Are ecological groups of species optimal for forest dynamics modelling?

The huge diversity of tree species in tropical rain-forests makes the modelling of its dynamics a difficult task. One-way to deal with it is to define species groups. A classical approach for building species groups consists in grouping species with nearby characteristics, using cluster analysis. A group of species is then characterized by the same list of attributes as a single species, and it is incorporated in the model of forest dynamics in the same way as a single species. In this paper, a new approach for building species group is proposed. It relies on the discrepancy between model predictions when all species are considered separately, and model predictions when species groups are used. An aggregation error that quantifies the bias in model predictions that results from species grouping is thus defined. We then define the optimal species grouping as the one that minimizes the aggregation error. Using data from a tropical rain-forest in French Guiana and a toy model of forest dynamics, this new method for species grouping is confronted to the classical method based on cluster analysis of the species characteristics, and to a combined method based on a cluster analysis that uses the aggregation error as a dissimilarity between species. The optimal species grouping is quite different from the classical species grouping. The ecological interpretation of the optimal groups is difficult, as there is no direct linkage between the species characteristics and the way that they are grouped. The combined approach yields species groups that are closed to the optimal ones, with much less computations. The optimal species groups are thus specific to the model of forest dynamics and lack the generality of those of the classical method, that in turn are not optimal.     

Model based grouping of species across environmental gradients

We present a novel approach to the statistical analysis and prediction of multispecies data. The approach allows the simultaneous grouping and quantification of multiple species’ responses to environmental gradients. The underlying statistical model is a finite mixture model, where mixing is performed over the individual species’ responses to environmental gradients. Species with similar responses are grouped with minimal information loss. We term these groups species archetypes. Each species archetype has an associated GLM that can be used to predict distributions with appropriate measures of uncertainty. Initially, we illustrate the concept and method using artificial data and then with application to real data comprising 200 species from the Great Barrier Reef (GBR) lagoon on 13 oceanographic and geological gradients from 12°S to 24°S. The 200 species from the GBR are well represented by 15 species archetypes. The model is interpreted through maps of the probability of presence for a fine scale set of locations throughout the study area. Maps of uncertainty are also produced to provide statistical context. The presence of each species archetype was strongly influenced by oceanographic gradients, principally temperature, oxygen and salinity. The number of species in each group ranged from 4 to 34. The method has potential application to the analysis of multispecies distribution patterns and for multispecies management.     

Sensitivity of species-distribution models to error,bias, and model design: An application to resource selection functions for woodland caribou

Models that predict distribution are now widely used to understand the patterns and processes of plant and animal occurrence as well as to guide conservation and management of rare or threatened species. Application of these methods has led to corresponding studies evaluating the sensitivity of model performance to requisite data and other factors that may lead to imprecise or false inferences. We expand upon these works by providing a relative measure of the sensitivity of model parameters and prediction to common sources of error, bias, and variability. We used a one-at-a-time sample design and GPS location data for woodland caribou (Rangifer tarandus caribou) to assess one common species-distribution model: a resource selection function. Our measures of sensitivity included change in coefficient values, prediction success, and the area of mapped habitats following the systematic introduction of geographic error and bias in occurrence data, thematic misclassification of resource maps, and variation in model design. Results suggested that error, bias and model variation have a large impact on the direct interpretation of coefficients. Prediction success and definition of important habitats were less responsive to the perturbations we introduced to the baseline model. Model coefficients, prediction success, and area of ranked habitats were most sensitive to positional error in species locations followed by sampling bias, misclassification of resources, and variation in model design. We recommend that researchers report, and practitioners consider, levels of error and bias introduced to predictive species-distribution models. Formal sensitivity and uncertainty analyses are the most effective means for evaluating and focusing improvements on input data and considering the range of values possible from imperfect models.     

