Evidence of an Absence of Inbreeding Depression in a Wild Population of Weddell Seals (Leptonychotes weddellii)

Inbreeding depression can reduce the viability of wild populations. Detecting inbreeding depression in the wild is difficult; developing accurate estimates of inbreeding can be time and labor intensive. In this study, we used a two-step modeling procedure to incorporate uncertainty inherent in estimating individual inbreeding coefficients from multilocus genotypes into estimates of inbreeding depression in a population of Weddell seals (Leptonychotes weddellii). The two-step modeling procedure presented in this paper provides a method for estimating the magnitude of a known source of error, which is assumed absent in classic regression models, and incorporating this error into inferences about inbreeding depression. The method is essentially an errors-in-variables regression with non-normal errors in both the dependent and independent variables. These models, therefore, allow for a better evaluation of the uncertainty surrounding the biological importance of inbreeding depression in non-pedigreed wild populations. For this study we genotyped 154 adult female seals from the population in Erebus Bay, Antarctica, at 29 microsatellite loci, 12 of which are novel. We used a statistical evidence approach to inference rather than hypothesis testing because the discovery of both low and high levels of inbreeding are of scientific interest. We found evidence for an absence of inbreeding depression in lifetime reproductive success, adult survival, age at maturity, and the reproductive interval of female seals in this population.

Entropy, Statistical Evidence, and Scientific Inference: Evidence Functions in Theory and Applications

Scope and Goals of the Special Issue: There is a growing realization that despite being the essential tool of modern data-based scientific discovery and model testing, statistics has major problems [...].

Assessing the Global and Local Uncertainty of Scientific Evidence in the Presence of Model Misspecification

Scientists need to compare the support for models based on observed phenomena. The main goal of the evidential paradigm is to quantify the strength of evidence in the data for a reference model relative to an alternative model. This is done via an evidence function, such as ΔSIC, an estimator of the sample size scaled difference of divergences between the generating mechanism and the competing models. To use evidence, either for decision making or as a guide to the accumulation of knowledge, an understanding of the uncertainty in the evidence is needed. This uncertainty is well characterized by the standard statistical theory of estimation. Unfortunately, the standard theory breaks down if the models are misspecified, as is commonly the case in scientific studies. We develop non-parametric bootstrap methodologies for estimating the sampling distribution of the evidence estimator under model misspecification. This sampling distribution allows us to determine how secure we are in our evidential statement. We characterize this uncertainty in the strength of evidence with two different types of confidence intervals, which we term “global” and “local.” We discuss how evidence uncertainty can be used to improve scientific inference and illustrate this with a reanalysis of the model identification problem in a prominent landscape ecology study using structural equations.

Model Projections in Model Space: A Geometric Interpretation of the AIC Allows Estimating the Distance Between Truth and Approximating Models

Information criteria have had a profound impact on modern ecological science. They allow researchers to estimate which probabilistic approximating models are closest to the generating process. Unfortunately, information criterion comparison does not tell how good the best model is. In this work, we show that this shortcoming can be resolved by extending the geometric interpretation of Hirotugu Akaike's original work. Standard information criterion analysis considers only the divergences of each model from the generating process. It is ignored that there are also estimable divergence relationships amongst all of the approximating models. We then show that using both sets of divergences and an estimator of the negative self entropy, a model space can be constructed that includes an estimated location for the generating process. Thus, not only can an analyst determine which model is closest to the generating process, she/he can also determine how close to the generating process the best approximating model is. Properties of the generating process estimated from these projections are more accurate than those estimated by model averaging. We illustrate in detail our findings and our methods with two ecological examples for which we use and test two different neg-selfentropy estimators. The applications of our proposed model projection in model space extend to all areas of science where model selection through information criteria is done.

