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.     

物种敏感度分布的非参数核密度估计模型

针对目前物种敏感度分布参数方法建模所存在的缺点,首次提出基于非参数核密度估计方法的物种敏感度分布模型,并提出相应的最优窗宽和检验方法。选用无机汞作为案例研究对象,利用非参数核密度估计方法和3种传统参数模型分别推导了保护我国水生生物的无机汞的急性水质基准值。结果表明,非参数核密度估计方法在推导无机汞水质基准中的稳健性和精确度都大大优于传统参数模型,能够更好地构建物种敏感度分布曲线。该方法的提出丰富了水质基准的理论方法学,为更好地保护水生生物提供了有力的支撑。     

A copula-based inference to piecewise exponential models under dependent censoring,with application to time to metamorphosis of salamander larvae

In ecology and evolutionary biology, controlled animal experiments are often conducted to measure time to metamorphosis which is possibly censored by the competing risk of death and the follow-up end. This paper considers the problem of estimating the survival function of time-to-event when it is subject to dependent censoring. When the censorship is due to competing risks, the traditional assumption of independent censorship may not be satisfied, and hence, the usual application of the Kaplan–Meier estimator yields a biased estimation for the survival function of the event time. This paper follows an assumed copula approach (Zheng and Klein in Biometrika 82(1):127–138, 1995) to adjust for dependence between the event time of interest and the competing event time. While the literature on an assumed copula approach has mostly focused on semiparametric settings, we alternatively consider a parametric approach with piecewise exponential models for fitting the survival function. We develop maximum likelihood estimation under the piecewise exponential models with an assumed copula. A goodness-of-fit procedure is also developed, which touches upon the identifiability issue of the copula. We conduct simulations to examine the performance of the proposed method and compare it with an existing semiparametric method. The method is applied to real data analysis on time to metamorphosis for salamander larvae living in Hokkaido, Japan (Michimae et al. in Evol Ecol Res 16:617–629, 2014).     

Use of individual-based models for population parameters estimation

A method for parameters estimation of stage-specific mortality and fecundity rate functions in poikilotherm organisms, and in particular for arthropod structured population, is proposed. The application of this method requires three types of information: stage-frequency data of a sampled population, development rate function and time evolution of forcing variables affecting the rate functions. By means of an individual-based model (a microscopic model) the number of eggs produced by the adults is generated starting from the number of individuals collected at each sampling time. Using a compartmental model (a macroscopic model) a stage-structured population dynamics is described and compared with observations. Non-linear regression methods based on least square principle are used to estimate the optimal parameters of the mortality and fecundity rate functions combining microscopic and macroscopic models. As a case study, the parameter estimation of the temperature-dependent mortality function of olives fruit fly Bactrocera oleae is 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.     

Estimation of spatiotemporal trends in bat abundance from mortality data collected at wind turbines

Renewable energy sources, such as wind energy, are essential tools for reducing the causes of climate change, but wind turbines can pose a collision risk for bats. To date, the population-level effects of wind-related mortality have been estimated for only 1 bat species. To estimate temporal trends in bat abundance, we considered wind turbines as opportunistic sampling tools for flying bats (analogous to fishing nets), where catch per unit effort (carcass abundance per monitored turbine) is a proxy for aerial abundance of bats, after accounting for seasonal variation in activity. We used a large, standardized data set of records of bat carcasses from 594 turbines in southern Ontario, Canada, and corrected these data to account for surveyor efficiency and scavenger removal. We used Bayesian hierarchical models to estimate temporal trends in aerial abundance of bats and to explore the effect of spatial factors, including landscape features associated with bat habitat (e.g., wetlands, croplands, and forested lands), on the number of mortalities for each species. The models showed a rapid decline in the abundance of 4 species in our study area; declines in capture of carcasses over 7 years ranged from 65% (big brown bat [Eptesicus fuscus]) to 91% (silver-haired bat [Lasionycteris noctivagans]). Estimated declines were independent of the effects of mitigation (increasing wind speed at which turbines begin to generate electricity from 3.5 to 5.5 m/s), which significantly reduced but did not eliminate bat mortality. Late-summer mortality of hoary (Lasiurus cinereus), eastern red (Lasiurus borealis), and silver-haired bats was predicted by woodlot cover, and mortality of big brown bats decreased with increasing elevation. These landscape predictors of bat mortality can inform the siting of future wind energy operations. Our most important result is the apparent decline in abundance of four common species of bat in the airspace, which requires further investigation.     

