Hidden variable models reveal the effects of infection from changes in host survival.

The impacts of disease on host vital rates can be demonstrated using longitudinal studies, but these studies can be expensive and logistically challenging. We examined the utility of hidden variable models to infer the individual effects of infectious disease from population-level measurements of survival when longitudinal studies are not possible. Our approach seeks to explain temporal deviations in population-level survival after introducing a disease causative agent when disease prevalence cannot be directly measured by coupling survival and epidemiological models. We tested this approach using an experimental host system (Drosophila melanogaster) with multiple distinct pathogens to validate the ability of the hidden variable model to infer per-capita disease rates. We then applied the approach to a disease outbreak in harbor seals (Phoca vituline) that had data on observed strandings but no epidemiological data. We found that our hidden variable modeling approach could successfully detect the per-capita effects of disease from monitored survival rates in both the experimental and wild populations. Our approach may prove useful for detecting epidemics from public health data in regions where standard surveillance techniques are not available and in the study of epidemics in wildlife populations, where longitudinal studies can be especially difficult to implement.

Ecological forecasts reveal limitations of common model selection methods: predicting changes in beaver colony densities.

Over the past two decades, there have been numerous calls to make ecology a more predictive science through direct empirical assessments of ecological models and predictions. While the widespread use of model selection using information criteria has pushed ecology toward placing a higher emphasis on prediction, few attempts have been made to validate the ability of information criteria to correctly identify the most parsimonious model with the greatest predictive accuracy. Here, we used an ecological forecasting framework to test the ability of information criteria to accurately predict the relative contribution of density dependence and density-independent factors (forage availability, harvest, weather, wolf [Canis lupus] density) on inter-annual fluctuations in beaver (Castor canadensis) colony densities. We modeled changes in colony densities using a discrete-time Gompertz model, and assessed the performance of four models using information criteria values: density-independent models with (1) and without (2) environmental covariates; and density-dependent models with (3) and without (4) environmental covariates. We then evaluated the forecasting accuracy of each model by withholding the final one-third of observations from each population and compared observed vs. predicted densities. Information criteria and our forecasting accuracy metrics both provided strong evidence of compensatory density dependence in the annual dynamics of beaver colony densities. However, despite strong within-sample performance by the most complex model (density-dependent with covariates) as determined using information criteria, hindcasts of colony densities revealed that the much simpler density-dependent model without covariates performed nearly as well predicting out-of-sample colony densities. The hindcast results indicated that the complex model over-fit our data, suggesting that parameters identified by information criteria as important predictor variables are only marginally valuable for predicting landscape-scale beaver colony dynamics. Our study demonstrates the importance of evaluating ecological models and predictions with long-term data and revealed how a known limitation of information criteria (over-fitting of complex models) can affect our interpretation of ecological dynamics. While incorporating knowledge of the factors that influence animal population dynamics can improve population forecasts, we suggest that comparing forecast performance metrics can likewise improve our knowledge of the factors driving population dynamics.

Reintroduced wolves and hunting limit the abundance of a subordinate apex predator in a multi-use landscape.

Top-down effects of apex predators are modulated by human impacts on community composition and species abundances. Consequently, research supporting top-down effects of apex predators occurs almost entirely within protected areas rather than the multi-use landscapes dominating modern ecosystems. Here, we developed an integrated population model to disentangle the concurrent contributions of a reintroduced apex predator, the grey wolf, human hunting and prey abundances on vital rates and abundance of a subordinate apex predator, the puma. Increasing wolf numbers had strong negative effects on puma fecundity, and subadult and adult survival. Puma survival was also influenced by density dependence. Overall, puma dynamics in our multi-use landscape were more strongly influenced by top-down forces exhibited by a reintroduced apex predator, than by human hunting or bottom-up forces (prey abundance) subsidized by humans. Quantitatively, the average annual impact of human hunting on equilibrium puma abundance was equivalent to the effects of 20 wolves. Historically, wolves may have limited pumas across North America and dictated puma scarcity in systems lacking sufficient refugia to mitigate the effects of competition.

A two-stage experimental design for dilution assays.

