Neighborhood and habitat effects on vital rates: expansion of the Barred Owl in the Oregon coast ranges

In this paper, we modify dynamic occupancy models developed for detection-nondetection data to allow for the dependence of local vital rates on neighborhood occupancy, where neighborhood is defined very flexibly. Such dependence of occupancy dynamics on the status of a relevant neighborhood is pervasive, yet frequently ignored. Our framework permits joint inference about the importance of neighborhood effects and habitat covariates in determining colonization and extinction rates. Our specific motivation is the recent expansion of the Barred Owl (Strix varia) in western Oregon, USA, over the period 1990-2010. Because the focal period was one of dramatic range expansion and local population increase, the use of models that incorporate regional occupancy (sources of colonists) as determinants of dynamic rate parameters is especially appropriate. We began our analysis of 21 years of Barred Owl presence/nondetection data in the Tyee Density Study Area (TDSA) by testing a suite of six models that varied only in the covariates included in the modeling of detection probability. We then tested whether models that used regional occupancy as a covariate for colonization and extinction outperformed models with constant or year-specific colonization or extinction rates. Finally we tested whether habitat covariates improved the AIC of our models, focusing on which habitat covariates performed best, and whether the signs of habitat effects are consistent with a priori hypotheses. We conclude that all covariates used to model detection probability lead to improved AIC, that regional occupancy influences colonization and extinction rates, and that habitat plays an important role in determining extinction and colonization rates. As occupancy increases from low levels toward equilibrium, colonization increases and extinction decreases, presumably because there are more and more dispersing juveniles. While both rates are affected, colonization increases more than extinction decreases. Colonization is higher and extinction is lower in survey polygons with more riparian forest. The effects of riparian forest on extinction rates are greater than on colonization rates. Model results have implications for management of the invading Barred Owl, both through habitat alteration and removal.     

Seasonal density dependence, timing of mortality, and sustainable harvesting

Birth-pulse populations are often characterized with discrete-time models, that use a single function to relate the post-breeding population size to the post-breeding size of the previous year. Recently, models of seasonal density dependence have been constructed that emphasize interactions during shorter time periods also. Here, we study two very simple forms of density-dependent mortality, that lead to Ricker and Beverton-Holt type population dynamics when viewed over the whole year. We explore the consequences of harvest timing to equilibrium population sizes under such density dependence. Whether or not individual mortality compensates for the harvested quota, the timing of harvesting has a strong impact on the sustainability of a harvesting quota. Further, we show that careless discretization of a continuous mortality scheme may seriously underestimate the reduction in population size caused by hunting and overestimate the sustainable yield. We also introduce the concept of the demographic value of an individual, which reflects the expected contribution to population size over time in the presence of density dependence. Finally, we discuss the possibility of calculating demographic values as means of optimizing harvest strategies. Here, a Pareto optimal harvest strategy will minimize the loss of demographic value from the population for a given yield.     

Reconstructibility of Density Dependence and the Conservative Assessment of Extinction Risks

Abstract: The probability of extinction is sensitive to the presence and character of density dependence controlling the dynamics of a population. This means that our capacity to estimate a population's risks of extinction under varying environmental conditions or competing management regimes is linked to our ability to reconstruct from data the density-dependence relationships governing the natural dynamics, especially when data do not reveal a trend of population growth or decline. In an example using Gadus morhua , we show that even 10- or 20-year data sets are too short to make precise estimates of these risks. We also observe, however, that under moderate or weak density dependence, the computed risks are lower than when density dependence is not included in the model. We propose, therefore, that when available data sets are insufficient for reconstructing reliable measurements of density dependence, conservative estimates of extinction probabilities can be made from models that simply omit density dependence.     

Ability of Matrix Models to Explain the Past and Predict the Future of Plant Populations

Uncertainty associated with ecological forecasts has long been recognized, but forecast accuracy is rarely quantified. We evaluated how well data on 82 populations of 20 species of plants spanning 3 continents explained and predicted plant population dynamics. We parameterized stage‐based matrix models with demographic data from individually marked plants and determined how well these models forecast population sizes observed at least 5 years into the future. Simple demographic models forecasted population dynamics poorly; only 40% of observed population sizes fell within our forecasts’ 95% confidence limits. However, these models explained population dynamics during the years in which data were collected; observed changes in population size during the data‐collection period were strongly positively correlated with population growth rate. Thus, these models are at least a sound way to quantify population status. Poor forecasts were not associated with the number of individual plants or years of data. We tested whether vital rates were density dependent and found both positive and negative density dependence. However, density dependence was not associated with forecast error. Forecast error was significantly associated with environmental differences between the data collection and forecast periods. To forecast population fates, more detailed models, such as those that project how environments are likely to change and how these changes will affect population dynamics, may be needed. Such detailed models are not always feasible. Thus, it may be wiser to make risk‐averse decisions than to expect precise forecasts from models. Habilidad de los Modelos Matriciales para Explicar el Pasado y Predecir el Futuro de las Poblaciones de Plantas     

