Effects of Point Pattern Shape on Home-Range Estimates

Abstract: Home-range estimators are commonly tested with simulated animal locational data in the laboratory before the estimators are used in practice. Although kernel density estimation (KDE) has performed well as a home-range estimator for simulated data, several recent studies have reported its poor performance when used with data collected in the field. This difference may be because KDE and other home-range estimators are generally tested with simulated point locations that follow known statistical distributions, such as bivariate normal mixtures, which may not represent well the space-use patterns of all wildlife species. We used simulated animal locational data of 5 point pattern shapes that represent a range of wildlife utilization distributions to test 4 methods of home-range estimation: 1) KDE with reference bandwidths, 2) KDE with least-squares cross-validation, 3) KDE with plug-in bandwidths, and 4) minimum convex polygon (MCP). For the point patterns we simulated, MCP tended to produce more accurate area estimates than KDE methods. However, MCP estimates were markedly unstable, with bias varying widely with both sample size and point pattern shape. The KDE methods performed best for concave distributions, which are similar to bivariate normal mixtures, but still overestimated home ranges by about 40–50% even in the best cases. For convex, linear, perforated, and disjoint point patterns, KDE methods overestimated home-range sizes by 50–300%, depending on sample size and method of bandwidth selection. These results indicate that KDE does not produce home-range estimates that are as accurate as the literature suggests, and we recommend exploring other techniques of home-range estimation.     

Extreme longevity in freshwater mussels revisited: sources of bias in age estimates derived from mark–recapture experiments

1. There may be bias associated with mark–recapture experiments used to estimate age and growth of freshwater mussels. Using subsets of a mark–recapture dataset for Quadrula pustulosa, I examined how age and growth parameter estimates are affected by (i) the range and skew of the data and (ii) growth reduction due to handling. I compared predictions from von Bertalanffy growth models based on mark–recapture data with direct observation of mussel age and growth inferred from validated shell rings. 2. Growth models based on a dataset that included observations from a wide range of length classes (spanning ≥ the upper 50% of the population length range) produced only slightly biased age estimates for small and medium‐sized individuals (overestimated by 1–2 years relative to estimates from validated shell rings) but estimates became increasingly biased for larger individuals. Growth models using data that included only observations of larger animals (< the upper 50% of length range) overestimated age for all length classes, and estimated maximum age was two to six times greater than the maximum age observed in the population (47 years). Similarly, growth models using a left‐skewed dataset overestimated age. 3. Reductions of growth due to repeated handling also resulted in overestimates of age. The estimated age of mussels that were handled in two consecutive years was as much as twice that of mussels that were handled only once over the same period. Assuming a constant reduction in the annual rate of growth, handling an individual for five consecutive years could result in an estimated age that is five times too high. 4. These findings show that mark–recapture methods have serious limitations for estimating mussel age and growth. A previous paper (Freshwater Biology, 46, 2001, 1349) presented longevity estimates for three mussel species that were an order of magnitude higher than estimates inferred from shell rings. Because those estimates of extreme longevity were based on mark–recapture methods and subject to multiple, additive sources of bias, they cannot be considered accurate representations of life span and cannot be used to conclude that traditional methods of bivalve ageing by interpretation of shell rings are flawed.     

Memory keeps you at home: a mechanistic model for home range emergence

Despite its central place in animal ecology no general mechanistic movement model with an emergent home-range pattern has yet been proposed. Random walk models, which are commonly used to model animal movement, show diffusion instead of a bounded home range and therefore require special modifications. Current approaches for mechanistic modeling of home ranges apply only to a limited set of taxa, namely territorial animals and/or central place foragers. In this paper we present a more general mechanistic movement model based on a biased correlated random walk, which shows the potential for home-range behavior. The model is based on an animal tracking a dynamic resource landscape, using a biologically plausible two-part memory system, i.e. a reference- and a working-memory. Our results show that by adding these memory processes the random walker produces home-range behavior as it gains experience, which also leads to more efficient resource use. Interestingly, home-range patterns, which we assessed based on home-range overlap and increase in area covered with time, require the combined action of both memory components to emerge. Our model has the potential to predict home-range size and can be used for comparative analysis of the mechanisms shaping home-range patterns.     