Semiparametric space–time survival modeling of chronic wasting disease in deer

In this paper, we propose a semiparametric survival model to investigate the pattern of spatial and temporal variation in disease prevalence of chronic wasting disease (CWD) in wild deer in Wisconsin over the years 2002 and 2006. The semiparametric survival model we suggested allows to build a more flexible model than the parametric model with fewer parametric assumptions by modeling the baseline hazard using a Gamma process prior. Based on the proposed model, we investigate the geographical distribution of CWD, and assess the effect of sex on disease prevalence. We use a Bayesian hierarchical framework where latent parameters capture temporal and spatial trends in disease incidence, incorporating sex and spatially correlated random effects. We also propose bivariate baseline hazard which change over age and time simultaneously to adopt different effects of age and time on the baseline hazard. Inference is carried out by using MCMC simulation techniques in a fully Bayesian framework. Our results suggest that disease has been spreaded mainly in the disease eradication zone and male deer show a significantly higher infection probability than female deer.     

Semi-parametric statistical approaches for space-time process prediction

The problem of estimation and prediction of a spatial-temporal stochastic process, observed at regular times and irregularly in space, is considered. A mixed formulation involving a non- parametric component, accounting for a deterministic trend and the effect of exogenous variables, and a parametric component representing the purely spatio-temporal random variation is proposed. Correspondingly, a two-step procedure, first addressing the estimation of the non- parametric component, and then the estimation of the parametric component is developed from the residual series obtained, with spatial-temporal prediction being performed in terms of suitable spatial interpolation of the temporal variation structure. The proposed model formula-tion, together with the estimation and prediction procedure, are applied using a Gaussian ARMA structure for temporal modelling to space-time forecasting from real data of air pollution concentration levels in the region surrounding a power station in northwest Spain.     

Propagation functions for monitoring distributional changes

In environmental assessment and monitoring, a primary objective of the investigator is to describe the changes occurring in the environmentally important variables over time. Propagation functions have been proposed to describe the distributional changes occurring in the variable of interest at two different times. McDonald et al. (1992, 1995) proposed an estimator of propagation function under the assumption of normality. We conduct a detailed sensitivity analysis of inference based on the normal model. It turns out that this model is appropriate only for small departures from normality whereas, for moderate to large departures, both estimation and testing of hypothesis break down. Non-parametric estimation of the propagation function based on kernel density estimation is also considered and the robustness of the choice of bandwidth for kernel density estimation is investigated. Bootstrapping is employed to obtain confidence intervals for the propagation function and also to determine the critical regions for testing the significance of distributional changes between two sampling epochs. Also studied briefly is the mathematical form and graphical shape of the propagation function for some parametric bivariate families of distributions. Finally, the proposed estimation techniques are illustrated on a data set of tree ring widths.     

Statistical Estimation and Model Selection of Species-Accumulation Functions

Abstract:  Soberón and Llorente (1993) proposed pure-birth stochastic processes as theoretical models for species-accumulation curves, and these processes have frequently been used to describe the progress of biological inventories. We describe, in algorithmic form, an alternative statistical analysis based on a likelihood approach ( Díaz-Francés & Gorostiza 2002 ) that provides mathematical rigor to the ideas in Soberón and Llorente (1993) and improves the estimation of the models by incorporating the facts that the variance of the error is not constant and that the observations are correlated. Additionally, we used the likelihood ratios between candidate models as an objective procedure for model selection, allowing comparison between the goodness of fit of various models. The software for these statistical methods can now be downloaded off the Internet. We used two examples of butterfly data sets to illustrate the use of the methods and the software.     

Seed terminal velocity, wind turbulence, and demography drive the spread of an invasive tree in an analytical model

Little is known about the relative importance of mechanistic drivers of plant spread, particularly when long-distance dispersal (LDD) events occur. Most methods to date approach LDD phenomenologically, and all mechanistic models, with one exception, have been implemented through simulation. Furthermore, the few recent mechanistically derived spread models have examined the relative role of different dispersal parameters using simulations, and a formal analytical approach has not yet been implemented. Here we incorporate an analytical mechanistic wind dispersal model (WALD) into a demographic matrix model within an analytical integrodifference equation spread model. We carry out analytical perturbation analysis on the combined model to determine the relative effects of dispersal and demographic traits and wind statistics on the spread of an invasive tree. Models are parameterized using data collected in situ and tested using independent data on historical spread. Predicted spread rates and direction match well the two historical phases of observed spread. Seed terminal velocity has the greatest potential influence on spread rate, and three wind properties (turbulence coefficient, mean horizontal wind speed, and standard deviation of vertical wind speed) are also important. Fecundity has marginal importance for spread rate, but juvenile survival and establishment are consistently important. This coupled empirical/theoretical framework enables prediction of plant spread rate and direction using fundamental dispersal and demographic parameters and identifies the traits and environmental conditions that facilitate spread. The development of an analytical perturbation analysis for a mechanistic spread model will enable multispecies comparative studies to be easily implemented in the future.     

