Analysis of binary data via a centered spatial-temporal autologistic regression model

A centered spatial-temporal autologistic model is developed for analyzing spatial-temporal binary data observed on a lattice over time. We propose expectation-maximization pseudolikelihood and Monte Carlo expectation-maximization likelihood as well as consider Bayesian inference to obtain the estimates of model parameters. Further, we compare the statistical efficiency of the three approaches for various sizes of sampling lattices and numbers of sampling time points. Regarding prediction, we use Monte Carlo to obtain predictive distributions at future time points and compare the performance of the model with the uncentered spatial-temporal autologistic regression model. The methodology is demonstrated via simulation studies and a real data example concerning southern pine beetle outbreak in North Carolina.     

Estimating population dynamics without population data

We develop a biologically correct cost system for production systems facing invasive pests that allows the estimation of population dynamics without a priori knowledge of their true values. We apply that model to a data set for olive producers in Crete and derive from it predictions about the underlying population dynamics. Those dynamics are compared to information on population dynamics obtained from pest sampling with extremely favorable results.     

Bayesian testing for trend in a power model for clustered binary data

Developmental toxicity studies are widely used to investigate the potential risk of environmental hazards. In dose–response experiments, subjects are randomly allocated to groups receiving various dose levels. Tests for trend are then often applied to assess possible dose effects. Recent techniques for risk assessment in this area are based on fitting dose–response models. The complexity of such studies implies a number of non-trivial challenges for model development and the construction of dose-related trend tests, including the hierarchical structure of the data, litter effects inducing extra variation, the functional form of the dose–response curve, the adverse event at dam or at fetus level, the inference paradigm, etc. The purpose of this paper is to propose a Bayesian trend test based on a non-linear power model for the dose effect and using an appropriate model for clustered binary data. Our work is motivated by the analysis of developmental toxicity studies, in which the offspring of exposed and control rodents are examined for defects. Simulations show the performance of the method over a number of samples generated under typical experimental conditions.     

Estimating age-specific hazards from wildlife telemetry data

We illustrate 2 techniques for estimating age-specific hazards with wildlife telemetry data: Siler’s (Ecology 60:750–757, 1979) competing risk model fit using maximum likelihood and a penalized likelihood estimate that only assumes the hazard varies smoothly with age. In most telemetry studies, animals enter at different points in time (and at different ages), leading to data that are left-truncated. In addition, death times may only be known to occur within an interval of time (interval-censoring). Observations may also be right-censored (e.g., due to the end of the study, radio-collar failure, or emigration from the study area). It is important to consider the observation process, since the contribution of each individual’s data to the likelihood will depend on whether data are left-truncated or censored. We estimate age-specific hazards using telemetry data collected in two Phases during a 13-year study of white-tailed deer (Odocoileus virginianus) in northern Minnesota. The hazards estimated from the two methods were similar for the full data set that included 302 adults and 76 neonates (followed since or shortly after birth). However, estimated hazards for early-aged individuals differed considerably for subsets of the data that did not include neonates. We discuss the advantages and disadvantages of these two modeling approaches and also compare the estimators using a short simulation study.     

Estimation and testing for covariance-spectral spatial-temporal models

Environmental and Ecological Statistics - In this paper we explore a covariance-spectral modelling strategy for spatial-temporal processes which involves a spectral approach for time but a...     

Estimating the functional form for the density dependence from life history data

Two contrasting approaches to the analysis of population dynamics are currently popular: demographic approaches where the associations between demographic rates and statistics summarizing the population dynamics are identified; and time series approaches where the associations between population dynamics, population density, and environmental covariates are investigated. In this paper, we develop an approach to combine these methods and apply it to detailed data from Soay sheep (Ovis aries). We examine how density dependence and climate contribute to fluctuations in population size via age- and sex-specific demographic rates, and how fluctuations in demographic structure influence population dynamics. Density dependence contributes most, followed by climatic variation, age structure fluctuations and interactions between density and climate. We then simplify the density-dependent, stochastic, age-structured demographic model and derive a new phenomenological time series which captures the dynamics better than previously selected functions. The simple method we develop has potential to provide substantial insight into the relative contributions of population and individual-level processes to the dynamics of populations in stochastic environments.     