Estimates of the average strength of natural selection are not inflated by sampling error or publication bias

Kingsolver et al.'s review of phenotypic selection gradients from natural populations provided a glimpse of the form and strength of selection in nature and how selection on different organisms and traits varies. Because this review's underlying database could be a key tool for answering fundamental questions concerning natural selection, it has spawned discussion of potential biases inherent in the review process. Here, we explicitly test for two commonly discussed sources of bias: sampling error and publication bias. We model the relationship between variance among selection gradients and sample size that sampling error produces by subsampling large empirical data sets containing measurements of traits and fitness. We find that this relationship was not mimicked by the review data set and therefore conclude that sampling error does not bias estimations of the average strength of selection. Using graphical tests, we find evidence for bias against publishing weak estimates of selection only among very small studies (N<38). However, this evidence is counteracted by excess weak estimates in larger studies. Thus, estimates of average strength of selection from the review are less biased than is often assumed. Devising and conducting straightforward tests for different biases allows concern to be focused on the most troublesome factors.     

Estimating environmental effects on population dynamics: consequences of observation error

Within the paradigm of population dynamics a central task is to identify environmental factors affecting population change and to estimate the strength of these effects. We here investigate the impact of observation errors in measurements of population densities on estimates of environmental effects. Adding observation errors may change the autocorrelation of a population time series with potential consequences for estimates of effects of autocorrelated environmental covariates. Using Monte Carlo simulations, we compare the performance of maximum likelihood estimates from three stochastic versions of the Gompertz model (log–linear first order autoregressive model), assuming 1) process error only, 2) observation error only, and 3) both process and observation error (the linear state–space model on log‐scale). We also simulated population dynamics using the Ricker model, and evaluated the corresponding maximum likelihood estimates for process error models. When there is observation error in the data and the considered environmental variable is strongly autocorrelated, its estimated effect is likely to be biased when using process error models. The environmental effect is overestimated when the sign of the autocorrelations of the intrinsic dynamics and the environment are the same and underestimated when the signs differ. With non‐autocorrelated environmental covariates, process error models produce fairly exact point estimates as well as reliable confidence intervals for environmental effects. In all scenarios, observation error models produce unbiased estimates with reasonable precision, but confidence intervals derived from the likelihood profiles are far too optimistic if there is process error present. The safest approach is to use state–space models in presence of observation error. These are factors worthwhile to consider when interpreting earlier empirical results on population time series, and in future studies, we recommend choosing carefully the modelling approach with respect to intrinsic population dynamics and covariate autocorrelation.     

Addressing Temporal Variability in Bird Calling with Design and Estimation: A Northern Bobwhite Example

Imprecise or biased density estimates can lead to inadequate conservation action, overexploitation of game species, or lost recreational opportunities. Common approaches to estimating density of avian populations often either ignore the probability that an individual is present within the sampling area but is not available to be sampled (e.g., not vocalizing), or do not consider covariates that could influence availability. Additionally, management decisions made at the management unit scale are often informed by inadequate monitoring practices, such as limited sampling intensity. In such cases, management agencies calculate density by applying correction factors (e.g., detection probabilities estimated using empirical data from a different study system) to count data, rather than estimating a detection function directly using statistical models. We conducted a simulation study using northern bobwhite (Colinus virginianus; bobwhite) as a model species to quantify the consequences of mis-specifying avian point count models on bias and precision of density estimates. We compared bias and precision of estimates from a fully specified distance-sampling model that estimates availability and detection to 4 different mis-specified approaches, including 2 approaches to calculating density using correction factors. Using correction factors to calculate density produced estimates with low bias but relatively lower precision compared to the fully specified model (CV of density estimates at 35 sites over 5 years: fully specified = 10%, correction factors = 25% and 30%). Although the mean precision and bias of the fully specified model improved with more data (70 sites over 5 years, CV = 9%; 35 sites over 10 years, CV = 9%), precision of correction factors did not (70 sites over 5 years, CV = 22% and 27%; 35 sites over 10 years, CV = 24% and 29%). The fully specified model captured the underlying temporal variation in detection and availability. Increasing sampling duration from 5 to 10 years improved modeled estimates of growth rate, even for mis-specified models, but not derived growth rates using pre-determined detection functions. We demonstrated that conducting point counts 3 times/year at a feasible number of sites can produce relatively unbiased estimates of bobwhite density. Pre-determined detection functions can be fortuitously unbiased for certain years, but they are not a reliable method for determining density or identifying trends in density over time. © 2020 The Wildlife Society.     

