Relationship between Population Size and Fitness

Abstract:  Long-term effective population size, which determines rates of inbreeding, is correlated with population fitness. Fitness, in turn, influences population persistence. I synthesized data from the literature concerning the effects of population size on population fitness in natural populations of plants to determine how large populations must be to maintain levels of fitness that will provide adequate protection against environmental perturbations that can cause extinction. Integral to this comment on what has been done and what needs to be done, sThe evidence suggests that there is a linear relationship between log population size and population fitness over the range of population sizes examined. More importantly, populations will have to be maintained at sizes of >2000 individuals to maintain population fitness at levels compatible with the conservation goal of long-term persistence. This approach to estimating minimum viable population size provides estimates that are in general agreement with those from numerous other studies and strengthens the argument that conservation efforts should ultimately aim at maintaining populations of several thousand individuals to ensure long-term persistence.     

Testing the effectiveness of capture mark recapture population estimation techniques using a computer simulation with known population size

Estimation of small mammal population sizes is important for monitoring ecosystem condition and for conservation. Here, we test the accuracy of standard methods of population size estimation using Capture-Mark-Recapture (CMR) on a simulated population of agents. The use of a computer simulation allows complete control of population sizes and behaviors, thereby avoiding assumptions that may be violated in real populations. We find that the recommended protocol for CMR sampling, using uniformly distributed traps, consistently overestimates population sizes by as much as 100% when studies are conducted over only two trapping periods. More than 20 trapping periods are required before this method, or that of placing traps randomly, gives an accurate estimation of population size (i.e., within a 95% confidence limit of the actual value). Non-random sampling, by placing traps on runways used by small mammals, produces the most accurate, and least variable, estimates of population. However, we show that around 10 trapping periods are still required to produce an accurate population estimate using this method. Given that most real populations do not comply with the ‘ideal’ assumptions made by CMR, we suggest that population estimates based on CMR may be fundamentally flawed, and recommend that protocols for CMR population estimation methods may need revising.     

Rapid Extinction of Mountain Sheep Populations Revisited

Abstract: Predicting extinction probabilities for populations of various sizes has been a primary focus of conservation biology. Berger (1990) presented an empirically based extinction model for mountain sheep ( Ovis canadensis ) populations in five southwestern states that predicted disappearance within 50 years of all populations estimated to number 50 sheep or fewer, but essentially no loss in that time period of populations estimated at over 100. The majority of the 122 populations he used in his analysis were from California, but his analysis did not use many of the historical size estimates for these populations. I tested Berger's (1990) model using the complete data set from California and found—contrary to his results—that, for all size classes of population estimates, at least 61% of the populations persisted for 50 years. Also, two predictions from Berger's model were not consistent with the data from California: (1) 10 populations have increased from estimates of 50 or fewer animals to over 100, whereas the Berger model predicted that these populations would only decline to extinction; and (2) of 27 extant populations with long enough records, 85% were estimated at least 50 years ago to be 50 individuals or fewer and should therefore be extinct by now. Berger's model has now failed tests in three states and therefore does not support the strong population size effect on extinction probability that it first appeared to provide, and it may serve conservation poorly through misdirected effort if it is used as the basis for setting policies or taking actions.     

Bayesian analysis of abundance for binomial sighting data with unknown number of marked individuals

The mark-resight method for estimating the size of a closed population can in many circumstances be a less expensive and less invasive alternative to traditional mark-recapture. Despite its potential advantages, one major drawback of traditional mark-resight methodology is that the number of marked individuals in the population available for resighting needs to be known exactly. In real field studies, this can be quite difficult to accomplish. Here we develop a Bayesian model for estimating abundance when sighting data are acquired from distinct sampling occasions without replacement, but the exact number of marked individuals is unknown. By first augmenting the data with some fixed number of individuals comprising a marked “super population,” the problem may then be reformulated in terms of estimating the proportion of this marked super population that was actually available for resighting. This then allows the data for the marked population available for resighting to be modeled as random realizations from a binomial logit-normal distribution. We demonstrate the use of our model to estimate the New Zealand robin (Petroica australis) population size in a region of Fiordland National Park, New Zealand. We then evaluate the performance of the proposed model relative to other estimators via a series of simulation experiments. We generally found our model to have advantages over other models when sample sizes are smaller with individually heterogeneous resighting probabilities. Due to limited budgets and the inherent variability between individuals, this is a common occurrence in mark-resight population studies. WinBUGS and R code to carry out these analyses is available from .     