Classification and ordination of benthic samples from Bedeque Bay,an estuary in Prince Edward Island,Canada

An attempt was made to identify the causes of the distribution of benthos within Bedeque Bay using multivariate techniques programmed for the computer. Both classification by a hierarchical cluster analysis, and ordination by principal components analysis suggested that a large proportion of the variance in the data was directly or indirectly correlated with a salinity gradient. Classification divided the species into two main groups, a in the upper half of the estuary where lower salinities and larger salinity fluctuations occurred, and group b in the lower half of the estuary with a more stable salinity regime. The group b species were further subdivided into those preferring soft mud and those preferring sandier sediments. The group a species were divided into a well-developed oyster association and various sub-groups less strongly associated with oysters. Five principal components were required to account for 50% of the variance in the data. The first axis accounted for 20% of the variance and was shown by a non-parametric test to be correlated with the salinity gradient. Axes II to V could not be interpreted, but possibly represented complex species interactions. By providing hard substrates and altering the natura of the sediment, oysters and mussels produced conditions suitable for many other species.     

Species-specific tuning increases robustness to sampling bias in models of species distributions: An implementation with Maxent

Various methods exist to model a species’ niche and geographic distribution using environmental data for the study region and occurrence localities documenting the species’ presence (typically from museums and herbaria). In presence-only modelling, geographic sampling bias and small sample sizes represent challenges for many species. Overfitting to the bias and/or noise characteristic of such datasets can seriously compromise model generality and transferability, which are critical to many current applications - including studies of invasive species, the effects of climatic change, and niche evolution. Even when transferability is not necessary, applications to many areas, including conservation biology, macroecology, and zoonotic diseases, require models that are not overfit. We evaluated these issues using a maximum entropy approach (Maxent) for the shrew Cryptotis meridensis, which is endemic to the Cordillera de Mérida in Venezuela. To simulate strong sampling bias, we divided localities into two datasets: those from a portion of the species’ range that has seen high sampling effort (for model calibration) and those from other areas of the species’ range, where less sampling has occurred (for model evaluation). Before modelling, we assessed the climatic values of localities in the two datasets to determine whether any environmental bias accompanies the geographic bias. Then, to identify optimal levels of model complexity (and minimize overfitting), we made models and tuned model settings, comparing performance with that achieved using default settings. We randomly selected localities for model calibration (sets of 5, 10, 15, and 20 localities) and varied the level of model complexity considered (linear versus both linear and quadratic features) and two aspects of the strength of protection against overfitting (regularization). Environmental bias indeed corresponded to the geographic bias between datasets, with differences in median and observed range (minima and/or maxima) for some variables. Model performance varied greatly according to the level of regularization. Intermediate regularization consistently led to the best models, with decreased performance at low and generally at high regularization. Optimal levels of regularization differed between sample-size-dependent and sample-size-independent approaches, but both reached similar levels of maximal performance. In several cases, the optimal regularization value was different from (usually higher than) the default one. Models calibrated with both linear and quadratic features outperformed those made with just linear features. Results were remarkably consistent across the examined sample sizes. Models made with few and biased localities achieved high predictive ability when appropriate regularization was employed and optimal model complexity was identified. Species-specific tuning of model settings can have great benefits over the use of default settings.     

Effects of sampling error and temporal correlations in population growth on process variance estimators

Estimates of a population’s growth rate and process variance from time-series data are often used to calculate risk metrics such as the probability of quasi-extinction, but temporal correlations in the data from sampling error, intrinsic population factors, or environmental conditions can bias process variance estimators and detrimentally affect risk predictions. It has been claimed (McNamara and Harding, Ecol Lett 7:16–20, 2004) that estimates of the long-term variance that incorporate observed temporal correlations in population growth are unaffected by sampling error; however, no estimation procedures were proposed for time-series data. We develop a suite of such long-term variance estimators, and use simulated data with temporally autocorrelated population growth and sampling error to evaluate their performance. In some cases, we get nearly unbiased long-term variance estimates despite ignoring sampling error, but the utility of these estimators is questionable because of large estimation uncertainty and difficulties in estimating correlation structure in practice. Process variance estimators that ignored temporal correlations generally gave more precise estimates of the variability in population growth and of the probability of quasi-extinction. We also found that the estimation of probability of quasi-extinction was greatly improved when quasi-extinction thresholds were set relatively close to population levels. Because of precision concerns, we recommend using simple models for risk estimates despite potential biases, and limiting inference to quantifying relative risk; e.g., changes in risk over time for a single population or comparative risk among populations.     