Combining multistate capture-recapture data with tag recoveries to estimate demographic parameters

Matrix population models that allow an animal to occupy more than one state over time are important tools for population and evolutionary ecologists. Definition of state can vary, including location for metapopulation models and breeding state for life history models. For populations whose members can be marked and subsequently reencountered, multistate mark-recapture models are available to estimate the survival and transition probabilities needed to construct population models. Multistate models have proved extremely useful in this context, but they often require a substantial amount of data and restrict estimation of transition probabilities to those areas or states subjected to formal sampling effort. At the same time, for many species, there are considerable tag recovery data provided by the public that could be modeled in order to increase precision and to extend inference to a greater number of areas or states. Here we present a statistical model for combining multistate capture-recapture data (e.g., from a breeding ground study) with multistate tag recovery data (e.g., from wintering grounds). We use this method to analyze data from a study of Canada Geese (Branta canadensis) in the Atlantic Flyway of North America. Our analysis produced marginal improvement in precision, due to relatively few recoveries, but we demonstrate how precision could be further improved with increases in the probability that a retrieved tag is reported.     

Joint modelling of breeding and survival in the kittiwake using frailty models

Assessment of population dynamics is central to population dynamics and conservation. In structured populations, matrix population models based on demographic data have been widely used to assess such dynamics. Although highlighted in several studies, the influence of heterogeneity among individuals in demographic parameters and of the possible correlation among these parameters has usually been ignored, mostly because of difficulties in estimating such individual-specific parameters. In the kittiwake (Rissa tridactyla), a long-lived seabird species, differences in survival and breeding probabilities among individual birds are well documented. Several approaches have been used in the animal ecology literature to establish the association between survival and breeding rates. However, most are based on observed heterogeneity between groups of individuals, an approach that seldom accounts for individual heterogeneity. Few attempts have been made to build models permitting estimation of the correlation between vital rates. For example, survival and breeding probability of individual birds were jointly modelled using logistic random effects models by [Cam, E., Link, W.A., Cooch, E.G., Monnat, J., Danchin, E., 2002. Individual covariation in life-history traits: seeing the trees despite the forest. Am. Naturalist, 159, in press]. This is the only example in wildlife animal populations we are aware of. Here we adopt the survival analysis approaches from epidemiology. We model the survival and the breeding probability jointly using a normally distributed random effect (frailty). Conditionally on this random effect, the survival time is modelled assuming a lognormal distribution, and breeding is modelled with a logistic model. Since the deaths are observed in year-intervals, we also take into account that the data are interval censored. The joint model is estimated using classic frequentist methods and also MCMC techniques in Winbugs. The association between survival and breeding attempt is quantified using the standard deviation of the random frailty parameters. We apply our joint model on a large data set of 862 birds, that was followed from 1984 to 1995 in Brittany (France). Survival is positively correlated with breeding indicating that birds with greater inclination to breed also had higher survival.     

Modelling the effects of UV radiation on the survival of Antarctic krill (Euphausia superba Dana) in the face of limited data

Antarctic krill, Euphausia superba, is a keystone species of the Antarctic ecosystem. A fishery for krill may compete with land-based predators (penguins and seals), particularly during the breeding season. The Commission for the Conservation of Antarctic Marine Living Resources (CCAMLR) is moving towards management in small scale units. The management models specify predation and fishing mortality as space and time dependent but do not yet include non-predation natural mortality. Krill are known to be highly susceptible to ultraviolet radiation (UV) but there are limited empirical data. We develop a model for krill mortality caused by UV and parameterize and assess it by comparison with experimental data. The analysis allows us to identify key parameters that should be measured in future experiments and also leads to suggestions about modification of experimental procedure. We illustrate the method for krill found in the Livingston Island area and show that (a) it is possible to estimate the component of natural mortality due to UV-induced damage and (b) that cohorts born in 1979, 1984, or 1997 have different survival in the first 5 years of life, associated with differential UV exposure. In particular, those born in 1997 may have experienced as much as 10% lower survival than those born in 1979. The method developed here allows a potentially important source of krill mortality to be incorporated into the management models and suggests key experiments and field work in the future.     

Incorporating diverse data and realistic complexity into demographic estimation procedures for sea otters.