Testing for environmentally induced bias in phenotypic estimates of natural selection: theory and practice

Measuring natural selection has been a fundamental goal of evolutionary biology for more than a century, and techniques developed in the last 20 yr have provided relatively simple means for biologists to do so. Many of these techniques, however, share a common limitation: when applied to phenotypic data, environmentally induced covariances between traits and fitness can lead to biased estimates of selection and misleading predictions about evolutionary change. Utilizing estimates of breeding values instead of phenotypic data with these methods can eliminate environmentally induced bias, although this approach is more difficult to implement. Despite this potential limitation to phenotypic methods and the availability of a potential solution, little empirical evidence exists on the extent of environmentally induced bias in phenotypic estimates of selection. In this article, we present a method for detecting bias in phenotypic estimates of selection and demonstrate its use with three independent data sets. Nearly 25% of the phenotypic selection gradients estimated from our data are biased by environmental covariances. We find that bias caused by environmental covariances appears mainly to affect quantitative estimates of the strength of selection based on phenotypic data and that the magnitude of these biases is large. As our estimates of selection are based on data from spatially replicated field experiments, we suggest that our findings on the prevalence of bias caused by environmental covariances are likely to be conservative.     

Modelling time to population extinction when individual reproduction is autocorrelated

In nature, individual reproductive success is seldom independent from year to year, due to factors such as reproductive costs and individual heterogeneity. However, population projection models that incorporate temporal autocorrelations in individual reproduction can be difficult to parameterise, particularly when data are sparse. We therefore examine whether such models are necessary to avoid biased estimates of stochastic population growth and extinction risk, by comparing output from a matrix population model that incorporates reproductive autocorrelations to output from a standard age‐structured matrix model that does not. We use a range of parameterisations, including a case study using moose data, treating probabilities of switching reproductive class as either fixed or fluctuating. Expected time to extinction from the two models is found to differ by only small amounts (under 10%) for most parameterisations, indicating that explicitly accounting for individual reproductive autocorrelations is in most cases not necessary to avoid bias in extinction estimates.     

Improving inference for nonlinear state‐space models of animal population dynamics given biased sequential life stage data

State‐space models (SSMs) are a popular tool for modeling animal abundances. Inference difficulties for simple linear SSMs are well known, particularly in relation to simultaneous estimation of process and observation variances. Several remedies to overcome estimation problems have been studied for relatively simple SSMs, but whether these challenges and proposed remedies apply for nonlinear stage‐structured SSMs, an important class of ecological models, is less well understood. Here we identify improvements for inference about nonlinear stage‐structured SSMs fit with biased sequential life stage data. Theoretical analyses indicate parameter identifiability requires covariates in the state processes. Simulation studies show that plugging in externally estimated observation variances, as opposed to jointly estimating them with other parameters, reduces bias and standard error of estimates. In contrast to previous results for simple linear SSMs, strong confounding between jointly estimated process and observation variance parameters was not found in the models explored here. However, when observation variance was also estimated in the motivating case study, the resulting process variance estimates were implausibly low (near‐zero). As SSMs are used in increasingly complex ways, understanding when inference can be expected to be successful, and what aids it, becomes more important. Our study illustrates (a) the need for relevant process covariates and (b) the benefits of using externally estimated observation variances for inference about nonlinear stage‐structured SSMs.     