Variances and variance estimators of the improved ratio estimators under adaptive cluster sampling

Although not design-unbiased, the ratio estimator is recognized as more efficient when a certain degree of correlation exists between the variable of primary interest and the auxiliary variable. Meanwhile, the Rao–Blackwell method is another commonly used procedure to improve estimation efficiency. Various improved ratio estimators under adaptive cluster sampling (ACS) that make use of the auxiliary information together with the Rao–Blackwellized univariate estimators have been proposed in past research studies. In this article, the variances and the associated variance estimators of these improved ratio estimators are proposed for a thorough framework of statistical inference under ACS. Performance of the proposed variance estimators is evaluated in terms of the absolute relative percentage bias and the empirical mean-squared error. As expected, results show that both the absolute relative percentage bias and the empirical mean-squared error decrease as the initial sample size increases for all the variance estimators. To evaluate the confidence intervals based on these variance estimators and the finite-population Central Limit Theorem, the coverage rate and the interval width are used. These confidence intervals suffer a disadvantage similar to that of the conventional ratio estimator. Hence, alternative confidence intervals based on a certain type of adjusted variance estimators are constructed and assessed in this article.     

Tropical coastal habitats as surrogates of fish community structure, grazing, and fisheries value

Habitat maps are frequently invoked as surrogates of biodiversity to aid the design of networks of marine reserves. Maps are used to maximize habitat heterogeneity in reserves because this is likely to maximize the number of species protected. However, the technique's efficacy is limited by intra-habitat variability in the species present and their abundances. Although communities are expected to vary among patches of the same habitat, this variability is poorly documented and rarely incorporated into reserve planning. To examine intra-habitat variability in coral-reef fishes, we generated a data set from eight tropical coastal habitats and six islands in the Bahamian archipelago using underwater visual censuses. Firstly, we provide further support for habitat heterogeneity as a surrogate of biodiversity as each predefined habitat type supported a distinct assemblage of fishes. Intra-habitat variability in fish community structure at scales of hundreds of kilometers (among islands) was significant in at least 75% of the habitats studied, depending on whether presence/absence, density, or biomass data were used. Intra-habitat variability was positively correlated with the mean number of species in that habitat when density and biomass data were used. Such relationships provide a proxy for the assessment of intra-habitat variability when detailed quantitative data are scarce. Intra-habitat variability was examined in more detail for one habitat (forereefs visually dominated by Montastraea corals). Variability in community structure among islands was driven by small, demersal families (e.g., territorial pomacentrid and labrid fishes). Finally, we examined the ecological and economic significance of intra-habitat variability in fish assemblages on Montastraea reefs by identifying how this variability affects the composition and abundances of fishes in different functional groups, the key ecosystem process of parrotfish grazing, and the ecosystem service of value of commercially important finfish. There were significant differences in a range of functional groups and grazing, but not fisheries value. Variability at the scale of tens of kilometers (among reefs around an island) was less than that among islands. Caribbean marine reserves should be replicated at scales of hundreds of kilometers, particularly for species-rich habitats, to capture important intra-habitat variability in community structure, function, and an ecosystem process.     

Adaptive two-stage one-per-stratum sampling

We briefly describe adaptive cluster sampling designs in which the initial sample is taken according to a Markov chain one-per-stratum design (Breidt, 1995) and one or more secondary samples are taken within strata if units in the initial sample satisfy a given condition C. An empirical study of the behavior of the estimation procedure is conducted for three small artificial populations for which adaptive sampling is appropriate. The specific sampling strategy used in the empirical study was a single random-start systematic sample with predefined systematic samples within strata when the initially sampled unit in that stratum satisfies C. The bias of the Horvitz-Thompson estimator for this design is usually very small when adaptive sampling is conducted in a population for which it is suited. In addition, we compare the behavior of several alternative estimators of the standard error of the Horvitz-Thompson estimator of the population total. The best estimator of the standard error is population-dependent but it is not unreasonable to use the Horvitz-Thompson estimator of the variance. Unfortunately, the distribution of the estimator is highly skewed hence the usual approach of constructing confidence intervals assuming normality cannot be used here.     

