Other-regarding preferences in a non-human primate: Common marmosets provision food altruistically

Burkart et al. 10.1073/pnas.0710310104.

Supporting Information

Files in this Data Supplement:

SI Text
SI Table 1
SI Table 2
SI Table 3
SI Figure 6
SI Figure 7
SI Table 4




SI Figure 6

Fig. 6. Experimental set-up viewed from above. The position of the mesh partition in front of the apparatus ensures that an animal facing the apparatus immediately experiences whether it can access the recipient compartment.

SI Figure 7

Fig. 7. Experimental apparatus. (a) Front view. (b) Top view. The upper tray contains the payoff distribution (0,1), the lower (0,0).

Table 1. Summary of performance of different regression models

The "X" symbols indicate whether a given variable was included in the regression. Int., intercept; Related, dummy for dyads in which the two subjects were related; Breeder, dummy indicating whether the donor was a breeding individual; Sex, dummy for male donors; Sex-breeder, the following three dummies were included in the regression as a means of classifying donors: (i) female breeders, (ii) male helpers, and (iii) male breeders (female helpers are the reference category specified by the intercept in this case); Donor, individual dummies for the donors. The last two columns of the table show the Akaike values and Akaike weights for each model. Higher Akaike weights mean more evidence in favor of a model.

Table 2. Summary of effects for model 5 from SI Table 4

A single asterisk indicates significance at the 0.05 level, whereas two asterisks indicate significance at the 0.01 level. Robust SEs are calculated by clustering on donor.

Table 3. Subjects and their roles in the experiments

Individuals were never paired with the same partner as both donor and recipient. For instance, Kaliper was a recipient when playing with Kalium but never played the donor role when paired with Kalium. For animals in experiment 2 indicated with an asterisk, data from the role not indicated were taken from experiment 1. D, donor; R, recipient {status according to Missler et al. [Missler M, Wolff JR, Rothe H, Heger W, Merker HJ, Treiber A, Scheid R, Crook GA (1992) J Med Primatol 21:285-298]}.

 

Session 1: With partner		Session 2: Without partner		Session 3: With partner
Motivation trial	(0,0) vs. (1,0)	Motivation trial	(1,0) vs. (0,0)	Motivation trial	(0,0) vs. (1,0)
Trial 1	(0,1) vs. (0,0)	Trial 1	(0,0) vs. (0,1)	Trial 1	(0,0) vs. (0,1)
Trial 2	(0,0) vs. (0,1)	Trial 2	(0,1) vs. (0,0)	Trial 2	(0,1) vs. (0,0)
Trial 3	(0,1) vs. (0,0)	Trial 3	(0,0) vs. (0,1)	Trial 3	(0,0) vs. (0,1)
Motivation trial	(1,0) vs. (0,0)	Motivation trial	(0,0) vs. (1,0)	Motivation trial	(1,0) vs. (0,0)
Trial 4	(0,0) vs. (0,1)	Trial 4	(0,1) vs. (0,0)	Trial 4	(0,1) vs. (0,0)
Trial 5	(0,1) vs. (0,0)	Trial 5	(0,0) vs. (0,1)	Trial 5	(0,0) vs. (0,1)
Trial 6	(0,0) vs. (0,1)	Trial 6	(0,1) vs. (0,0)	Trial 6	(0,1) vs. (0,0)
Motivation trial	(0,0) vs. (1,0)	Motivation trial	(1,0) vs. (0,0)	Motivation trial	(0,0) vs. (1,0)

The first payoff distribution listed in a given cell refers to the distribution on the upper tray.

SI Text

Additional Statistical Analyses

Choice of Categories. To confirm our conclusions and determine whether structuring the treatment effect by the sex-breeder class of the donor is better than the possible alternatives, we analyzed the data using linear regressions and an information theoretic approach to model selection. For all regressions, as our response variable we calculated by dyad the proportion of (0,1) choices when a partner was present minus the proportion of (0,1) choices when a partner was absent. This produced 57 observations. SI Table 1 summarizes the results of the model selection exercise.