Dilution assays to determine solute concentration have found wide use in biomedical research. Many dilution assays return imprecise concentration estimates because they are only done to orders of magnitude. Previous statistical work has focused on how to design efficient experiments that can return more precise estimates, however this work has not considered the practical difficulties of implementing these designs in the laboratory. We developed a two-stage experiment with a first stage that obtains an order of magnitude estimate and a second stage that concentrates effort on the most informative dilution to increase estimator precision. We show using simulations and an empirical example that the best two-stage experimental designs yield estimates that are remarkably more accurate than standard methods with equivalent effort. This work demonstrates how to utilize previous advances in experimental design in a manner consistent with current laboratory practice. We expect that multi-stage designs will prove to be useful for obtaining precise estimates with minimal experimental effort.

Inference from the stationary distribution of allele frequencies in a family of Wright-Fisher models with two levels of genetic variability.

The distribution of allele frequencies obtained from diffusion approximations to Wright-Fisher models is useful in developing intuition about the population level effects of evolutionary processes. The statistical properties of the stationary distributions of K-allele models have been extensively studied under neutrality or under selection. Here, we introduce a new family of Wright-Fisher models in which there are two hierarchical levels of genetic variability. The genotypes composed of alleles differing from each other at the selected level have fitness differences with respect to each other and evolve under selection. The genotypes composed of alleles differing from each other only at the neutral level have the same fitness and evolve under neutrality. We show that with an appropriate scaling of the mutation parameter with respect to the number of alleles at each level, the frequencies of alleles at the selected and the neutral level are conditionally independent of each other, conditional on knowing the number of alleles at all levels. This conditional independence allows us to simulate from the joint stationary distribution of the allele frequencies. We use these simulated frequencies to perform inference on parameters of the model with two levels of genetic variability using Approximate Bayesian Computation.

Evidence and implications of higher-order scaling in the environmental variation of animal population growth.

Environmental stochasticity is an important concept in population dynamics, providing a quantitative model of the extrinsic fluctuations driving population abundances. It is typically formulated as a stochastic perturbation to the maximum reproductive rate, leading to a population variance that scales quadratically with abundance. However, environmental fluctuations may also drive changes in the strength of density dependence. Very few studies have examined the consequences of this alternative model formulation while even fewer have tested which model better describes fluctuations in animal populations. Here we use data from the Global Population Dynamics Database to determine the statistical support for this alternative environmental variance model in 165 animal populations and test whether these models can capture known population-environment interactions in two well-studied ungulates. Our results suggest that variation in the density dependence is common and leads to a higher-order scaling of the population variance. This scaling will often stabilize populations although dynamics may also be destabilized under certain conditions. We conclude that higher-order environmental variation is a potentially ubiquitous and consequential property of animal populations. Our results suggest that extinction risk estimates may often be overestimated when not properly taking into account how environmental fluctuations affect population parameters.

Detecting population-environmental interactions with mismatched time series data.

Time series analysis is an essential method for decomposing the influences of density and exogenous factors such as weather and climate on population regulation. However, there has been little work focused on understanding how well commonly collected data can reconstruct the effects of environmental factors on population dynamics. We show that, analogous to similar scale issues in spatial data analysis, coarsely sampled temporal data can fail to detect covariate effects when interactions occur on timescales that are fast relative to the survey period. We propose a method for modeling mismatched time series data that couples high-resolution environmental data to low-resolution abundance data. We illustrate our approach with simulations and by applying it to Florida's southern Snail kite population. Our simulation results show that our method can reliably detect linear environmental effects and that detecting nonlinear effects requires high-resolution covariate data even when the population turnover rate is slow. In the Snail kite analysis, our approach performed among the best in a suite of previously used environmental covariates explaining Snail kite dynamics and was able to detect a potential phenological shift in the environmental dependence of Snail kites. Our work provides a statistical framework for reliably detecting population-environment interactions from coarsely surveyed time series. An important implication of this work is that the low predictability of animal population growth by weather variables found in previous studies may be due, in part, to how these data are utilized as covariates.

Loss of animal seed dispersal increases extinction risk in a tropical tree species due to pervasive negative density dependence across life stages.

