Computational aspects of N-mixture models

The N-mixture model is widely used to estimate the abundance of a population in the presence of unknown detection probability from only a set of counts subject to spatial and temporal replication (Royle, 2004, Biometrics 60,105–115). We explain and exploit the equivalence of N-mixture and multivariate Poisson and negative-binomial models, which provides powerful new approaches for fitting these models. We show that particularly when detection probability and the number of sampling occasions are small, infinite estimates of abundance can arise. We propose a sample covariance as a diagnostic for this event, and demonstrate its good performance in the Poisson case. Infinite estimates may be missed in practice, due to numerical optimization procedures terminating at arbitrarily large values. It is shown that the use of a bound, K, for an infinite summation in the N-mixture likelihood can result in underestimation of abundance, so that default values of K in computer packages should be avoided. Instead we propose a simple automatic way to choose K. The methods are illustrated by analysis of data on Hermann’s tortoise Testudo hermanni

Occupancy modelling : study design and models for data collected along transects

Occupancy, defined as the proportion of sites occupied by a species, is a state variable of interest in ecology and conservation. When modelling species occupancy it is crucial to account for the detection process, as most species can remain undetected at sites where present. This is usually achieved by carrying out separate repeat visits to each sampling site but other methods are sometimes used, such as surveying spatial sub-units within each sampling site, or even collecting detection data continuously along a transect, during a single visit. This thesis deals with two aspects of occupancy modelling: (i) we explore issues related to the design of occupancy studies, including the trade-off in survey effort allocation between sites and repeat visits, sample size determination and the impact of sampling with replacement in studies based on spatial replication; and (ii) we develop and evaluate new models to estimate occupancy from species detection data collected along transects, motivated by the analysis of a data set from a Surnatran tiger Panthera tigris sumatrae survey which followed this type of sampling protocol. The models we propose, which describe the detection process as a continuous point process, can account for clustering and/or abundance-induced heterogeneity in the detection process and represent a step forward with respect to current modelling approaches which involve data discretisation and two-stage ad hoc procedures

Using occupancy analysis to validate the use of footprint tunnels as a method for monitoring the hedgehog Erinaceus europaeus

Indirect survey methods are often used in studies of mammals, but are susceptible to biases caused by failure to detect species where they are present. Occupancy analysis is an analytical technique which enables non-detection rates to be estimated and which can be used to develop and refine novel survey methods. In this study, we investigated the use of footprint tunnels by volunteers as a method for surveying occupancy of sites by hedgehogs Erinaceus europaeus. The survey protocol led to a very low non-detection rate and could reasonably be used to detect occupancy changes of 25% with statistical power of 0.95 in a national survey

Valid auto-models for spatially autocorrelated occupancy and abundance data

Auto-logistic and related auto-models, implemented approximately as autocovariate regression, provide simple and direct modelling of spatial dependence. The autologistic model has been widely applied in ecology since Augustin, Mugglestone and Buckland (J. Appl. Ecol., 1996, 33, 339) analysed red deer census data using a hybrid estimation approach, combining maximum pseudo-likelihood estimation with Gibbs sampling of missing data. However Dormann (Ecol. Model., 2007, 207, 234) questioned the validity of auto-logistic regression, giving examples of apparent underestimation of covariate parameters in analysis of simulated "snouter" data. Dormann et al. (Ecography, 2007, 30, 609) extended this analysis to auto-Poisson and auto-normal models, reporting similar anomalies. All the above studies employ neighbourhood weighting schemes inconsistent with conditions (Besag, J. R. Stat. Soc., Ser. B, 1974, 36, 192) required for auto-model validity; furthermore the auto-Poisson analysis fails to exclude cooperative interactions. We show that all "snouter" anomalies are resolved by correct auto-model implementation. Re-analysis of the red deer data shows that invalid neighbourhood weightings generate only small estimation errors for the full dataset, but larger errors occur on geographic subsamples. A substantial fraction of papers applying auto-logistic regression to ecological data use these invalid weightings, which are default options in the widely used "spdep" spatial dependence package for R. Auto-logistic analyses using invalid neighbourhood weightings will be erroneous to an extent that can vary widely. These analyses can easily be corrected by using valid neighbourhood weightings available in "spdep". The hybrid estimation approach for missing data is readily adapted for valid neighbourhood weighting schemes and is implemented here in R for application to sparse presence-absence data.Comment: Typos corrected in Table 1. Note that defaults in R package 'spdep' have changed in response to this paper; some results using defaults are therefore now version-dependen

Monitoring and conservation of the Critically Endangered Alaotran gentle lemur Hapalemur alaotrensis

