Revisão de modelos probabilísticos de distribuição: uma aplicação para peixes migradores - Barradas, José Ricardo de Souza (2012)
Given the limitations of the logit model, represented by the equation P = e(b0 + b1 x1 + b2 x2 + ... + bi xi) . (1 + e(b0 + b1 x1 + b2 x2 + ... + bi xi))-1, where: P is the probability of occurrence of the species (0-1), x1, x2 and xi are the environmental descriptors, b0, b1, b2 and bi are coefficients of the model calibration, and LOGITm, represented by the equation P = e(b1 . (Altitude - PMFAltitude) + b2 . (Área de Bacia PMFÁrea de Bacia)) . (1 + e (b1 . (Altitude - PMFAltitude) + b2 . (Área de Bacia PMFÁrea de Bacia)))-1, where: P is the probability of occurrence of the species (0-1), , b1 and b2 are coefficients related to altitude and basin area, respectively, and PMF is the point of changing phase of each parameter, as described in the literature for prediction of probability distribution of species in extreme situations due to compensatory mechanisms resulting from the design of these models, the goal of this study was to propose a new statistical model for the distribution of species of migratory fish and compare it with the models mentioned above. It was used the available database derived from the project PEIXES MIGRADORES E POTENCIAL HIDRELÉTRICO: GESTÃO INTEGRADA DA BACIA URUGUAI (RS/SC), which is composed of 167 points distributed throughout the Brazilian territory of the watershed. The model proposed in this study (Logistic Product - LP) is represented by the following equation: P = (1 b0) + b0 . (1 + e(TAXAAltitude . (Altitude PMFAltitude)))-1 . (1 + e(-TAXAÁrea de Bacia . (Área de Bacia PMFÁrea de Bacia)))-1, where: P is the probability of occurrence of the species (0-1), b0 is a fraction of the likelihood of unexplained by any of the descriptors; TAXA is a parameter indicative of the relative speed of change of absent/presence and PMF is the point of changing phase of each parameter. The models were adjusted for four species of migratory large Uruguay River basin: Leporinus obtusidens (piava), Prochilodus lineatus (grumatã) Pseudoplatystoma corruscans (pintado) and Salminus brasiliensis (dourado). The models were analyzed according to (1) adherence between their expected occurrence and estimated, (2) formats dimensional fields of the residual variance as a function of the variables altitude and basin area, (3) the formats dimensional fields of probability of occurrence in function of the variables altitude and basin area, and (4) through statistical criteria of Akaike Information Criterion (AIC) and Dimensional Stability Index (DSI), the latter being developed in this study and represented by the following equation: D.S.I. = (CvP1 . CvP2 . CvP3 . ... . CvPi )1/ i, where: CvP1, CvP2, CvP3, CvPi is the coefficient of variation for each parameter. The percentage of adherence obtained were generally around 80%, and, in general, the LP model showed adherence rates between 1% and 4% lower than the other models. The PMFAltitude obtained with the LP model were higher for all species, being 672 m for S. brasiliensis, 516 m for P. lineatus, 651 m for L. obtusidens and 509 m for P. corruscans. The PMFBasin Area were higher for the model LOGITm, except for P. lineatus, where the models LOGITm and LP had the same value (101 km2) and P. corruscans, where the LP model showed a value of 1623 km2 and LOGITm model showed a value of 709 km2. The fields of probability of occurrence for the LOGIT and LOGITm models for all species had the same general behavior in the form of an oblique cross-section sigmoid. However, the fields formed by the residual sum of squares (RSS) obtained with the model LOGITm for all species behaved like a "trough" of lower values of variance, indicating the same statistical quality ara a wide range of combinations of PMFaltitude and PMFBasin Area, which results in lack of stability of the fitting parameters. The LP model presented only one point of lower value of RSS in all settings, showing better stability of the final answer, however, the minimum value obtained was always a little higher than in other models. The fields of probability of occurrence showed that the LP model shows the interaction between environmental variables closer to the biological reality that LOGIT and LOGITm, not being checked the compensatory mechanisms presented in the models LOGIT and LOGITm. The LP model presented the highest values of AIC for all species, and 34.3 for S. brasiliensis, 35.0 for P. lineatus, 35.2 for L. obtusidens and 33.7 for P. corruscans.The model presented in this criterion is less suitable than others to describe the distribution of species. With the DSI method, however, the LP model obtained the lowest values, except for S. brasiliensis, which achieved results slightly higher than the model LOGITm. In the present study we noted the similarity between models LOGIT and LOGITm because, except for L.obtusidens, the differences between them were extremely small, not representative for the studies on this scale. The LP model showed no compensatory mechanisms such as the LOGIT and LOGITm, therefore, although the worst results obtained in the AIC criterion, the resulting improvements in the statistical stability, shape of dimensional field and better predictive ability in extreme situations justify its use.