication of Invasive Predators

Abstract: Introduced predators can have pronounced effects on naïve prey species; thus, predator control is often essential for conservation of threatened native species. Complete eradication of the predator, although desirable, may be elusive in budget‐limited situations, whereas predator suppression is more feasible and may still achieve conservation goals. We used a stochastic predator–prey model based on a Lotka‐Volterra system to investigate the cost‐effectiveness of predator control to achieve prey conservation. We compared five control strategies: immediate eradication, removal of a constant number of predators (fixed‐number control), removal of a constant proportion of predators (fixed‐rate control), removal of predators that exceed a predetermined threshold (upper‐trigger harvest), and removal of predators whenever their population falls below a lower predetermined threshold (lower‐trigger harvest). We looked at the performance of these strategies when managers could always remove the full number of predators targeted by each strategy, subject to budget availability. Under this assumption immediate eradication reduced the threat to the prey population the most. We then examined the effect of reduced management success in meeting removal targets, assuming removal is more difficult at low predator densities. In this case there was a pronounced reduction in performance of the immediate eradication, fixed‐number, and lower‐trigger strategies. Although immediate eradication still yielded the highest expected minimum prey population size, upper‐trigger harvest yielded the lowest probability of prey extinction and the greatest return on investment (as measured by improvement in expected minimum population size per amount spent). Upper‐trigger harvest was relatively successful because it operated when predator density was highest, which is when predator removal targets can be more easily met and the effect of predators on the prey is most damaging. This suggests that controlling predators only when they are most abundant is the “best” strategy when financial resources are limited and eradication is unlikely.     

Analysis of a Fisheries Model for Harvest of Hawksbill Sea Turtles (Eretmochelys imbricata)

The hawksbill sea turtle ( Eretmochelys imbricata ) is valued for its mottled shell, called bekko in Japan. Populations of hawksbills have declined worldwide, and currently there is a ban on all international trade of hawksbill shell and products (Convention on International Trade of Endangered Species of Wild Fauna and Flora). In 1992 the Bekko Association of Japan introduced a fisheries model for hawksbill sea turtles in Cuba. The model estimated a sustainable yield of 5500 turtles from Cuban feeding grounds. We examined the model to determine whether this level of harvest was reasonable. Little biological information is available for hawksbills, so the model contained a number of simplifying assumptions, and several of its parameters were unsupported by data. The population was assumed to be at equilibrium, with a constant number of recruits (1-year-old turtles) and constant annual survival and growth rates. We analyzed the model to see how population size and sustainable yield results were affected by changes in various model parameters, and we found that the model was most sensitive to annual survival probability, which was assumed to be a constant 90% per year for all turtles greater than 1 year old. When we entered growth curves generated by mark-recapture data from other hawksbill populations, the model predicted a wide range of population sizes and sustainable yields. We determined that the assumptions of the current model make it unreliable for predicting sustainable yield of hawksbills, and that much research is needed to produce a more accurate model for management of this endangered species.     

The onset of natural convection in lakes and reservoirs due to night time cooling

A theoretical model, based on linear stability analysis, is proposed to predict the onset of natural convection in lakes and reservoirs due to night time cooling. To such purpose, the system was modelled as a initially quiescent deep Boussinesq fluid reservoir, whose upper boundary temperature changes sinusoidally. From scaling analysis, it is found that critical onset times for convection are proportional to R ^−2/7, where R is a Rayleigh number including fluid properties and forcing frequency. The proportionality constant was found, from the solution of an eigenvalue problem, as a function of the Prandtl number. The onset time for convection was easily observed from experiments and quantitatively detected as a rapid increase of the RMS of the computed velocity field obtained using PIV. In this controlled conditions, differences close to 10% between predicted and observed times for the start of the convective flow was found. It is apparent from the present set of results that predictions are reasonable.     