Estimating soil carbon turnover using radiocarbon data: A case-study for European Russia

Turnover rates of soil carbon for 20 soil types typical for a 3.7 million km² area of European Russia were estimated based on ¹⁴C data. The rates are corrected for bomb radiocarbon which strongly affects the topsoil ¹⁴C balance. The approach is applied for carbon stored in the organic and mineral layers of the upper 1 m of the soil profile. The turnover rates of carbon in the upper 20 cm are relatively high for forest soils (0.16–0.78% year⁻¹), intermediate for tundra soils (0.25% year⁻¹), and low for grassland soils (0.02–0.08% year⁻¹) with the exception of southern Chernozems (0.32% year⁻¹). In the soil layer of 20–100 cm depth, the turnover rates were much lower for all soil types (0.01–0.06% year⁻¹) except for peat bog soils of the southern taiga (0.14% year⁻¹). Combined with a map of soil type distribution and a dataset of several hundred soil carbon profiles, the method provides annual fluxes for the slowest components of soil carbon assuming that the latter is in equilibrium with climate and vegetation cover. The estimated carbon flux from the soil is highest for forest soils (12–147 gC/(m² year)), intermediate for tundra soils (33 gC/(m² year)), and lowest for grassland soils (1–26 gC/(m² year)). The approach does not distinguish active and recalcitrant carbon fractions and this explains the low turnover rates in the top layer. Since changes in soil types will follow changes in climate and land cover, we suggest that pedogenesis is an important factor influencing the future dynamics of soil carbon fluxes. Up to now, both the effect of soil type changes and the clear evidence from ¹⁴C measurements that most soil organic carbon has a millennial time scale, are basically neglected in the global carbon cycle models used for projections of atmospheric CO₂ in 21st century and beyond.     

Estimating survival rates with time series of standing age-structure data

It has long been recognized that age-structure data contain useful information for assessing the status and dynamics of wildlife populations. For example, age-specific survival rates can be estimated with just a single sample from the age distribution of a stable, stationary population. For a population that is not stable, age-specific survival rates can be estimated using techniques such as inverse methods that combine time series of age-structure data with other demographic data. However, estimation of survival rates using these methods typically requires numerical optimization, a relatively long time series of data, and smoothing or other constraints to provide useful estimates. We developed general models for possibly unstable populations that combine time series of age-structure data with other demographic data to provide explicit maximum likelihood estimators of age-specific survival rates with as few as two years of data. As an example, we applied these methods to estimate survival rates for female bison (Bison bison) in Yellowstone National Park, USA. This approach provides a simple tool for monitoring survival rates based on age-structure data.     

Estimating a distance dependent contagion function using point sample data

Natural events and human activities cause changes in landscape structure. Landscape metrics are used as a useful tool to study landscape trends and ecological processes related to the landscape structure. These metrics are commonly calculated on wall-to-wall raster data from remote sensing. A recent trend is to use sample data to estimate landscape metrics. In this study, point sampling was used to estimate a vector-based and distance dependent contagion metric. The metric is an extension of the established contagion. The statistical properties, for both unconditional and conditional contagions, were assessed by a point (point pairs) sampling experiment in maps from the National Inventory of landscapes in Sweden. Random and systematic sampling designs were tested for nine point distances and five sample sizes and for two classification systems. The systematic design showed slightly smaller root mean square error (RMSE) and bias than the random design. Both true and estimated values were calculated using computer programs in FORTRAN, which was specifically written for the purpose of the study. For a given sample size, RMSE and bias increased with increasing point distance. The estimator of unconditional contagion had acceptable RMSE and bias for moderate sample sizes, but in the conditional case the bias (and thus the RMSE) was unacceptably large. The main reason for this is that small classes (by area) affect both the true value of the contagion and are often missing in the sample. The method proposed can be adopted in gradient-based model of landscape structure where no distinct border is assumed between polygons. The method can also be applied in field-based inventories.     

