On estimating Hooded crow density from line transect data through exponential mixture models

Line transect sampling is a distance sampling method widely used for estimating wildlife population density. Since the usual approach assumes a model for the detection function, the estimate depends on the shape of such a function. In particular, the estimate is influenced by the so-called shoulder condition, which ensures that detection is nearly certain at small distances from the line transect. For instance, the half-normal model satisfies this condition, whereas the negative exponential model does not. The aim of this paper is to propose the exponential mixture model of the half-normal and the negative exponential in order to estimate the population density in the case where the shoulder condition is not guaranteed. Such a case study on Hooded crow is described in the paper.     

Modelling the property of compounds from structure: statistical methods for models validation

This study discusses some statistical methods used in quantitative structure–property relationships model’s validation and comparison. The paper also introduces a series of online tools for model’s validation. The implemented diagnostic tool that incorporated analytical approaches are exemplified on a series of models which estimate and predict the boiling points of a sample of 73 alkanes. The used parameters and methods are presented, and some reference values are provided.     

Methods for estimating the uncertainty in emergy table-form models

Emergy studies have suffered criticism due to the lack of uncertainty analysis and this shortcoming may have directly hindered the wider application and acceptance of this methodology. Recently, to fill this gap, the sources of uncertainty in emergy analysis were described and analytical and stochastic methods were put forward to estimate the uncertainty in unit emergy values (UEVs). However, the most common method used to determine UEVs is the emergy table-form model, and only a stochastic method (i.e., the Monte Carlo method) was provided to estimate the uncertainty of values calculated in this way. To simplify the determination of uncertainties in emergy analysis using table-form calculations, we introduced two analytical methods provided by the Guide to the Expression of Uncertainty in Measurement (GUM), i.e., the Variance method and the Taylor method, to estimate the uncertainty of emergy table-form calculations for two different types of data, and compared them with the stochastic method in two case studies. The results showed that, when replicate data are available at the system level, i.e., the same data on inputs and output are measured repeatedly in several independent systems, the Variance method is the simplest and most reliable method for determining the uncertainty of the model output, since it considers the underlying covariance of the inputs and requires no assumptions about the probability distributions of the inputs. However, when replicate data are only available at the subsystem level, i.e., repeat samples are measured on subsystems without specific correspondence between an output and a certain suite of inputs, the Taylor method will be a better option for calculating uncertainty, since it requires less information and is easier to understand and perform than the Monte Carlo method.     

A new algorithm for estimating the parameters of the spatial generalized linear mixed models

Non-Gaussian spatial responses are usually modeled using a spatial generalized linear mixed model with location specific latent variables. The likelihood function of this model cannot usually be given in a closed form, thus the maximum likelihood approach is very challenging. So far, several numerical algorithms to solve the problem of calculating maximum likelihood estimates of this model have been presented. In this paper to estimate the parameters an approximate method is considered and a new algorithm is introduced that is much faster than existing algorithms but just as accurate. This is called the Approximate Expectation Maximization Gradient algorithm. The performance of the proposed algorithm and is illustrated with a simulation study and on a real data set.     

Modified Weibull multi-state models for the analysis of animal carcinogenicity data

The Peto test is the standard method of analysis used in carcinogenicity studies to compare tumor incidence in groups of animals. It assumes that tumors are either instantly fatal or have no effect on mortality and requires a judgement of the lethality of each tumor. To avoid this requirement, parametric multi-state models have been proposed. In addition these allow estimation of tumor onset and mortality rates. This paper considers two such models and presents a modification. It is shown that the modified models provide a better fit to carcinogenicity data and simulated data are used to show that the modified models provide a modest increase in test power relative to the Peto test.     

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.     

On the functional extinction of the Passenger Pigeon

The Passenger Pigeon (Ectopistes migratorius) was a social breeder, and it has been suggested that the species experienced functional extinction, defined as a total reproductive failure, prior to its actual extinction in the early years of the 20th century. We applied a novel randomization test based on the relative times of the most recent egg‐ and skin‐specimen sightings (i.e., recorded date of specimen collection) to test for functional extinction. For a total of 6 eggs and 27 skins, the observed significance level was 0.38, which indicated that the species did not become functionally extinct. Thus, proposals to reverse its rapid decline in the late 19th century could have been successful.     

Comparison of statistical and theoretical habitat models for conservation planning: the benefit of ensemble prediction

