Tests for a biased sex ratio when the data are clustered

In behavioral ecology the overall sex ratio in a population of birds is often tested to see if it differs from a 50/50 ratio. In recent publications the binomial test or the ² test are carried out although the sexes of chicks within the same nest may not be independent. The lack of independence occurs since female birds can adjust the sex ratio in an adaptive way as demonstrated in recent studies. In order to take dependence into consideration the Wilcoxon signed rank test based on the within-brood differences between the proportions of sons and daughters was performed in a study investigating great tit hatchling sex ratios. We compare this test with a test based on an optimally weighted estimator recently proposed for medical studies with clustered binary data. According to our simulation results, this novel test is more powerful than the Wilcoxon signed rank test and should be used for the analysis of avian sex ratios. The methods are illustrated with real data from the great reed warbler.     

Robust benchmark dose determination based on profile score methods

We investigate several methods commonly used to obtain a benchmark dose and show that those based on full likelihood or profile likelihood methods might have severe shortcomings. We propose two new profile likelihood-based approaches which overcome these problems. Another contribution is the extension of the benchmark dose determination to non full likelihood models, such as quasi-likelihood, generalized estimating equations, which are widely used in settings such as developmental toxicity where clustered data are encountered. This widening of the scope of application is possible by the use of (robust) score statistics. Benchmark dose methods are applied to a data set from a developmental toxicity study.     

Nonparametric MLE incorporation of heterogeneity and model testing into premarked cohort studies

We utilize mixture models and nonparametric maximum likelihood estimation to both develop a likelihood ratio test (lrt) for a common simplifying assumption and to allow heterogeneity within premarked cohort studies. Our methods allow estimation of the entire probability model and thus one can not only estimate many parameters of interest but one can also bootstrap from the estimated model to predict many things, including the standard deviations of estimators. Simulations suggest that our lrt has the appropriate protection for Type I error and often has good power. In practice, our lrt is important for determining the appropriateness of estimators and in examining if a simple design with only one capture period could be utilized for a future similar study.     

Time series analysis of elemental and isotopic data from biomineralized whale tissue

A temporal record of environmental conditions is often contained within accretionary biological tissue. These records can provide knowledge of the environmental conditions that existed at the time the tissue was formed. In this study, we look at trace element concentrations and isotopic ratios of carbon and nitrogen as contained in baleen from bowhead whales in the eastern and western Arctic Ocean. Time series techniques, including maximum likelihood method and likelihood ratio tests, are applied to analysis of data and inference about their mean structures.     

Maximum likelihood method for parameter estimation in non-linear models with below detection data

The maximum likelihood (ML) method for regression analyzes of censored data (below detection limit) for nonlinear models is presented. The proposed ML method has been translated into an equivalent least squares method (ML-LS). A two stage iterative algorithm is proposed to estimate statistical parameters from the derived least squares translation. The developed algorithm is applied to a nonlinear model for prediction of ambient air CO concentration in terms of concentrations of respirable particulate matter (RSPM) and NO₂. It has been shown that if censored data are ignored or estimated through simplifications such as (i) censored data are equal to detection limit, (ii) censored data are half of the difference between detection limit and lower limit (e.g., zero or background level) or (iii) censored data are equal to lower limit, this can cause significant bias in estimated parameters. The developed ML-LS method provided better estimates of parameters than any of the simplifications in censored data.     

A pioneer validation of a state-space model of vessel trajectories (VMS) with observers’ data

In the context of the expansion of animal tracking and bio-logging, state-space models have been developed with the objective to characterise animals’ trajectories and to understand the factors controlling their behaviour. In the fisheries community, the electronic tagging of vessels commonly designated by Vessel Monitoring Systems (VMS) is developing and provides a new insight for the understanding, the analysis and the modelling of the trajectories of vessels and their prospecting behaviour. VMS data are thus a clue for the proper definition of fishing effort which remains a fundamental parameter of tuna stock assessments. In this context, we used the VMS (recording of hourly positions) of the French tropical tuna purse-seiners operating in the Indian Ocean to characterise three types of movement (states) on the VMS trajectories (stillness, tracking, and cruising). Based on empirical evidences, and on the regular frequency of VMS acquisition, this was achieved by the development of a Bayesian Hidden Markov model for the speeds and turning angles derived from the hourly steps of the trajectories. In a second phase, states were related to activities disentangling stillness into fishing or stop at sea. Finally the quality of the model performances was rigorously quantified thanks to observers’ data. Confronting model prediction and true activities allowed estimating that 10% of the hourly steps were misclassified. The assumptions and model’ choices are discussed, highlighting the fact that VMS data and observers’ data having different time resolutions, the effective use of validating data was troublesome. However, without validation, these analyses remain speculative. The validation part of this work represents an important step for the operational use of state-space models in ecology in the broad sense (predators’ tracking data, e.g. birds or mammals trajectories).     

