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

Estimating demographic parameters using a combination of known-fate and open N-mixture models

1. Accurate estimates of demographic parameters are required to infer appropriate ecological relationships and inform management actions. Recently developed N-mixture models use count data from unmarked individuals to estimate demographic parameters, but a joint approach combining the strengths of both analytical tools has not been developed. 2. We present an integrated model combining known-fate and open N-mixture models, allowing the estimation of detection probability, recruitment, and the joint estimation of survival. We first use a simulation study to evaluate the performance of the model relative to known values. We then provide an applied example using 4 years of wolf survival data consisting of relocations of radio-collared wolves within packs and counts of associated pack-mates. The model is implemented in both maximum-likelihood and Bayesian frameworks using a new R package kfdnm and the BUGS language. 3. The simulation results indicated that the integrated model was able to reliably recover parameters with no evidence of bias, and estimates were more precise under the joint model as expected. Results from the applied example indicated that the marked sample of wolves was biased towards individuals with higher apparent survival rates (including losses due to mortality and emigration) than the unmarked pack-mates, suggesting estimates of apparent survival based on joint estimation could be more representative of the overall population. Estimates of recruitment were similar to direct observations of pup production, and overlap of the credible intervals suggested no clear differences in recruitment rates. 4. Our integrated model is a practical approach for increasing the amount of information gained from future and existing radio-telemetry and other similar mark-resight datasets.Comment: 22 pages, 2 figures, 2 appendice

Disappearance of Spurious States in Analog Associative Memories

We show that symmetric n-mixture states, when they exist, are almost never stable in autoassociative networks with threshold-linear units. Only with a binary coding scheme we could find a limited region of the parameter space in which either 2-mixtures or 3-mixtures are stable attractors of the dynamics.Comment: 5 pages, 3 figures, accepted for publication in Phys Rev

Modeling abundance using N-mixture models: the importance of considering ecological mechanisms

Predicting abundance across a species' distribution is useful for studies of ecology and biodiversity management. Modeling of survey data in relation to environmental variables can be a powerful method for extrapolating abundances across a species' distribution and, consequently, calculating total abundances and ultimately trends. Research in this area has demonstrated that models of abundance are often unstable and produce spurious estimates, and until recently our ability to remove detection error limited the development of accurate models. The N-mixture model accounts for detection and abundance simultaneously and has been a significant advance in abundance modeling. Case studies that have tested these new models have demonstrated success for some species, but doubt remains over the appropriateness of standard N-mixture models for many species. Here we develop the N-mixture model to accommodate zero-inflated data, a common occurrence in ecology, by employing zero-inflated count models. To our knowledge, this is the first application of this method to modeling count data. We use four variants of the N-mixture model (Poisson, zero-inflated Poisson, negative binomial, and zero-inflated negative binomial) to model abundance, occupancy (zero-inflated models only) and detection probability of six birds in South Australia. We assess models by their statistical fit and the ecological realism of the parameter estimates. Specifically, we assess the statistical fit with AIC and assess the ecological realism by comparing the parameter estimates with expected values derived from literature, ecological theory, and expert opinion. We demonstrate that, despite being frequently ranked the “best model” according to AIC, the negative binomial variants of the N-mixture often produce ecologically unrealistic parameter estimates. The zero-inflated Poisson variant is preferable to the negative binomial variants of the N-mixture, as it models an ecological mechanism rather than a statistical phenomenon and generates reasonable parameter estimates. Our results emphasize the need to include ecological reasoning when choosing appropriate models and highlight the dangers of modeling statistical properties of the data. We demonstrate that, to obtain ecologically realistic estimates of abundance, occupancy and detection probability, it is essential to understand the sources of variation in the data and then use this information to choose appropriate error distributions. Copyright ESA. All rights reserved

Analysis of auto-ignition of heated hydrogen-air mixtures with different detailed reaction mechanisms

Auto-ignition processes of hydrogen, diluted with nitrogen, in heated air are numerically investigated by means of an unsteady laminar flamelet approach in mixture fraction space. The focus is on the auto-ignition delay time and the most reactive mixture fraction as obtained with five chemical mechanisms. Two strongly different levels of dilution, corresponding to experiments in the open literature, are considered. This concerns low-temperature chemistry at atmospheric pressure. The temperature of the air stream is much higher than the temperature of the fuel stream in the cases under study. We extensively investigate the effect of the co-flow temperature, the conditional scalar dissipation rate and the resolution in mixture fraction space for one case. With respect to the conditional scalar dissipation rate, we discuss the Amplitude Mapping Closure (AMC) model with imposed maximum scalar dissipation rate at mixture fraction equal to 0.5, as well as a constant conditional scalar dissipation rate value over the entire mixture fraction value range. We also illustrate that an auto-ignition criterion, based on a temperature rise, leads to similar results as an auto-ignition criterion, based on OH mass fraction, provided that the hydrogen is not too strongly diluted

Advocating better habitat use and selection models in bird ecology

Studies on habitat use and habitat selection represent a basic aspect of bird ecology, due to its importance in natural history, distribution, response to environmental changes, management and conservation. Basically, a statistical model that identifies environmental variables linked to a species presence is searched for. In this sense, there is a wide array of analytical methods that identify important explanatory variables within a model, with higher explanatory and predictive power than classical regression approaches. However, some of these powerful models are not widespread in ornithological studies, partly because of their complex theory, and in some cases, difficulties on their implementation and interpretation. Here, I describe generalized linear models and other five statistical models for the analysis of bird habitat use and selection outperforming classical approaches: generalized additive models, mixed effects models, occupancy models, binomial N-mixture models and decision trees (classification and regression trees, bagging, random forests and boosting). Each of these models has its benefits and drawbacks, but major advantages include dealing with non-normal distributions (presence-absence and abundance data typically found in habitat use and selection studies), heterogeneous variances, non-linear and complex relationships among variables, lack of statistical independence and imperfect detection. To aid ornithologists in making use of the methods described, a readable description of each method is provided, as well as a flowchart along with some recommendations to help them decide the most appropriate analysis. The use of these models in ornithological studies is encouraged, given their huge potential as statistical tools in bird ecology.Fil: Palacio, Facundo Xavier. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Naturales y Museo. División Zoología de Vertebrados. Sección Ornitología; Argentin

Bestimmung der Fledermausaktivität in Agroforstsystemen und angrenzenden Habitaten mittels N-mixture Modellen

Bat activity in agroforestry systems at the research station Scheyern was analyzed using a N-mixture model approach. Results show low bat activity but provide hints that agroforestry structures can increase bat activity in open agricultural habitats