Measuring Selectivity from Multiple Choice Feeding-Preference Experiments

Abstract

SUMMARY A selection index that has been used in the past for the analysis of multiple choice feedingpreference experiments with discrete items of food is extended for use with experiments where amounts of food are measured on a continuous scale and time changes may occur even in the absence of consumers. Estimation equations with approximate variances and covariances are provided. Confidence intervals and a test for significant selection are briefly discussed. There are many examples in the biological literature of the use of multiple choice feeding experiments that involve consumers being simultaneously offered the choice of two or more types of food, and then a comparison being made between the amounts of different foods consumed. With these experiments there are two situations that need to be considered separately as far as the analysis of data is concerned, depending upon whether the abundance of foods is determined by counting discrete units (e.g., individual items of prey) or by measuring continuous amounts (e.g., weighing seaweed). With discrete units, methods that are reviewed by Manly (1985, Chapter 5) can be used to test for significant selection and to estimate selection indices. Generally, analyses are well developed for this situation, which will not be discussed further here. Instead, the present note concentrates on experiments with measured food consumption. An important factor that is taken into account is the fact that in many experiments the amounts of different types of food are subject to autogenic changes (i.e., natural changes that occur in the absence of consumers). For this reason it is necessary to run control trials at the same time as trials with consumers. Differences between the results for the consumer and the control trials can then be used to estimate true consumption (Peterson and Renaud, 1989). In an important paper, Roa (1992) discussed the problem of testing for selection using the results from consumer and control trials. He noted the importance of allowing for possible correlation between the results for different foods within one trial due to there being different environmental conditions for each trial and (for consumer trials) due to the fact that if a large amount of one food is taken then there is likely to be less of other foods taken, even when there is no selection taking place. He also proposed a test for selection that is based on Hotelling's T2 statistic, which he claimed allows for correlation. Subsequently, Manly (1993) pointed out certain problems with Roa's test and suggested an alternative one that uses Yao's (1965) degrees-of-freedom approximation for comparing the means of two samples from multivariate normal distributions with different covariance matrices.