Locus-specific heritability estimation via the bootstrap in linkage scans for quantitative trait loci

BACKGROUND/AIMS: In genome-wide linkage analysis of quantitative trait loci (QTL), locus-specific heritability estimates are biased when the original data are used to both localize linkage and estimate effects, due to maximization of the LOD score over the genome. Positive bias is increased by adoption of stringent significance levels to control genome-wide type I error. We propose multi-locus bootstrap resampling estimators for bias reduction in the situation in which linkage peaks at more than one QTL are of interest. METHODS: Bootstrap estimates were based on repeated sample splitting in the original dataset. We conducted simulation studies in nuclear families with 0 to 5 QTLs and applied the methods in a genome-wide analysis of a blood pressure phenotype in extended pedigrees from the Framingham Heart Study (FHS). RESULTS: Compared to na?ve estimates in the original simulation samples, bootstrap estimates had reduced bias and smaller mean squared error. In the FHS pedigrees, the bootstrap yielded heritability estimates as much as 70% smaller than in the original sample. CONCLUSIONS: Because effect estimates obtained in an initial study are typically inflated relative to those expected in an independent replication study, successful replication will be more likely when sample size requirements are based on bias-reduced estimates.     

Modelling occurrence and abundance of species when detection is imperfect

Relationships between species abundance and occupancy are of considerable interest in metapopulation biology and in macroecology. Such relationships may be described concisely using probability models that characterize variation in abundance of a species. However, estimation of the parameters of these models in most ecological problems is impaired by imperfect detection. When organisms are detected imperfectly, observed counts are biased estimates of true abundance, and this induces bias in stated occupancy or occurrence probability. In this paper we consider a class of models that enable estimation of abundance/occupancy relationships from counts of organisms that result from surveys in which detection is imperfect. Under such models, parameter estimation and inference are based on conventional likelihood methods. We provide an application of these models to geographically extensive breeding bird survey data in which alternative models of abundance are considered that include factors that influence variation in abundance and detectability. Using these models, we produce estimates of abundance and occupancy maps that honor important sources of spatial variation in avian abundance and provide clearly interpretable characterizations of abundance and occupancy adjusted for imperfect detection.     

Describing Directional Cell Migration with a Characteristic Directionality Time

Many cell types can bias their direction of locomotion by coupling to external cues. Characteristics such as how fast a cell migrates and the directedness of its migration path can be quantified to provide metrics that determine which biochemical and biomechanical factors affect directional cell migration, and by how much. To be useful, these metrics must be reproducible from one experimental setting to another. However, most are not reproducible because their numerical values depend on technical parameters like sampling interval and measurement error. To address the need for a reproducible metric, we analytically derive a metric called directionality time, the minimum observation time required to identify motion as directionally biased. We show that the corresponding fit function is applicable to a variety of ergodic, directionally biased motions. A motion is ergodic when the underlying dynamical properties such as speed or directional bias do not change over time. Measuring the directionality of nonergodic motion is less straightforward but we also show how this class of motion can be analyzed. Simulations are used to show the robustness of directionality time measurements and its decoupling from measurement errors. As a practical example, we demonstrate the measurement of directionality time, step-by-step, on noisy, nonergodic trajectories of chemotactic neutrophils. Because of its inherent generality, directionality time ought to be useful for characterizing a broad range of motions including intracellular transport, cell motility, and animal migration.     

Scaling Occupancy Estimates up to Abundance for Wolves

Management of wildlife populations often requires reliable estimates of population size or distribution. Estimating abundance can be logistically difficult, and occupancy models have been used as a less expensive proxy for abundance estimation. Another alternative is to use independent estimates of home-range size and mean group size to directly scale occupancy estimates up to abundance. We used simulations to explore when scaling occupancy up to abundance is reliable, and as an example we applied an occupancy approach to estimate abundance of wolves (Canis lupus) from roadside snow-tracking surveys in northern Wisconsin, USA, in 2016 and 2018. Estimates of wolf abundance were plausible and compared favorably with independent estimates produced by territory mapping, and snow-tracking data requirements were lower than for territory mapping. Simulation results suggested that reasonable abundance estimates could be obtained under some conditions but also that severe positive bias could result under other conditions, especially when populations were small and dispersed, home range size was small, and areal sampling units were large. Positive bias in abundance estimates occurs because of closure assumption violations when tracks from a single wolf or pack are detected in >1 sample unit, and the sum of the sample unit areas where tracks were detected exceed the sum of the home range areas. Bias was minimized when sampling units were small relative to home range size or when sampling units were route segments that approximate point sample units, and when home ranges were highly aggregated. We conclude that, although caution is warranted when scaling occupancy estimates up to abundance, scaled occupancy models can provide feasible and reliable estimates of abundance, assuming home range size and mean group size are accurately known or estimated, sampling units are appropriately chosen, and covariates that aggregate home ranges can be used to accurately predict occupancy probability. © 2021 The Authors. The Journal of Wildlife Management published by Wiley Periodicals LLC on behalf of The Wildlife Society.     

