INFERRING ECOLOGICAL RELATIONSHIPS FROM THE EDGES OF SCATTER DIAGRAMS- COMPARISON OF REGRESSION TECHNIQUES

Scatter diagrams have historically proved useful in the study of assoc iative relationships in ecology. Several important ecological question s involve correlations between variables resulting in polygonal shapes , Two examples that have received considerable attention are patterns between prey size and predator size in animal populations and the rela tionship between animal abundance and body size. Each is typically ill ustrated using scatter diagrams with upper and lower boundaries of res ponse variables often changing at different rates with changes in the independent variables, Despite recent statistical contributions that h ave stimulated an interest in characterizing the limits of a variable, a consensus on an appropriate methodology to quantify the boundaries of scatter diagrams has not yet been achieved, We tested regression te chniques based on least squares and least absolute values models using several independent data sets on prey length and predator length for piscivorous fishes and compared estimated slopes for consistency, Our results indicated that least squares regression techniques were partic ularly sensitive to outlying y values and irregularities in the distri bution of observations, and that they frequently produced inconsistent estimates of slope for upper and lower bounds. In contrast, quantile regression techniques based on least absolute values models appeared r obust to outlying y values and sparseness within data sets, while prov iding consistent estimates of upper and lower bound slopes. Moreover, the use of quantile regression eliminated the need for an excess of ar bitrary decision-making on the part of the investigator. We recommend quantile regression as an improvement to currently available technique s used to examine potential ecological relationships dependent upon qu antitative information on the boundaries of polygonal relationships.