Environmental variability and allocation trade-offs maintain species diversity in a process-based model of succulent plant communities

Ecological theory suggests that environmental variability can promote coexistence, provided that species occupy differential niches. In this study, we focus on two questions: (1) Do allocation trade-offs provide a sufficient basis for niche differentiation in succulent plant communities? (2) What is the relative importance of different forms of environmental variability on species diversity and community composition? We approach these questions with a generic, individual-based simulation model. In our model, plants compete for water in a spatially explicit environment. Species differ in their size at maturity and in the allocation of carbon to roots, leaves and storage tissue. The model was fully specified with independent literature data. Model output was compared to characteristics of a species-rich community in the semi-arid Richtersveld (South Africa). The model reproduced the coexistence of plants with different sizes at maturity, the dominance of succulent shrubs, and the level of vegetation cover. We analyzed the effects of three forms of environmental variability: (a) temporal fluctuations in precipitation (rain and fog), (b) spatial heterogeneity of water supply due to run-on and run-off processes and (c) ‘rock pockets’ that limit root competition in space. The three types of variability had differential effects on diversity: diversity exhibited a strong hump-shaped response to temporal variation. Spatial variability increased diversity, with the strongest increase occurring at intermediate levels of temporal variability. Finally, rock pockets had the weakest effect, but contributed to diversity by providing refuges for small species, particularly at low temporal variability. The model thus shows that spatio-temporal variation of resource supply can maintain diversity over long time scales even in small systems, as is the case in the Richtersveld succulent communities. Trade-offs in allocation provide the basis for necessary niche differentiation. By describing resource competition between individual plants, our model provides a mechanistic basis for the link from species traits to community composition at given environmental conditions. It thereby contributes to an understanding of the forces shaping plant communities. Such an understanding is critical to reduce the threats environmental change poses to biodiversity and ecosystem services.     

Trait groups as management entities in a complex,multispecies reef fishery

Localized stressors compound the ongoing climate-driven decline of coral reefs, requiring natural resource managers to work with rapidly shifting paradigms. Trait-based adaptive management (TBAM) is a new framework to help address changing conditions by choosing and implementing management actions specific to species groups that share key traits, vulnerabilities, and management responses. In TBAM maintenance of functioning ecosystems is balanced with provisioning for human subsistence and livelihoods. We first identified trait-based groups of food fish in a Pacific coral reef with hierarchical clustering. Positing that trait-based groups performing comparable functions respond similarly to both stressors and management actions, we ascertained biophysical and socioeconomic drivers of trait-group biomass and evaluated their vulnerabilities with generalized additive models. Clustering identified 7 trait groups from 131 species. Groups responded to different drivers and displayed divergent vulnerabilities; human activities emerged as important predictors of community structuring. Biomass of small, solitary reef-associated species increased with distance from key fishing ports, and large, solitary piscivores exhibited a decline in biomass with distance from a port. Group biomass also varied in response to different habitat types, the presence or absence of reported dynamite fishing activity, and exposure to wave energy. The differential vulnerabilities of trait groups revealed how the community structure of food fishes is driven by different aspects of resource use and habitat. This inherent variability in the responses of trait-based groups presents opportunities to apply selective TBAM strategies for complex, multispecies fisheries. This approach can be widely adjusted to suit local contexts and priorities.     

Automatic construction of concept hierarchies: The case of foliage-dwelling spiders

In this paper, we present the hierarchical variable dependencies that were obtained from raw data with the use of two machine learning techniques on an ecological data set. The data set contains features of field margins and the corresponding number of spider species inhabiting them. This data set was used before by domain experts to construct a fuzzy qualitative model with hierarchical variable dependencies, which we use for comparison with our results. One of the machine learning methods constructs a hierarchical structure similar to the one in the experts’ model, while revealing some additional interesting relations of environmental features with respect to the number of spider species. The other method constructs a different hierarchy from the one proposed by the experts, which, according to our classification performance experiments, might be even more appropriate.     