Conservation Genetics at the Species Boundary

Abstract: Conservation genetics has expanded its purview such that molecular techniques are now used routinely to prioritize populations for listing and protection and infer their historical relationships in addition to addressing more traditional questions of heterozygosity and inbreeding depression. Failure to specify whether molecular data are being used for diagnosis-related questions or for population viability questions, however, can lead either to misinterpretation of character data as adaptive information or to misinterpretation of frequency or distance data as diagnostic or historical information. Each of these misinterpretations will confound conservation programs. The character-based approach to delimiting phylogenetic species is both operationally and logically superior to "diagnostic" methods that involve distance- or frequency-based routines, which are unstable over time. Tree-based criteria for the diagnosis of conservation "units" are also inappropriate because they can depend on patterns inferred without reference to diagnostic characters. Intraspecific studies, conservation-related or otherwise, that adopt terminology and methods designed to infer nested hierarchic relationships confuse diagnosis with historical inferences by treating diagnoses as outcomes rather than as precursors to phylogeny reconstruction. A character-based diagnostic approach recognizes the analytical dichotomy between species hierarchies and population statistics and provides a framework for the understanding of each. No species concept, however, should be viewed as an absolute criterion for protecting populations, but as part of a framework from within which identification of protection and management goals can be achieved effectively and defensibly.     

Designing Species Translocation Strategies When Population Growth and Future Funding Are Uncertain

Abstract: When translocating individuals to found new populations, managers must allocate limited funds among release and monitoring activities that differ in method, cost, and probable result. In addition, managers are increasingly expected to justify the funding decisions they have made. Within the framework of decision analysis, we used robust optimization to formulate and solve different translocation problems in which both population growth and future funding were uncertain. Performance criteria included maximizing mean population size and minimizing the risk of undesirable population-size outcomes. Robust optimization provided several insights into the design of translocation strategies: (1) risk reduction is obtained at the expense of mean population size; (2) as survival of released animals becomes more important, funds should be allocated to release methods with lower risks of failure, regardless of costs; (3) the performance gain from monitoring drops as the proportion of a fixed budget required to pay for monitoring increases; and (4) as the likelihood of obtaining future funding increases, more of the existing budget should be spent on building release capacity rather than saved for future operating costs. These relationships highlight the importance of performance criteria and economic costs in determining optimal release and monitoring strategies.     

Estimation methods for nonlinear state-space models in ecology

The use of nonlinear state-space models for analyzing ecological systems is increasing. A wide range of estimation methods for such models are available to ecologists, however it is not always clear, which is the appropriate method to choose. To this end, three approaches to estimation in the theta logistic model for population dynamics were benchmarked by Wang (2007). Similarly, we examine and compare the estimation performance of three alternative methods using simulated data. The first approach is to partition the state-space into a finite number of states and formulate the problem as a hidden Markov model (HMM). The second method uses the mixed effects modeling and fast numerical integration framework of the AD Model Builder (ADMB) open-source software. The third alternative is to use the popular Bayesian framework of BUGS. The study showed that state and parameter estimation performance for all three methods was largely identical, however with BUGS providing overall wider credible intervals for parameters than HMM and ADMB confidence intervals.     

Site-selection bias and apparent population declines in long-term studies

Detecting population declines is a critical task for conservation biology. Logistical difficulties and the spatiotemporal variability of populations make estimation of population declines difficult. For statistical reasons, estimates of population decline may be biased when study sites are chosen based on abundance of the focal species. In this situation, apparent population declines are likely to be detected even if there is no decline. This site-selection bias is mentioned in the literature but is not well known. We used simulations and real population data to examine the effects of site-selection biases on inferences about population trends. We used a left-censoring method to detect population-size patterns consistent with site-selection bias. The site-selection bias is an important consideration for conservation biologists, and we offer suggestions for minimizing or mitigating it in study design and analysis. Article impact statement: Estimates of population declines are biased if studies begin in large populations, and time-series data show a signature of such an effect.     

Multivariate bootstrap confidence regions for abundance vector using

Abundance vector estimation is a well investigated problem in statistical ecology. The use of simple random sampling with replacement or replicated sampling ensures good asymptotic properties of the abundance vector estimators. However, real surveys are based on small sample sizes, and assuming any specific distribution of the abundance vector estimator may be hazardous.In this paper we focus our attention on situations where the population is not too large and the sample size is small. We propose bootstrap multivariate confidence regions based on data depth. Data depth is a geometrical concept of ordering data from the center outwardly in higher dimensions. The Simplicial depth, the Tukey's depth and the Mahalanobis depth are presented. In order to build confidence regions in the presence of a skewed distribution of the abundance vector estimator, the use of Tukey's depth is suggested. The proposed method has been applied to the benthic community of Lake Lesina. A comparison with Mahalanobis depth and standard existing methods is reported.     

