AIC model selection and multimodel inference in behavioral ecology: some background,observations, and comparisons

We briefly outline the information-theoretic (I-T) approaches to valid inference including a review of some simple methods for making formal inference from all the hypotheses in the model set (multimodel inference). The I-T approaches can replace the usual t tests and ANOVA tables that are so inferentially limited, but still commonly used. The I-T methods are easy to compute and understand and provide formal measures of the strength of evidence for both the null and alternative hypotheses, given the data. We give an example to highlight the importance of deriving alternative hypotheses and representing these as probability models. Fifteen technical issues are addressed to clarify various points that have appeared incorrectly in the recent literature. We offer several remarks regarding the future of empirical science and data analysis under an I-T framework.     

Determination of average individual dry weights and ash-free dry weights in different sieve fractions of marine meiofauna

Individual dry weights and ash-free dry weights for different meiofauna taxa from two soft bottom localities (31 and 117 m depth) in Gullmar Fjord on the Swedish west coast were determined. Samples from August 1980 and February 1981 of about 100 to 600 formalin-preserved specimens of each of the different taxa from each of four sieve fractions were weighed on a microbalance. Individual dry weights ranging from 0.12 g (nematodes in the 0.040-mm fraction) to 172 g (polythalamous, arenaceous Foraminifera in the 0.500-mm fraction) and ash-free dry weights ranging from 0.10 g (nematodes in the 0.040-mm fraction) to 37 g (polychaetes in the 0.500-mm fraction) were obtained. Great similarities were noted between corresponding values from the two stations as well as between summer and winter values. The percentage of organic matter, determined by ashing, in the body weight differed greatly among taxa. Some standard individual dry weight and ash-free dry weight values, to be used for re-calculation of abundance values into biomass, are presented.     

An estimating function approach to the inference of catch-effort models

A class of catch-effort models, which allows for heterogeneous removal probabilities, is proposed for closed populations. The model includes three types of removal probabilities: multiplicative, Poisson and logistic. The usual removal and generalized removal models then become special cases. The equivalence of the proposed model and a special type of capture-recapture model is discussed. A unified estimating function approach is used to estimate the initial population size. For the homogeneous model, the resulting population size estimator based on optimal estimating functions is asymptotically equivalent to the maximum likelihood estimator. One advantage for our approach is that it can be extended to handle the heterogeneous populations in which the maximum likelihood estimators do not exist. The bootstrap method is applied to construct variance estimators and confidence intervals. We illustrate the method by two real data examples. Results of a simulation study investigating the performance of the proposed estimation procedure are presented.     

Probability distributions and statistical inference for axial data

Observations on axes which lack information on the direction of propagation are referred to as axial data. Such data are often encountered in enviromental sciences, e.g. observations on propagations of cracks or on faults in mining walls. Even though such observations are recorded as angles, circular probability models are inappropriate for such data since the constraint that observations lie only in [0, π) needs to be enforced. Probability models for such axial data are argued here to have a general structure stemming from that of wrapping a circular distribution on a semi-circle. In particular, we consider the most popular circular model, the von Mises or circular normal distribution, and derive the corresponding axial normal distribution. Certain properties of this distribution are established. Maximum likelihood estimation of its parameters are shown to be surprisingly, in contrast to trigonometric moment estimation, numerically quite appealing. Finally we illustrate our results by several real life axial data sets. Received: September 2004/ Revised: December 2004     

Estimation and inference for upper hinge regression models

Environmental and Ecological Statistics - We introduce a new type of threshold regression models called upper hinge models. Under this type of threshold models, there only exists an association...     

Theoretical foundations of learning processes for sustainable development

Social-ecological systems are co-evolving systems. Of particular relevance are here: (1) co-evolution of the environment and governance, (2) co-evolution of technology and governance, and (3) co-evolution of human behaviour and culture. The co-evolutionary perspective has helped to understand the processes which led to the present unsustainable situation. This paper highlights different types of learning processes which occur in co-evolving systems and explores learning processes on the macro-, meso- and micro-levels for moving onto more sustainable paths. While the literature in environmental management, ecological economics or sustainability science often refers to the need for learning processes, the conceptualisation of learning and the link to learning theories is weak. This paper draws on learning theories from psychology, social psychology, education, evolutionary economics and political science and offers a first step toward theoretical foundations of learning processes for sustainable development. An improved understanding of these learning processes will provide important clues for policy recommendations on multiple scales.     