Selection of a modeling approach is an important step in the conservation planning process, but little guidance is available. We compared two statistical and three theoretical habitat modeling approaches representing those currently being used for avian conservation planning at landscape and regional scales: hierarchical spatial count (HSC), classification and regression tree (CRT), habitat suitability index (HSI), forest structure database (FS), and habitat association database (HA). We focused our comparison on models for five priority forest-breeding species in the Central Hardwoods Bird Conservation Region: Acadian Flycatcher, Cerulean Warbler, Prairie Warbler, Red-headed Woodpecker, and Worm-eating Warbler. Lacking complete knowledge on the distribution and abundance of each species with which we could illuminate differences between approaches and provide strong grounds for recommending one approach over another, we used two approaches to compare models: rank correlations among model outputs and comparison of spatial correspondence. In general, rank correlations were significantly positive among models for each species, indicating general agreement among the models. Worm-eating Warblers had the highest pairwise correlations, all of which were significant (P < 0.05). Red-headed Woodpeckers had the lowest agreement among models, suggesting greater uncertainty in the relative conservation value of areas within the region. We assessed model uncertainty by mapping the spatial congruence in priorities (i.e., top ranks) resulting from each model for each species and calculating the coefficient of variation across model ranks for each location. This allowed identification of areas more likely to be good targets of conservation effort for a species, those areas that were least likely, and those in between where uncertainty is higher and thus conservation action incorporates more risk. Based on our results, models developed independently for the same purpose (conservation planning for a particular species in a particular geography) yield different answers and thus different conservation strategies. We assert that using only one habitat model (even if validated) as the foundation of a conservation plan is risky. Using multiple models (i.e., ensemble prediction) can reduce uncertainty and increase efficacy of conservation action when models corroborate one another and increase understanding of the system when they do not.     

The optimal harvest and management in the models of animal populations

We extended zero-cost optimization model for population of domestic animals. Also the model of hiring of labor in cattle-breeding farm is constructed and investigated.     

On estimating the exponent of power-law frequency distributions

Power-law frequency distributions characterize a wide array of natural phenomena. In ecology, biology, and many physical and social sciences, the exponents of these power laws are estimated to draw inference about the processes underlying the phenomenon, to test theoretical models, and to scale up from local observations to global patterns. Therefore, it is essential that these exponents be estimated accurately. Unfortunately, the binning-based methods traditionally used in ecology and other disciplines perform quite poorly. Here we discuss more sophisticated methods for fitting these exponents based on cumulative distribution functions and maximum likelihood estimation. We illustrate their superior performance at estimating known exponents and provide details on how and when ecologists should use them. Our results confirm that maximum likelihood estimation outperforms other methods in both accuracy and precision. Because of the use of biased statistical methods for estimating the exponent, the conclusions of several recently published papers should be revisited.     

On inferring population trends of mobile waterbirds from aerial transect surveys in variable environments

Environmental and Ecological Statistics - Monitoring waterbird populations in Australia is challenging for reasons of counting logistics, and because population aggregation and dispersion can shift...     

Group navigation and the "many-wrongs principle" in models of animal movement

Traditional studies of animal navigation over both long and short distances have usually considered the orientation ability of the individual only, without reference to the implications of group membership. However, recent work has suggested that being in a group can significantly improve the ability of an individual to align toward and reach a target direction or point, even when all group members have limited navigational ability and there are no leaders. This effect is known as the "many-wrongs principle" since the large number of individual navigational errors across the group are suppressed by interactions and group cohesion. In this paper, we simulate the many-wrongs principle using a simple individual-based model of movement based on a biased random walk that includes group interactions. We study the ability of the group as a whole to reach a target given different levels of individual navigation error, group size, interaction radius, and environmental turbulence. In scenarios with low levels of environmental turbulence, simulation results demonstrate a navigational benefit from group membership, particularly for small group sizes. In contrast, when movement takes place in a highly turbulent environment, simulation results suggest that the best strategy is to navigate as individuals rather than as a group.     

Sensitivity of ecological models to their climate drivers: statistical ensembles for forcing.

Global and regional numerical models for terrestrial ecosystem dynamics require fine spatial resolution and temporally complete historical climate fields as input variables. However, because climate observations are unevenly spaced and have incomplete records, such fields need to be estimated. In addition, uncertainty in these fields associated with their estimation are rarely assessed. Ecological models are usually driven with a geostatistical model's mean estimate (kriging) of these fields without accounting for this uncertainty, much less evaluating such errors in terms of their propagation in ecological simulations. We introduce a Bayesian statistical framework to model climate observations to create spatially uniform and temporally complete fields, taking into account correlation in time and space, spatial heterogeneity, lack of normality, and uncertainty about all these factors. A key benefit of the Bayesian model is that it generates uncertainty measures for the generated fields. To demonstrate this method, we reconstruct historical monthly precipitation fields (a driver for ecological models) on a fine resolution grid for a climatically heterogeneous region in the western United States. The main goal of this work is to evaluate the sensitivity of ecological models to the uncertainty associated with prediction of their climate drivers. To assess their numerical sensitivity to predicted input variables, we generate a set of ecological model simulations run using an ensemble of different versions of the reconstructed fields. We construct such an ensemble by sampling from the posterior predictive distribution of the climate field. We demonstrate that the estimated prediction error of the climate field can be very high. We evaluate the importance of such errors in ecological model experiments using an ensemble of historical precipitation time series in simulations of grassland biogeochemical dynamics with an ecological numerical model, Century. We show how uncertainty in predicted precipitation fields is propagated into ecological model results and that this propagation had different modes. Depending on output variable, the response of model dynamics to uncertainty in inputs ranged from uncertainty in outputs that matched that of inputs to those that were muted or that were biased, as well as uncertainty that was persistent in time after input errors dropped.     

