Estimation of capture probabilities using generalized estimating equations and mixed effects approaches

Modeling individual heterogeneity in capture probabilities has been one of the most challenging tasks in capture-recapture studies. Heterogeneity in capture probabilities can be modeled as a function of individual covariates, but correlation structure among capture occasions should be taking into account. A proposed generalized estimating equations (GEE) and generalized linear mixed modeling (GLMM) approaches can be used to estimate capture probabilities and population size for capture-recapture closed population models. An example is used for an illustrative application and for comparison with currently used methodology. A simulation study is also conducted to show the performance of the estimation procedures. Our simulation results show that the proposed quasi-likelihood based on GEE approach provides lower SE than partial likelihood based on either generalized linear models (GLM) or GLMM approaches for estimating population size in a closed capture-recapture experiment. Estimator performance is good if a large proportion of individuals are captured. For cases where only a small proportion of individuals are captured, the estimates become unstable, but the GEE approach outperforms the other methods

Standardized Assessment of Biodiversity Trends in Tropical Forest Protected Areas: The End Is Not in Sight

Extinction rates in the Anthropocene are three orders of magnitude higher than background and disproportionately occur in the tropics, home of half the world’s species. Despite global efforts to combat tropical species extinctions, lack of high-quality, objective information on tropical biodiversity has hampered quantitative evaluation of conservation strategies. In particular, the scarcity of population-level monitoring in tropical forests has stymied assessment of biodiversity outcomes, such as the status and trends of animal populations in protected areas. Here, we evaluate occupancy trends for 511 populations of terrestrial mammals and birds, representing 244 species from 15 tropical forest protected areas on three continents. For the first time to our knowledge, we use annual surveys from tropical forests worldwide that employ a standardized camera trapping protocol, and we compute data analytics that correct for imperfect detection. We found that occupancy declined in 22%, increased in 17%, and exhibited no change in 22% of populations during the last 3–8 years, while 39% of populations were detected too infrequently to assess occupancy changes. Despite extensive variability in occupancy trends, these 15 tropical protected areas have not exhibited systematic declines in biodiversity (i.e., occupancy, richness, or evenness) at the community level. Our results differ from reports of widespread biodiversity declines based on aggregated secondary data and expert opinion and suggest less extreme deterioration in tropical forest protected areas. We simultaneously fill an important conservation data gap and demonstrate the value of large-scale monitoring infrastructure and powerful analytics, which can be scaled to incorporate additional sites, ecosystems, and monitoring methods. In an era of catastrophic biodiversity loss, robust indicators produced from standardized monitoring infrastructure are critical to accurately assess population outcomes and identify conservation strategies that can avert biodiversity collapse. © 2016 Beaudrot et al

Minimisation of functions of a positive semidefinite matrix A subject to AX = 0

A common problem in multivariate analysis is that of minimising or maximising a function f of a positive semidefinite matrix A subject possibly to AX = 0. Typically A is a variance-covariance matrix. Using the theory of nearest point projections in Hilbert spaces, it is shown that the solution satisfies the equation f'(A) + M - A = 0, where A = P0(M) and P0 is a certain projection operator.Positive semidefinite matrices maximum likelihood estimation projections in Hilbert space

Capture-recapture parameter estimation for open animal populations

This comprehensive book, rich with applications, offers a quantitative framework for the analysis of the various capture-recapture models for open animal populations, while also addressing associated computational methods. The state of our wildlife populations provides a litmus test for the state of our environment, especially in light of global warming and the increasing pollution of our land, seas, and air. In addition to monitoring our food resources such as fisheries, we need to protect endangered species from the effects of human activities (e.g. rhinos, whales, or encroachments on the habitat of orangutans). Pests must be be controlled, whether insects or viruses, and we need to cope with growing feral populations such as opossums, rabbits, and pigs. Accordingly, we need to obtain information about a given population’s dynamics, concerning e.g. mortality, birth, growth, breeding, sex, and migration, and determine whether the respective population is increasing , static, or declining. There are many methods for obtaining population information, but the most useful (and most work-intensive) is generically known as “capture-recapture,” where we mark or tag a representative sample of individuals from the population and follow that sample over time using recaptures, resightings, or dead recoveries. Marks can be natural, such as stripes, fin profiles, and even DNA; or artificial, such as spots on insects. Attached tags can, for example, be simple bands or streamers, or more sophisticated variants such as radio and sonic transmitters. To estimate population parameters, sophisticated and complex mathematical models have been devised on the basis of recapture information and computer packages. This book addresses the analysis of such models. It is primarily intended for ecologists and wildlife managers who wish to apply the methods to the types of problems discussed above, though it will also benefit researchers and graduate students in ecology. Familiarity with basic statistical concepts is essential

Linear Regression Analysis

Concise, mathematically clear, and comprehensive treatment of the subject.* Expanded coverage of diagnostics and methods of model fitting.* Requires no specialized knowledge beyond a good grasp of matrix algebra and some acquaintance with straight-line regression and simple analysis of variance models.* More than 200 problems throughout the book plus outline solutions for the exercises.* This revision has been extensively class-tested