Using hidden Markov chains and empirical Bayes change-point estimation for transect data

Consider a lattice of locations in one dimension at which data are observed. We model the data as a random hierarchical process. The hidden process is assumed to have a (prior) distribution that is derived from a two-state Markov chain. The states correspond to the mean values (high and low) of the observed data. Conditional on the states, the observations are modelled, for example, as independent Gaussian random variables with identical variances. In this model, there are four free parameters: the Gaussian variance, the high and low mean values, and the transition probability in the Markov chain. A parametric empirical Bayes approach requires estimation of these four parameters from the marginal (unconditional) distribution of the data and we use the EM-algorithm to do this. From the posterior of the hidden process, we use simulated annealing to find the maximum a posteriori (MAP) estimate. Using a Gibbs sampler, we also obtain the maximum marginal posterior probability (MMPP) estimate of the hidden process. We use these methods to determine where change-points occur in spatial transects through grassland vegetation, a problem of considerable interest to plant ecologists.     

On parametric estimation of population abundance for line transect sampling

Despite recent advances in nonparametric methods for estimating animal abundance, parametric methods are still used widely among biometricians due to their simplicity. In this paper, we propose an optimal shrinkage-type estimator and an empirical Bayes estimator for estimating animal density from line transect sampling data. The performances of the proposed estimators are compared with those of the maximum likelihood estimator and a bias-corrected maximum likelihood estimator both theoretically and numerically. Simulation results show that the optimal shrinkage-type estimator works the best if the detection function has a very thin tail (for example, the half normal detection function), while the maximum likelihood estimator is the best estimator if the detection function has relatively thick tail (for example, the polynomial detection function).     

Animal abundance estimation in independent observer line transect surveys

The theory of conventional line transect surveys is based on an essential assumption that 100% detection of animals right on the transect lines can be achieved. When this assumption fails, independent observer line transect surveys are used. This paper proposes a general approach, based on a conditional likelihood, which can be carried out either parametrically or nonparametrically, to estimate the abundance of non-clustered biological populations using data collected from independent observer line transect surveys. A nonparametric estimator is specifically proposed which combines the conditional likelihood and the kernel smoothing method. It has the advantage that it allows the data themselves to dictate the form of the detection function, free of any subjective choice. The bias and the variance of the nonparametric estimator are given. Its asymptotic normality is established which enables construction of confidence intervals. A simulation study shows that the proposed estimator has good empirical performance, and the confidence intervals have good coverage accuracy.     

A combination line transect and capture-recapture sampling model for multiple observers in aerial surveys

We present a robust sampling methodology to estimate population size using line transect and capture-recapture procedures for aerial surveys. Aerial surveys usually underestimate population density due to animals being missed. A combination of capture-recapture and line transect sampling methods with multiple observers allows violation of the assumption that all animals on the centreline are sighted from the air. We illustrate our method with an example of inanimate objects which shows evidence of failure of the assumption that all objects on the centreline have probability 1 of being detected. A simulation study is implemented to evaluate the performance of three variations of the Lincoln-Petersen estimator: the overall estimator, the stratified estimator, and the general stratified estimator based on the combined likelihood proposed in this paper. The stratified Lincoln-Petersen estimator based on the combined likelihood is found to be generally superior to the other estimators.     

Efficient statistical mapping of avian count data

We develop a spatial modeling framework for count data that is efficient to implement in high-dimensional prediction problems. We consider spectral parameterizations for the spatially varying mean of a Poisson model. The spectral parameterization of the spatial process is very computationally efficient, enabling effective estimation and prediction in large problems using Markov chain Monte Carlo techniques. We apply this model to creating avian relative abundance maps from North American Breeding Bird Survey (BBS) data. Variation in the ability of observers to count birds is modeled as spatially independent noise, resulting in over-dispersion relative to the Poisson assumption. This approach represents an improvement over existing approaches used for spatial modeling of BBS data which are either inefficient for continental scale modeling and prediction or fail to accommodate important distributional features of count data thus leading to inaccurate accounting of prediction uncertainty.     

Line transect sampling of Karner blue butterflies ( Lycaeides melissa samuelis)

Line transect sampling is an effective survey method for estimating butterfly densities because it provides unbiased estimates of site-density (provided key assumptions are met), and estimates are comparable among sites. For monitoring Karner blue butterflies in Wisconsin, USA, comparable estimates are required because each year a different selection of sites will be monitored. Annual state-wide indices of species abundance can be derived from the site-surveys and compared to previous year's indices to monitor trends. We advocate that line transect sampling is preferable to Pollard-Yates transects as a survey technique for monitoring Karner blue butter- flies. The Pollard-Yates surveys do not adjust for diferences in site detectability. As a consequence, estimates of among-site from Pollard-Yates surveys can be biased. © Rapid Science 1998     