Estimating the extinction date of the thylacine with mixed certainty data

The thylacine (Thylacinus cynocephalus), one of Australia's most characteristic megafauna, was the largest marsupial carnivore until hunting, and potentially disease, drove it to extinction in 1936. Although thylacines were restricted to Tasmania for 2 millennia prior to their extinction, recent so‐called plausible sightings on the Cape York Peninsula in northern Queensland have emerged, leading some to speculate the species may have persisted undetected. We compiled a data set that included physical evidence, expert‐validated sightings, and unconfirmed sightings up to the present day and implemented a range of extinction models (focusing on a Bayesian approach that incorporates all 3 types of data by modeling valid and invalid sightings as independent processes) to evaluate the likelihood of the thylacine's persistence. Although the last captive individual died in September 1936, our results suggested that the most likely extinction date would be 1940. Our other extinction models estimated the thylacine's extinction date between 1936 and 1943, and the most optimistic scenario indicated that the species did not persist beyond 1956. The search for the thylacine, much like similar efforts to rediscover other recently extinct charismatic taxa, is likely to be fruitless, especially given that persistence on Tasmania would have been no guarantee the species could reappear in regions that had been unoccupied for millennia. The search for the thylacine may become a rallying point for conservation and wildlife biology and could indirectly help fund and support critical research in understudied areas such as Cape York. However, our results suggest that attempts to rediscover the thylacine will be unsuccessful and that the continued survival of the thylacine is entirely implausible based on most current mathematical theories of extinction.     

Estimating age from recapture data: integrating incremental growth measures with ancillary data to infer age-at-length

Estimating the age of individuals in wild populations can be of fundamental importance for answering ecological questions, modeling population demographics, and managing exploited or threatened species. Significant effort has been devoted to determining age through the use of growth annuli, secondary physical characteristics related to age, and growth models. Many species, however, either do not exhibit physical characteristics useful for independent age validation or are too rare to justify sacrificing a large number of individuals to establish the relationship between size and age. Length-at-age models are well represented in the fisheries and other wildlife management literature. Many of these models overlook variation in growth rates of individuals and consider growth parameters as population parameters. More recent models have taken advantage of hierarchical structuring of parameters and Bayesian inference methods to allow for variation among individuals as functions of environmental covariates or individual-specific random effects. Here, we describe hierarchical models in which growth curves vary as individual-specific stochastic processes, and we show how these models can be fit using capture-recapture data for animals of unknown age along with data for animals of known age. We combine these independent data sources in a Bayesian analysis, distinguishing natural variation (among and within individuals) from measurement error. We illustrate using data for African dwarf crocodiles, comparing von Bertalanffy and logistic growth models. The analysis provides the means of predicting crocodile age, given a single measurement of head length. The von Bertalanffy was much better supported than the logistic growth model and predicted that dwarf crocodiles grow from 19.4 cm total length at birth to 32.9 cm in the first year and 45.3 cm by the end of their second year. Based on the minimum size of females observed with hatchlings, reproductive maturity was estimated to be at nine years. These size benchmarks are believed to represent thresholds for important demographic parameters; improved estimates of age, therefore, will increase the precision of population projection models. The modeling approach that we present can be applied to other species and offers significant advantages when multiple sources of data are available and traditional aging techniques are not practical.     

Estimating trend precision and power to detect trends across grouped count data

Ecologists commonly use grouped or clustered count data to estimate temporal trends in counts, abundance indices, or abundance. For example, the U.S. Breeding Bird Survey data represent multiple counts of birds from within each of multiple, spatially defined routes. Despite a reliance on grouped counts, analytical methods for prospectively estimating precision of trend estimates or statistical power to detect trends that explicitly acknowledge the characteristics of grouped count data are undescribed. These characteristics include the fact that the sampling variance is an increasing function of the mean, and that sampling and group-level variance estimates are generally estimated on different scales (the sampling and log scales, respectively). We address these issues for repeated sampling of a single population using an analytical approach that has the flavor of a generalized linear mixed model, specifically that of a negative binomial-distributed count variable with random group effects. The count mean, including grand intercept, trend, and random group effects, is modeled linearly on the log scale, while sampling variance of the mean is estimated on the log scale via the delta method. Results compared favorably with those derived using Monte Carlo simulations. For example, at trend = 5% per temporal unit, differences in standard errors and in power were modest relative to those estimated by simulation (< or = /11/% and < or = /16/%, respectively), with relative differences among power estimates decreasing to < or = /7/% when power estimated by simulations was > or = 0.50. Similar findings were obtained using data from nine surveys of fingernail clams in the Mississippi River. The proposed method is suggested (1) where simulations are not practical and relative precision or power is desired, or (2) when multiple precision or power calculations are required and where the accuracy of a fraction of those calculations will be confirmed using simulations.     

