Bifurcating Markov chains (BMCs) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We provide a central limit theorem for additive functionals of BMCs under $L^2$ -ergodic conditions with three different regimes. This completes the pointwise approach developed in a previous work. As an application, we study the elementary case of a symmetric bifurcating autoregressive process, which justifies the nontrivial hypothesis considered on the kernel transition of the BMCs. We illustrate in this example the phase transition observed in the fluctuations.

For many mammal species, converting dung density into population density requires accurate estimates of defaecation rate and dung survival time. The latter parameter probably varies seasonally. In Nki National Park, south-east Cameroon, we monitored 216 dung piles of the blue duiker Philantomba monticola and 373 of the red duiker group (Cephalophus spp.), major game animals in Central Africa, and estimated dung survival time across seasons. Mean survival time was 6.83 days in the major dry season and 1.21–1.81 in other seasons for the blue duiker, and 7.37 and 1.53–4.05 for red duikers, lower than the values conventionally used for density estimations in Central Africa (i.e. 18 days for the blue duiker and 21 days for red duikers). Overall, beetles removed half of the dung within 1 day of deposition. However, the proportion of dung piles that beetles removed was significantly lower in the major dry season, and other dung piles remained longer until they disappeared as a result of other factors. As shorter dung survival time results in higher estimates of population density, our findings imply that in forests with intense beetle activity, duiker densities are higher than those based on the conventional values of dung survival time. Duiker densities and dung survival time should be estimated simultaneously. To minimize the bias introduced by rapid removal of fresh dung by beetles, only fresh dung (< 3 hours old) should be monitored when estimating mean dung survival time.

Populations of the globally endangered Giant Nuthatch Sitta magna have declined significantly throughout their small world range in southern China and northern continental South-East Asia. Distance sampling and direct observations were used to estimate the density and habitat use of the Giant Nuthatch in a potential stronghold for the species, Chiang Dao Wildlife Sanctuary, Thailand. Thirteen line transects covering 6.2 km were established in open, pine-oak habitat favoured by the nuthatch, during November 2014 to December 2015. The mean density of Giant Nuthatch was 3.94±1.22 (95% CI = 2.15–7.22) individuals/km2. Hierarchical distance sampling models indicated that habitat use by Giant Nuthatch was strongly correlated with trees of large diameter. A pair of Giant Nuthatches was radio-tracked as they fed nestlings during the 2016 breeding season. The female’s home range, centred on the nest, was 7.79 ha (95% kernel home range), approximately one-fourth of that of the male, 32.01 ha. Giant Nuthatches showed a significant preference for foraging on pines Pinus spp. and used the fissured bark of mature pines in which to store acorns of deciduous tree species. Our research indicates the importance of large, mature trees in open pine-oak forest in supporting Giant Nuthatch populations.

The giant otter Pteronura brasiliensis, categorized as Endangered on the IUCN Red List, was once widely distributed throughout South America. By the middle of the 20th century the giant otter had become locally extinct along the main rivers of the Orinoco basin. Although some populations seem to have recovered, the paucity of information available does not permit a full evaluation of the species' conservation status. The objective of this study was to estimate the abundance and density of the giant otter population along the Orinoco river in the municipality of Puerto Carreño, Vichada, Colombia, where there is important commercial and recreational fishing. Thirty-nine linear km were surveyed, repeatedly, with a total of 315 km of surveys. Population size was estimated by direct counts of individuals. All individuals detected were photographed and identified individually from their throat pelage patterns. In total, 30 otters were identified, giving a minimum density of 0.77 individuals per km, one of the highest reported for the species in Colombia. Given the high density in this well-developed area, our results highlight the importance of this population for the conservation of the species.