Estimation of population density by spatially explicit capture-recapture analysis of data from area searches

The recent development of capture-recapture methods for estimating animal population density has focused on passive detection using devices such as traps or automatic cameras. Some species lend themselves more to active searching: a polygonal plot may be searched repeatedly and the locations of detected individuals recorded, or a plot may be searched just once and multiple cues (feces or other sign) identified as belonging to particular individuals. This report presents new likelihood-based spatially explicit capture-recapture (SECR) methods for such data. The methods are shown to be at least as robust in simulations as an equivalent Bayesian analysis, and to have negligible bias and near-nominal confidence interval coverage with parameter values from a lizard data set. It is recommended on the basis of simulation that plots for SECR should be at least as large as the home range of the target species. The R package "secr" may be used to fit the models. The likelihood-based implementation extends the spatially explicit analyses available for search data to include binary data (animal detected or not detected on each occasion) or count data (multiple detections per occasion) from multiple irregular polygons, with or without dependence among polygons. It is also shown how the method may be adapted for detections along a linear transect.     

Effects of anthropogenic disturbance on primate density at the landscape scale

Accurate estimations of the abundance of threatened animal populations are required for assessment of species’ status and vulnerability and conservation planning. However, density estimation is usually difficult and resource demanding, so researchers often collect data at local scales. However, anthropogenic pressures most often have landscape-level effects, for example, through habitat loss and fragmentation. We applied hierarchical distance sampling (HDS) to transect count data to determine the effect of habitat and anthropogenic factors on the density of 3 arboreal primate species inhabiting 5 distinct tropical forests across a landscape of 19,000 km² in the Udzungwa Mountains of Tanzania. We developed a novel, multiregion extension of HDS that allowed us to model density and detectability jointly across forests without losing site-specific information. For all species, the effect of anthropogenic disturbance on density was overwhelmingly negative among metapopulations: −0.63 Angolan colobus (Colobus angolensis palliatus) (95% Bayesian CI −1.03 to −0.27), −0.54 Udzungwa red colobus (Procolobus gordonorum) (−0.89 to −0.22), and −0.33 Sykes' monkey (Cercopithecus mitis monoides) (−0.63 to −0.07). Some responses to habitat factors were shared, notably the negative effect of elevation and the positive effect of climber coverage. These results are important for conservation science and practice because: the among-populations negative responses to anthropogenic disturbance provides a foundation for development of conservation plans that hold at the landscape scale, which is a comprehensive and cost-efficient approach; the among-species consistency in responses suggests conservation measures may be generalized at the guild level, which is especially relevant given the functional importance of primates in tropical rainforests; and the greater primate densities in areas at low elevation, which are closer to human settlements, point to specific management recommendations, such as the creation of buffer zones and prioritization of areas for protection.     

Sample based estimation of landscape metrics; accuracy of line intersect sampling for estimating edge density and Shannon’s diversity index

A recent trend is to estimate landscape metrics using sample data and cost-efficiency is one important reason for this development. In this study, line intersect sampling (LIS) was used as an alternative to wall-to-wall mapping for estimating Shannon’s diversity index and edge length and density. Monte Carlo simulation was applied to study the statistical performance of the estimators. All combinations of two sampling designs (random and systematic distribution of transects), four sample sizes, five transect configurations (straight line, L, Y, triangle, and quadrat), two transect orientations (fixed and random), and three configuration lengths were tested, each with a large number of simulations. Reference was 50 photos of size 1 km², already manually delineated in vector format by photo interpreters using GIS environment. The performance was compared by root mean square error (RMSE) and bias. The best combination for all three metrics was found to be the systematic design and as response design the straight line configuration with random orientation of transects, with little difference between the fixed and random orientation of transects. The rate of decrease of RMSE for increasing sample size and line length was studied with a mixed linear model. It was found that the RMSE decreased to a larger degree with the systematic design than the random one, especially with increasing sample size. Due to the nonlinearity in the definition of Shannon diversity estimator its estimator has a small and negative bias, decreasing with sample size and line length. Finally, a time study was conducted, measuring the time for registration of line intersections and their lengths on non-delineated aerial photos. The time study showed that long sampling lines were more cost-efficient than short ones for photo-interpretation.     

The reflection method of line intercept sampling to eliminate boundary bias

When a line transect overlaps the boundary of the sampled region, it can be reflected back on top of itself into the region, thereby making it possible to include elements near the edge twice from the same transect. A practical advantage of doing so is the reduction of field time and effort compared to the customary procedure of folding the transect back into another part of the region. An estimator is presented which accounts for this procedure in a way that preserves design-unbiased estimation.     