Order restricted randomized designs and two sample inference

This paper develops a new design that relies on subjective judgment ranking to compare subsets of experimental units. This judgment ranking is used along with restricted randomization to improve statistical inference for the contrast between two levels of a treatment. The new design assigns the judgment ranked units in a subset to different treatments. Such an assignment translates the positive dependence among units within each subset into negative dependence for the estimators of treatment means, and hence leads to a reduction in variance for the contrast. For the proposed design, a test for the difference in means of two treatment levels is developed along with an associated confidence interval. It is shown that the null distribution of the proposed test is approximated reasonably well with the Student’s t-distribution for sample sizes as small as 6. A simulation study indicates that the proposed design is advantageous compared to its competitors in the literature for both high and low quality rankings. The new design’s advantage increases with the quality of rankings.     

Modeling and inference of animal movement using artificial neural networks

Movement of animals in relation to objects in their environment is important in many areas of ecology and wildlife conservation. Tools for analysis of movement data, however, still remain rather limited. In previous work, we developed nonlinear regression models for movement in relation to a single landscape feature. Here we greatly expand these previous models by using artificial neural networks. The new models add substantial flexibility and capabilities, including the ability to incorporate multiple factors and covariates. We devise a likelihood-based model fitting procedure that utilizes genetic algorithms and demonstrate the approach with movement data for red diamond rattlesnakes. The proposed methodology can be useful for global positioning system tracking data that are becoming more common in studies of animal movement behavior.     

Bayesian nonparametric inference for the overlap of daily animal activity patterns

The study of the interaction among species is an active area of research in Ecology. In particular, it is of interest to evaluate the overlap of their ecological niches. Temporal activity is one of the niche’s axes most commonly used to explore ecological segregation among animal species, and many contributions focus on the overlap of this variable. Once the information of the temporal activity is obtained in the wild, the data is treated as a random sample. There exist different methods to estimate the overlap. Specifically, in the case of two species, one possibility is to estimate the density of the temporal activity of each species and then evaluate the overlap between these density functions. This leads naturally to the analysis of circular data. Most of the procedures currently in use impose some rather restrictive assumptions on the probabilistic models used to describe the phenomena, and only provide approximate measures of the uncertainty involved in the process. In this article, we propose a Bayesian nonparametric approach which incorporates a well-defined noninformative prior. We take advantage of the data structure to define such a prior in terms of the predictive distribution. To the best of our knowledge, this is a novel approach. Our procedure is compared with a well-known method using simulated data, and applied to the analysis of real camera-trap data concerning two mammalian species from the El Triunfo biosphere reserve (Chiapas, Mexico).     

Methods for joint inference from panel survey and demographic data

A number of methods for joint inference from animal abundance and demographic data have been proposed in recent years, each with its own advantages. A new approach to analyzing panel survey and demographic data simultaneously is described. The approach fits population-dynamics models to the survey data, rather than to a single index of abundance derived from them and thus avoids disadvantages inherent in analyzing such an index. The methodology is developed and illustrated with British Lapwing data, and the results are compared with those obtained from existing approaches. The estimates of demographic parameters and population indices are similar for all methods. The results of a simulation study show that the new method performs well in terms of mean squared error.     

