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.     

Assemblage stability in stream fishes: A review

We quantified the stability of nine stream fish assemblages by calculating coefficients of variation of population size for assemblage members. Coefficients of variation were high and averaged over 96%; indicating that most assemblages were quite variable. Coefficient of variation (CV) estimates were not significantly affected by: (1) years of study, (2) mean abundance, (3) familial classification, or (4) mean interval between collections. We also detected minor regional differences in CVs. The high variability exhibited by many stream fish assemblages suggests that it may be difficult to detect the effects of anthropogenic disturbances using population data alone. Consequently, we urge managers to exercise caution in the evaluation of the effects of these disturbances. More long-term studies of the ecological characteristics of undisturbed stream fish assemblages are needed to provide a benchmark against which disturbed systems can be compared. We suggest that CVs are a better estimator of population/assemblage stability, than either Kendall's W or the standard deviation of the logarithms of numerical censuses. This conclusion is based on the following reasons. First, CVs scale population variation by the mean and, hence, more accurately measure population variability. Second, this scaling permits the comparison of populations with different mean abundances. Finally, the interpretation of CV values is less ambiguous than either of the aforementioned metrics.     

A new policy‐related measure of population dispersal and sparsity using GIS

Policy indicators applied at a national scale can have considerable financial impact for resource allocations to individual counties, especially if there are extreme local factors. This article develops arid explores a new measure of population dispersal and sparsity and discusses the impact of this indicator in a variety of locations, by using GIS techniques.     

Bison and elk in the American Southwest: In search of the pristine

Ecosystem managers often use the early historic condition of the fauna in an area as the model for restoration or management. West of the Pecos River in the American Southwest, present-day abundances and distributional ranges of bison and American elk exceed those reported in early historic times. I evaluate several potential causes for the historic scarcity of these animals—inadequate forage, insufficient water, nonhuman predation, disease, and hunting by late-prehistoric humans. Archaeological and ecological evidence suggest that restricted availability of water coupled with hunting by late-prehistoric peoples probably were the most important causes. Perennial water is more widely distributed now than previously, mainly because of water well and water catchment construction. Proliferation of agriculture-based human economies in the region from AD 0–1500 led to rapid population growth of aboriginal peoples, with resulting increased harvests of resources. The likelihood that late-prehistoric humans severely depleted the abundances of large mammals indicates a need to reevaluate the exclusive use of early-historic conditions as the basis for setting goals for ecosystem management. Implications of reintroducing large herbivores to ecosystems are discussed.     

Population viability analysis as a tool in wildlife conservation policy: With reference to Australia

Wildlife conservation policy for endangered species restoration follows a six-phase process. Population viability analysis (PVA) can play a major contributing role in four of these. PVA, as discussed here, is a technique where extinction vulnerabilities of small populations are estimated using computer simulation modeling. The benefits and limitations of using PVA in wildlife decision and policy processes are reviewed based on our direct experience. PVA permits decision makers to set time frames for management, estimate the required magnitude of restoration efforts, identify quantitative targets for species recovery, and select, implement, monitor, and evaluate management strategies. PVA is of greatest value for rare species policy and management. However, a limitation of PVA simulation models is that they are constrained by the amount of biological data available, and such data are difficult to obtain from small populations that are at immediate risk of extinction. These problems may be overcome with improved models and more data. Our experience shows benefits of PVA far outweigh its limitations, and applications of the approach are most useful when integrated with decision analysis and completed within an adaptive management philosophy. PVAs have been carried out for 14 Victorian species and less used elsewhere in Australia. Management and recovery plans are developed from these PVAs. We recommend that PVA be used to guide research programs, develop conservation strategies, and inform decision and policy making for both endangered and nonendangered species because it can significantly improve many aspects of natural resource policy and management.     

A method for prediction of extent of microbial pollution of seawater and carrying capacity of beaches

The increase in the number of tourists visiting a coast is desired by most of the countries for economic reasons. However, this increase in tourism may cause pollution of the sea. This can be only avoided by proper planning and by predicting the carrying capacity of the coast in terms of sea pollution. This is especially important for developing countries where part of the wastewater is discharged without any treatment into the sea.In the present study the beaches were classified according to their use — and consequently the amount of waste discharged into the sea — into four groups: (1) coasts that are used only for swimming and recreational purposes; (2) coasts used simultaneously for dwelling, swimming, and recreational purposes; (3) coasts along which only dwellings exist; and (4) natural and man-made harbors, i.e., coasts used as shelters. During the survey,40,320 observations were made between December 1985 and February 1988 to determine the effect of the number of tourists on seawater quality. The results obtained were analyzed by a multilinear regression program to obtain an empirical equation giving the extent of the sea pollution in terms of coliform concentration as a function of population density and some other environmental factors.The equations derived in this study enable the determination of the carrying capacity of a beach in terms of pollution as well as the expected degree of pollution corresponding to a given population density. Furthermore, it allows the prediction of the extra carrying capacity that can be obtained by improving the waste-disposal conditions.     