A resource-based approach to modelling the dynamics of interacting populations

The procedure for modelling the growth of single-species populations [Sakanoue, S., 2007. Extended logistic model for growth of single-species populations. Ecol. Model. 205, 159–168] is improved to be applicable to the study of the dynamics of interacting populations. The improved procedure is based on three assumptions: resource availability changes with population size as a variable, resource supply to populations and population demand for resources are defined as functions of resource availability and population size, and the variables of resource availability and population size shift in the supply function attracted to the demand function. These assumptions are organized into three equations. The equations can generate the dynamics models of plant, herbivore, and detritivore populations, and their own resources. The models can be used to describe prey–predator dynamics. They naturally contain nonlinear terms for the predator’s numerical and functional responses. Depending on the terms, the fluctuations in resource availability and population size stabilize. The three equations can also generate the dynamics models of different populations consuming the same resources. The analysis of zero isoclines of the models shows that a superior population can be simply defined as one with a higher intrinsic rate of natural increase, that a stable coexistence may be realized with the intraspecific interference or the interspecific facilitation of superiors, and that the interspecific interference or the intraspecific facilitation of inferiors may make the coexistence unstable and the inferiors winners depending on their initial population size.     

Population inertia and its sensitivity to changes in vital rates and population structure

Because the (st)age structure of a population may rarely be stable, studies of transient population dynamics and population momentum are becoming ever more popular. Yet, studies of "population momentum" are restricted in the sense that they describe the inertia of population size resulting from a demographic transition to the stationary population growth rate. Although rarely mentioned, inertia in population size is a general phenomenon and can be produced by any demographic transition or perturbation. Because population size is of central importance in demography, conservation, and management, formulas relating the sensitivity of population inertia to changes in underlying vital rates and population structure could provide much-needed insight into the dynamics of populations with unstable (st)age structure. Here, we derive such formulas, which are readily computable, and provide examples of their potential use in studies of life history and applied arenas of population study.     

Extinction-effective population index: incorporating life-history variations in population viability analysis

Viability status of populations is a commonly used measure for decision-making in the management of populations. One of the challenges faced by managers is the need to consistently allocate management effort among populations. This allocation should in part be based on comparison of extinction risks among populations. Unfortunately, common criteria that use minimum viable population size or count-based population viability analysis (PVA) often do not provide results that are comparable among populations, primarily because they lack consistency in determining population size measures and threshold levels of population size (e.g., minimum viable population size and quasi-extinction threshold). Here I introduce a new index called the "extinction-effective population index," which accounts for differential effects of demographic stochasticity among organisms with different life-history strategies and among individuals in different life stages. This index is expected to become a new way of determining minimum viable population size criteria and also complement the count-based PVA. The index accounts for the difference in life-history strategies of organisms, which are modeled using matrix population models. The extinction-effective population index, sensitivity, and elasticity are demonstrated in three species of Pacific salmonids. The interpretation of the index is also provided by comparing them with existing demographic indices. Finally, a measure of life-history-specific effect of demographic stochasticity is derived.     

Modeling the brown bear population in Slovenia: A tool in the conservation management of a threatened species

In this paper, we address three aspects of the brown bear population in Slovenia: its size (and its evolution over time), its spatial expansion out of the core area, and its potential habitat based on natural habitat suitability. Data collected through measurement/observation of the bear population and from the literature are used. A model is developed for each aspect. The results are estimates of population size, a picture of the spatial expansion of the population and maps of its optimal and maximal potential habitat (based on natural suitability). Overall, the brown bear population has been increasing since the establishment of a core protective area and has been expanding outside this area. The habitat suitability maps show that there is room for further expansion. Based on habitat suitability and bear population density, as well as human activity and current damage reports, we recommend that the Alps should be temporarily kept free of the bears, until the necessary mitigation measures regarding human–bear conflicts are carried out. On the other hand it is of crucial importance to adapt human activities and improve bear management in the optimal habitat, with which the goals of successful conservation of the species might be achieved.     

