An Analysis of Forage Preference Indices

Of those models currently used to describe the preference of animals for various plants undeigiven conditions, all have serious shortcomings for purposes of accurately explaining the data, in the regression sense. When five equations, based in various ways on preference and availability, were used to estimate diets of cattle and sheep, no clear advantage of one expression over another could be found. All models tested with the sheep data resulted in increased predicted sums of squares compared with total sums of squares. In contrast, models tested with the cattle data showed some reduction in unexplained variation in diet estimates during the entire year, spring, and summer, but not during fall. This improvement was probably because the cattle pastures were more homogeneous than the sheep pastures and species were aggregated. The best model was Ratio 4 (preference -availability) but it requires a complex and expensive parameter estimation technique. It was concluded that sampling problems combine with inadequacies of the preference indexes to prevent accurate representation of the concept of diet preference. It was also concluded that sampling problems arise when the fecal, rumen fistula, or esophageal fistual techniques are used to estimate diets. A technique for adjusting these techniques to make them suitable for predicting diets was described. Further investigations into animal behavior are needed to determine variables which affect what the animal perceives as being desirable in relation to what is available. Preference indices in range work are used to summarize grazing trials, to draw conclusions about animal behavior (Krueger 1972), and to incorporate into diet prediction models (Nelson 1977, Nelson 1978) or simulation models (Anway 1976). However, the concept of preference has never been given a rigorous test. The objective of this paper is to approach such a test by analyzing the indices which purport to measure preference. All models that could be located in the literature which incorporated preference were examined for usefulness in the context of large herbivores, particularly domestic stock. Those that passed logical examination were tested against grazing study data. Only one model (Silen and Dimock 1978) had been previously tested. None had been tested against data from natural pastures. Review of Previous Indices Many authors have developed indices of preference for animal diets. Some of the models developed for predation can be adapted to herbivory with suitable changes of definition. Many of the models developed are limited to the 2-prey case. Chesson ( 1978) and Cock ( 1978) review and discuss many of these models. It is often stated (e.g., Cock 1978) that 2-prey models can be extended to the n-prey case by pooling all prey except type 1 into Authors are research associate and associate professor, Department of Range Science, Colorado State University, Fort Collins, Colorado 80523. Research was supported by the Colorado State Univ. Exp. Sta. and published as Sci. Series Pap. No. 2601 in cooperation with Regional Project W 151. The authors would like to express their appreciation to persons who reviewed this manuscript and for their many helpful suggestions. Further, we would like to thank Drs. Anderson and Krueger for having conducted such thorough studies and for allowing us to use their data for statistical analysis. Manuscript received May 29, 1980. the type 2 category and then treating as a 2-prey situation. This technique has never been validated and in fact is not tenable unless the pooled species are equally preferred. Consider, for example, an animal (predator or herbivore) with 3 food items. Species 1 and 2 are greatly preferred but are much rarer than species 3. Normally, the diet consists of equal parts of 1 an.d 2 plus a small amount of 3. If 2 and 3 are pooled into a new class 2’, the desirable characteristics of species 2 are overwhelmed by the undesirable character of 3. This approach leads us to conclude, then, that the animal will eat almost entirely items of type 1. The problem is that there is no tenable rationale for pooling species with different probabilities of encounter for herbivores or of capture for predators, frequencies in the habitat, and desirabilities to the predator (or herbivore). There are times when pooling species is unavoidable, but pooling into 2 classes as a standard procedure is an unjustified oversimplification. Similarly, pooling of plant parts may be an unjustified oversimplification (D. Swift, personal communication). Because, in general, large herbivores consume more than two types of food, the many models that can represent only choices between two food items are not deemed useful. For these reasons such models will not be considered further in this paper. Four relative preference indices (RPI’s) are discussed by Krueger (1972). He rejects two of the indices because they do not meet the criterion that every plant has the same value when selection by animals is completely random. The models which pass Krueger’s (1972) random grazer test are RPIl and RPlz, which correspond to Ratio 1 and Ratio 2, discussed in the following section. Prediction Using Preference Ratios In this section, four preference ratio models are analyzed for logical validity. Those that meet this criteria are tested against data in the next section. Ratio 1 Ratio 1 (R I) is the same as RPIl (Krueger 1972) and is given by Rli = fdi l Dr (1) fri l RAi where Rli is the value of Ratio 1 for the i’th plant species; fdi = frequency of species i in the diet; fri = frequency of species i in the pasture; Di = percent by weight of the diet for species i; and RAi = relative availability (percent by weight) of species i in the pasture. Used as a predictive formula, we get &= fri l Rli*R&. (2) This index has problemfdarising from the use of frequency. Because frequency depends on plot size and shape, and different management agencies and research workers use different sampling schemes, it would be very hard to get comparable results from place to place. In addition, the frequency of a food item to a herbivore depends on its mobility, the visibility of the food item under various conditions, and other factors. For these reasons, the usefulness of this index seemed dubious and it was not considered further. 316 JOURNAL OF RANGE MANAGEMENT 35(3), May 1982 Ratio 2 This ratio has been used frequently (Krueger 1972, Jacobs 1974, Cock 1978) and is commonly called the forage ratio in range work. It is given other names in other fields of ecology. It is described as the ratio of the percent of a species in the diet to the percent on the range. Its computational formula is