Comparison of some homogeneity tests in analysis of over-dispersed binomial data

This paper compares the procedures based on the extended quasi-likelihood, pseudo-likelihood and quasi-likelihood approaches for testing homogeneity of several proportions for over-dispersed binomial data. The type I error of the Wald tests using the model-based and robust variance estimates, the score test, and the extended quasi-likelihood ratio test (deviance reduction test) were examined by simulation. The extended quasi-likelihood method performs less well when mean responses are close to 1 or 0. The model-based Wald test based on the quasi-likelihood performs the best in maintaining the nominal level. The score test performs less well when the intracluster correlations are large or heterogeneous. In summary: (i) both the quasilikelihood and pseudo-likelihood methods appear to be acceptable but care must be taken when overfitting a variance function with small sample sizes; (ii) the extended quasi-likelihood approach is the least favourable method because its nominal level is much too high; and (iii) the robust variance estimator performs poorly, particularly when the sample size is small.     

Estimating the complexity of bird song by using capture-recapture approaches from community ecology

Repertoire size, the number of unique song or syllable types in the repertoire, is a widely used measure of song complexity in birds, but it is difficult to calculate this exactly in species with large repertoires. A new method of repertoire size estimation applies species richness estimation procedures from community ecology, but such capture-recapture approaches have not been much tested. Here, we establish standardized sampling schemes and estimation procedures using capture-recapture models for syllable repertoires from 18 bird species, and suggest how these may be used to tackle problems of repertoire estimation. Different models, with different assumptions regarding the heterogeneity of the use of syllable types, performed best for different species with different song organizations. For most species, models assuming heterogeneous probability of occurrence of syllables (so-called detection probability) were selected due to the presence of both rare and frequent syllables. Capture-recapture estimates of syllable repertoire size from our small sample did not differ significantly from previous estimates using larger samples of count data. However, the enumeration of syllables in 15 songs yielded significantly lower estimates than previous reports. Hence, heterogeneity in detection probability of syllables should be addressed when estimating repertoire size. This is neglected using simple enumeration procedures, but is taken into account when repertoire size is estimated by appropriate capture-recapture models adjusted for species-specific song organization characteristics. We suggest that such approaches, in combination with standardized sampling, should be applied in species with potentially large repertoire size. On the other hand, in species with small repertoire size and homogenous syllable usage, enumerations may be satisfactory. Although researchers often use repertoire size as a measure of song complexity, listeners to songs are unlikely to count entire repertoires and they may rely on other cues, such as syllable detection probability.Communicated by A. Cockburn     

Inference about the ratio of means from Negative Binomial paired count data

We derive some statistical properties of the distribution of two Negative Binomial random variables conditional on their total. This type of model can be appropriate for paired count data with Poisson over-dispersion such that the variance is a quadratic function of the mean. This statistical model is appropriate in many ecological applications including comparative fishing studies of two vessels and or gears. The parameter of interest is the ratio of pair means. We show that the conditional means and variances are different from the more commonly used Binomial model with variance adjusted for over-dispersion, or the Beta-Binomial model. The conditional Negative Binomial model is complicated because it does not eliminate nuisance parameters like in the Poisson case. Maximum likelihood estimation with the unconditional Negative Binomial model can result in biased estimates of the over-dispersion parameter and poor confidence intervals for the ratio of means when there are many nuisance parameters. We propose three approaches to deal with nuisance parameters in the conditional Negative Binomial model. We also study a random effects Binomial model for this type of data, and we develop an adjustment to the full-sample Negative Binomial profile likelihood to reduce the bias caused by nuisance parameters. We use simulations with these methods to examine bias, precision, and accuracy of estimators and confidence intervals. We conclude that the maximum likelihood method based on the full-sample Negative Binomial adjusted profile likelihood produces the best statistical inferences for the ratio of means when paired counts have Negative Binomial distributions. However, when there is uncertainty about the type of Poisson over-dispersion then a Binomial random effects model is a good choice.     