Errors in Statistical Inference Under Model Misspecification: Evidence, Hypothesis Testing, and AIC

The methods for making statistical inferences in scientific analysis have diversified even within the frequentist branch of statistics, but comparison has been elusive. We approximate analytically and numerically the performance of Neyman-Pearson hypothesis testing, Fisher significance testing, information criteria, and evidential statistics (Royall, 1997). This last approach is implemented in the form of evidence functions: statistics for comparing two models by estimating, based on data, their relative distance to the generating process (i.e., truth) (Lele, 2004). A consequence of this definition is the salient property that the probabilities of misleading or weak evidence, error probabilities analogous to Type 1 and Type 2 errors in hypothesis testing, all approach 0 as sample size increases. Our comparison of these approaches focuses primarily on the frequency with which errors are made, both when models are correctly specified, and when they are misspecified, but also considers ease of interpretation. The error rates in evidential analysis all decrease to 0 as sample size increases even under model misspecification. Neyman-Pearson testing on the other hand, exhibits great difficulties under misspecification. The real Type 1 and Type 2 error rates can be less, equal to, or greater than the nominal rates depending on the nature of model misspecification. Under some reasonable circumstances, the probability of Type 1 error is an increasing function of sample size that can even approach 1! In contrast, under model misspecification an evidential analysis retains the desirable properties of always having a greater probability of selecting the best model over an inferior one and of having the probability of selecting the best model increase monotonically with sample size. We show that the evidence function concept fulfills the seeming objectives of model selection in ecology, both in a statistical as well as scientific sense, and that evidence functions are intuitive and easily grasped. We find that consistent information criteria are evidence functions but the MSE minimizing (or efficient) information criteria (e.g., AIC, AICc, TIC) are not. The error properties of the MSE minimizing criteria switch between those of evidence functions and those of Neyman-Pearson tests depending on models being compared.

Strong Evidence for an Intraspecific Metabolic Scaling Coefficient Near 0.89 in Fish

As an example of applying the evidential approach to statistical inference, we address one of the longest standing controversies in ecology, the evidence for, or against, a universal metabolic scaling relationship between metabolic rate and body mass. Using fish as our study taxa, we curated 25 studies with measurements of standard metabolic rate, temperature, and mass, with 55 independent trials and across 16 fish species and confronted this data with flexible random effects models. To quantify the body mass - metabolic rate relationship, we perform model selection using the Schwarz Information Criteria (ΔSIC), an established evidence function. Further, we formulate and justify the use of ΔSIC intervals to delineate the values of the metabolic scaling relationship that should be retained for further consideration. We found strong evidence for a metabolic scaling coefficient of 0.89 with a ΔSIC interval spanning 0.82 to 0.99, implying that mechanistically derived coefficients of 0.67, 0.75, and 1, are not supported by the data. Model selection supports the use of a random intercepts and random slopes by species, consistent with the idea that other factors, such as taxonomy or ecological or lifestyle characteristics, may be critical for discerning the underlying process giving rise to the data. The evidentialist framework applied here, allows for further refinement given additional data and more complex models.

Ecological change points: The strength of density dependence and the loss of history

Change points in the dynamics of animal abundances have extensively been recorded in historical time series records. Little attention has been paid to the theoretical dynamic consequences of such change-points. Here we propose a change-point model of stochastic population dynamics. This investigation embodies a shift of attention from the problem of detecting when a change will occur, to another non-trivial puzzle: using ecological theory to understand and predict the post-breakpoint behavior of the population dynamics. The proposed model and the explicit expressions derived here predict and quantify how density dependence modulates the influence of the pre-breakpoint parameters into the post-breakpoint dynamics. Time series transitioning from one stationary distribution to another contain information about where the process was before the change-point, where is it heading and how long it will take to transition, and here this information is explicitly stated. Importantly, our results provide a direct connection of the strength of density dependence with theoretical properties of dynamic systems, such as the concept of resilience. Finally, we illustrate how to harness such information through maximum likelihood estimation for state-space models, and test the model robustness to widely different forms of compensatory dynamics. The model can be used to estimate important quantities in the theory and practice of population recovery.