Understanding the Lessons and Limitations of Conservation and Development

Abstract: The lack of concrete instances in which conservation and development have been successfully merged has strengthened arguments for strict exclusionist conservation policies. Research has focused more on social cooperation and conflict of different management regimes and less on how these factors actually affect the natural environments they seek to conserve. Consequently, it is still unknown which strategies yield better conservation outcomes? We conducted a meta‐analysis of 116 published case studies on common resource management regimes from Africa, south and central America, and southern and Southeast Asia. Using ranked sociodemographic, political, and ecological data, we analyzed the effect of land tenure, population size, social heterogeneity, as well as internally devised resource‐management rules and regulations (institutions) on conservation outcome. Although land tenure, population size, and social heterogeneity did not significantly affect conservation outcome, institutions were positively associated with better conservation outcomes. There was also a significant interaction effect between population size and institutions, which implies complex relationships between population size and conservation outcome. Our results suggest that communities managing a common resource can play a significant role in conservation and that institutions lead to management regimes with lower environmental impacts.     

Integral projection models for finite populations in a stochastic environment

Continuous types of population structure occur when continuous variables such as body size or habitat quality affect the vital parameters of individuals. These structures can give rise to complex population dynamics and interact with environmental conditions. Here we present a model for continuously structured populations with finite size, including both demographic and environmental stochasticity in the dynamics. Using recent methods developed for discrete age-structured models we derive the demographic and environmental variance of the population growth as functions of a continuous state variable. These two parameters, together with the expected population growth rate, are used to define a one-dimensional diffusion approximation of the population dynamics. Thus, a substantial reduction in complexity is achieved as the dynamics of the complex structured model can be described by only three population parameters. We provide methods for numerical calculation of the model parameters and demonstrate the accuracy of the diffusion approximation by computer simulation of specific examples. The general modeling framework makes it possible to analyze and predict future dynamics and extinction risk of populations with various types of structure, and to explore consequences of changes in demography caused by, e.g., climate change or different management decisions. Our results are especially relevant for small populations that are often of conservation concern.     

Diagnosing Units of Conservation Management

Species-oriented conservation programs attempt to analyze and maintain intra-specific variation in order to maximally preserve biological diversity. The "evolutionarily significant unit" has become an operational term for a group of organisms that should be the minimial unit for conservation management. No generally accepted definition for this term exists that would be the basis for the evaluation of these units in practical conservation situations. Currently, taxonomic decisions in species conservation are mostly based on the biological species concept. But the universal application of criteria of reproductive isolation or phenetic similarity to delimit conservation units is problematical. We favor a definition for evolutionarily significant units based on patterns of variation. In the theoretical framework of the phylogenetic species concept, conservation units are delimited by characters that diagnose clusters of individuals or populations to the exclusion of other such clusters. Characters are used for cladistic analysis to infer hypotheses of the phylogenetic relationships of individuals, and differentiated populations are diagnosed using population aggregation analysis. Characters can be based on genetic, morphological, ecological, or behavioral information, provided they are inferred to be heritable. The use of cladistics and population aggregation analysis has the potential to make the evaluation of evoluntionarily significant units objective and testable, an important consideration in politically controversial cases. Our cladistic approach is demonstrated by the evaluation of potential conservation units in the endangered tiger beetles Cicindela dorsalis and C. puritana .     

Lessons from other disciplines for setting management thresholds for biodiversity conservation

Successful, state-dependent management, in which the goal of management is to maintain a system in a desired state, involves defining the boundaries between different states. Once these boundaries have been defined, managers require a strategic action plan with thresholds that initiate management interventions to either maintain or return the system to a desired state. This approach to management is widely used across diverse industries from agriculture, to medicine, to information technology, but it has only been adopted in conservation management relatively recently. Conservation practitioners have expressed a willingness to integrate this structured approach in their management systems, but they have also voiced concerns, including lack of a robust process for doing so. Given the widespread use of state-dependent management in other fields, we conducted an extensive review of the literature on threshold-based management to gain insight into how and where it is applied and identify potential lessons for conservation management. We identified 22 industries using 75 different methods for setting management thresholds in 843 studies. Methods spanned six broad approaches, including expert driven, statistical, predictive, optimization, experimental, and artificial intelligence methods. The objectives of each of these studies influenced the approaches used, including the methods for setting thresholds and selecting actions, and the number of thresholds set. The role of value judgments in setting thresholds was clear; studies across all industries frequently involved experts in setting thresholds, often accompanied by computational tools to simulate the consequences of proposed thresholds under different conditions. Of the 30 conservation studies examined, two-thirds used expert-driven methods, consistent with prior evidence that experience-based information often drives conservation management decisions. The methods we identified from other disciplines could help conservation decision makers set thresholds for management interventions in different contexts, linking monitoring to management actions and ensuring that conservation interventions are timely and effective.     