Performance of a Bayesian state-space model of semelparous species for stock-recruitment data subject to measurement error

Measurement errors in spawner abundance create problems for fish stock assessment scientists. To deal with measurement error, we develop a Bayesian state-space model for stock-recruitment data that contain measurement error in spawner abundance, process error in recruitment, and time series bias. Through extensive simulations across numerous scenarios, we compare the statistical performance of the Bayesian state-space model with that of standard regression for a traditional stock-recruitment model that only considers process error. Performance varies depending on the information content in data, as determined by stock productivity, types of harvest situations, and amount of measurement error. Overall, in terms of estimating optimal spawner abundance S_MSY, the Ricker density-dependence parameter β, and optimal harvest rate h_MSY, the Bayesian state-space model works best for informative data from low and variable harvest rate situations for high-productivity salmon stocks. The traditional stock-recruitment model (TSR) may be used for estimating α and h_MSY for low-productivity stocks from variable and high harvest rate situations. However, TSR can severely overestimate S_MSY when spawner abundance is measured with large error in low and variable harvest rate situations. We also found that there is substantial merit in using h_MSY (or benchmarks derived from it) instead of S_MSY as a management target.     

A Bayesian hierarchical model for monitoring harbor seal changes in Prince William Sound, Alaska

Bayesian hierarchical models were used to assess trends of harbor seals, Phoca vitulina richardsi, in Prince William Sound, Alaska, following the 1989 Exxon Valdez oil spill. Data consisted of 4–10 replicate observations per year at 25 sites over 10 years. We had multiple objectives, including estimating the effects of covariates on seal counts, and estimating trend and abundance, both per site and overall. We considered a Bayesian hierarchical model to meet our objectives. The model consists of a Poisson regression model for each site. For each observation the logarithm of the mean of the Poisson distribution was a linear model with the following factors: (1) intercept for each site and year, (2) time of year, (3) time of day, (4) time relative to low tide, and (5) tide height. The intercept for each site was then given a linear trend model for year. As part of the hierarchical model, parameters for each site were given a prior distribution to summarize overall effects. Results showed that at most sites, (1) trend is down; counts decreased yearly, (2) counts decrease throughout August, (3) counts decrease throughout the day, (4) counts are at a maximum very near to low tide, and (5) counts decrease as the height of the low tide increases; however, there was considerable variation among sites. To get overall trend we used a weighted average of the trend at each site, where the weights depended on the overall abundance of a site. Results indicate a 3.3% decrease per year over the time period.     

A process-based model designed for filling of large data gaps in tower-based measurements of net ecosystem productivity

In this paper we present a simple hybrid gap-filling model (GFM) designed with a minimum number of parameters necessary to capture the ecological processes important for filling medium-to-large gaps in Flux data. As the model is process-based, the model has potential to be used in filling large gaps exhibiting a broad range of micro-meteorological and site conditions. The GFM performance was evaluated using “Punch hole” and extrapolation experiments based on data collected in west-central New Brunswick. These experiments indicated that the GFM is able to provide acceptable results (r² > 0.80) when >500 data points are used in model parameterization. The GFM was shown to address daytime evolution of NEP reasonably well for a wide range of weather and site conditions. An analysis of residuals indicated that for the most part no obvious trends were evident; although a slight bias was detected in NEP with soil temperature. To explore the portability of the GFM across ecosystem types, a transcontinental validation was conducted using NEP and ancillary data from seven ecosystems along a north-south transect (i.e., temperature–moisture gradient) from northern Europe (Finland) to the Middle East (Israel). The GFM was shown to explain over 75% of the variability in NEP measured at most ecosystems, which strongly suggests that the GFM maybe successfully applied to forest ecosystems outside Canada.     

