Categorising count data into ordinal responses with application to ecological communities

Count data sets may involve overdispersion from a set of species and underdispersion from another set which would require fitting different models (e.g. a negative binomial model for the overdispersed set and a binomial model for the underdispersed one). Additionally, many count data sets have very high counts and very low counts. Categorising these counts into ordinal categories makes the actual counts less influential in the model fitting, giving broad categories which enable us to detect major broadly based patterns of turnover or nestedness shown by groups of species. In this paper, a strategy of categorising count data into ordinal data was carried out and also we implemented measures to compare different cluster structures. The application of this categorising strategy and a comparison of clustering results between count and categorised ordinal data in two ecological community data sets are shown. A major advantage of using our ordinal approach is that it allows for the inclusion of all different levels of dispersion in the data in one methodology, without treating the data differently. This reduction of the parameters on modelling different levels of dispersion does not substantially change the results in clustering structure. In the two data sets used in this paper, we observed ordinal clustering structure up to 93.1 % similar to those from the count data approaches. This has the important implication of supporting simpler, faster data collection using ordinal scales only.Peer ReviewedPostprint (author's final draft

Introducing spaced mosaic plots

Informe de com fer spaced mosaic plots en RRecent research has developed a group of likelihood-based finite mixture mod- els for a data matrix with ordinal data, establishing likelihood-based multivari- ate methods which applies fuzzy clustering via finite mixtures to the ordered stereotype model. There are many visualisation tools which depict reduction of dimensionality in matrices of ordinal data. This technical report introduces the spaced mosaic plot which is one new graphical tool for ordinal data when the or- dinal stereotype model is used. It takes advantage of the fitted score parameters to determine the spacing between two adjacent ordinal categories. We develop a function in R and its documentation is presented. Finally, the description of a spaced mosaic plot is shown.Preprin

Mixture-based clustering for the ordered stereotype model

Many of the methods which deal with the reduction of dimensionality in matrices of data are based on mathematical techniques such as distance-based algorithms or matrix decomposition and eigenvalues. Recently a group of likelihood-based finite mixture models for a data matrix with binary or count data, using basic Bernoulli or Poisson building blocks has been developed. This is extended and establishes likelihood-based multivariate methods for a data matrix with ordinal data which applies fuzzy clustering via finite mixtures to the ordered stereotype model. Model-fitting is performed using the expectation–maximization (EM) algorithm, and a fuzzy allocation of rows, columns, and rows and columns simultaneously to corresponding clusters is obtained. A simulation study is presented which includes a variety of scenarios in order to test the reliability of the proposed model. Finally, the results of the application of the model in two real data sets are shown.Peer ReviewedPostprint (author's final draft

Finite mixture biclustering of discrete type multivariate data

Many of the methods which deal with clustering in matrices of data are based on mathematical techniques such as distance-based algorithms or matrix decomposition and eigenvalues. In general, it is not possible to use statistical inferences or select the appropriateness of a model via information criteria with these techniques because there is no underlying probability model. This article summarizes some recent model-based methodologies for matrices of binary, count, and ordinal data, which are modelled under a unified statistical framework using finite mixtures to group the rows and/or columns. The model parameter can be constructed from a linear predictor of parameters and covariates through link functions. This likelihood-based one-mode and two-mode fuzzy clustering provides maximum likelihood estimation of parameters and the options of using likelihood information criteria for model comparison. Additionally, a Bayesian approach is presented in which the parameters and the number of clusters are estimated simultaneously from their joint posterior distribution. Visualization tools focused on ordinal data, the fuzziness of the clustering structures, and analogies of various standard plots used in the multivariate analysis are presented. Finally, a set of future extensions is enumerated

Integrated analysis of capture-recapture-resighting data and counts of unmarked birds at stop-over sites