Overhunting in tropical forests reduces populations of vertebrate seed dispersers. If reduced seed dispersal has a negative impact on tree population viability, overhunting could lead to altered forest structure and dynamics, including decreased biodiversity. However, empirical data showing decreased animal-dispersed tree abundance in overhunted forests contradict demographic models which predict minimal sensitivity of tree population growth rate to early life stages. One resolution to this discrepancy is that seed dispersal determines spatial aggregation, which could have demographic consequences for all life stages. We tested the impact of dispersal loss on population viability of a tropical tree species, Miliusa horsfieldii, currently dispersed by an intact community of large mammals in a Thai forest. We evaluated the effect of spatial aggregation for all tree life stages, from seeds to adult trees, and constructed simulation models to compare population viability with and without animal-mediated seed dispersal. In simulated populations, disperser loss increased spatial aggregation by fourfold, leading to increased negative density dependence across the life cycle and a 10-fold increase in the probability of extinction. Given that the majority of tree species in tropical forests are animal-dispersed, overhunting will potentially result in forests that are fundamentally different from those existing now.

Optimal sampling strategies for detecting zoonotic disease epidemics.

The early detection of disease epidemics reduces the chance of successful introductions into new locales, minimizes the number of infections, and reduces the financial impact. We develop a framework to determine the optimal sampling strategy for disease detection in zoonotic host-vector epidemiological systems when a disease goes from below detectable levels to an epidemic. We find that if the time of disease introduction is known then the optimal sampling strategy can switch abruptly between sampling only from the vector population to sampling only from the host population. We also construct time-independent optimal sampling strategies when conducting periodic sampling that can involve sampling both the host and the vector populations simultaneously. Both time-dependent and -independent solutions can be useful for sampling design, depending on whether the time of introduction of the disease is known or not. We illustrate the approach with West Nile virus, a globally-spreading zoonotic arbovirus. Though our analytical results are based on a linearization of the dynamical systems, the sampling rules appear robust over a wide range of parameter space when compared to nonlinear simulation models. Our results suggest some simple rules that can be used by practitioners when developing surveillance programs. These rules require knowledge of transition rates between epidemiological compartments, which population was initially infected, and of the cost per sample for serological tests.

Predicting the process of extinction in experimental microcosms and accounting for interspecific interactions in single-species time series.

Predicting population extinction risk is a fundamental application of ecological theory to the practice of conservation biology. Here, we compared the prediction performance of a wide array of stochastic, population dynamics models against direct observations of the extinction process from an extensive experimental data set. By varying a series of biological and statistical assumptions in the proposed models, we were able to identify the assumptions that affected predictions about population extinction. We also show how certain autocorrelation structures can emerge due to interspecific interactions, and that accounting for the stochastic effect of these interactions can improve predictions of the extinction process. We conclude that it is possible to account for the stochastic effects of community interactions on extinction when using single-species time series.

The importance of long-distance seed dispersal for the demography and distribution of a canopy tree species.

Long-distance seed dispersal (LDD) is considered a crucial determinant of tree distributions, but its effects depend on demographic processes that enable seeds to establish into adults and that remain poorly understood at large spatial scales. We estimated rates of seed arrival, germination, and survival and growth for a canopy tree species (Miliusa horsfieldii), in a landscape ranging from evergreen forest, where the species' abundance is high, to deciduous forest, where it is extremely low. We then used an individual-based model (IBM) to predict sapling establishment and to compare the relative importance of seed arrival and establishment in explaining the observed distribution of seedlings. Individuals in deciduous forest, far from the source population, experienced multiple benefits (e.g., increased germination rate and seedling survival and growth) from being in a habitat where conspecifics were almost absent. The net effect of these spatial differences in demographic processes was significantly higher estimated sapling establishment probabilities for seeds dispersed long distances into deciduous forest. Despite the high rate of establishment in this habitat, Miliusa is rare in the deciduous forest because the arrival of seeds at long distances from the source population is extremely low. Across the entire landscape, the spatial pattern of seed arrival is much more important than the spatial pattern of establishment for explaining observed seedling distributions. By using dynamic models to link demographic data to spatial patterns, we show that LDD plays a pivotal role in the distribution of this tree in its native habitat.

A framework for modeling the impacts of adaptive search intensity on the efficiency of abundance surveys.

