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Little is known about interactions between the critically endangered Sumatran tiger Panthera tigris sumatrae and its prey because of the difficulties associated with detecting these species. In this study, we quantify temporal overlap between the Sumatran tiger and five of its presumed prey species from four study areas comprising disturbed lowland to primary submontane forest. Data from 126 camera traps over 8984 camera days were used to estimate species activity patterns and, in turn, their overlap through the coefficient D (ranging from 0 to 1, i.e. no overlap to complete overlap). A newly developed statistical technique was applied to determine confidence intervals associated with respective overlap, which is important, as such measures of precision are usually not estimated in these types of study. Strong temporal overlap was found between tiger and muntjac Muntiacus muntjac (D = 0.80, 95%CI= 0.71-0.84) and tiger and sambar Cervus unicolor (D =0.81, 0.55-0.85), with the latter illustrating the importance of measuring precision. According to the foraging theory, Sumatran tigers should focus on expending lower levels of energy searching for and then capturing larger bodied prey that present the least risk. Hence, surprisingly, there was little overlap between the crepuscular tiger and the largest-bodied prey species available, the nocturnal tapir Tapirus indicus (0.52, 0.44-0.60), suggesting that it is not a principal prey species. This study provides the first insights into Sumatran tiger-prey temporal interactions. The ability to estimate overlap statistics with measures of precision has obvious and wide benefits for other predator-prey and interspecific competition studies.

Count data often show a higher incidence of zero counts than would be expected if the data were Poisson distributed. Zero-inflated Poisson regression models are a useful class of models for such data, but parameter estimates may be seriously biased if the nonzero counts are overdispersed in relation to the Poisson distribution. We therefore provide a score test for testing zero-inflated Poisson regression models against zero-inflated negative binomial alternatives.

Summary 1.Occupancy is an important concept in ecology. To obtain an unbiased estimator of occupancy it is necessary to address the issue of imperfect detection, which requires conducting replicate surveys at the sites being sampled. As the allocation of total effort can be done in different ways, occupancy studies should be designed carefully to ensure an efficient use of available resources. 2. In this paper we address the design of single-season single-species occupancy studies with a focus on: (1) issues relating to small sample sizes and (2) the potential relevance of including the precision of the detectability estimator as a criterion for design. We explore analytically the model with constant probabilities and examine how bias and precision are affected by the numbers of sites and replicates used. 3. We show how, for small sample sizes, the estimator properties depart from those predicted by large sample approximations, emphasize the need to use simulations when designing for small sample sizes and provide a new software tool that can assist in this process. 4. We offer advice on the amount of replication needed when the probability of detection is a quantity of interest and show that, in this case, it is more efficient to reduce the number of sites and increase the amount of replication per site compared with situations where only occupancy is of concern. 5. Synthesis and applications. It is essential to have clearly stated objectives before starting a study and to design the sampling accordingly. As the allocation of effort into replication and sites can be done in different ways, occupancy studies should be designed carefully to ensure an efficient use of available resources. To avoid waste, it is crucial to anticipate the quality of the estimates that can be expected from a particular study design. The discussion and guidance provided here is of special interest for those designing occupancy studies with small sample sizes, something not uncommon in the context of ecology and conservation.

This paper reviews many different estimators of intraclass correlation that have been proposed for binary data and compares them in an extensive simulation study. Some of the estimators are very specific, while others result from general methods such as pseudo-likelihood and extended quasi-likelihood estimation. The simulation study identifies several useful estimators, one of which does not seem to have been considered previously for binary data. Estimators based on extended quasi-likelihood are found to have a substantial bias in some circumstances.