The importance of proper model assumption in bayesian phylogenetics

We studied the importance of proper model assumption in the context of Bayesian phylogenetics by examining >5,000 Bayesian analyses and six nested models of nucleotide substitution. Model misspecification can strongly bias bipartition posterior probability estimates. These biases were most pronounced when rate heterogeneity was ignored. The type of bias seen at a particular bipartition appeared to be strongly influenced by the lengths of the branches surrounding that bipartition. In the Felsenstein zone, posterior probability estimates of bipartitions were biased when the assumed model was underparameterized but were unbiased when the assumed model was overparameterized. For the inverse Felsenstein zone, however, both underparameterization and overparameterization led to biased bipartition posterior probabilities, although the bias caused by overparameterization was less pronounced and disappeared with increased sequence length. Model parameter estimates were also affected by model misspecification. Underparameterization caused a bias in some parameter estimates, such as branch lengths and the gamma shape parameter, whereas overparameterization caused a decrease in the precision of some parameter estimates. We caution researchers to assure that the most appropriate model is assumed by employing both a priori model choice methods and a posteriori model adequacy tests.     

The influence of environmentally induced heterogeneity on age-specific genetic variance for mortality rates

Using parametric models that describe the increase in mortality rates with age, we demonstrate that environmentally induced heterogeneity among genetically identical individuals is sufficient to generate biased estimates of age-specific genetic variance. Although the magnitude of the bias may change with age, one general trend emerges: the true genetic variance at the oldest ages is likely to be dramatically underestimated. Our results are robust to different manifestations of heterogeneity and suggest that such a bias is a general feature of these models. We note that age-dependent estimates of genetic variance for characters that are correlated with mortality (either genetically or environmentally) can be expected to be similarly affected. The results are independent of sample size and suggest that the bias may be more widespread in the literature than is currently appreciated. Our results are discussed with reference to existing data on mortality variance in Drosophila melanogaster.     

Precision and accuracy of divergence time estimates from STR and SNPSTR variation

Inference of intraspecific population divergence patterns typically requires genetic data for molecular markers with relatively high mutation rates. Microsatellites, or short tandem repeat (STR) polymorphisms, have proven informative in many such investigations. These markers are characterized, however, by high levels of homoplasy and varying mutational properties, often leading to inaccurate inference of population divergence. A SNPSTR is a genetic system that consists of an STR polymorphism closely linked (typically < 500 bp) to one or more single-nucleotide polymorphisms (SNPs). SNPSTR systems are characterized by lower levels of homoplasy than are STR loci. Divergence time estimates based on STR variation (on the derived SNP allele background) should, therefore, be more accurate and precise. We use coalescent-based simulations in the context of several models of demographic history to compare divergence time estimates based on SNPSTR haplotype frequencies and STR allele frequencies. We demonstrate that estimates of divergence time based on STR variation on the background of a derived SNP allele are more accurate (3% to 7% bias for SNPSTR versus 11% to 20% bias for STR) and more precise than STR-based estimates, conditional on a recent SNP mutation. These results hold even for models involving complex demographic scenarios with gene flow, population expansion, and population bottlenecks. Varying the timing of the mutation event generating the SNP revealed that estimates of divergence time are sensitive to SNP age, with more recent SNPs giving more accurate and precise estimates of divergence time. However, varying both mutational properties of STR loci and SNP age demonstrated that multiple independent SNPSTR systems provide less biased estimates of divergence time. Furthermore, the combination of estimates based separately on STR and SNPSTR variation provides insight into the age of the derived SNP alleles. In light of our simulations, we interpret estimates from data for human populations.     