Regression analysis of forest damage by marginal models for correlated ordinal responses

Studies on forest damage generally cannot be carried out by common regression models, for two main reasons: Firstly, the response variable, damage state of trees, is usually observed in ordered categories. Secondly, responses are often correlated, either serially, as in a longitudinal study, or spatially, as in the application of this paper, where neighbourhood interactions exist between damage states of spruces determined from aerial pictures. Thus so-called marginal regression models for ordinal responses, taking into account dependence among observations, are appropriate for correct inference. To this end we extend the binary models of Liang and Zeger (1986) and develop an ordinal GEEI model, based on parametrizing association by global cross-ratios. The methods are applied to data from a survey conducted in Southern Germany. Due to the survey design, responses must be assumed to be spatially correlated. The results show that the proposed ordinal marginal regression models provide appropriate tools for analysing the influence of covariates, that characterize the stand, on the damage state of spruce.     

Condition dependence of male display coloration in a jumping spider (Habronattus pyrrithrix)

In many animals, conspicuous coloration functions as a quality signal. Indicator models predict that such colors should be variable and condition dependent. In Habronattus pyrrithrix jumping spiders, females are inconspicuously colored, while males display brilliant red faces, green legs, and white pedipalps during courtship. We tested the predictions of the indicator model in a field study and found that male body condition was positively correlated with the size, hue, and red chroma of a male’s facial patch and negatively correlated with the brightness of his green legs. These traits were more condition dependent than non-display colors. We then tested a dietary mechanism for condition dependence using two experiments. To understand how juvenile diet affects the development of coloration, we reared juvenile spiders on high- and low-quality diets and measured coloration at maturity. To understand how adult diet affects the maintenance of coloration, we fed wild-caught adults with high- or low-quality diets and compared their coloration after 45 days. In the first experiment, males fed high-quality diet had redder faces, suggesting that condition dependence is mediated by juvenile diet. In the second experiment, red coloration did not differ between treatments, suggesting that adult diet is not important for maintaining the color after it is produced at maturity. Diet had no effect on green coloration in either experiment. Our results show different degrees of condition dependence for male display colors. Because red is dependent on juvenile diet, it may signal health or foraging ability. We discuss evidence that green coloration is age dependent and alternatives to indicator models for colorful displays in jumping spiders.     

Simulating the fate of Florida Snowy Plovers with sea-level rise: Exploring research and management priorities with a global uncertainty and sensitivity analysis perspective

Changes in coastal habitats due to sea-level rise provide an uncertain, yet significant threat to shoreline dependent birds. Rising sea levels can cause habitat fragmentation and loss which can result in considerable reduction in their foraging and nesting areas. Computational models and their algorithmic assumptions play an integral role in exploring potential mitigation responses to uncertain and potentially adverse ecological outcomes. The presence of uncertainty in metapopulation models is widely acknowledged but seldom considered in their development and evaluation, specifically the effects of uncertain model inputs on the model outputs. This paper was aimed to (1) quantify the contribution of each uncertain input factor to the uncertainty in the output of a metapopulation model which evaluated the effects of long-term sea-level rise on the population of Snowy Plovers (Charadrius alexandrinus) found in the Gulf Coast of Florida, and (2) determine the ranges of model inputs that produced a specific output for the purpose of formulating environmental management decisions. This was carried out by employing global sensitivity and uncertainty analysis (GSA) using two generic (model independent) methods, the qualitative screening Morris method and a quantitative variance-based Sobol’ method coupled with Monte Carlo filtering. The analyses were applied to three density dependence scenarios: assuming a ceiling-type density dependence, assuming a contest-type density dependence, and assuming that density dependence is uncertain as to being ceiling- or contest-dependent. The sources of uncertainty in the outputs depended strongly on the type of density dependence considered in the model. In general, uncertainty in the outputs highly depended on the uncertainty in stage matrix elements (fecundity, adult survival, and juvenile survival), dispersal rate from central areas with low current populations (the “Big Bend” area of Florida) to the northern, panhandle populations, the maximum growth rate, and density dependence type. Our results showed that increasing the maximum growth rate to a value of 1.2 or larger will increase the final average population of Snowy Plovers assuming a contest-type density dependence. Results suggest that studies that further quantify which density dependence relationship best describes Snowy Plover population dynamics should be conducted since this is the main driver of uncertainty in model outcomes. Furthermore, investigating the presence of Snowy Plovers in the Big Bend region may be important for providing connection between the panhandle and peninsula populations.     