Disentangling the effects of heterogeneity, stochastic dynamics and sampling in a community of aquatic insects

A dynamic and heterogeneous species abundance model generating the lognormal species abundance distribution is fitted to time series of species data from an assemblage of stoneflies and mayflies (Plecoptera and Ephemeroptera) of an aquatic insect community collected over a period of 15 years. In each year except one, we analyze 5 parallel samples taken at the same time of the season giving information about the over-dispersion in the sampling relative to the Poisson distribution. Results are derived from a correlation analysis, where the correlation in the bivariate normal distribution of log abundance is used as measurement of similarity between communities. The analysis enables decomposition of the variance of the lognormal species abundance distribution into three components due to heterogeneity among species, stochastic dynamics driven by environmental noise, and over-dispersion in sampling, accounting for 62.9, 30.6 and 6.5% of the total variance, respectively. Corrected for sampling the heterogeneity and stochastic components accordingly account for 67.3 and 32.7% of the among species variance in log abundance. By using this method, it is possible to disentangle the effect of heterogeneity and stochastic dynamics by quantifying these components and correctly remove sampling effects on the observed species abundance distribution.     

Hierarchical Bayesian space-time models

Space-time data are ubiquitous in the environmental sciences. Often, as is the case with atmo- spheric and oceanographic processes, these data contain many different scales of spatial and temporal variability. Such data are often non-stationary in space and time and may involve many observation/prediction locations. These factors can limit the effectiveness of traditional space- time statistical models and methods. In this article, we propose the use of hierarchical space-time models to achieve more flexible models and methods for the analysis of environmental data distributed in space and time. The first stage of the hierarchical model specifies a measurement- error process for the observational data in terms of some 'state' process. The second stage allows for site-specific time series models for this state variable. This stage includes large-scale (e.g. seasonal) variability plus a space-time dynamic process for the anomalies'. Much of our interest is with this anomaly proc ess. In the third stage, the parameters of these time series models, which are distributed in space, are themselves given a joint distribution with spatial dependence (Markov random fields). The Bayesian formulation is completed in the last two stages by speci- fying priors on parameters. We implement the model in a Markov chain Monte Carlo framework and apply it to an atmospheric data set of monthly maximum temperature.     

Improving occupancy estimation when two types of observational error occur: non-detection and species misidentification

Efforts to draw inferences about species occurrence frequently account for false negatives, the common situation when individuals of a species are not detected even when a site is occupied. However, recent studies suggest the need to also deal with false positives, which occur when species are misidentified so that a species is recorded as detected when a site is unoccupied. Bias in estimators of occupancy, colonization, and extinction can be severe when false positives occur. Accordingly, we propose models that simultaneously account for both types of error. Our approach can be used to improve estimates of occupancy for study designs where a subset of detections is of a type or method for which false positives can be assumed to not occur. We illustrate properties of the estimators with simulations and data for three species of frogs. We show that models that account for possible misidentification have greater support (lower AIC for two species) and can yield substantially different occupancy estimates than those that do not. When the potential for misidentification exists, researchers should consider analytical techniques that can account for this source of error, such as those presented here.     

Quasi-Poisson vs. negative binomial regression: how should we model overdispersed count data?

Quasi-Poisson and negative binomial regression models have equal numbers of parameters, and either could be used for overdispersed count data. While they often give similar results, there can be striking differences in estimating the effects of covariates. We explain when and why such differences occur. The variance of a quasi-Poisson model is a linear function of the mean while the variance of a negative binomial model is a quadratic function of the mean. These variance relationships affect the weights in the iteratively weighted least-squares algorithm of fitting models to data. Because the variance is a function of the mean, large and small counts get weighted differently in quasi-Poisson and negative binomial regression. We provide an example using harbor seal counts from aerial surveys. These counts are affected by date, time of day, and time relative to low tide. We present results on a data set that showed a dramatic difference on estimating abundance of harbor seals when using quasi-Poisson vs. negative binomial regression. This difference is described and explained in light of the different weighting used in each regression method. A general understanding of weighting can help ecologists choose between these two methods.