Trends in Vegetation Degradation in Relation to Land Tenure, Rainfall, and Population Changes in Peddie District, Eastern Cape, South Africa

Spatial and temporal variations in vegetation are examined in relation to land tenure, population increase, and rainfall variation in a part of Peddie district, Eastern Cape. Sequential aerial photographs between 1938 and 1988 are analyzed to determine trends in vegetation and population change in three different land-tenure units. The areal extent at each date of four distinct vegetation categories is determined using PC ARC/INFO GIS. Long-term annual rainfall trends for the area are analyzed and juxtaposed with vegetation changes. Extensive ground-truthing exercises are carried out to verify the present condition of vegetation condition in terms of cover and species composition. Differences in land-tenure systems are discerned as the dominant factor controlling variations in vegetation degradation. The study also reveals that neither population changes nor rainfall variations can explain the observed trends in vegetation degradation. Earlier injudicious land-use practices, sustained since the turn of the last century, may provide plausible explanations for the trends and present status of vegetation degradation in the area.     

Modeling individual and population dynamics in a consumer–resource system: Behavior under food limitation and crowding and the effect on population cycling in Daphnia

In population modeling, a considerable level of complexity is often required to provide trustworthy results, comparable with field observations. By assuring sufficient detail at the individual level while preserving the potential to explore the consequences at higher levels, individual-based modeling may thus provide a useful tool to investigate dynamics at different levels of organization. Still, population dynamics resulting from such models are often at odds with observations from the field. This may be partly caused by a lack of focus on the individual dynamics under conditions of food stress and starvation. I developed a physiologically structured, individual-based simulation model to investigate life history of Daphnia and its effect on population dynamics in response to the productivity of the system. In verifying model behavior with available literature data on life history and physiology, I paid special attention to the dynamics of food intake and the verification of individual level results under conditions of food limitation and starvation. I show that the maximum filtering rates under low food levels used in the current model are much closer to measured filtering rates than the ones used in other models. Being consistent with results on physiology and life history from experiments at a wide range of food availability (including starvation), the model generates low amplitude or high amplitude population density cycles depending on the productivity of the system, as observed in field and experimental populations of Daphnia and with the minimum population densities being one to two orders of magnitude lower in the high amplitude than in the low amplitude cycles. To generate results which are not only qualitatively but also quantitatively comparable to experimental and field observations, however, a crowding effect on the filtering response has to be incorporated in the model.     

Predation affects the susceptibility of hard clam Meretrix lusoria to Hg-stressed birnavirus

Predator–prey interaction in aquatic ecosystem is one of the simplest drivers affecting the species population dynamics. Predation controls are recognized as important aspects of ecosystem husbandry and management. In this paper we investigated how predation control cause an increase in host growth in the abundance of hard clam (Meretrix lusoria) populations subject to mercury (Hg)-stressed birnavirus. Here we linked predator–prey relationships with a bioenergetic matrix population model (MPM) associated with a susceptible–infectious–mortality (SIM) model based on a host–pathogen–predator framework to quantify the predator effects on population dynamics of disease in hard clam populations. Our results indicated that relative high predation rates could promote the hard clam abundances in relation to predators that selectively captured the infected hard clam, by which the disease transmission was suppressed. The results also demonstrated that predator-induced modifications in host behavior could have potential negative or positive effects on host growth depending on relative species density and resource dynamics. The most immediate implication of this study for the management of aquatic ecosystem is that, beyond the potential for causing a growth in abundance, predation might provoke greater predictability in aquatic ecosystem species populations and thereby increase the safety of ecosystem production from stochastic environmental events.     

Convexity in projection matrices: Projection to a calibration problem

Convexity, as a fundamental property of sets and functions defined on convex sets, plays an important role in many mathematical and applied disciplines, including extremal and optimal-control problems. We prove the set of all feasible projection matrices in a general class of matrix models for stage-structured population dynamics to be convex and the dominant eigenvalue (λ₁) of any projection 2 × 2 matrix to be either a convex, or a concave function on a simplex of the matrix first-row entries (i.e., stage-specific reproduction rates). The latter is also conjectured for the general n × n case. Though looking far from practical needs of matrix population models, this mathematical result has appeared to be quite useful in solving a practical problem to calibrate the projection matrix, i.e., to estimate all the stage-specific vital rates, from empirical data. The data from monitoring of individual life histories of marked plants on permanent sample plots during successive years enable direct calculation of the stage-specific survival and ontogenetic transition rates, but the rates of reproduction do remain uncertain as far as the parent plants can hardly be determined for the (not yet marked!) recruitment.