Composite likelihood approach to the regression analysis of spatial multivariate ordinal data and spatial compositional data with exact zero values

In many environmental and ecological studies, it is of interest to model compositional data. One approach is to consider positive random vectors that are subject to a unit-sum constraint. In landscape ecological studies, it is common that compositional data are also sampled in space with some elements of the composition absent at certain sampling sites. In this paper, we first propose a practical spatial multivariate ordered probit model for multivariate ordinal data, where the response variables can be viewed as the discretized non-negative compositions without the unit-sum constraint. We then propose a novel two-stage spatial mixture Dirichlet regression model. The first stage models the spatial dependence and the presence of exact zero values, and the second stage models all the non-zero compositional data. A maximum composite likelihood approach is developed for parameter estimation and inference in both the spatial multivariate ordered probit model and the two-stage spatial mixture Dirichlet regression model. The standard errors of the parameter estimates are computed by an estimate of the Godambe information matrix. A simulation study is conducted to evaluate the performance of the proposed models and methods. A land cover data example in landscape ecology further illustrates that accounting for spatial dependence can improve the accuracy in the prediction of presence/absence of different land covers as well as the magnitude of land cover compositions.     

Confronting two-sex demographic models with data

Most population dynamics models explicitly track the density of a single sex. When the operational sex ratio can vary, two-sex models may be needed to understand and predict population trajectories. Various functions have been proposed to describe the relative contributions of females and males to recruitment, and these functions can differ qualitatively in the patterns that they generate. Which mating function best describes the dynamics of real populations is not known, since alternative two-sex models have not been confronted with experimental data. We conducted the first such comparison, using laboratory populations of the bean beetle Callosobruchus maculatus. Manipulations of the operational sex ratio and total density provided strong support for a demographic model in which the birth rate was proportional to the harmonic mean of female and male densities, and females, males, and their offspring made unique contributions to density dependence. We offer guidelines for transferring this approach to other, less tractable systems in which possibilities for sex ratio manipulations are more limited. We show that informative experimental designs require strong perturbations of the operational sex ratio. The functional form of density dependence (saturating vs. over-compensatory) and the relative contributions of each sex to density dependence can both determine in which direction and at which population densities such perturbations would be most informative. Our experimental results and guidelines for design strategies promote synthesis of two-sex population dynamics theory with empirical data.     

Removing the boundary influence on negatively buoyant jets

A comprehensive laboratory study of negatively buoyant discharges is presented. Unlike previous studies, here the focus is on generating data sets where influences of the bottom boundary have been eliminated. There are significant discrepancies in the published dilution data for these flows and a contributing factor is the large variation in the bottom boundary condition. A Laser-induced Fluorescence system is employed to gather flow spread, peak concentration (minimum dilution) and trajectory data for a wide range of densimetric Froude numbers and initial discharge angles. Data from these experiments are compared with previously published data, along with predictions from integral models and a revised form of the previously published semi-analytical solutions. The new data sets are not distorted by mixing processes associated with the bottom boundary and therefore provide the basis for more meaningful assessments of the predictive capabilities of existing models, given that the influences of the bottom boundary on contaminant mixing are not incorporated into these models. In general the models assessed are able to predict key geometric quantities with reasonable accuracy, but their minimum dilution predictions are conservative. Importantly dilution at the return point shows a strong dependence on the initial discharge angle and this could have important implications for the design of discharge systems.     

Traps and transformations influencing the financial viability of tourism on private‐land conservation areas