The models presented in this paper are motivated by a stop-over study of semipalmated sandpipers, Callidris pussila. Two sets of data were collected at the stop-over site: a capture-recapture-resighting data set and a vector of counts of unmarked birds. The two data sets are analysed simultaneously by combining a new model for the capture-recapture-resighting data set with a binomial likelihood for the counts. The aim of the analysis is to estimate the total number of birds that used the site and the average duration of stop-over. The combined analysis is shown to be highly efficient when just 1% of birds are recaptured, and is recommended for similar investigations

Plasticity in feeding selectivity and trophic structure of kelp forest associated fishes from northern Chile Plasticidad en la selección de alimento y estructura trófica de los peces asociados a bosques de macroalgas pardas del norte de Chile

One of the primary ways in which species interact with their environment is through foraging; thereby directly consuming some fraction of their surrounding habitat. The habitat itself, in turn, may dictate the types of foraging opportunities that are available to the inhabitants. To investigate the relationship between habitat availability and diet composition of habitat-associated fishes, we estimated the relative abundance of the potential sessile and mobile prey items and the diet of the fish species assemblage associated to kelp forest. Specifically, diet and feeding selectivity of the kelp-forest associated fish assemblage were determined by calculating Manly's alpha selectivity index. We determined the diet of kelp forest associated fishes and their foraging behavior by comparing prey availability with those items present in the stomachs of fishes captured by gill net and spear gun. We calculated the degree of dietary overlap among fishes from four locations along the northern coast of Chile. Results indicate that utilization of prey by predators is predominantly affected by potential prey availability. With the exception of the two carnivorous species such as Pinguipes chilensis (Valenciennes, 1883) and Paralabrax humeralis (Cuvier & Valenciennes, 1828), whose diet did not change among sites, all other kelp-associated fishes changed their dietary habitats to consistent with the availability of local resources. Benthic resources changed among the different study sites, which led to differing diets even in the same species from different locations. Eleven of the 12 kelp forest fishes also showed some selectively for benthic prey. We conclude that the ability of fishes to be plastic in their feeding preference and, therefore, partition the benthic resources may set adaptations to co-exist in a dynamic environment such as kelp forest.<br>Una de las principales formas en que las especies interactúan con su medio ambiente es a través de la alimentación, consumiendo directamente una fracción de los componentes del hábitat circundante. El propio hábitat, a su vez, puede determinar la conducta de forrajeo y los tipos de alimentación de sus depredadores. Para investigar la relación entre la disponibilidad de alimento y la composición de la dieta de los peces asociados a hábitat dominados por macroalgas pardas, se estimó la abundancia de las presas potenciales tanto especies sésiles como móviles y se comparó con la dieta de las especies de los peces en cuatro diferentes sitios de la costa del norte de Chile. Se determinó la dieta de los peces y su plasticidad alimentaria mediante la comparación entre la disponibilidad de presas con los ítemes presentes en los estómagos de los peces que fueron capturados por de red de enmalle y arpón de mano. Además se calculó el índice de selectividad alfa de Manly y el grado de sobreposición de la dieta de los peces costeros. Los resultados muestran que la utilización de las presas por los depredadores es afectada principalmente por la disponibilidad de presas potenciales. La mayoría de los peces asociados a las macroalgas difieren en su dieta en consonancia con la disponibilidad de los recursos a escalas locales, con la excepción de dos especies carnívoras tales como Pinguipes chilensis (Valenciennes, 1883) y Paralabrax humeralis (Cuvier & Valenciennes, 1828), cuya dieta no cambió entre los sitios estudiados. Las diferencias en la dieta de las especies son explicadas por los cambios en los recursos bentónicos que varían entre los sitios de estudio. Once de las 12 especies de peces asociados a los bosques de macroalgas pardas mostraron algún grado de selectividad de presas de origen bentónico. Se concluye que la habilidad de los peces de cambiar sus preferencias de alimentación y, por tanto, la partición de los recursos bentónicos puede obedecer a las adaptaciones para coexistir en un ambiente dinámico como aquel dominado por bosques de macroalgas pardas