Space–time home-range estimates and resource selection for the Critically Endangered Philippine Eagle on Mindanao

Quantifying home-range size and habitat resource selection are important elements in wildlife ecology and are useful for informing conservation action. Many home-range estimators and resource selection functions are currently in use. However, both methods are fraught with analytical issues inherent within autocorrelated movement data from irregular sampling and interpretation of resource selection model parameters to inform conservation management. Here, we apply satellite remote sensing technologies to provide updated estimates of home-range size and first estimates of fine-scale resource selection for six adult Philippine Eagles Pithecophaga jefferyi using a space–time autocorrelated kernel density estimate (AKDE) home-range estimator and non-parametric resource selection functions. All six adult Eagles showed distinct site fidelity, with continuous range residency between 2 and 18 km, 1 month after tagging. The space–time AKDE home-range estimators had a median 95% home-range size = 68 km² (95% confidence interval (95% CI) 62–74 km², range: 39–161 km²), with the median 50% core range size = 13 km² (95% CI 11–14 km², range 9–33 km²). From the resource selection functions, all adult Philippine Eagles used habitat high in photosynthetic leaf and canopy structure but avoided areas of old-growth biomass and denser areas of vegetation. This is possibly due to foraging forays into secondary forest and fragmented agricultural areas away from nesting sites. For the first time, we determine two important fine-scale spatial processes for this Critically Endangered raptor that can help in directing conservation management. Rather than employing traditional home-range estimators and resource selection functions, we recommend that analysts consider space–time approaches and non-parametric resource selection functions to animal movement data to explore fully space–time and resource selection.     

The Effect of Selection Bias in Studies of Fads and Fashions

Most studies of fashion and fads focus on objects and practices that once were popular. We argue that limiting the sample to such trajectories generates a selection bias that obscures the underlying process and generates biased estimates. Through simulations and the analysis of a data set that has previously not been used to analyze the rise and fall of cultural practices, the New York Times text archive, we show that studying a whole range of cultural objects, both popular and less popular, is essential for understanding the drivers of popularity. In particular, we show that estimates of statistical models of the drivers of popularity will be biased if researchers use only trajectories of those practices that once were popular.     

Estimating the Rate of Adaptive Molecular Evolution When the Evolutionary Divergence Between Species is Small

We investigate the extent by which the estimates of the rate of adaptive molecular evolution obtained by extending the McDonald-Kreitman test are biased if the species, subjected to analysis, diverged recently. We show that estimates can be biased if the nucleotide divergence between the species is low relative to within species variation, and that the magnitude of the bias depends on the rate of adaptive evolution and the distribution of fitness effects of new mutations. Bias appears to be because of three factors: (1) misattribution of polymorphism to divergence; (2) the contribution of ancestral polymorphism to divergence; and (3) different rates of fixation of neutral and advantageous mutations. If there is little adaptive molecular evolution, then slightly deleterious mutations inflate estimates of the rate of adaptive evolution, because these contribute proportionately more to polymorphism than to nucleotide divergence than neutral mutations. However, if there is substantial adaptive evolution, polymorphism contributing to apparent divergence may downwardly bias estimates. We propose a simple method for correcting the different contributions of slightly deleterious and neutral mutations to polymorphism and divergence, and apply it to datasets from several species. We find that estimates of the rate of adaptive molecular evolution from closely related species may be underestimates by ~10% or more. However, after the contribution of polymorphism to divergence is removed, the rate of adaptive evolution may still be overestimated as a consequence of ancestral polymorphism and time for fixation effects. This bias may be substantial if branch lengths are less than 10N (e) generations.     

Reduction of bias in estimating the frequency of recessive genes.

The standard approach to estimating the frequency of a completely recessive autosomal gene is to use the maximum-likelihood estimator (MLE), q = square root q2. Since the expectation oof Q using MLE is systematically less than the true value, this estimator always gives a negatively biased estimate of q. Here we describe the bias associated the MLE over a range of q and N values, explore some of the properties of this estimator, and propose new estimators which reduce the bias. We also describe some of the new estimators' properties, as well as the remaining bias associated with them for varying q and N values. We further propose one of these estimators as the one which most effectively reduces bias over a specific q value range of approximately .005 to .05, and which is less biased than JLE over essentially all q and N values. The proposed estimator also is directly compared with MLE in calculating various available estimates of q, demonstrating the percentage of reduction in bias achieved. This reduction varies from negligible for estimates of q above .3 and N greater than 100, to a 23% reduction in bias for a q value of .09 and an N value of 215.