Scale, Variable Density, and Conservation Planning for Mammalian Carnivores

Abstract: Many mammalian carnivores are in local or global decline. To slow this process, continued planning to protect these species is warranted, Still, the data bases that we have at our disposal do not adequately document population requirements for space at scales appropriate for conservation planning. To illustrate this problem, we have collected published data for 214 population censuses of carnivores. We tested for a relationship between the number of individuals censused and the size of study site for our entire data set. We conducted the same test for each family, for which we obtained sufficient and qualifying census data With areas ranging from less than 10 km² to over 40,000 km², we obtained a significant regression (p < .001; r²= 76%) for the sample as a whole. We examined the distribution of densities with increasing area and found that the relationship was not constant but decreased We noticed that numbers per census-area size increased with a slope (m < 1). We also noticed that the sizes of study areas were unevenly distributed Only 7% of the studies in our sample censused regions larger than 10,000 km². It remains unclear to what extent and how the density decreases with increasing scale We expect that extrapolations from small scales to larger ones are likely to underestimate space requirements for carnivores.     

Use made in marine ecology of methods for estimating demographic parameters from size/frequency data

Macdonald and Pitcher's method of decomposing a sizefrequency histogram into cohorts (mathematical optimization of the fit of the distribution function to the histogram) has been used to estimate the composition of random samples drawn from populations with known cohort structure. The large-sample behaviour of the method is in accordance with the results of asymptotic theory. With sample sizes typical of those used in many ecological studies, good estimates often could not be obtained without imposing constraints upon the estimation procedure, even when the number of age classes in the population was known. If the number of age classes was not known, it was frequently difficult to determine from small samples. When unconstrained solutions were obtainable, confidence limits about estimates were often very wide. Our results and information in the theoretical literature indicate that if the Petersen method (whereby several modes on a size-frequency histogram are taken to represent single age classes and all age classes to be present) does not work, accurate estimates of demographic parameters are unlikely to be obtainable using more rigorous methods. In view of these difficulties, we recommend that an iptimization method, such as that described by Macdonald and Pitcher, be used to estimate demographic parameters. Standard errors of estimates should be reported. Optimization methods give an indication when the data is inadequate to obtain accurate parameter estimates, either by failing to converge or by placing large standard errors about the estimates. Graphical methods do not give a clear warning of this, and should be avoided except where the modes on the size-frequency histogram are very well separated and sample sizes are large. Often, assumptions must be made about population parameters to enable their estimation. This may involve constraining some parameters to particular values, assuming a fixed relationship between cohort mean sizes and their standard deviations, or by assuming that individuals grow according to a von Bertalanffy curve. Any such assumptions need detailed justification in each case.     

Evaluation of variance approximation techniques for non-linear photosynthesis—irradiance models

Parameters derived from photosynthesis-irradiance (P-I) models, although often empirical in nature, are useful indicators of the photoadaptive state of phytoplankton in culture and in situ. However objective criteria for determining significant changes in P-I curves are rarely provided, because confidence intervals for parameters of non-linear models are not estimated easily. Examination of least-squares residuals in parameter space and Monte Carlo approaches have been used to estimate confidence regions around parameter values, but the computationally intensive nature of these methods has prevented their routine application. We present an alternative method of estimating confidence intervals for parameters of P-I curves that runs quickly on a microcomputer and is easily combined with common parameter-estimation routines. This algorithm was tested using a 3-parameter P-I model and curves describing a wide range of photoadaptive states, with different numbers of observations and different amounts of inherent variability. The method produced results comparable to the Monte Carlo technique. This analysis makes it possible to specify the sample size required to define parameters with acceptable confidence as a function of data variance and photoadaptive state. In most reasonable situations, 25 observations are sufficient.     