Hitching a ride: Seed accrual rates on different types of vehicles

Human activities, from resource extraction to recreation, are increasing global connectivity, especially to less-disturbed and previously inaccessible places. Such activities necessitate road networks and vehicles. Vehicles can transport reproductive plant propagules long distances, thereby increasing the risk of invasive plant species transport and dispersal. Subsequent invasions by less desirable species have significant implications for the future of threatened species and habitats. The goal of this study was to understand vehicle seed accrual by different vehicle types and under different driving conditions, and to evaluate different mitigation strategies. Using studies and experiments at four sites in the western USA we addressed three questions: How many seeds and species accumulate and are transported on vehicles? Does this differ with vehicle type, driving surface, surface conditions, and season? What is our ability to mitigate seed dispersal risk by cleaning vehicles? Our results demonstrated that vehicles accrue plant propagules, and driving surface, surface conditions, and season affect the rate of accrual: on- and off-trail summer seed accrual on all-terrain vehicles was 13 and 3508 seeds km^-1, respectively, and was higher in the fall than in the summer. Early season seed accrual on 4-wheel drive vehicles averaged 7 and 36 seeds km^-1 on paved and unpaved roads respectively, under dry conditions. Furthermore, seed accrual on unpaved roads differed by vehicle type, with tracked vehicles accruing more than small and large 4-wheel drives; and small 4-wheel drives more than large. Rates were dramatically increased under wet surface conditions. Vehicles indiscriminately accrue a wide diversity of seeds (different life histories, forms and seed lengths); total richness, richness of annuals, biennials, forbs and shrubs, and seed length didn't differ among vehicle types, or additional seed bank samples. Our evaluation of portable vehicle wash units showed that approximately 80% of soil and seed was removed from dirty vehicles. This suggests that interception programs to reduce vehicular seed transportation risk are feasible and should be developed for areas of high conservation value, or where the spread of invasive species is of special concern.

MODELS OF CHARACTER DISPLACEMENT AND THE THEORETICAL ROBUSTNESS OF TAXON CYCLES

The appropriateness of the techniques used in modeling character displacement has been the focus of vigorous debate. In this paper, the three competing methods (the coevolutionarily stable community (CSC), the evolutionarily stable strategy (ESS), and quantitative genetic recursion (QGR)) are compared in models using a common ecological setting. Specific predictions of the CSC model have been used to understand features of character displacement among Cnemidophorous lizards on islands off Mexico, Anolis lizards in the Lesser Antilles and Galápagos finches. Nonetheless, the validity of the approach has been repeatedly questioned. Conceptually the three formalisms vary in the degree to which within species variability is allowed in the models. The predictions of the CSC are found not to be robust to even small violation of its fundamental assumption of absolute species monomorphy. We show by simulation and analytical observations that the CSC is not valid under frequency dependent selection, and that the ESS is the limiting case of QGR as intraspecific phenotypic variation goes to zero. Thus the ESS and the QGR models agree closely when the between-phenotype component (BPC) of the niche width is small. However, as the BPC increases, quantitative discrepancies between ESS and QGR predictions increase, although model behavior remains qualitatively similar. A fourth approach, termed "Quantitative Genetic Optimization" (QGO) analysis, is suggested, combining advantages of both the ESS and QGR. Although all approaches support the possibility of taxon cycles, the cycle patterns predicted are qualitatively different and strongly model dependent.

ON THE COEXISTENCE AND COEVOLUTION OF ASEXUAL AND SEXUAL COMPETITORS

The coexistence and coevolution of sexual and asexual species under resource competition are explored with three models: a nongenetic ecological model, a model including single locus genetics, and a quantitative-genetic model. The basic assumption underlying all three models is that genetic differences are translated into ecological differences. Hence if sexual species are genetically more variable, they will be ecologically more variable. Under classical competition theory, this increased ecological variability can, in many cases, be an advantage to individual sexual genotypes and to the sexual species as a whole. The purpose of this paper is to determine the conditions when this advantage will outway three disadvantages of sexuality: the costs of males, of segregation, and of the additive component of recombination. All three models reach similar conclusions. Although asexuality confers an advantage, it is much less than a two-fold advantage because minor increases in the overall species niche width of the sexual species will offset the reproductive advantage of the asexual species. This occurs for two reasons. First, an increase in species niche width increases the resource base of the sexual species. Second, to the extent that the increase in niche width is due to increased differences between individuals, a reduction in intraspecific competition will result. This is not to imply that the sexual species will always win. The prime conditions that enable sexual species to stably coexist with or even supplant an asexual sister species are: relatively high between-genotype (but within-species) niche differentiation; significant niche differences between the species; low environmental variance; severe resource exploitation; larger within-phenotype niche width in the sexual species than in the asexual species. Spatial or temporal heterogeneities are not required in this model. This is an important difference between this model and other models for sexual advantage. Instead, depletion of resources used by common genotypes creates a rare-genotype advantage. The sexual species, with its great diversity of genotypes, is better equipped to capture this advantage. Although the mechanisms of our model are framed in terms of competition for shared resources, the important factor is that it generates frequency-dependent fitnesses. Other frequency-dependent ecological mechanisms, such as shared predators with functional responses, or shared genotypically-specific parasites, would work as well.