Statistical inference using the g or K point pattern spatial statistics

Spatial point pattern analysis provides a statistical method to compare an observed spatial pattern against a hypothesized spatial process model. The G statistic, which considers the distribution of nearest neighbor distances, and the K statistic, which evaluates the distribution of all neighbor distances, are commonly used in such analyses. One method of employing these statistics involves building a simulation envelope from the result of many simulated patterns of the hypothesized model. Specifically, a simulation envelope is created by calculating, at every distance, the minimum and maximum results computed across the simulated patterns. A statistical test is performed by evaluating where the results from an observed pattern fall with respect to the simulation envelope. However, this method, which differs from P. Diggle's suggested approach, is invalid for inference because it violates the assumptions of Monte Carlo methods and results in incorrect type I error rate performance. Similarly, using the simulation envelope to estimate the range of distances over which an observed pattern deviates from the hypothesized model is also suspect. The technical details of why the simulation envelope provides incorrect type I error rate performance are described. A valid test is then proposed, and details about how the number of simulated patterns impacts the statistical significance are explained. Finally, an example of using the proposed test within an exploratory data analysis framework is provided.     

Oxidative stress in the blood of pregnant rats and reduction of organ weights caused by the polychlorinated biphenyl congener 77

3,3′,4,4′-Tetrachlorobiphenyl (PCB 77), one of the environmentally persistent polychlorinated biphenyls that have been used for industrial purposes, was repeatedly administered to pregnant rats by gavage at a dose of minimal, non-lethal toxicity in order to study its effects on routine blood variables, parameters of oxidative stress and hematopoietic organs in pregnant female rats. Of the routine blood parameters, PCB 77 reduced the mean corpuscular hemoglobin concentration and platelet counts; the levels of malondialdehyde and glutathione peroxidase in the blood were higher during the first days of gestation (1–7), as compared to the respective controls. In the subsequent period between days 8 and 18, these parameters did not show any significant change after PCB 77 treatment. Routine blood parameters and oxidative stress parameters indicated a moderate degree of oxidative stress which alone could not bring about the serious weight reduction of the thymus, pituitary, and kidneys. The extent of oxidative stress did not correlate with the weight reduction of some of the blood-forming organs.     

Statistical inference on patch-specific survival and movement rates from marked animals

Empirical estimates of patch-specific survival and movement rates are needed to parametrize spatially explicit population models, and for inference on the effects of habitat quality and fragmentation on populations. Data from radio-marked animals, in which both the fates and habitat locations of animals are known over time, can be used in conjunction with continuous-time proportional hazards models to obtain inferences on survival rates. Discrete-time conditional logistic models may provide inference on both survival and movement rates. We use Monte Carlo simulation to investigate accuracy of estimates of survival from both approaches, and movement rates from conditional logistic regression, for two habitats. Bias was low (relative bias < 0.04) and interval coverage accurate (close to the nominal 0.95) for estimates of habitat effect on survival based on proportional hazards. Bias was high ( relative bias 0.60) and interval coverage poor ( = 0.26 vs. nominal 0.95) for estimates of habitat effect based on conditional logistic regression; bias was especially influenced by heterogeneity in survival and the shape of the hazard function, whereas both bias and coverage were affected by ‘memory’ effects in movement patterns. Bias estimates of movement rate was low ( relative bias < 0.05), but interval coverage was poor ( = 0.48–0.80), possibly as a result of poor performance of a Taylor series estimate of variance. An example is provided from a radio-telemetry study of 47 wintering American woodcock (Scolopax minor), illustrating practical difficulties in field studies to parametrize these models. We also discuss extensions of continuous-time models to explicitly include a movement process, and further examine tradeoffs between continuous and discrete models.     

Tree growth inference and prediction from diameter censuses and ring widths.

Estimation of tree growth is based on sparse observations of tree diameter, ring widths, or increments read from a dendrometer. From annual measurements on a few trees (e.g., increment cores) or sporadic measurements from many trees (e.g., diameter censuses on mapped plots), relationships with resources, tree size, and climate are extrapolated to whole stands. There has been no way to formally integrate different types of data and problems of estimation that result from (1) multiple sources of observation error, which frequently result in impossible estimates of negative growth, (2) the fact that data are typically sparse (a few trees or a few years), whereas inference is needed broadly (many trees over many years), (3) the fact that some unknown fraction of the variance is shared across the population, and (4) the fact that growth rates of trees within competing stands are not independent. We develop a hierarchical Bayes state space model for tree growth that addresses all of these challenges, allowing for formal inference that is consistent with the available data and the assumption that growth is nonnegative. Prediction follows directly, incorporating the full uncertainty from inference with scenarios for "filling the gaps" for past growth rates and for future conditions affecting growth. An example involving multiple species and multiple stands with tree-ring data and up to 14 years of tree census data illustrates how different levels of information at the tree and stand level contribute to inference and prediction.     