The ability of private conservation organizations to remain financially viable is a key factor influencing their effectiveness. One‐third of financially motivated private‐land conservation areas (PLCAs) surveyed in South Africa are unprofitable, raising questions about landowners’ abilities to effectively adapt their business models to the socioeconomic environment. In any complex system, options for later adaptation can be constrained by starting conditions (path dependence). We tested 3 hypothesized drivers of path dependence in PLCA ecotourism and hunting business models: (H1) the initial size of a PLCA limits the number of mammalian game and thereby predators that can be sustained; (H2) initial investments in infrastructure limit the ability to introduce predators; and (H3) rainfall limits game and predator abundance. We further assessed how managing for financial stability (optimized game stocking) or ecological sustainability (allowing game to fluctuate with environmental conditions) influenced the ability to overcome path dependence. A mechanistic PLCA model based on simple ecological and financial rules was run for different initial conditions and management strategies, simulating landowner options for adapting their business model annually. Despite attempts by simulated landowners to increase profits, adopted business models after 13 years were differentiated by initial land and infrastructural assets, supporting H1 and H2. A conservation organization's initial assets can cause it to become locked into a financially vulnerable business model. In our 50‐year simulation, path dependence was overcome by fewer of the landowners who facilitated natural ecological variability than those who maintained constant hunting rates and predator numbers, but the latter experienced unsustainably high game densities in low rainfall years. Management for natural variability supported long‐term ecological sustainability but not shorter term socioeconomic sustainability for PLCAs. Our findings highlight trade‐offs between ecological and economic sustainability and suggest a role for governmental support of the private conservation industry.     

Strength of evidence for density dependence in abundance time series of 1198 species

Population limitation is a fundamental tenet of ecology, but the relative roles of exogenous and endogenous mechanisms remain unquantified for most species. Here we used multi-model inference (MMI), a form of model averaging, based on information theory (Akaike's Information Criterion) to evaluate the relative strength of evidence for density-dependent and density-independent population dynamical models in long-term abundance time series of 1198 species. We also compared the MMI results to more classic methods for detecting density dependence: Neyman-Pearson hypothesis-testing and best-model selection using the Bayesian Information Criterion or cross-validation. Using MMI on our large database, we show that density dependence is a pervasive feature of population dynamics (median MMI support for density dependence = 74.7-92.2%), and that this holds across widely different taxa. The weight of evidence for density dependence varied among species but increased consistently, with the number of generations monitored. Best-model selection methods yielded similar results to MMI (a density-dependent model was favored in 66.2-93.9% of species time series), while the hypothesis-testing methods detected density dependence less frequently (32.6-49.8%). There were no obvious differences in the prevalence of density dependence across major taxonomic groups under any of the statistical methods used. These results underscore the value of using multiple modes of analysis to quantify the relative empirical support for a set of working hypotheses that encompass a range of realistic population dynamical behaviors.     

Host-parasitoid dynamics: Effects of the position of density dependence

Four models are presented, two of which have density-dependent regulation in the hosts and two in the parasitoids. Host and parasitoid equilibria are both less with density-dependent regulation in the hosts than in the parasitoids. The percent of hosts parasitized at equilibrium is also less with density dependence in the hosts than in the parasitoids. These results are compared with those from other models.     

Fitting complex population models by combining particle filters with Markov chain Monte Carlo

We show how a recent framework combining Markov chain Monte Carlo (MCMC) with particle filters (PFMCMC) may be used to estimate population state-space models. With the purpose of utilizing the strengths of each method, PFMCMC explores hidden states by particle filters, while process and observation parameters are estimated using an MCMC algorithm. PFMCMC is exemplified by analyzing time series data on a red kangaroo (Macropus rufus) population in New South Wales, Australia, using MCMC over model parameters based on an adaptive Metropolis-Hastings algorithm. We fit three population models to these data; a density-dependent logistic diffusion model with environmental variance, an unregulated stochastic exponential growth model, and a random-walk model. Bayes factors and posterior model probabilities show that there is little support for density dependence and that the random-walk model is the most parsimonious model. The particle filter Metropolis-Hastings algorithm is a brute-force method that may be used to fit a range of complex population models. Implementation is straightforward and less involved than standard MCMC for many models, and marginal densities for model selection can be obtained with little additional effort. The cost is mainly computational, resulting in long running times that may be improved by parallelizing the algorithm.     

The scale and cause of spatial heterogeneity in strength of temporal density dependence

The importance of density dependence in natural communities continues to spark much debate because it is fundamental to population regulation. We used temporal manipulations of density to explore potentially stabilizing density dependence in early survivorship among six local populations of a tropical damselfish (Dascyllus flavicaudus). Specifically, we tested the premise that spatial heterogeneity in the strength of temporal density dependence would reflect variation in density of predators, the agent of mortality. Our field manipulations revealed that mortality among successive cohorts of young fishes was density dependent at each reef, but that its strength varied by approximately 1.5 orders of magnitude. This spatial heterogeneity was well predicted by variation among the six reefs in the density of predatory fishes that consume juvenile damselfishes. Because density dependence arose from competition for enemy-free space within a shelter coral, the mortality consequence of the competition depended on the neighborhood density of predators. Thus, the scale of heterogeneity in the density dependence largely reflected attributes of the environment that shaped the local abundance of predators. These results have important implications for how ecologists explore regulatory processes in nature. Failure to account for spatial variation could frequently yield misleading conclusions regarding density dependence as a stabilizing process, obscure underlying mechanisms influencing its strength, and provide no insight into the spatial scale of the heterogeneity. Further, models of population dynamics will be improved when experimental approaches better estimate the magnitude and causes of variation in strength of stabilizing density dependence.     