The Alaotran gentle lemur Hapalemur alaotrensis is a Critically Endangered lemur, which exclusively inhabits the marshes around Lac Alaotra in northeast Madagascar. In the past decades the population of H. alaotrensis has experienced a dramatic decline due to poaching, habitat destruction and degradation. Surveys have been carried out periodically to follow the status of the population. Here we present the results of a survey carried out between May and June 2008 in the southwestern part of the marshes around Alaotra and discuss the key findings derived from the analysis of the data collected. Our study indicates that the probability of detecting the species in an area where it is present is very low and depends on factors that vary in space and time. These results stress the need to account for imperfect detection when monitoring this species, an issue especially relevant when reporting population trends. Our analyses also show that habitat fragmentation is a key determinant of habitat suitability for H. alaotrensis, with fragmented areas of marsh showing low suitability. Finally, our observations and analysis suggest that the protection provided by the local community to H. alaotrensis in Andreba is contributing to the conservation of this Critically Endangered species. This highlights the need to continue working on engaging the local communities in the conservation of the marshes at Lac Alaotra as a critical element to secure the future of H. alaotrensis. KEYWORDS: bandro, habitat suitability, habitat fragmentation, imperfect detection, Maxent

Optical Absorption by Indirect Excitons in a Transition Metal Dichalcogenide Double Layer

We calculate the binding energy, transition energies, oscillator strength, and absorption coefficient of indirect excitons in transition metal dichalcogenide (TMDC) double layers separated by an integer number of hexagonal boron nitride (h-BN) monolayers. The absorption factor, a dimensionless quantity which gives the fraction of incoming photons absorbed by the indirect excitons in the double layer, is evaluated. The aforementioned optical quantities are obtained for transitions from the ground state to the first two excited states. All quantities are studied as a function of the interlayer separation, which may be experimentally controlled by varying the number of h-BN monolayers between the TMDC layers. Calculations are performed by using the exciton wave function and eigenenergies obtained for the Keldysh potential. For each material, we choose a combination of the exciton reduced mass and the dielectric screening length from the existing literature which give the largest and the smallest indirect exciton binding energy. These combinations of material parameters provide upper and lower bounds on all quantities presented. Our findings can be examined experimentally via two-photon spectroscopy.Comment: 13 pages, 3 figure

Monitoring and conservation of the critically endangered Alaotran gentle lemur Hapalemur alaotrensis

The Alaotran gentle lemur Hapalemur alaotrensis is a Critically Endangered lemur, which exclusively inhabits the marshes around Lac Alaotra in northeast Madagascar. In the past decades the population of H. alaotrensis has experienced a dramatic decline due to poaching, habitat destruction and degradation. Surveys have been carried out periodically to follow the status of the population. Here we present the results of a survey carried out between May and June 2008 in the southwestern part of the marshes around Alaotra and discuss the key findings derived from the analysis of the data collected. Our study indicates that the probability of detecting the species in an area where it is present is very low and depends on factors that vary in space and time. These results stress the need to account for imperfect detection when monitoring this species, an issue especially relevant when reporting population trends. Our analyses also show that habitat fragmentation is a key determinant of habitat suitability for H. alaotrensis, with fragmented areas of marsh showing low suitability. Finally, our observations and analysis suggest that the protection provided by the local community to H. alaotrensis in Andreba is contributing to the conservation of this Critically Endangered species. This highlights the need to continue working on engaging the local communities in the conservation of the marshes at Lac Alaotra as a critical element to secure the future of H. alaotrensis

Cost-efficient effort allocation for camera-trap occupancy surveys of mammals

Camera-traps are increasingly used to survey threatened mammal species and are an important tool for estimating habitat occupancy. To date, cost-efficient occupancy survey effort allocation studies have focused on trade-offs between number of sample units (SUs) and sampling occasions, with simplistic accounts of associated costs which do not reflect camera-trap survey realities. Here we examine camera-trap survey costs as a function of the number of SUs, survey duration and camera-traps per SU, linking costs to precision in occupancy estimation. We evaluate survey effort trade-offs for hypothetical species representing different levels of occupancy (?) and detection (p) probability to identify optimal design strategies. We apply our cost function to three threatened species as worked examples. Additionally, we use an extensive camera-trap data set to evaluate independence between multiple camera traps per SU. The optimal number of sampling occasions that result in minimum cost decrease as detection probability increases, irrespective of whether the species is rare (? 0.5). The most expensive survey scenarios occur for elusive (p 10 km2), where the survey is conducted on foot. Minimum survey costs for elusive species can be achieved with fewer sampling occasions and multiple cameras per SU. Multiple camera-traps set within a single SU can yield independent species detections. We provide managers and researchers with guidance for conducting cost-efficient camera-trap occupancy surveys. Efficient use of survey budgets will ultimately contribute to the conservation of threatened and data deficient mammals