The random encounter model, a method for estimating animal density using camera traps without the need for individual recognition, has been developed over the past decade. A key assumption of this model is that cameras are placed randomly in relation to animal movements, requiring that cameras are not set only at sites thought to have high animal traffic. The aim of this study was to define a correction factor that allows the random encounter model to be applied in photo-trapping surveys in which cameras are placed along tracks to maximize capture probability. Our hypothesis was that applying such a correction factor would compensate for the different rates at which lynxes use tracks and the surrounding area, and should thus improve the estimates obtained with the random encounter model. We tested this using data from a well-known Iberian lynx Lynx pardinus population. Firstly, we estimated Iberian lynx densities using a traditional camera-trapping design followed by spatially explicit capture–recapture analyses. We estimated the differential use rate for tracks vs the surrounding area using data from a lynx equipped with a GPS collar, and subsequently calculated the correction factor. As expected, the random encounter model overestimated densities by 378%. However, the application of the correction factor improved the estimate and reduced the error to 16%. Although there are limitations to the application of the correction factor, the corrected random encounter model shows potential for density estimation of species for which individual identification is not possible.

All gibbon species are declining throughout South and South-east Asia because of habitat loss and human activities such as hunting. Lao still contains a relatively large area of forest habitat suitable for gibbons, but their status in the country remains poorly known. Here we present the first density estimate of the Critically Endangered northern white-cheeked gibbon Nomascus leucogenys in Nam Et-Phou Louey National Protected Area, northern Lao. We conducted gibbon surveys using an auditory sampling technique during May–August 2014 and May 2015, at 40 sites, covering 125.6 km2. We applied N-mixture models to analyse group counts, investigating which landscape and human disturbance covariates influenced the spatial variation of gibbon abundance across the study area. We estimated the average gibbon density to be 0.4 groups/km2. Gibbon density was higher in mixed deciduous forest (0.74 groups/km2) than in evergreen forest (0.09 groups/km2), which could be a result of long-term hunting in evergreen forest areas. Thus, future gibbon protection plans should consider not only evergreen forest as priority habitat, but also deciduous forest, which tends to receive less attention in conservation planning. We also highlight key areas containing gibbons where law enforcement patrols should be focussed, to limit threats such as poaching. Future forest management plans should aim to maximize the size and connectivity of suitable gibbon habitat, to enable exchange between subpopulations.

Rigorous status estimates of populations of large carnivores are necessary to inform their management and help evaluate the effectiveness of conservation interventions. The African leopard Panthera pardus faces rising anthropogenic pressures across most of its contracting sub-Saharan range, but the scarcity of reliable population estimates means that management decisions often have to rely on expert opinion rather than being based on sound evidence. This is particularly true for Mozambique, where little is known about the ecology or conservation status of leopard populations as a result of prolonged armed conflict. We used camera trapping and spatially explicit capture–recapture models to provide a leopard density estimate in Xonghile Game Reserve in southern Mozambique, which is part of the Greater Limpopo Transfrontier conservation initiative. The estimated population density was 2.60 ± SE 0.96 leopards/100 km2. Our study provides a baseline leopard density for the region and the first empirical density estimate for southern Mozambique. Our results also suggest that current methods used to set trophy hunting quotas for leopards, both in Mozambique and elsewhere in Africa, may be leading to unsustainable quotas, which highlights the importance of robust empirical data in guiding conservation policy.

Insurance regulation often dictates that insurers monitor their solvency risk in real time and take appropriate actions whenever the risk exceeds their tolerance level. Bayesian methods are appealing for prediction problems thanks to their ability to naturally incorporate both sample variability and parameter uncertainty into a predictive distribution. However, handling data arriving in real time requires a flexible non-parametric model, and the Monte Carlo methods necessary to evaluate the predictive distribution in such cases are not recursive and can be too expensive to rerun each time new data arrives. In this paper, we apply a recently developed alternative perspective on Bayesian prediction based on copulas. This approach facilitates recursive Bayesian prediction without computing a posterior, allowing insurers to perform real-time updating of risk measures to assess solvency risk, and providing them with a tool for carrying out dynamic risk management strategies in today’s “big data” era.

Conditional Monte Carlo replaces a naive estimate Z of a number z by its conditional expectation given a suitable piece of information. It always reduces variance and its traditional applications are in that vein. We survey here other potential uses such as density estimation and calculations for Value-at-Risk and/or expected shortfall, going in part into the implementation in various copula structures. Also the interplay between these different aspects comes into play.