Accounting for large-scale factors in the study of understory vegetation using a conditional logistic model

Local-scale and large-scale factors can affect the presence of a species of understory vegetation in the forest. Local-scale factors may be the influence of surrounding trees, while climate and latitude are typically considered large-scale factors. A model for the presence of a species needs to take into account both scales. A conditional logistic model is proposed for those studies where only the local-scale factors are of interest and that avoids estimating the large-scale parameters. Conditioning is carried out by the number of quadrats in the plot where the vegetation is found. As the latter is a sufficient statistic for the large-scale factors, a model free from these parameters is obtained. Data gathered in the permanent sample plots of the 1985–1986 National Forest Inventory of Finland is used for illustration, where the local-scale factor of interest is the influence of the trees, quantified by an index based on the size and location of the trees. The model fitted to Vaccinium vitis-idaea showed a significant and positive influence of Scots pine on the presence of this species, while for Calamagrostis arundinacea, a decrease in the odds ratio was observed due to the influence of Norway spruce.     

Uncertainty analyses for calibrating a soil carbon balance model to agricultural field trial data in Sweden and Kenya

How do additional data of the same and/or different type contribute to reducing model parameter and predictive uncertainties? Most modeling applications of soil organic carbon (SOC) time series in agricultural field trial datasets have been conducted without accounting for model parameter uncertainty. There have been recent advances with Monte Carlo-based uncertainty analyses in the field of hydrological modeling that are applicable, relevant and potentially valuable in modeling the dynamics of SOC. Here we employed a Monte Carlo method with threshold screening known as Generalized Likelihood Uncertainty Estimation (GLUE) to calibrate the Introductory Carbon Balance Model (ICBM) to long-term field trail data from Ultuna, Sweden and Machang’a, Kenya. Calibration results are presented in terms of parameter distributions and credibility bands on time series simulations for a number of case studies. Using these methods, we demonstrate that widely uncertain model parameters, as well as strong covariance between inert pool size and rate constant parameters, exist when root mean square simulation errors were within uncertainties in input estimations and data observations. We show that even rough estimates of the inert pool (perhaps from chemical analysis) can be quite valuable to reduce uncertainties in model parameters. In fact, such estimates were more effective at reducing parameter and predictive uncertainty than an additional 16 years time series data at Ultuna. We also demonstrate an effective method to jointly, simultaneously and in principle more robustly calibrate model parameters to multiple datasets across different climatic regions within an uncertainty framework. These methods and approaches should have benefits for use with other SOC models and datasets as well.     

Integrating soil carbon cycling with that of nitrogen and phosphorus in the watershed model SWAT: Theory and model testing

In this paper we describe and test a sub-model that integrates the cycling of carbon (C), nitrogen (N) and phosphorus (P) in the Soil Water Assessment Tool (SWAT) watershed model. The core of the sub-model is a multi-layer, one-pool soil organic carbon (S_C) algorithm, in which the decomposition rate of S_C and input rate to S_C (through decomposition and humification of residues) depend on the current size of S_C. The organic N and P fluxes are coupled to that of C and depend on the available mineral N and P, and the C:N and N:P ratios of the decomposing pools. Tillage explicitly affects the soil organic matter turnover rate through tool-specific coefficients. Unlike most models, the turnover of soil organic matter does not follow first order kinetics. Each soil layer has a specific maximum capacity to accumulate C or C saturation (S_x) that depends on texture and controls the turnover rate. It is shown in an analytical solution that S_x is a parameter with major influence in the model C dynamics. Testing with a 65-yr data set from the dryland wheat growing region in Oregon shows that the model adequately simulates the S_C dynamics in the topsoil (top 0.3 m) for three different treatments. Three key model parameters, the optimal decomposition and humification rates and a factor controlling the effect of soil moisture and temperature on the decomposition rate, showed low uncertainty as determined by generalized likelihood uncertainty estimation. Nonetheless, the parameter set that provided accurate simulations in the topsoil tended to overestimate S_C in the subsoil, suggesting that a mechanism that expresses at depth might not be represented in the current sub-model structure. The explicit integration of C, N, and P fluxes allows for a more cohesive simulation of nutrient cycling in the SWAT model. The sub-model has to be tested in forestland and rangeland in addition to agricultural land, and in diverse soils with extreme properties such high or low pH, an organic horizon, or volcanic soils.