Miguel Nakamura

Niches and distributional areas: Concepts, methods, and assumptions

Estimating actual and potential areas of distribution of species via ecological niche modeling has become a very active field of research, yet important conceptual issues in this field remain confused. We argue that conceptual clarity is enhanced by adopting restricted definitions of “niche” that enable operational definitions of basic concepts like fundamental, potential, and realized niches and potential and actual distributional areas. We apply these definitions to the question of niche conservatism, addressing what it is that is conserved and showing with a quantitative example how niche change can be measured. In this example, we display the extremely irregular structure of niche space, arguing that it is an important factor in understanding niche evolution. Many cases of apparently successful models of distributions ignore biotic factors: we suggest explanations to account for this paradox. Finally, relating the probability of observing a species to ecological factors, we address the issue of what objects are actually calculated by different niche modeling algorithms and stress the fact that methods that use only presence data calculate very different quantities than methods that use absence data. We conclude that the results of niche modeling exercises can be interpreted much better if the ecological and mathematical assumptions of the modeling process are made explicit.

Sequential stopping rules for species accumulation

Identifying and counting the total number of biological species observed to date, and plotting versusa measure of the effort used to record them, gives rise to a species accumulation curve. Interest typically is concerned with estimating the total number of species in the area of study, having observed only the accumulation curve, having no information on species frequencies. This article considers the problem of optimally stopping the sampling process. We use a sequential procedure with a fixed maximum horizon for accumulation. A utility function based on the number of new species to be observed and the effort saved from the maximum horizon is adopted, and a workable algorithm based on backward induction is obtained. An example in accumulation of bat species is also presented.

Prediction of potential areas of species distributions based on presence-only data

We introduce a methodology to infer zones of high potential for the habitat of a species, useful for management of biodiversity, conservation, biogeography, ecology, or sustainable use. Inference is based on a set of sites where the presence of the species has been reported. Each site is associated with covariate values, measured on discrete scales. We compute the predictive probability that the species is present at each node of a regular grid. Possible spatial bias for sites of presence is accounted for. Since the resulting posterior distribution does not have a closed form, a Markov chain Monte Carlo (MCMC) algorithm is implemented. However, we also describe an approximation to the posterior distribution, which avoids MCMC. Relevant features of the approach are that specific notions of data acquisition such as sampling intensity and detectability are accounted for, and that available a priori information regarding areas of distribution of the species is incorporated in a clear-cut way. These concepts, arising in the presence-only context, are not addressed in alternative methods. We also consider an uncertainty map, which measures the variability for the predictive probability at each node on the grid. A simulation study is carried out to test and compare our approach with other standard methods. Two case studies are also presented.

Empirical probability generating function: An overview

Abstract A convenient approach to the statistical analysis of distributions for counts is possible using the empirical probability generating function. In this paper we give an overview of recent results and show the usefulness and advantages of this methodology. On one hand, there are some stochastic models in which the probability generating function arises naturally and therefore it seems reasonable to use its empirical counterpart. On the other hand, this statistical tool has demonstrated to be useful in the study of classical statistical problems of distributions for counts, especially in exploratory data analysis, rapid multi-parameter estimation and testing the goodness of fit. Our recommendation is to make allowance for the empirical probability generating function when dealing with statistical inference for discrete distributions.

Estimating parameters for discrete distributions via the empirical probability generating function

We consider parameter estimation for a family of discrete distributions characterized by probability generating functions (pgfs). Kemp and Kemp (1988) suggest estimators based on the empirical probability generating function (epgf) the methods involve solving estimating equations obtained by equating functionals of the epgf and pgf on a fixed, finite set of values. We derive asymptotic theory for these estimators and consider some examples. Graphical techniques based on the theory are shown to be useful for exploratory analysis

Exploratory data analysis for counts using the empirical probability generating function 1

We present a graphical method based on the empirical probability generating function for preliminary statistical analysis of distributions for counts. The method is especially useful in fitting a Poisson model, or for identifying alternative models as well as possible outlying observations from general discrete distributions.