Logging Concessions Can Extend the Conservation Estate for Central African Tropical Forests

Abstract:  The management of tropical forest in timber concessions has been proposed as a solution to prevent further biodiversity loss. The effectiveness of this strategy will likely depend on species-specific, population-level responses to logging. We conducted a survey (749 line transects over 3450 km) in logging concessions (1.2 million ha) in the northern Republic of Congo to examine the impact of logging on large mammal populations, including endangered species such as the elephant ( Loxodonta africana ), gorilla ( Gorilla gorilla ), chimpanzee ( Pan troglodytes ), and bongo ( Tragelaphus eurycerus ). When we estimated species abundance without consideration of transect characteristics, species abundances in logged and unlogged forests were not different for most species. When we modeled the data with a hurdle model approach, however, analyzing species presence and conditional abundance separately with generalized additive models and then combining them to calculate the mean species abundance, species abundance varied strongly depending on transect characteristics. The mean species abundance was often related to the distance to unlogged forest, which suggests that intact forest serves as source habitat for several species. The mean species abundance responded nonlinearly to logging history, changing over 30 years as the forest recovered from logging. Finally the distance away from roads, natural forest clearings, and villages also determined the abundance of mammals. Our results suggest that logged forest can extend the conservation estate for many of Central Africa's most threatened species if managed appropriately. In addition to limiting hunting, logging concessions must be large, contain patches of unlogged forest, and include forest with different logging histories.     

Using accelerometer,high sample rate GPS and magnetometer data to develop a cattle movement and behaviour model

The study described in this paper developed a model of animal movement, which explicitly recognised each individual as the central unit of measure. The model was developed by learning from a real dataset that measured and calculated, for individual cows in a herd, their linear and angular positions and directional and angular speeds. Two learning algorithms were implemented: a Hidden Markov model (HMM) and a long-term prediction algorithm. It is shown that a HMM can be used to describe the animal's movement and state transition behaviour within several “stay” areas where cows remained for long periods. Model parameters were estimated for hidden behaviour states such as relocating, foraging and bedding. For cows’ movement between the “stay” areas a long-term prediction algorithm was implemented. By combining these two algorithms it was possible to develop a successful model, which achieved similar results to the animal behaviour data collected. This modelling methodology could easily be applied to interactions of other animal species.     

Predicting the variation in detection function in line transect sampling through random parameter model

A method for calibrating (localizing) detection function models in line transect sampling is proposed. The method is based on a random parameter model which supplies localized predictions of detection function parameters utilizing a few sample data points from the concerned location(s). The method has the clear advantage of being able to provide density estimates based on very few observations from a location which would be impossible through traditional methods. The method is successfully illustrated using census data on sambar (Cervus unicolor) from a set of wildlife sanctuaries in Kerala, India. The need for further research in this direction is indicated.     

Mapping species distributions in one dimension by non-homogeneous hidden Markov models: the case of freshwater pearl mussels in the River Dee

The investigation of species distributions in rivers involves data which are inherently sequential and unlikely to be fully independent. To take these characteristics into account, we develop a Bayesian hierarchical model for mapping the distribution of freshwater pearl mussels in the River Dee (Scotland). At the top of the hierarchy the likelihood is used to describe the sequence of sites in which mussels were observed or not. Given that false observations can occur, and that “not observed” means both that the species was not present and that it was not observed, a Markov prior is introduced at the second level of the hierarchy to represent the sequence of sites in which mussels are estimated to occur. The Markov prior allows modelling the spatial dependency between neighbouring sites. A third level in the hierarchy is given by the representation of the transition probabilities of the Markov chain in terms of site-specific explanatory variables, through a logistic regression. The selection of the explanatory variables which influence the Markov process is performed by means of a simulation-based procedure, in the complex case of association between covariates. Four features were found to be associated with reduced chance of finding a local mussel population: tributaries, bridges, dredging, and waste water treatment works. These results complement the results of a previous study, providing new evidence for the causes of the deterioration of a highly threatened species.     

Use of non-homogeneous Poisson process (NHPP) in presence of change-points to analyze drought periods: a case study in Brazil

Rain precipitation in the last years has been very atypical in different regions of the world, possibly, due to climate changes. We analyze Standard Precipitation Index (SPI) measures (1, 3, 6 and 12-month timescales) for a large city in Brazil: Campinas located in the southeast region of Brazil, São Paulo State, ranging from January 01, 1947 to May 01, 2011. A Bayesian analysis of non-homogeneous Poisson processes in presence or not of change-points is developed using Markov Chain Monte Carlo methods in the data analysis. We consider a special class of models: the power law process. We also discuss some discrimination methods for the choice of the better model to be used for the rain precipitation data.     

