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Competitive order as a measure of social dominance in dairy cattle: A criticism of the paper by Friend and Polan
191
COMPETITIVE ORDER CATTLE: A CRITICISM
AS A MEASURE OF SOCIAL OF THE PAPER BY FRIEND
DOMINANCE AND POLAN
IN DAIRY
Friend and Polan (1978) concluded “.... The dominance values used in this study failed as adequate measures of a socially mediated priority of access . . . . From these data, we doubt the existence of a classical hierarchy in dairy cows . . . . Production variables were most important and described in a positive direction access to limited amounts of feed, dry matter intake, and time at the feed trough . . . .” The authors utilised a multiple regression analysis in which the relative importance of twelve independent variables (dominance value, age, body weight, daily milk production during the treatment, mature equivalent milk production and percent milk fat, and their squares) was to be determined in predicting a number of dependent variables (including time at feed trough when either concentrate or hay was fed, and dry matter intake). The aim of the work was sound. Unfortunately, the authors based their conclusions on a comparison of standardized partial regression coefficients, which cannot, by itself, give evidence about which independent variables contribute most importantly to the variation in the dependent variable. Partial regression coefficients (whether standarized or not is not important in this context) show the relation between the dependent variable and one independent variable with all other independent variables held constant. That is, partial regression coefficients tell us something about the extra relationship of Y to Xi after all the other Xs have been allowed for. If the partial regression of Y on Xi is small this does not mean that Y is not determined, or caused by, or associated with Xi. It merely shows that Xi has no extra relationship after the other Xs have been allowed for. Thus, even if Xi determines both Y and Xj, but so that Xj is closely correlated with Xi, there need not be a high partial regression coefficient of Y and Xi with any model that also includes Xj. In view of this, Friend and Polan have not shown that their dominance values failed as measures of a socially mediated priority of access. In fact, they found a simple correlation coefficient of 0.60 (P < 0.01) between time spent eating concentrate and dominance value. I suggest that a more correct interpretation of at least some of their results is as follows: (1) Dominance value affected the time spent eating, at least the concentrate. (2) As dominance value has elsewhere been found to be correlated with age and/or weight (see their introduction), similar correlations are likely to have been present here. This could lead to small partial regression coefficients for dependent variables with dominance value, age and weight (as actually found). (3) Daily production was probably closely related to time spent eating (of concentrate in particular) and therefore was also correlated to some extent with dominance value. This will have resulted in relatively small par&J
192
regression coefficients of time spent eating (concentrate in particular) with daily production. Further, dominance value is likely to have affected both time in stalls and time spent eating, which in turn affected daily production, leading to relatively small partial regression coefficients of time in stalls on daily production. The data generally fit this explanation. (4) Mature equivalent production and percent fat were the variables furthest removed from the intercorrelated variables of the experimental period (dominance value, age, weight, time spent eating, daily production). They are therefore expected to have had the lowest correlations with any of the other variables and as a consequence to provide the highest amount of extra association with, e.g., time spent eating, after all other variables have been allowed for. This was found and mistakenly used by Friend and Polan to conclude that these variables were most important in determining time spent eating, etc. The underlying biology implied by my interpretation is that: (a) Social dominance was present. (b) Dominance value was important, at least in affecting time spent eating concentrate. (c) The amount of concentrate eaten had some effect on daily production during the experiments and (d) Measures of production of the total lactation were less closely related to the amount of feed eaten during the experimental period. The suggestion made by Friend and Polan that highly producing cows have a need to eat more for reasons unrelated to dominance is very reasonable and entirely consistent with my interpretation above. R.G. BEILHARZ Agriculture and Forestry University of Melbourne Parkville, Victoria 3052 Australia (Received 7 April 1978)
REFERENCE Friend, T.H. and Polan, C.E., 1978. Competitive in dairy cattle. Appl. Anim. Ethol., 4: 61-70.
order as a measure of social dominance
COMPETITIVE ORDER CATTLE: A CRITICISM
AS A MEASURE OF SOCIAL OF THE PAPER BY FRIEND
DOMINANCE AND POLAN
IN DAIRY
Friend and Polan (1978) concluded “.... The dominance values used in this study failed as adequate measures of a socially mediated priority of access . . . . From these data, we doubt the existence of a classical hierarchy in dairy cows . . . . Production variables were most important and described in a positive direction access to limited amounts of feed, dry matter intake, and time at the feed trough . . . .” The authors utilised a multiple regression analysis in which the relative importance of twelve independent variables (dominance value, age, body weight, daily milk production during the treatment, mature equivalent milk production and percent milk fat, and their squares) was to be determined in predicting a number of dependent variables (including time at feed trough when either concentrate or hay was fed, and dry matter intake). The aim of the work was sound. Unfortunately, the authors based their conclusions on a comparison of standardized partial regression coefficients, which cannot, by itself, give evidence about which independent variables contribute most importantly to the variation in the dependent variable. Partial regression coefficients (whether standarized or not is not important in this context) show the relation between the dependent variable and one independent variable with all other independent variables held constant. That is, partial regression coefficients tell us something about the extra relationship of Y to Xi after all the other Xs have been allowed for. If the partial regression of Y on Xi is small this does not mean that Y is not determined, or caused by, or associated with Xi. It merely shows that Xi has no extra relationship after the other Xs have been allowed for. Thus, even if Xi determines both Y and Xj, but so that Xj is closely correlated with Xi, there need not be a high partial regression coefficient of Y and Xi with any model that also includes Xj. In view of this, Friend and Polan have not shown that their dominance values failed as measures of a socially mediated priority of access. In fact, they found a simple correlation coefficient of 0.60 (P < 0.01) between time spent eating concentrate and dominance value. I suggest that a more correct interpretation of at least some of their results is as follows: (1) Dominance value affected the time spent eating, at least the concentrate. (2) As dominance value has elsewhere been found to be correlated with age and/or weight (see their introduction), similar correlations are likely to have been present here. This could lead to small partial regression coefficients for dependent variables with dominance value, age and weight (as actually found). (3) Daily production was probably closely related to time spent eating (of concentrate in particular) and therefore was also correlated to some extent with dominance value. This will have resulted in relatively small par&J
192
regression coefficients of time spent eating (concentrate in particular) with daily production. Further, dominance value is likely to have affected both time in stalls and time spent eating, which in turn affected daily production, leading to relatively small partial regression coefficients of time in stalls on daily production. The data generally fit this explanation. (4) Mature equivalent production and percent fat were the variables furthest removed from the intercorrelated variables of the experimental period (dominance value, age, weight, time spent eating, daily production). They are therefore expected to have had the lowest correlations with any of the other variables and as a consequence to provide the highest amount of extra association with, e.g., time spent eating, after all other variables have been allowed for. This was found and mistakenly used by Friend and Polan to conclude that these variables were most important in determining time spent eating, etc. The underlying biology implied by my interpretation is that: (a) Social dominance was present. (b) Dominance value was important, at least in affecting time spent eating concentrate. (c) The amount of concentrate eaten had some effect on daily production during the experiments and (d) Measures of production of the total lactation were less closely related to the amount of feed eaten during the experimental period. The suggestion made by Friend and Polan that highly producing cows have a need to eat more for reasons unrelated to dominance is very reasonable and entirely consistent with my interpretation above. R.G. BEILHARZ Agriculture and Forestry University of Melbourne Parkville, Victoria 3052 Australia (Received 7 April 1978)
REFERENCE Friend, T.H. and Polan, C.E., 1978. Competitive in dairy cattle. Appl. Anim. Ethol., 4: 61-70.
order as a measure of social dominance