Reliable information on wildlife populations and the threats they face is crucial for assessing the performance of conservation strategies. As part of its efforts to improve the effectiveness of Bukit Barisan Selatan National Park in Sumatra, Indonesia, and aid the recovery of flagship species, the Park's management authority designated a 1,000 km2 forest block an Intensive Protection Zone. To set a baseline from which to evaluate the performance of this zone, we investigated the density of tigers Panthera tigris sumatrae, and spatio-temporal interactions between tigers, their principle prey and threats. The estimated density of tigers was 2.8 per 100 km2, whereas in 2002 camera-trapping failed to record any tigers in the Intensive Protection Zone. We found the study area contained a rich prey base, with muntjac deer Muntiacus muntjak, macaques Macaca nemestrina and wild pigs Sus scrofa occupying 85–98% of the area, and sambar Rusa unicolor 61%. Despite these promising findings we also recorded a relatively high number of people entering the Park illegally, with 77 incidents over 6 months, of which 20% involved armed poachers. The poachers operated mainly at night and were concentrated in two locations. Law enforcement patrol teams were active during the day, and therefore had little overlap with the poachers. Prioritizing these at-risk areas for increased protection by rangers would further secure the Intensive Protection Zone, and expanding ranger activity across the Park would support efforts to remove the Park from UNESCO's List of World Heritage In Danger.

Nominally protected areas in Papua are under threat from encroachment, logging and hunting. The northern cassowary Casuarius unappendiculatus is the largest frugivore of the lowland rainforest of New Guinea and is endemic to this region, and therefore it is an important conservation target and a potential flagship species. We investigated effects of habitat degradation on the species by means of distance sampling surveys of 58 line transects across five distinct habitats, from primary forest to forest gardens. Estimated cassowary densities ranged from 14.1 (95% CI 9.2–21.4) birds km−2 in primary forest to 1.4 (95% CI 0.4–5.6) birds km−2 in forest garden. Density estimates were intermediate in unlogged but hunted natural forest and in > 30 year-old secondary forest, and considerably lower in recently logged (< 3 years) forest. Cassowary abundance was positively correlated with canopy cover and with tree height and diameter, and negatively correlated with hunting traps and human trails. In generalized linear models cassowary abundance was best explained by the number of fruiting trees and potential water sources. The results suggest that although the northern cassowary is moderately tolerant of intermediate disturbance it is relatively intolerant of heavy disturbance such as intensive logging. To secure the populations of northern cassowary and of other large animal species in Papua, forest degradation needs to be addressed by enforcing regulations in existing protection forest and/or establishing new protected areas, such as wildlife reserves.

Methods that accurately estimate animal abundance or density are crucial for wildlife management. Although numerous techniques are available, there have been few comparisons of the precision and cost-effectiveness of different approaches. We assess the precision and cost of three methods for estimating densities of the Endangered Grevy's zebra Equus grevyi. We compare distance sampling and photographic capture–recapture, and a new technique, the random encounter model (REM) that uses camera-trap encounter rates to estimate density. All three methods provide comparable density estimates for Grevy's zebra and are preferable to the common practice of raw counts. Photographic capture–recapture is the most precise and line-transect distance sampling the least precise. Line transects and photographic capture–recapture surveys are cost-effective in the first year and REM is most cost-effective in the long-term. The methods used here for Grevy's zebra may be applied to other rangeland ungulates. We suggest that for single species monitoring programmes in which individuals can be identified, photographic capture–recapture surveys may be the preferred method for estimating wildlife abundances. When encounter rates are low, distance sampling lacks the precision of the other methods but its cost advantage may make it appropriate for long-term or multi-species monitoring programmes. The REM is an efficient and precise method of estimating densities but has high initial equipment costs. We believe REM has the potential to work well for many species but it requires independent estimates of animal movements and group size.