When planning abundance surveys, the impact of search intensity on the quality of the density estimates is rarely considered. We constructed a time-budget modeling framework for abundance surveys using principles from optimal foraging theory. We link search intensity to the number of sample units surveyed, searcher detection probability, the number of detections made, and the precision of the estimated population density. This framework allowed us to determine how a searcher should behave to produce optimized density estimates. Using data collected from quadrat and removal surveys of zebra mussels (Dreissena polymorpha) in central Minnesota, we applied this framework to evaluate potential improvements. We found that by tuning searcher behavior, density estimates from removal surveys of zebra mussels could be improved by up to 60% in some cases, without changing the overall survey time. Our framework also predicts a critical population density where the best survey method switches from removal surveys at low densities to quadrat surveys at high densities, consistent with past empirical work. In addition, we provide simulation tools to apply this form of analysis to a number of other commonly used survey designs. Our results provide insights into how to improve the performance of many survey methods in high-density environments by either tuning searcher behavior or decoupling the estimation of population density and detection probability.

A comparison of survey method efficiencies for estimating densities of zebra mussels (Dreissena polymorpha).

Abundance surveys are commonly used to estimate plant or animal densities and frequently require estimating detection probabilities to account for imperfect detection. The estimation of detection probabilities requires additional measurements that take time, potentially reducing the efficiency of the survey when applied to high-density populations. We conducted quadrat, removal, and distance surveys of zebra mussels (Dreissena polymorpha) in three central Minnesota lakes and determined how much survey effort would be required to achieve a pre-specified level of precision for each abundance estimator, allowing us to directly compare survey design efficiencies across a range of conditions. We found that the required sampling effort needed to achieve our precision goal depended on both the survey design and population density. At low densities, survey designs that could cover large areas but with lower detection probabilities, such as distance surveys, were more efficient (i.e., required less sampling effort to achieve the same level of precision). However, at high densities, quadrat surveys, which tend to cover less area but with high detection rates, were more efficient. These results demonstrate that the best survey design is likely to be context-specific, requiring some prior knowledge of the underlying population density and the cost/time needed to collect additional information for estimating detection probabilities.

Linking beaver dam affected flow dynamics to upstream passage of Arctic grayling.

Beaver reintroductions and beaver dam structures are an increasingly utilized ecological tool for rehabilitating degraded streams, yet beaver dams can potentially impact upstream fish migrations. We collected two years of data on Arctic grayling movement through a series of beaver dams in a low gradient mountain stream, utilizing radio-telemetry techniques, to determine how hydrology, dam characteristics, and fish attributes impeded passage and movement rates of spawning grayling. We compared fish movement between a "normal" flow year and a "low" flow year, determined grayling passage probabilities over dams in relation to a suite of factors, and predicted daily movement rates in relation to the number of dams each fish passed and distance between dams during upstream migration to spawning areas. We found that the average passage probability over unbreached beaver dams was 88%, though we found that it fell below 50% at specific dams. Upstream passage of grayling was affected by three main characteristics: (a) temperature, (b) breach status, and (c) hydrologic linkages that connect sections of stream above and below the dam. Other variables influence passage, but to a lesser degree. Cumulative passage varied with distance upstream and total number of dams passed in low versus normal flow years, while movement rates upstream slowed as fish swam closer to dams. Our findings demonstrate that upstream passage of fish over beaver dams is strongly correlated with hydrologic conditions with moderate controls by dam- and fish-level characteristics. Our results provide a framework that can be applied to reduce barrier effects when and where beaver dams pose a significant threat to the upstream migration of fish populations while maintaining the diverse ecological benefits of beaver activity when dams are not a threat to fish passage.

Metrics for Performance Evaluation of Patient Exercises during Physical Therapy.

OBJECTIVE: The article proposes a set of metrics for evaluation of patient performance in physical therapy exercises. METHODS: Taxonomy is employed that classifies the metrics into quantitative and qualitative categories, based on the level of abstraction of the captured motion sequences. Further, the quantitative metrics are classified into model-less and model-based metrics, in reference to whether the evaluation employs the raw measurements of patient performed motions, or whether the evaluation is based on a mathematical model of the motions. The reviewed metrics include root-mean square distance, Kullback Leibler divergence, log-likelihood, heuristic consistency, Fugl-Meyer Assessment, and similar. RESULTS: The metrics are evaluated for a set of five human motions captured with a Kinect sensor. CONCLUSION: The metrics can potentially be integrated into a system that employs machine learning for modelling and assessment of the consistency of patient performance in home-based therapy setting. Automated performance evaluation can overcome the inherent subjectivity in human performed therapy assessment, and it can increase the adherence to prescribed therapy plans, and reduce healthcare costs.

