APPENDIX 4: Statistical methods for determining gastrointestinal (GI) quotients in |

- Martin
et al. [1985] eliminate the differences in body size via the use of quotients (defined below); however, allometric (non-linear) scaling models are used to calculate estimated organ sizes for the GI quotients. - Using major axis methods, linear equations were fitted between the (dependent variable) log of the surface areas of the stomach, intestines, cecum, and colon, and (independent variable) log of body weight. Such equations relate the size (surface area) of each organ to overall body weight, in an equation analogous to Kleiber's Law. They found a slope of 0.75 (i.e., Kleiber's Law) to be within the 95% confidence intervals for the data set for each GI component, except for the colon. They chose to use 0.75 for producing estimates for the colon anyway, for consistency with the other three gut components, which scaled according to Kleiber's Law.
- They next calculate 4 GI quotients for each animal in the study. These are
defined as: __surface area of GI component--actual__

surface area of GI component--predictedwhere the predicted surface area is based on actual weight and scaling equations (above) similar to Kleiber's Law. Separate GI quotients are computed for the stomach, intestines, cecum, and colon. Note that quotient values greater than 1 indicate actual surface area is greater than predicted, while quotient values less than 1 indicate that actual surface area is less than predicted.

- Multivariate (simultaneous multiple-
variable) techniques were used to attempt to group the data set (4 GI coefficients for each animal in the sample) in a way that would provide insight into the actual diets of each animal, as follows:- The technique of multi-
dimensional scaling (MDS) was used to analyze the multivariate GI- quotient data set. The results from MDS roughly agreed with the dendrogram results (below), but were difficult to interpret because a large group of primates clustered together. - A dendrogram--
a "tree" diagram-- based on distances between points in the study data set was calculated. (See Figure 11, p. 81 of Martinet al. [1985].) Developing a dendrogram is the first step in a procedure known as clustering. The object of clustering is to determine groupings for multivariate data. The next step is to examine the possible groupings in the dendrogram to see if the clusters can be interpreted in ameaningful way.

- The technique of multi-

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