Estimating preferences for outdoor recreation:: a comparison of continuous and count data demand system frameworks

Continuous and count data demand system models have emerged as attractive alternatives to the discrete choice random utility maximization models (RUMs) that currently dominate the seasonal, multi-site recreation demand literature. This paper compares the frameworks conceptually and investigates their empirical performance with a common data set. Although the two modeling approaches employ substantially different behavioral and econometric assumptions, results from a recreation application based on the 1997 Iowa Wetlands Survey suggest that qualitatively similar policy inferences arise from the competing structures.     

Estimating wildfire growth from noisy and incomplete incident data using a state space model

Wildfire behaviors are complex and are of interest to fire managers and scientists for a variety of reasons. Many of these important behaviors are directly measured from the cumulative burn area time series of individual wildfires; however, estimating cumulative burn area time series is challenging due to the magnitude of measurement errors and missing entries. To resolve this, we introduce two state space models for reconstructing wildfire burn area using repeated observations from multiple data sources that include different levels of measurement error and temporal gaps. The constant growth parameter model uses a few parameters and assumes a burn area time series that follows a logistic growth curve. The non-constant growth parameter model uses a time-varying logistic growth curve to produce detailed estimates of the burn area time series that permit sudden pauses and pulses of growth. We apply both reconstruction models to burn area data from 13 large wildfire incidents to compare the quality of the burn area time series reconstructions and computational requirements. The constant growth parameter model reconstructs burn area time series with minimal computational requirements, but inadequately fits observed data in most cases. The non-constant growth parameter model better describes burn area time series, but can also be highly computationally demanding. Sensitivity analyses suggest that in a typical application, the reconstructed cumulative burn area time series is fairly robust to minor changes in the prior distributions.     

Adapting empirical equations to Lake Kinneret data by using three calibration methods

This paper examines whether the relationships between a number of characteristic limnological variables (suspended particulate matter, turbidity, Secchi depth, light attenuation, and chlorophyll a) determined for temperate lakes are consistent with the relationships found in Mediterranean lakes such as Lake Kinneret. We found that the use of published relationships between lake variables may lead to erroneous results when applied indiscriminately to other lake types.     

Estimating historic movement of a climatological variable from a pair of misaligned functional data sets

Environmental and Ecological Statistics - We consider the problem of estimating the mean function from a pair of paleoclimatic functional data sets after one of them has been registered with the...     

Estimating parameters of hidden Markov models based on marked individuals: use of robust design data

Development and use of multistate mark-recapture models, which provide estimates of parameters of Markov processes in the face of imperfect detection, have become common over the last 20 years. Recently, estimating parameters of hidden Markov models, where the state of an individual can be uncertain even when it is detected, has received attention. Previous work has shown that ignoring state uncertainty biases estimates of survival and state transition probabilities, thereby reducing the power to detect effects. Efforts to adjust for state uncertainty have included special cases and a general framework for a single sample per period of interest. We provide a flexible framework for adjusting for state uncertainty in multistate models, while utilizing multiple sampling occasions per period of interest to increase precision and remove parameter redundancy. These models also produce direct estimates of state structure for each primary period, even for the case where there is just one sampling occasion. We apply our model to expected-value data, and to data from a study of Florida manatees, to provide examples of the improvement in precision due to secondary capture occasions. We have also implemented these models in program MARK. This general framework could also be used by practitioners to consider constrained models of particular interest, or to model the relationship between within-primary-period parameters (e.g., state structure) and between-primary-period parameters (e.g., state transition probabilities).     

Estimating the status of nearshore rockfish (Sebastes spp.) populations with length frequency data.