Importance of Accounting for Detection Heterogeneity When Estimating Abundance: the Case of French Wolves

Abstract: Assessing conservation strategies requires reliable estimates of abundance. Because detecting all individuals is most often impossible in free‐ranging populations, estimation procedures have to account for a <1 detection probability. Capture–recapture methods allow biologists to cope with this issue of detectability. Nevertheless, capture–recapture models for open populations are built on the assumption that all individuals share the same detection probability, although detection heterogeneity among individuals has led to underestimating abundance of closed populations. We developed multievent capture–recapture models for an open population and proposed an associated estimator of population size that both account for individual detection heterogeneity (IDH). We considered a two‐class mixture model with weakly and highly detectable individuals to account for IDH. In a noninvasive capture–recapture study of wolves we based on genotypes identified in feces and hairs, we found a large underestimation of population size (27% on average) occurred when IDH was ignored.     

Supportive Breeding and Variance Effective Population Size

The practice of supporting weak, wild populations through release of individuals bred in captivity is becoming an increasingly important conservation measure. A frequently recommended form of such breeding-release activity refers to supportive breeding: a fraction of the target population is brought into captivity for reproduction, and the resulting progeny are released to mix with the wild segment of the population. We derived an expression for the variance effective size of a population managed through supportive breeding and discuss its relationship to previously published equations that are based on the assumption of random mating. We show that the effect of supportive breeding may be quite different on the inbreeding and the variance effective sizes. Whereas supportive breeding always results in a reduction of the inbreeding effective number, the variance effective number may either decrease, increase, or remain unchanged. We discuss these observations in relation to conservation management and suggest some general guidelines for supportive breeding situations. Our recommendations include making a distinction between inbreeding and variance effective numbers; taking particular care when dealing with organisms with high reproductive potential; assuring that the amount of drift be no larger than it would be without supportive breeding; and focusing primarily on the variance effective size of a population-that is, on the effective number directly related to the rate of loss of gene diversity.     

Untested assumptions about within-species sample size and missing data in interspecific studies

Phylogenetic comparative studies rely on species-specific data that often contain missing values and/or differ in sample size among species. These phenomena may violate statistical assumptions about the non-random variance component in sampling effort. A major reason why this assumption is often not fulfilled is because the probability of being sampled (i.e., being captured or observed) may depend on species-specific characteristics. Here, we test this assumption by using information on within-species sample sizes and missing data from five independent comparative datasets of European birds. First, we show that the two estimates of data availability (missing values and within-species sample size) are positively correlated and are associated with research effort in general (the number of papers published). Second, we demonstrate biologically meaningful relationships between data availability and phenotypic traits. For example, population size, risk-taking, and habitat specialization independently predicted within-species sample size. The key determinants of missing data were population size and distribution range. However, data availability was not structured by phylogenetic relationships. These results indicate that the accuracy of sampling is repeatable and distributed non-randomly among species, as several species-specific attributes determined the probability of observation. Therefore, data availability seems to be a species-specific trait that can be shaped by ecology, life history, and behavior. Such relationships raise issues about non-random sampling, which requires attention in comparative studies.     

Long-term demographic and genetic effects of releasing captive-born individuals into the wild

Because of continued habitat destruction and species extirpations, the need to use captive breeding for conservation purposes has been increasing steadily. However, the long-term demographic and genetic effects associated with releasing captive-born individuals with varied life histories into the wild remain largely unknown. To address this question, we developed forward-time, agent-based models for 4 species with long-running captive-breeding and release programs: coho salmon (Oncorhynchus kisutch), golden lion tamarin (Leontopithecus rosalia), western toad (Anaxyrus boreas), and Whooping Crane (Grus americana). We measured the effects of supplementation by comparing population size and neutral genetic diversity in supplemented populations to the same characteristics in unaltered populations 100 years after supplementation ended. Releasing even slightly less fit captive-born individuals to supplement wild populations typically resulted in reductions in population sizes and genetic diversity over the long term when the fitness reductions were heritable (i.e., due to genetic adaptation to captivity) and populations continued to be regulated by density-dependent mechanisms over time. Negative effects for species with longer life spans and lower rates of population replacement were smaller than for species with shorter life spans and higher rates of population replacement. Programs that released captive-born individuals over fewer years or that avoided breeding individuals with captive ancestry had smaller reductions in population size and genetic diversity over the long term. Relying on selection in the wild to remove individuals with reduced fitness mitigated some negative demographic effects, but at a substantial cost to neutral genetic diversity. Our results suggest that conservation-focused captive-breeding programs should take measures to prevent even small amounts of genetic adaptation to captivity, quantitatively determine the minimum number of captive-born individuals to release each year, and fully account for the interactions among genetic adaptation to captivity, population regulation, and life-history variation.