An updated perspective on the role of environmental autocorrelation in animal populations

Ecological theory predicts that the presence of temporal autocorrelation in environments can considerably affect population extinction risk. However, empirical estimates of autocorrelation values in animal populations have not decoupled intrinsic growth and density feedback processes from environmental autocorrelation. In this study we first discuss how the autocorrelation present in environmental covariates can be reduced through nonlinear interactions or by interactions with multiple limiting resources. We then estimated the degree of environmental autocorrelation present in the Global Population Dynamics Database using a robust, model-based approach. Our empirical results indicate that time series of animal populations are affected by low levels of environmental autocorrelation, a result consistent with predictions from our theoretical models. Claims supporting the importance of autocorrelated environments have been largely based on indirect empirical measures and theoretical models seldom anchored in realistic assumptions. It is likely that a more nuanced understanding of the effects of autocorrelated environments is necessary to reconcile our conclusions with previous theory. We anticipate that our findings and other recent results will lead to improvements in understanding how to incorporate fluctuating environments into population risk assessments.

Development and Validation of the Conceptual Assessment of Natural Selection (CANS)

We developed and validated the Conceptual Assessment of Natural Selection (CANS), a multiple-choice test designed to assess how well college students understand the central principles of natural selection. The expert panel that reviewed the CANS concluded its questions were relevant to natural selection and generally did a good job sampling the specific concepts they were intended to assess. Student interviews confirmed questions on the CANS provided accurate reflections of how students think about natural selection. And, finally, statistical analysis of student responses using item response theory showed that the CANS did a very good job of estimating how well students understood natural selection. The empirical reliability of the CANS was substantially higher than the Force Concept Inventory, a highly regarded test in physics that has a similar purpose.

Assessing parameter identifiability in phylogenetic models using data cloning

The success of model-based methods in phylogenetics has motivated much research aimed at generating new, biologically informative models. This new computer-intensive approach to phylogenetics demands validation studies and sound measures of performance. To date there has been little practical guidance available as to when and why the parameters in a particular model can be identified reliably. Here, we illustrate how Data Cloning (DC), a recently developed methodology to compute the maximum likelihood estimates along with their asymptotic variance, can be used to diagnose structural parameter nonidentifiability (NI) and distinguish it from other parameter estimability problems, including when parameters are structurally identifiable, but are not estimable in a given data set (INE), and when parameters are identifiable, and estimable, but only weakly so (WE). The application of the DC theorem uses well-known and widely used Bayesian computational techniques. With the DC approach, practitioners can use Bayesian phylogenetics software to diagnose nonidentifiability. Theoreticians and practitioners alike now have a powerful, yet simple tool to detect nonidentifiability while investigating complex modeling scenarios, where getting closed-form expressions in a probabilistic study is complicated. Furthermore, here we also show how DC can be used as a tool to examine and eliminate the influence of the priors, in particular if the process of prior elicitation is not straightforward. Finally, when applied to phylogenetic inference, DC can be used to study at least two important statistical questions: assessing identifiability of discrete parameters, like the tree topology, and developing efficient sampling methods for computationally expensive posterior densities.