Ecologists often point to excessive truncation of a population's size-structure as a deleterious effect of exploitation, yet the effect of this truncation on population persistence is seldom quantified. While persistence of marine populations requires maintenance of a sufficient level of lifetime reproduction, fishing reduces lifetime reproduction by increasing the total mortality rate, preventing individuals from growing old, large, and highly fecund. We employ a new method of estimating changes in lifetime egg production (LEP) using two samples of the size structure, one in the past and one current, to assess persistence of five species of nearshore rockfish (Sebastes spp.) in California and Oregon, U.S.A. Using length frequency data from catch in the recreational fishery, we estimate that since 1980, four of the five rockfish species considered have experienced declines in LEP to levels that suggest that persistence is impaired. When changes in LEP were estimated for subsets of the data corresponding to neighboring geographical regions, differences in LEP levels were apparent in the neighboring regions, implying that the effects of fishing mortality are not evenly distributed over space. We conclude by discussing the use of this estimation approach to assess the status of other species in data-poor situations.     

Estimating California ecosystem carbon change using process model and land cover disturbance data: 1951-2000

Land use change, natural disturbance, and climate change directly alter ecosystem productivity and carbon stock level. The estimation of ecosystem carbon dynamics depends on the quality of land cover change data and the effectiveness of the ecosystem models that represent the vegetation growth processes and disturbance effects. We used the Integrated Biosphere Simulator (IBIS) and a set of 30- to 60-m resolution fire and land cover change data to examine the carbon changes of California's forests, shrublands, and grasslands. Simulation results indicate that during 1951-2000, the net primary productivity (NPP) increased by 7%, from 72.2 to 77.1 Tg C yr⁻¹ (1 teragram = 10¹² g), mainly due to CO₂ fertilization, since the climate hardly changed during this period. Similarly, heterotrophic respiration increased by 5%, from 69.4 to 73.1 Tg C yr⁻¹, mainly due to increased forest soil carbon and temperature. Net ecosystem production (NEP) was highly variable in the 50-year period but on average equalled 3.0 Tg C yr⁻¹ (total of 149 Tg C). As with NEP, the net biome production (NBP) was also highly variable but averaged −0.55 Tg C yr⁻¹ (total of -27.3 Tg C) because NBP in the 1980s was very low (-5.34 Tg C yr⁻¹). During the study period, a total of 126 Tg carbon were removed by logging and land use change, and 50 Tg carbon were directly removed by wildland fires. For carbon pools, the estimated total living upper canopy (tree) biomass decreased from 928 to 834 Tg C, and the understory (including shrub and grass) biomass increased from 59 to 63 Tg C. Soil carbon and dead biomass carbon increased from 1136 to 1197 Tg C.Our analyses suggest that both natural and human processes have significant influence on the carbon change in California. During 1951-2000, climate interannual variability was the key driving force for the large interannual changes of ecosystem carbon source and sink at the state level, while logging and fire were the dominant driving forces for carbon balances in several specific ecoregions. From a long-term perspective, CO₂ fertilization plays a key role in maintaining higher NPP. However, our study shows that the increase in C sequestration by CO₂ fertilization is largely offset by logging/land use change and wildland fires.     

Selecting a binary Markov model for a precipitation process

This paper uses rth-order categorical Markov chains to model the probability of precipitation. Several stationary and non-stationary high-order Markov models are proposed and compared using BIC. The number of parameters increases exponentially by adding the Markov order. Several classes of high-order Markov models are proposed which their increase of number of parameters are modest. For example models that use the number of precipitation days in a period prior to date, temperature of the previous day and sines/cosines periodic functions (to model the seasonality) are considered. The theory of partial likelihood is used to estimate the parameters. Parsimonious non-stationary first order Markov models with few seasonal terms are found optimal using BIC and temperature does not turn out to be a useful covariate. However BIC seems to underestimate the number of seasonal terms. We have also compared the results with AIC in some cases which tends to pick parsimonious models with more seasonal terms and higher order. We also show that ignoring seasonal terms result in picking higher order Markov chains. Finally we apply the methods to build confidence intervals for the probability of periods with no precipitation or low number of precipitation days in Calgary using historical data from 1980 to 2000.