Comparative performance of generalized additive models and multivariate adaptive regression splines for statistical modelling of species distributions

Two statistical modelling techniques, generalized additive models (GAM) and multivariate adaptive regression splines (MARS), were used to analyse relationships between the distributions of 15 freshwater fish species and their environment. GAM and MARS models were fitted individually for each species, and a MARS multiresponse model was fitted in which the distributions of all species were analysed simultaneously. Model performance was evaluated using changes in deviance in the fitted models and the area under the receiver operating characteristic curve (ROC), calculated using a bootstrap assessment procedure that simulates predictive performance for independent data. Results indicate little difference between the performance of GAM and MARS models, even when MARS models included interaction terms between predictor variables. Results from MARS models are much more easily incorporated into other analyses than those from GAM models. The strong performance of a MARS multiresponse model, particularly for species of low prevalence, suggests that it may have distinct advantages for the analysis of large datasets. Its identification of a parsimonious set of environmental correlates of community composition, coupled with its ability to robustly model species distributions in relation to those variables, can be seen as converging strongly with the purposes of traditional ordination techniques.     

A comparison of two models with Landsat data for estimating above ground grassland biomass in Inner Mongolia,China

Two models, artificial neural network (ANN) and multiple linear regression (MLR), were developed to estimate typical grassland aboveground dry biomass in Xilingol River Basin, Inner Mongolia, China. The normalized difference vegetation index (NDVI) and topographic variables (elevation, aspect, and slope) were combined with atmospherically corrected reflectance from the Landsat ETM+ reflective bands as the candidate input variables for building both models. Seven variables (NDVI, aspect, and bands 1, 3, 4, 5 and 7) were selected by the ANN model (implemented in Statistica 6.0 neural network module), while six (elevation, NDVI, and bands 1, 3, 5 and 7) were picked to fit the MLR function after a stepwise analysis was executed between the candidate input variables and the above ground dry biomass. Both models achieved reasonable results with RMSEs ranging from 39.88% to 50.08%. The ANN model provided a more accurate estimation (RMSE_r = 39.88% for the training set, and RMSE_r = 42.36% for the testing set) than MLR (RMSE_r = 49.51% for the training, and RMSE_r = 53.20% for the testing). The final above ground dry biomass maps of the research area were produced based on the ANN and MLR models, generating the estimated mean values of 121 and 147 g/m², respectively.     

Uncertain sightings and the extinction of the Ivory-billed Woodpecker

The extinction of a species can be inferred from a record of its sightings. Existing methods for doing so assume that all sightings in the record are valid. Often, however, there are sightings of uncertain validity. To date, uncertain sightings have been treated in an ad hoc way, either excluding them from the record or including them as if they were certain. We developed a Bayesian method that formally accounts for such uncertain sightings. The method assumes that valid and invalid sightings follow independent Poisson processes and use noninformative prior distributions for the rate of valid sightings and for a measure of the quality of uncertain sightings. We applied the method to a recently published record of sightings of the Ivory-billed Woodpecker (Campephilus principalis). This record covers the period 1897-2010 and contains 39 sightings classified as certain and 29 classified as uncertain. The Bayes factor in favor of extinction was 4.03, which constitutes substantial support for extinction. The posterior distribution of the time of extinction has 3 main modes in 1944, 1952, and 1988. The method can be applied to sighting records of other purportedly extinct species.     

Inferring extinction of mammals from sighting records, threats, and biological traits

For species with five or more sightings, quantitative techniques exist to test whether a species is extinct on the basis of distribution of sightings. However, 70% of purportedly extinct mammals are known from fewer than five sightings, and such models do not include some important indicators of the likelihood of extinction such as threats, biological traits, search effort, and demography. Previously, we developed a quantitative method that we based on species' traits in which we used Cox proportional hazards regression to calculate the probability of rediscovery of species regarded as extinct. Here, we used two versions of the Cox regression model to determine the probability of extinction in purportedly extinct mammals and compared the results of these two models with those of stationary Poisson, nonparametric, and Weibull sighting-distribution models. For mammals with five or more sightings, the stationary Poisson model categorized all but two critically endangered (flagged as possibly extinct) species in our data set as extinct, and results with this model were consistent with current categories of the International Union for the Conservation of Nature. The scores of probability of rediscovery for individual species in one version of our Cox regression model were correlated with scores assigned by the stationary Poisson model. Thus, we used this Cox regression model to determine the probability of extinction of mammals with sparse records. On the basis of the Cox regression model, the most likely mammals to be rediscovered were the Montane monkey-faced bat (Pteralopex pulchra), Armenian myotis (Myotis hajastanicus), Alcorn's pocket gopher (Pappogeomys alcorni), and Wimmer's shrew (Crocidura wimmeri). The Cox model categorized two species that have recently disappeared as extinct: the baiji (Lipotes vexillifer) and the Christmas Island pipistrelle (Pipistrellus murrayi). Our new method can be used to test whether species with few records or recent last-sighting dates are likely to be extinct.