Replicated sampling increases efficiency in monitoring biological populations

Observation or sampling error in population monitoring can cause serious degradation of the inferences, such as estimates of trend or risk, that ecologists and managers frequently seek to make with time-series observations of population abundances. We show that replicating the sampling process can considerably improve the information obtained from population monitoring. At each sampling time the sampling method would be repeated, either simultaneously or within a short time. In this study we examine the potential value of replicated sampling to population monitoring using a density-dependent population model. We modify an existing population time-series model, the Gompertz state-space model, to incorporate replicated sampling, and we develop maximum-likelihood and restricted maximum-likelihood estimates of model parameters. Depending on sampling protocols, replication may or may not entail substantial extra cost. Some sampling programs already have replicated samples, but the samples are aggregated or pooled into one estimate of population abundance; such practice of aggregating samples, according to our model, loses considerable information about model parameters. The gains from replicated sampling are realized in substantially improved statistical inferences about model parameters, especially inferences for sorting out the contributions of process noise and observation error to observed population variability.

Hybridization rapidly reduces fitness of a native trout in the wild

Human-mediated hybridization is a leading cause of biodiversity loss worldwide. How hybridization affects fitness and what level of hybridization is permissible pose difficult conservation questions with little empirical information to guide policy and management decisions. This is particularly true for salmonids, where widespread introgression among non-native and native taxa has often created hybrid swarms over extensive geographical areas resulting in genomic extinction. Here, we used parentage analysis with multilocus microsatellite markers to measure how varying levels of genetic introgression with non-native rainbow trout (Oncorhynchus mykiss) affect reproductive success (number of offspring per adult) of native westslope cutthroat trout (Oncorhynchus clarkii lewisi) in the wild. Small amounts of hybridization markedly reduced fitness of male and female trout, with reproductive success sharply declining by approximately 50 per cent, with only 20 per cent admixture. Despite apparent fitness costs, our data suggest that hybridization may spread due to relatively high reproductive success of first-generation hybrids and high reproductive success of a few males with high levels of admixture. This outbreeding depression suggests that even low levels of admixture may have negative effects on fitness in the wild and that policies protecting hybridized populations may need reconsideration.

Relative growth rates of predator and prey dinosaurs reflect effects of predation

Hadrosaurs grew rapidly, and quantifying their growth is key to understanding life-history interactions between predators and prey during the Late Cretaceous. In this study, we longitudinally sampled a sequence of lines of arrested growth (LAGs) from an essentially full-grown hadrosaur Hypacrosaurus stebingeri (MOR 549). Spatial locations of LAGs in the femoral and tibial transverse sections of MOR 549 were measured and circumferences were calculated. For each bone, a time series of circumference data was fitted to several stochastic, discrete growth models. Our results suggest that the femur and the tibia of this specimen of Hypacrosaurus probably followed a Gompertz curve and that LAGs reportedly missing from early ontogeny were obscured by perimedullary resorption. In this specimen, death occurred at 13 years and took approximately 10-12 years to reach 95 per cent asymptotic size. The age at growth inflection, which is a proxy for reproductive maturity, occurred at approximately 2-3 years. Comparisons with several small and large predatory theropods reveal that MOR 549 grew faster and matured sooner than they did. These results suggest that Hypacrosaurus was able to partly avoid predators by outgrowing them.

Effects of tourists on behavior and demography of Olympic marmots

If changes in animal behavior resulting from direct human disturbance negatively affect the persistence of a given species or population, then these behavioral changes must necessarily lead to reduced demographic performance. We tested for the effects of human disturbance on Olympic marmots (Marmota olympus), a large ground-dwelling squirrel that has disappeared from several areas where recreation levels are high. We assessed the degree to which antipredator and foraging behavior and demographic rates (survival and reproduction) differed between sites with high recreation levels (high use) and those with little or no recreation (low use). Compared with the marmots at low-use sites, marmots at high-use sites displayed significantly reduced responses to human approach, which could be construed as successful accommodation of disturbance or as a decrease in predator awareness. The marmots at high-use sites also looked up more often while foraging, which suggests an increased wariness. Marmots at both types of sites had comparable reproductive and survival rates and were in similar body condition. Until now, the supposition that marmots can adjust their behavior to avoid negative demographic consequences when confronted with heavy tourism has been based on potentially ambiguous behavioral data. Our results support this hypothesis in the case of Olympic marmots and demonstrate the importance of considering demographic data when evaluating the impacts of recreation on animal populations.