Reliable information on historical and current population dynamics is central to understanding patterns of growth and decline in animal populations. We developed a maximum likelihood-based analysis to estimate spatial and temporal trends in age/sex-specific survival rates for the threatened southern sea otter (Enhydra lutris nereis), using annual population censuses and the age structure of salvaged carcass collections. We evaluated a wide range of possible spatial and temporal effects and used model averaging to incorporate model uncertainty into the resulting estimates of key vital rates and their variances. We compared these results to current demographic parameters estimated in a telemetry-based study conducted between 2001 and 2004. These results show that survival has decreased substantially from the early 1990s to the present and is generally lowest in the north-central portion of the population's range. The greatest temporal decrease in survival was for adult females, and variation in the survival of this age/sex class is primarily responsible for regulating population growth and driving population trends. Our results can be used to focus future research on southern sea otters by highlighting the life history stages and mortality factors most relevant to conservation. More broadly, we have illustrated how the powerful and relatively straightforward tools of information-theoretic-based model fitting can be used to sort through and parameterize quite complex demographic modeling frameworks.     

Modelling the distribution of plant species using the autologistic regression model

For modeling the distribution of plant species in terms of climate covariates, we consider an autologistic regression model for spatial binary data on a regularly spaced lattice. This model belongs to the class of autologistic models introduced by Besag (1974). Three estimation methods, the coding method, maximum pseudolikelihood method and Markov chain Monte Carlo method are studied and comparedvia simulation and real data examples. As examples, we use the proposed methodology to model the distributions of two plant species in the state of Florida.     

Intercomparison of Two Models,ETA and RAMS,with TRACT Field Campaign Data

In this work a model intercomparison between RAMS and ETA models is carried out, with the aim of evaluating the quality and accuracy of these mesoscale models in reproducing the time evolution of the meteorology in real complex terrain. This is of great importance not only for meteorological forecast but also for air quality assessment. Numerical simulations are performed to reproduce the mean variables' fields and to compare them with measurements collected during the field campaign TRACT. The domain covers the Rhine valley and surrounding mountainous region and we consider a time period of two days. Results from simulations are compared to observations relative to ground stations and radiosoundings. A qualitative analysis is joined to a quantitative estimation of some reference statistical indexes. Both RAMS and ETA models performances are satisfactory when compared to the measured data and also their relative agreement is good. The mean variable fields are reproduced with a satisfactory degree of reliability, even if the simulated profiles are not able to describe the largest fluctuations of the variables. At the surface stations, the best agreement between predictions and observations is obtained for the wind velocity, while the quality of the results is lower for temperature and humidity.     

Estimating equations for separable spatial-temporal binary data

For binary data with correlation across space and over time, the literature concerning the estimation of fixed effects in marginal models is limited. In this paper, we model the marginal probability of binary responses in terms of parameters of interest by a logistic function. An estimating equation based on the quasi-likelihood concept is developed to estimate parameters. Under separable correlation models, we show that the quasi-likelihood estimate is asymptotically optimal. A series of simulations is conducted to evaluate how the efficiency varies with the regression coefficients. We also compare the relative efficiency with another estimating equation by simulations. The proposed method is applied to an ecological study of forest decline to test independence of two spatial-temporal binary outcomes.     

On spline-based approaches to spatial linear regression for geostatistical data

For spatial linear regression, the traditional approach to capture spatial dependence is to use a parametric linear mixed-effects model. Spline surfaces can be used as an alternative to capture spatial variability, giving rise to a semiparametric method that does not require the specification of a parametric covariance structure. The spline component in such a semiparametric method, however, impacts the estimation of the regression coefficients. In this paper, we investigate such an impact in spatial linear regression with spline-based spatial effects. Statistical properties of the regression coefficient estimators are established under the model assumptions of the traditional spatial linear regression. Further, we examine the empirical properties of the regression coefficient estimators under spatial confounding via a simulation study. A data example in precision agriculture research regarding soybean yield in relation to field conditions is presented for illustration.     

Flexible modeling for stock-recruitment relationships using Bayesian nonparametric mixtures

The stock and recruitment relationship is fundamental to the management of fishery natural resources. However, inferring stock-recruitment relationships is a challenging problem because of the limited available data, the collection of plausible models, and the biological characteristics that should be reflected in the model. Motivated by limitations of traditional parametric stock-recruitment models, we propose a Bayesian nonparametric approach based on a mixture model for the joint distribution of log-reproductive success and stock biomass. Flexible mixture modeling for this bivariate distribution yields rich inference for the stock-recruitment relationship through the implied conditional distribution of log-reproductive success given stock biomass. The method is illustrated with cod data from six regions of the North Atlantic, including comparison with simpler Bayesian parametric and semiparametric models.