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Arita H.T.,National Autonomous University of Mexico | Christen A.,Research Center en Matematicas | Rodriguez P.,Comision Nacional para el Conocimiento y Uso de la Biodiversidad | Soberon J.,University of Kansas
Global Ecology and Biogeography | Year: 2012

Aim A great deal of information on distribution and diversity can be extracted from presence-absence matrices (PAMs), the basic analytical tool of many biogeographic studies. This paper presents numerical procedures that allow the analysis of such information by taking advantage of mathematical relationships within PAMs. In particular, we show how range-diversity (RD) plots summarize much of the information contained in the matrices by the simultaneous depiction of data on distribution and diversity. Innovation We use matrix algebra to extract and process data from PAMs. Information on the distribution of species and on species richness of sites is computed using the traditional R (by rows) and Q (by columns) procedures, as well as the new Rq (by rows, considering the structure of columns) and Qr (by columns, considering the structure by rows) methods. Matrix notation is particularly suitable for summarizing complex calculations using PAMs, and the associated algebra allows the implementation of efficient computational programs. We show how information on distribution and species richness can be depicted simultaneously in RD plots, allowing a direct examination of the relationship between those two aspects of diversity. We explore the properties of RD plots with a simple example, and use null models to show that while parameters of central tendency are not affected by randomization, the dispersion of points in RD plots does change, showing the significance of patterns of co-occurrence of species and of similarity among sites. Main conclusion Species richness and range size are both valid measures of diversity that can be analysed simultaneously with RD plots. A full analysis of a system requires measures of central tendency and dispersion for both distribution and species richness. © 2011 Blackwell Publishing Ltd.

Brian D.,University of Idaho | Ponciano J.M.,Research Center en Matematicas | Taper M.L.,Montana State University
Ecology | Year: 2010

Observation or sampling error in population monitoring can cause serious degradation of the inferences, such as estimates of trend or risk, that ecologists and managers frequently seek to make with time-series observations of population abundances. We show that replicating the sampling process can considerably improve the information obtained from population monitoring. At each sampling time the sampling method would be repeated, either simultaneously or within a short time. In this study we examine the potential value of replicated sampling to population monitoring using a density-dependent population model. We modify an existing population time-series model, the Gompertz state-space model, to incorporate replicated sampling, and we develop maximum-likelihood and restricted maximum-likelihood estimates of model parameters. Depending on sampling protocols, replication may or may not entail substantial extra cost. Some sampling programs already have replicated samples, but the samples are aggregated or pooled into one estimate of population abundance; such practice of aggregating samples, according to our model, loses considerable information about model parameters. The gains from replicated sampling are realized in substantially improved statistical inferences about model parameters, especially inferences for sorting out the contributions of process noise and observation error to observed population variability. © 2010 by the Ecological Society of America.

Fernandez D.,Victoria University of Wellington | Nakamura M.,Research Center en Matematicas
Ecological Modelling | Year: 2015

Sampling bias contained in data of biological surveys is very common. Bias is clearly a function of roads, cities, rivers, or other physical features that determines accessibility of collectors, and many data sets of species are presence-only. We set out to estimate spatial sampling bias in a region, based on presence-only data, by explicitly incorporating information on these accessibility factors, and by considering a target group of species that may share a common search pattern. In order to indirectly estimate the number of individuals, we also resort to the concept of species richness. A probabilistic (multinomial) model is proposed, enabling standard likelihood inference procedures to be implemented. Simulation scenarios for exploration of the model and experimentation with the estimation procedure are included. Illustrative examples over a region of Mexico with mammals and butterflies are also reported with insightful results. Our model is able to estimate the sampling bias in a region and enhance the inferences regarding presence-only data. © 2015 Elsevier B.V.

Cavazos-Cadena R.,Antonio Narro Agrarian Autonomous University | Hernandez-Hernandez D.,Research Center en Matematicas
Mathematics of Operations Research | Year: 2011

This work concerns Markov decision processes with finite state space and compact action set. The performance of a control policy is measured by a risk-sensitive average costcriterion and, under standard continuity-compactness conditions, it is shown that the discounted approximations converge to the optimal value function, and that the superior and inferior limit average criteria have the same optimal value function. These conclusions are obtained for every nonnull risk-sensitivity coefficient, and regardless of the communication structure induced by the transition law. © 2011 INFORMS.

Ponciano J.M.,University of Florida | Capistran M.A.,Research Center en Matematicas
PLoS Computational Biology | Year: 2011

In this paper we used a general stochastic processes framework to derive from first principles the incidence rate function that characterizes epidemic models. We investigate a particular case, the Liu-Hethcote-van den Driessche's (LHD) incidence rate function, which results from modeling the number of successful transmission encounters as a pure birth process. This derivation also takes into account heterogeneity in the population with regard to the per individual transmission probability. We adjusted a deterministic SIRS model with both the classical and the LHD incidence rate functions to time series of the number of children infected with syncytial respiratory virus in Banjul, Gambia and Turku, Finland. We also adjusted a deterministic SEIR model with both incidence rate functions to the famous measles data sets from the UK cities of London and Birmingham. Two lines of evidence supported our conclusion that the model with the LHD incidence rate may very well be a better description of the seasonal epidemic processes studied here. First, our model was repeatedly selected as best according to two different information criteria and two different likelihood formulations. The second line of evidence is qualitative in nature: contrary to what the SIRS model with classical incidence rate predicts, the solution of the deterministic SIRS model with LHD incidence rate will reach either the disease free equilibrium or the endemic equilibrium depending on the initial conditions. These findings along with computer intensive simulations of the models' Poincaré map with environmental stochasticity contributed to attain a clear separation of the roles of the environmental forcing and the mechanics of the disease transmission in shaping seasonal epidemics dynamics. © 2011 Ponciano, Capistrán.

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