Selecting the best stable isotope mixing model to estimate grizzly bear diets in the Greater Yellowstone Ecosystem.

Past research indicates that whitebark pine seeds are a critical food source for Threatened grizzly bears (Ursus arctos) in the Greater Yellowstone Ecosystem (GYE). In recent decades, whitebark pine forests have declined markedly due to pine beetle infestation, invasive blister rust, and landscape-level fires. To date, no study has reliably estimated the contribution of whitebark pine seeds to the diets of grizzlies through time. We used stable isotope ratios (expressed as δ13C, δ15N, and δ34S values) measured in grizzly bear hair and their major food sources to estimate the diets of grizzlies sampled in Cooke City Basin, Montana. We found that stable isotope mixing models that included different combinations of stable isotope values for bears and their foods generated similar proportional dietary contributions. Estimates generated by our top model suggest that whitebark pine seeds (35±10%) and other plant foods (56±10%) were more important than meat (9±8%) to grizzly bears sampled in the study area. Stable isotope values measured in bear hair collected elsewhere in the GYE and North America support our conclusions about plant-based foraging. We recommend that researchers consider model selection when estimating the diets of animals using stable isotope mixing models. We also urge researchers to use the new statistical framework described here to estimate the dietary responses of grizzlies to declines in whitebark pine seeds and other important food sources through time in the GYE (e.g., cutthroat trout), as such information could be useful in predicting how the population will adapt to future environmental change.

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.

Animal-borne imaging reveals novel insights into the foraging behaviors and Diel activity of a large-bodied apex predator, the American alligator (Alligator mississippiensis).

Large-bodied, top- and apex predators (e.g., crocodilians, sharks, wolves, killer whales) can exert strong top-down effects within ecological communities through their interactions with prey. Due to inherent difficulties while studying the behavior of these often dangerous predatory species, relatively little is known regarding their feeding behaviors and activity patterns, information that is essential to understanding their role in regulating food web dynamics and ecological processes. Here we use animal-borne imaging systems (Crittercam) to study the foraging behavior and activity patterns of a cryptic, large-bodied predator, the American alligator (Alligator mississippiensis) in two estuaries of coastal Florida, USA. Using retrieved video data we examine the variation in foraging behaviors and activity patterns due to abiotic factors. We found the frequency of prey-attacks (mean = 0.49 prey attacks/hour) as well as the probability of prey-capture success (mean = 0.52 per attack) were significantly affected by time of day. Alligators attempted to capture prey most frequently during the night. Probability of prey-capture success per attack was highest during morning hours and sequentially lower during day, night, and sunset, respectively. Position in the water column also significantly affected prey-capture success, as individuals' experienced two-fold greater success when attacking prey while submerged. These estimates are the first for wild adult American alligators and one of the few examples for any crocodilian species worldwide. More broadly, these results reveal that our understandings of crocodilian foraging behaviors are biased due to previous studies containing limited observations of cryptic and nocturnal foraging interactions. Our results can be used to inform greater understanding regarding the top-down effects of American alligators in estuarine food webs. Additionally, our results highlight the importance and power of using animal-borne imaging when studying the behavior of elusive large-bodied, apex predators, as it provides critical insights into their trophic and behavioral interactions.

Estimating the diets of animals using stable isotopes and a comprehensive Bayesian mixing model.

Using stable isotope mixing models (SIMMs) as a tool to investigate the foraging ecology of animals is gaining popularity among researchers. As a result, statistical methods are rapidly evolving and numerous models have been produced to estimate the diets of animals--each with their benefits and their limitations. Deciding which SIMM to use is contingent on factors such as the consumer of interest, its food sources, sample size, the familiarity a user has with a particular framework for statistical analysis, or the level of inference the researcher desires to make (e.g., population- or individual-level). In this paper, we provide a review of commonly used SIMM models and describe a comprehensive SIMM that includes all features commonly used in SIMM analysis and two new features. We used data collected in Yosemite National Park to demonstrate IsotopeR's ability to estimate dietary parameters. We then examined the importance of each feature in the model and compared our results to inferences from commonly used SIMMs. IsotopeR's user interface (in R) will provide researchers a user-friendly tool for SIMM analysis. The model is also applicable for use in paleontology, archaeology, and forensic studies as well as estimating pollution inputs.