Optimal exploitation of a fishery employing a non-linear harvesting function

A harvesting function is developed to described the rate of removal of fish from a fish population. The function incorporates the effects of both the handling or processing time of the catch and the competition, between boats in the fleet, for the fish.We will assume that the growth rate of the fish population can be modelled with a concave, dome shaped growth curve. With this assumption, it has been shown that if the rate of harvesting the fish is linearly related to both effort (which can be thought of as some measure of the number of boats in the fleet) and the population size, then the population will tend towards a single equilibrium level which is globally stable. This paper shows that the saturation effects due to the handling time may generate two equilibrium levels (one stable, one unstable) rather than a single globally stable equilibrium. The results of competition between boats are economically undesirable because of the decrease in efficiency. However, this competition may be beneficial to the exploited fish population.Using the harvesting model derived earlier, the steady state or long term optimal harvesting policies as well as the transition paths to these states are developed. The only constraint is on the maximum allowable effort which is effectively an upper limitation on the fleet size or number of man-hours of fishing.     

Variation in life-history patterns of the grass shrimp Palaemonetes pugio in two South Carolina estuarine systems

A population of Palaemonetes pugio Holthuis 1949, inhabiting a fairly constant high salinity estuarine environment (North Inlet), exhibited more rapid growth, earlier first reproduction, a smaller clutch size, more fluctuating sex ratio, and shorter life span. A population in a less saline environment (Minim Creek) showed relatively slower growth, delayed first reproduction, larger clutch size, female-dominated sex ratio, and longer life span. Growth in both areas was rapid in summer and slower in winter, with the females growing much larger than the males. Summer generation females first reproduced at the age of 3.5 months in North Inlet and at 4.8 months in Minim Creek. Minim Creek females larger than 30-mm TL carried more eggs than North Inlet females of similar sizes. Life span in North Inlet was calculated to be 6–7 months for the summer generation and 9–10 months for the winter generation; in Minim Creek, the corresponding longevity estimates were 9–10 months and 12–13 months, respectively. Variations in life history patterns are hypothesized to be the results of numerous environmental factors acting differentially on the various life-stages of the organism. The results suggest that the reproductive flexibility of P. pugio enhances its ability to persist in a variety of environments.Contribution no. 426 of the Belle W. Baruch Institute for Marine Biology and Coastal Research     

The interplay of sex ratio, male success and density-independent mortality affects population dynamics

Environmental constraints can limit a population to a certain size, which is usually called the carrying capacity of a habitat. Besides to this ‘external’ factor, which is mainly determined by the limitation of resources, we investigate here another set of population-intrinsic factors that can limit a population size significantly below the maximum sustainable size. Firstly, density-independent mortality is a prominent factor in all organisms that show age-related and/or accidental death. Secondly, in sexually reproducing organisms the sex ratio and the success of pairing is important for finding reproductive partners. Using a simple model, we demonstrate how sex ratio, mating success and gender-specific mortality can strongly affect the speed of population growth and the maximum population size. In addition, we demonstrate that density-independent mortality, which is often neglected in population models, adds a very important feature to the system: it strongly enhances the negative influence of unbiased sex ratios and inefficient pairing to the maximum sustainable population size. A decrease of the maximum population size significantly affects a population's survival chance in inter-specific competition. Thus, we conclude that the inclusion of density-independent mortality is crucial, especially for models of species that reproduce sexually. We show that density-independent mortality, together with biased sex ratios, can significantly lower the abilities of a population to survive in conditions of strong inter-specific competition and due to the Allee effect. We emphasize that population models should incorporate the sex ratio, male success and density-independent mortality to make plausible predictions of the population dynamics in a gender-structured population. We show that the population size is limited by these intrinsic factors. This is of high ecological significance, because it means that there will always be resources available in any habitat that allows other species (e.g., invaders) to use these resources and settle successfully, if they are sufficiently adapted.