Laboratory evaluation of kinetic parameters for lake sediment denitrification models

Laboratory experiments using the acetylene blockage technique showed that denitrification rates in sediments from Lake Okeechobee, Florida, are described by Michaelis-Menten nitrate dependence and Arrhenius temperature dependence (E_act = 15.5 kcal, but do not appear to be affected by seasonal differences in the supply of carbon substrates in this eutrophic lake. Peak nitrate concentrations in the sediments are in the range of the half-saturation constant, and thus, for a given temperature, k_d varies by a factor of approximately two over the typical range of nitrate concentrations. Most diagenetic sediment denitrification models employ a single-valued rate constant k_d, to describe nitrate dependence. However, the use of a constant k_d for eutrophic lake sediments may result in a significantly erroneous estimate of annual denitrification loss.     

On the choice of statistical models for estimating occurrence and extinction from animal surveys

In surveys of natural animal populations the number of animals that are present and available to be detected at a sample location is often low, resulting in few or no detections. Low detection frequencies are especially common in surveys of imperiled species; however, the choice of sampling method and protocol also may influence the size of the population that is vulnerable to detection. In these circumstances, probabilities of animal occurrence and extinction will generally be estimated more accurately if the models used in data analysis account for differences in abundance among sample locations and for the dependence between site-specific abundance and detection. Simulation experiments are used to illustrate conditions wherein these types of models can be expected to outperform alternative estimators of population site occupancy and extinction.     

Detecting and Modeling Spatial and Temporal Dependence in Conservation Biology

Abstract: Due to the structuring forces and large-scale physical processes that shape our biosphere, we often find that environmental and ecological data are either spatially or temporally—or both spatially and temporally—dependent. When these data are analyzed, statistical techniques and models are frequently applied that were developed for independent data. We describe some of the detrimental consequences, such as inefficient parameter estimators, biased hypothesis test results, and inaccurate predictions, of ignoring spatial and temporal data dependencies, and we cite an example of adverse statistical results occurring when spatial dependencies were disregarded. We also discuss and recommend available techniques used to detect and model spatial and temporal dependence, including variograms, covariograms, autocorrelation and partial autocorrelation plots, geostatistical techniques, Gaussian autoregressive models, K functions, and ARIMA models, in environmental and ecological research to avoid the aforementioned difficulties.     

Building statistical models to analyze species distributions.

Models of the geographic distributions of species have wide application in ecology. But the nonspatial, single-level, regression models that ecologists have often employed do not deal with problems of irregular sampling intensity or spatial dependence, and do not adequately quantify uncertainty. We show here how to build statistical models that can handle these features of spatial prediction and provide richer, more powerful inference about species niche relations, distributions, and the effects of human disturbance. We begin with a familiar generalized linear model and build in additional features, including spatial random effects and hierarchical levels. Since these models are fully specified statistical models, we show that it is possible to add complexity without sacrificing interpretability. This step-by-step approach, together with attached code that implements a simple, spatially explicit, regression model, is structured to facilitate self-teaching. All models are developed in a Bayesian framework. We assess the performance of the models by using them to predict the distributions of two plant species (Proteaceae) from South Africa's Cape Floristic Region. We demonstrate that making distribution models spatially explicit can be essential for accurately characterizing the environmental response of species, predicting their probability of occurrence, and assessing uncertainty in the model results. Adding hierarchical levels to the models has further advantages in allowing human transformation of the landscape to be taken into account, as well as additional features of the sampling process.     

Multistate models for monitoring individual trees in permanent observation plots

This interdisciplinary research on forest ecosystems begins with some characteristics of ecosystems which are the basis for the derivation of statistical models for the development and vitality of trees. Several ecological problems which could be solved by longitudinal studies are mentioned. Statistical methods for the evaluation of the crowns of spruce trees (Picea abies Karst) in three permanent observation plots in Switzerland are described. In particular, the time-dependent proportional odds model and a transitional model are used. Through application of these multistate models the data give information on the dependence of an ordered categorical response variable on covariates characterizing the ecosystem. The response variable is observed through infrared aerial photographs. This monitoring system gives insight into the dynamic behaviour of the forest ecosystem. The need for more eco-systematically motivated statistical research using longitudinal studies is identified.