Extrapolating cetacean densities to quantitatively assess human impacts on populations in the high seas

As human activities expand beyond national jurisdictions to the high seas, there is an increasing need to consider anthropogenic impacts to species inhabiting these waters. The current scarcity of scientific observations of cetaceans in the high seas impedes the assessment of population‐level impacts of these activities. We developed plausible density estimates to facilitate a quantitative assessment of anthropogenic impacts on cetacean populations in these waters. Our study region extended from a well‐surveyed region within the U.S. Exclusive Economic Zone into a large region of the western North Atlantic sparsely surveyed for cetaceans. We modeled densities of 15 cetacean taxa with available line transect survey data and habitat covariates and extrapolated predictions to sparsely surveyed regions. We formulated models to reduce the extent of extrapolation beyond covariate ranges, and constrained them to model simple and generalizable relationships. To evaluate confidence in the predictions, we mapped where predictions were made outside sampled covariate ranges, examined alternate models, and compared predicted densities with maps of sightings from sources that could not be integrated into our models. Confidence levels in model results depended on the taxon and geographic area and highlighted the need for additional surveying in environmentally distinct areas. With application of necessary caution, our density estimates can inform management needs in the high seas, such as the quantification of potential cetacean interactions with military training exercises, shipping, fisheries, and deep‐sea mining and be used to delineate areas of special biological significance in international waters. Our approach is generally applicable to other marine taxa and geographic regions for which management will be implemented but data are sparse.     

Hidden process models for animal population dynamics.

Hidden process models are a conceptually useful and practical way to simultaneously account for process variation in animal population dynamics and measurement errors in observations and estimates made on the population. Process variation, which can be both demographic and environmental, is modeled by linking a series of stochastic and deterministic subprocesses that characterize processes such as birth, survival, maturation, and movement. Observations of the population can be modeled as functions of true abundance with realistic probability distributions to describe observation or estimation error. Computer-intensive procedures, such as sequential Monte Carlo methods or Markov chain Monte Carlo, condition on the observed data to yield estimates of both the underlying true population abundances and the unknown population dynamics parameters. Formulation and fitting of a hidden process model are demonstrated for Sacramento River winter-run chinook salmon (Oncorhynchus tshawytsha).     

Estimation bias under model selection for distance sampling detection functions

Many simulation studies have examined the properties of distance sampling estimators of wildlife population size. When assumptions hold, if distances are generated from a detection model and fitted using the same model, they are known to perform well. However, in practice, the true model is unknown. Therefore, standard practice includes model selection, typically using model comparison tools like Akaike Information Criterion. Here we examine the performance of standard distance sampling estimators under model selection. We compare line and point transect estimators with distances simulated from two detection functions, hazard-rate and exponential power series (EPS), over a range of sample sizes. To mimic the real-world context where the true model may not be part of the candidate set, EPS models were not included as candidates, except for the half-normal parameterization. We found median bias depended on sample size (being asymptotically unbiased) and on the form of the true detection function: negative bias (up to 15% for line transects and 30% for point transects) when the shoulder of maximum detectability was narrow, and positive bias (up to 10% for line transects and 15% for point transects) when it was wide. Generating unbiased simulations requires careful choice of detection function or very large datasets. Practitioners should collect data that result in detection functions with a shoulder similar to a half-normal and use the monotonicity constraint. Narrow-shouldered detection functions can be avoided through good field procedures and those with wide shoulder are unlikely to occur, due to heterogeneity in detectability.     

Feeding over the 24-h cycle: dietary flexibility of cathemeral collared lemurs (<Emphasis Type="Italic">Eulemur collaris</Emphasis>)

Animals show specific morphological, physiological and behavioural adaptations to diurnal or nocturnal activity. Cathemeral species, i.e. animals with activities distributed over the 24-h period, have to compromise between these specific adaptations. The driving evolutionary forces and the proximate costs and benefits of cathemerality are still poorly understood. Our goal was to evaluate the role of predator avoidance, food availability and diet quality in shaping cathemeral activity of arboreal mammals using a lemur species as an example. For this, two groups of collared lemurs, Eulemur collaris, were studied for 14 months in the littoral forest of southeastern Madagascar. Data on feeding behaviour were collected during all-day and all-night follows by direct observation. A phenological transect containing 78 plant species was established and monitored every 2 weeks to evaluate food availability during the study period. Characteristics of food items and animal nutritional intake were determined via biochemical analyses. The ratio of diurnal to nocturnal feeding was used as response variable in the analyses. The effects of abiotic environmental variables were removed statistically before the analyses of the biotic variables. We found that diurnal feeding lasted longer during the hot–wet season (December–February), whereas nocturnal feeding peaked during the hot–dry and cool–wet seasons (March–August). Although the lemurs foraged mostly in lower forest strata during daylight and used emergent trees preferably at night, the variables which measured animal exposure to birds of prey failed to predict the variation of the ratio of diurnal/nocturnal feeding. Ripe fruit availability and fiber intake are the two variables which best predicted the annual variation of the lemur diurnality. The data indicate that feeding over the whole 24-h cycle is advantageous during lean periods when animals have a fibre-rich, low-quality diet.