A prospective cohort study to evaluate peridomestic infection as a determinant of dengue transmission: Protocol

BackgroundVector control programs, which have focused mainly on the patient house and peridomestic areas around dengue cases, have not produced the expected impact on transmission. This project will evaluate the assumption that the endemic/epidemic transmission of dengue begins around peridomestic vicinities of the primary cases. Its objective is to assess the relationship between symptomatic dengue case exposure and peridomestic infection incidence.Methods/DesignA prospective cohort study will be conducted (in Tepalcingo and Axochiapan, in the state of Morelos, Mexico), using the state surveillance system for the detection of incident cases. Paired blood specimens will be collected from both the individuals who live with the incident cases and a sample of subjects residing within a 25-meter radius of such cases (exposed cohort), in order to measure dengue-specific antibodies. Other subjects will be selected from areas which have not presented any incident cases within 200 meters, during the two months preceding the sampling (non-exposed cohort). Symptomatic/asymptomatic incident infection will be considered as the dependent variable, exposure to confirmed dengue cases, as the principal variable, and the socio-demographic, environmental and socio-cultural conditions of the subjects, as additional explanatory variables.DiscussionResults indicating a high infection rate among the exposed subjects would justify the application of peridomestic control measures and call for an evaluation of alternate causes for insufficient program impact. On the other hand, a low incidence of peridomestic-infected subjects would support the hypothesis that infection occurs outside the domicile, and would thus explain why the vector control measures applied in the past have exerted such a limited impact on cases incidence rates. The results of the present study may therefore serve to reassess site selection for interventions of this type.

ESTIMATION OF A MULTIVARIATE BOX-COX TRANSFORMATION TO ELLIPTICAL SYMMETRY VIA THE EMPIRICAL CHARACTERISTIC FUNCTION*

Let X=(X1, X2,..., Xd)t be a random vector of positive entries, such that for some λ=(λ1,λ2,...,λd)t, the vector X(λ) defined by % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GaamiwamaaDaaaleaamiaadMgaaSqaaWGaaiikaiabeU7aSnaaBaaa% baGaamyAaiaacMcaaeqaaaaakiabg2da9iaacIcadaWcgaqaaiaadI% fadaqhaaWcbaadcaWGPbaaleaamiabeU7aSnaaBaaabaGaamyAaaqa% baaaaOGaeyOeI0IaaGymaiaacMcaaeaacqaH7oaBdaWgaaWcbaadca% WGPbGaaiilaaWcbeaakiaadMgacqGH9aqpcaaIXaGaeSOjGSKaaiil% aiaadsgaaaaaaa!53BB!\[X_i^{(\lambda _{i)} } = ({{X_i^{\lambda _i } - 1)} \mathord{\left/ {\vphantom {{X_i^{\lambda _i } - 1)} {\lambda _{i,} i = 1 \ldots ,d}}} \right. \kern-\nulldelimiterspace} {\lambda _{i,} i = 1 \ldots ,d}}\]is elliptically symmetric. We describe a procedure based on the multivariate empirical characteristic function for estimating the λis. Asymptotic results regarding consistency of the estimators are given and we evaluate their performance in simulated data. In a one-dimensional setting, comparisons are made with other available transformations to symmetry.

Statistical inference for extinction rates based on last sightings

Rates of extinction can be estimated from sighting records and are assumed to be implicitly constant by many data analysis methods. However, historical sightings are scarce. Frequently, the only information available for inferring extinction is the date of the last sighting. In this study, we developed a probabilistic model and a corresponding statistical inference procedure based on last sightings. We applied this procedure to data on recent marine extirpations and extinctions, seeking to test the null hypothesis of a constant extinction rate. We found that over the past 500 years extirpations in the ocean have been increasing but at an uncertain rate, whereas a constant rate of global marine extinctions is statistically plausible. The small sample sizes of marine extinction records generate such high uncertainty that different combinations of model inputs can yield different outputs that fit the observed data equally well. Thus, current marine extinction trends may be idiosyncratic.

Macro-Scale Patterns in Upwelling/Downwelling Activity at North American West Coast.

The seasonal and interannual variability of vertical transport (upwelling/downwelling) has been relatively well studied, mainly for the California Current System, including low-frequency changes and latitudinal heterogeneity. The aim of this work was to identify potentially predictable patterns in upwelling/downwelling activity along the North American west coast and discuss their plausible mechanisms. To this purpose we applied the min/max Autocorrelation Factor technique and time series analysis. We found that spatial co-variation of seawater vertical movements present three dominant low-frequency signals in the range of 33, 19 and 11 years, resembling periodicities of: atmospheric circulation, nodal moon tides and solar activity. Those periodicities might be related to the variability of vertical transport through their influence on dominant wind patterns, the position/intensity of pressure centers and the strength of atmospheric circulation cells (wind stress). The low-frequency signals identified in upwelling/downwelling are coherent with temporal patterns previously reported at the study region: sea surface temperature along the Pacific coast of North America, catch fluctuations of anchovy Engraulis mordax and sardine Sardinops sagax, the Pacific Decadal Oscillation, changes in abundance and distribution of salmon populations, and variations in the position and intensity of the Aleutian low. Since the vertical transport is an oceanographic process with strong biological relevance, the recognition of their spatio-temporal patterns might allow for some reasonable forecasting capacity, potentially useful for marine resources management of the region.