Population dynamics and control of invasive Spartina alterniflora: inference and forecasting under uncertainty

Managing invaded ecosystems entails making decisions about control strategies in the face of scientific uncertainty and ecological stochasticity. Statistical tools such as model selection and Bayesian decision analysis can guide decision-making by estimating probabilities of outcomes under alternative management scenarios, but these tools have seldom been applied in invasion ecology. We illustrate the use of model selection and Bayesian methods in a case study of smooth cordgrass (Spartina alterniflora) invading Willapa Bay, Washington. To address uncertainty in model structure, we quantified the weight of evidence for two previously proposed hypotheses, that S. alterniflora recruitment varies with climatic conditions (represented by sea surface temperature) and that recruitment is subject to an Allee effect due to pollen limitation. By fitting models to time series data, we found strong support for climate effects, with higher per capita seedling production in warmer years, but no evidence for an Allee effect based on either the total area invaded or the mean distance between neighboring clones. We used the best-supported model to compare alternative control strategies, incorporating uncertainty in parameter estimates and population dynamics. For a fixed annual removal effort, the probability of eradication in 10 years was highest, and final invaded area lowest, if removals targeted the smallest clones rather than the largest or randomly selected clones. The relationship between removal effort and probability of eradication was highly nonlinear, with a sharp threshold separating -0% and -100% probability of success, and this threshold was 95% lower in simulations beginning early rather than late in the invasion. This advantage of a rapid response strategy is due to density-dependent population growth, which produces alternative stable equilibria depending on the initial invasion size when control begins. Our approach could be applied to a wide range of invasive species management problems where appropriate data are available.     

The effect of species response form on species distribution model prediction and inference

Ecological theory and current evidence support the validity of various species response curves according to a variety of environmental gradients. Various methods have been developed for building species distribution models but it is not well known how these methods perform under various assumptions about the form of the underlying species response. It is also not well known how spatial correlation in species occurrence affects model performance. These effects were investigated by applying an environmental envelope method (BIOCLIM) and three regression-based methods: logistic regression (LR), generalized additive modelling (GAM), and classification and regression tree (CART) to simulated species occurrence data. Each simulated species was constructed as a sum of responses with varying weights. Three basic species response curves were assumed: Gaussian (bell-shaped), Beta (skew) and linear. The two non-linear responses conform to standard ecological niche theory. All three responses were applied in turn to three simulated environmental variables, each with varying degrees of spatial autocorrelation. GAM produced the most consistent model performance over all forms of simulated species response. BIOCLIM and CART were inclined to underrate the performance of variables with a linear response. BIOCLIM was less sensitive to data density. LR was susceptible to model misspecification. The use of a linear function in LR underestimated the performance of variables with non-linear species response and contributed to increased spatial autocorrelation in model residuals. Omission of important environmental variables with non-linear species response also contributed to increased spatial autocorrelation in model residuals. Adding a spatial autocovariate term to the LR model (autologistic model) reduced the spatial autocorrelation and improved model performance, but did not correct the misidentification of the dominant environmental determinant. This is to be expected since the autologistic approach was designed primarily for prediction and not for inference. Given that various forms of species response to environmental determinants arise commonly in nature: (1) higher order functions should always be tested when applying LR in modelling species distribution; (2) spatial autocorrelation in species distribution model residuals can indicate that environmental determinants with non-linear response are missing from the model; and (3) deficiencies in LR model performance due to model misspecification can be addressed by adding a spatial autocovariate to the model, but care should be taken when interpreting the coefficients of the model parameters.