Recently the Sunda clouded leopard Neofelis diardi was recognized as a separate species distinct from the clouded leopard Neofelis nebulosa of mainland Asia. Both species are categorized as Vulnerable on the IUCN Red List. Little is known about the newly identified species and, in particular, information from forests outside protected areas is scarce. Here we present one of the first density estimates calculated with spatial capture–recapture models using camera-trap data. In two commercial forest reserves in Sabah (both certified for their sustainable management practices) the density of the Sunda clouded leopard was estimated to be c. 1 per 100 km2 (0.84±SE 0.42 and 1.04±SE 0.58). The presence of the Sunda clouded leopard in such forests is encouraging for its conservation but additional studies from other areas, including protected forests, are needed to compare and evaluate these densities.

We build confidence balls for the common density s of a real valued sample X1,...,Xn. We use resampling methods to estimate the projection of s onto finite dimensional linear spaces and a model selection procedure to choose an optimal approximation space. The covering property is ensured for all n ≥ 2 and the balls are adaptive over a collection of linear spaces.

The aim of this paper is to find a concrete bound for the error involved when approximating the nth Hermite function (in the oscillating range) by an asymptotic formula due to D. Dominici. This bound is then used to study the accuracy of certain approximations to Hermite expansions and to Fourier transforms. A way of estimating an unknown probability density is proposed.

We propose a feature selection method for density estimation withquadratic loss. This method relies on the study of unidimensionalapproximation models and on the definition of confidence regions forthe density thanks to these models. It is quite general and includescases of interest like detection of relevant wavelets coefficientsor selection of support vectors in SVM. In the general case, weprove that every selected feature actually improves the performanceof the estimator. In the case where features are defined bywavelets, we prove that this method is adaptative near minimax (upto a log term) in some Besov spaces. We end the paper bysimulations indicating that it must be possible to extend theadaptation result to other features.


We develop an integration by parts technique for point processes, with application to the computation of sensitivities via Monte Carlo simulations in stochastic models with jumps. The method is applied to density estimation with respect to the Lebesgue measure via a modified kernel estimator which is less sensitive to variations of the bandwidth parameter than standard kernel estimators. This applies to random variables whose densities are not analytically known and requires the knowledge of the point process jump times.

Given an n-sample from some unknown density f on [0,1], it is easy to construct anhistogram of the data based on some given partition of [0,1], but not so much is knownabout an optimal choice of the partition, especially when the data set is not large, even ifone restricts to partitions into intervals of equal length. Existing methods are either rulesof thumbs or based on asymptotic considerations and often involve some smoothnessproperties of f. Our purpose in this paper is to give an automatic, easy to program andefficient method to choose the number of bins of the partition from the data. It is based on boundson the risk of penalized maximum likelihood estimators due to Castellan and heavy simulationswhich allowed us to optimize the form of the penalty function. These simulations show that themethod works quite well for sample sizes as small as 25.

This paper deals with semiparametric convolution models, where thenoise sequence has a Gaussian centered distribution, with unknownvariance. Non-parametric convolution models are concerned with the case of anentirely known distribution for the noise sequence, and they havebeen widely studied in the past decade. The main property of thosemodels is the following one: the more regular the distribution of thenoise is, the worst the rate of convergence for the estimation of thesignal's density g is [5]. Nevertheless, regularity assumptionson the signal density g improve those rates of convergence [15].In this paper, we show that whenthe noise (assumed tobe Gaussian centered) has a varianceσ2 that is unknown (actually, it is always the case inpractical applications), the rates of convergence for the estimation ofg are seriously deteriorated, whatever its regularity is supposed to be.More precisely, the minimax risk for the pointwise estimation of g over aclass of regular densities is lower bounded by a constant over log n. We construct two estimators of σ2, andmore particularly, an estimator which is consistent as soon as the signal hasa finite first order moment.We also mention as a consequence the deterioration of therate of convergence in the estimation of the parameters in the nonlinearerrors-in-variables model.

The subject of this paper is to estimate adaptively the common probabilitydensity of n independent, identically distributed random variables. Theestimation is done at a fixed point $x_{0}\in \mathbb R$ , over the densityfunctions that belong to the Sobolev class Wn(β,L). We consider theadaptive problem setup, where the regularity parameter β is unknownand varies in a given set B n . A sharp adaptive estimator is obtained,and the explicit asymptotical constant, associated to its rate ofconvergence is found.