Revising how the computer program CERVUS accommodates genotyping error increases success in paternity assignment

Genotypes are frequently used to identify parentage. Such analysis is notoriously vulnerable to genotyping error, and there is ongoing debate regarding how to solve this problem. Many scientists have used the computer program CERVUS to estimate parentage, and have taken advantage of its option to allow for genotyping error. In this study, we show that the likelihood equations used by versions 1.0 and 2.0 of CERVUS to accommodate genotyping error miscalculate the probability of observing an erroneous genotype. Computer simulation and reanalysis of paternity in Rum red deer show that correcting this error increases success in paternity assignment, and that there is a clear benefit to accommodating genotyping errors when errors are present. A new version of CERVUS (3.0) implementing the corrected likelihood equations is available at http://www.fieldgenetics.com.

Can random mutation mimic design?: a guided inquiry laboratory for undergraduate students

Complex biological structures, such as the human eye, have been interpreted as evidence for a creator for over three centuries. This raises the question of whether random mutation can create such adaptations. In this article, we present an inquiry-based laboratory experiment that explores this question using paper airplanes as a model organism. The main task for students in this investigation is to figure out how to simulate paper airplane evolution (including reproduction, inheritance, mutation, and selection). In addition, the lab requires students to practice analytic thinking and to carefully delineate the implications of their results.

How are humans related to other primates? A guided inquiry laboratory for undergraduate students

Understanding that phylogenies depict the evolutionary history of species is a critical concept for undergraduate biology students. We present an inquiry-based laboratory exercise exploring this concept in the context of the human phylogeny. This activity reinforces several important biological concepts and skills. Bolstered concepts include that evolution is descent with modification, that evolution is a genetic process, and that humans are closely related to apes. In terms of thinking skills, the lab gives students practice with hypothetical-deductive thinking, quantifying patterns from complex data, and evaluating evidence.

Interspecific Competition, Environmental Gradients, Gene Flow, and the Coevolution of Species' Borders

Darwin viewed species range limits as chiefly determined by an interplay between the abiotic environment and interspecific interactions. Haldane argued that species' ranges could be set intraspecifically when gene flow from a species' populous center overwhelms local adaptation at the periphery. Recently, Kirkpatrick and Barton have modeled Haldane's process with a quantitative genetic model that combines density-dependent local population growth with dispersal and gene flow across a linear environmental gradient in optimum phenotype. To address Darwin's ideas, we have extended the Kirkpatrick and Barton model to include interspecific competition and the frequency-dependent selection that it generates, as well as stabilizing selection on a quantitative character. Our model includes local population growth, movements over space, natural selection, and gene flow. It simultaneously addresses the evolution of character displacement and species borders. It reproduces the Kirkpatrick and Barton single-species result that limited ranges can be produced with sufficiently steep environmental gradients and strong dispersal. Further, in the absence of environmental gradients or barriers to dispersal, interspecific competition will not limit species ranges at evolutionary equilibrium. However, interspecific competition can interact with environmental gradients and gene flow to generate limited ranges with much less extreme gradient and dispersal parameters than in the single-species case. Species display character displacement in sympatry, yet the reduction in competition that results from this displacement does not necessarily allow the two species to become sympatric everywhere. When species meet, competition reduces population densities in the region of overlap, which, in turn, intensifies the asymmetry in gene flow from center to margin. This reduces the ability of each species to adapt to local physical conditions at their range limits. If environmental gradients are monotonic but not linear, the transition zone between species at coevolutionary equilibrium occurs where the environmental gradient is steepest. If productivity gradients are also introduced into the model, then patterns similar to Rapoport's rule emerge. Interacting species respond to climate change, as it affects the optimal phenotype over space, by a combination of range shifts and local evolution in mean phenotype, while solitary species respond solely by range shifts. Finally, we compare empirical estimates for intrinsic growth rates and diffusion coefficients for several species to those needed by the single-species model to produce a stable limited range. These empirical values are generally insufficient to produce limited ranges in the model suggesting a role for interspecific interactions.