More precisely, the conclusion presented in the main text is that marmosets exhibited other-regarding preferences in the experiment, but these preferences are best understood by structuring the analysis according to the sex and breeding status of the donor. This, however, is not the only way to decompose the effect associated with the presence of a recipient. The question thus arises whether the sex/breeder categorization is a comparatively good categorization. Specifically, one can instead distinguish between related and unrelated dyads (SI Table 1, model 2). It is also possible to consider a pure sex effect (SI Table 1, model 4) or a pure effect associated with breeding status (SI Table 1, model 3) without classifying donors jointly by their sex and breeding class (SI Table 1, model 5). Moreover, one can simply use individual fixed effects for the donors as predictors without classifying dyads into particular categories (SI Table 1, model 6). Lastly, one can compare the rate of choosing (0,1) with and without the presence of a recipient without addressing such distinctions, i.e., by ignoring structure based on different types of dyads completely (SI Table 1, model 1). We conducted all of these analyses and in sum the exercise confirmed that a statistical model that takes into account the sex and breeding status of the donor (SI Table 1, model 5) performs best.

With respect to our use of information theory, P-values are a widely used method for reporting the statistical significance of variables, but they are ill suited to the task of choosing which model is best among an arbitrary number of models (1). We instead used a derivative form (AIC_c) of Akaike's information criterion (2) discussed in ref. 1 (p. 66) to compare the fits of various ordinary least squares regression models. This approach allows one to consider simultaneously a set of models composed of an arbitrary number of candidate models and identify the model that explains the data best. In particular, when one fits a model to data, one loses information in the sense that the model never fully captures all of the processes that generated the actual data. The Akaike-selected model is the model that is estimated to lose the least amount of information, and it thus has an intuitive and compelling interpretation. The use of AIC_c validates the increased predictive power of included explanatory variables after adjusting for the number of parameters and the number of observations while making it possible to select the model that best summarizes the data. In addition, the model with the smallest AIC_c value tends to make the best out-of-sample predictions. Lastly, one can rescale AIC_c values by computing Akaike weights for each model. Akaike weights are unit-free measures of fit. They sum to 1, and each Akaike weight captures the proportional weight of evidence in the data for the associated model, where higher Akaike weights mean more evidence in favor of the model.

As the Akaike weights in SI Table 1 indicate, the proportional weight of evidence favors models that account for the sex and/or breeding status of the donor. It is also interesting to see that a model that accounts for relatedness is far worse than models that account for sex or breeding status. In fact, adding the relatedness variable to the intercept (see model 2) decreases the Akaike weight relative to a model without the relatedness variable (model 1). This means that the relatedness variable explains almost nothing compared with the other variables considered in SI Table 1. In addition, SI Table 1 shows that individual variation across subjects is not important for explaining the data. This result is indicated by the very low Akaike weight for model 6, which is also related to the fact that most individual dummies in model 6 are not significant. Model 5, the model that categorizes donors into four classes by considering sex and breeding status jointly, is by far the best fitting model. Thus, this analysis confirms that categorizing donors by their sex and breeding status is comparatively the best approach to analyzing the other-regarding tendencies among marmoset subjects.

SI Table 2 shows the parameter estimates, robust SEs, and statistical significance for the coefficients in model 5.

SI Table 2 confirms that female helpers chose (0,1) in the presence of a partner as often as in the absence of a partner. This result is indicated by the lack of significance and the nearly zero estimated value for the intercept. However, all three of the remaining sex-breeder categories (female breeders, male breeders, and male helpers) exhibit significantly higher proportions of (0,1) choices in the presence of the partner than the female helpers. Thus, our regression analysis confirms the results presented in Fig. 2.

Are There Time Trends Across Trials and Sessions? One important question is whether subjects' choices exhibited a time trend across trials or across sessions. We tested for this possibility in several ways. First, we conducted a direct comparison between session 1 and session 3, which revealed that the animals did not choose the prosocial tray more often in session 1 than in session 3 [t(18) = 1.254, P = 0.226], arguing against the potential influence of a training effect that decays over time. Second, we conducted logistic regressions with subjects' choices as the dependent variable. In these regressions, we controlled for individual variation, the presence of a partner, and time effects by including a period variable indicating the sequence of choices by dyad (e.g., 1-18). We included both linear and quadratic terms in the period variable. However, both the linear and the quadratic term had no explanatory value; the coefficient of the linear period term in the regression is -0.0280 (P = 0.71), whereas the coefficient of the quadratic period term is -0.001 (P = 0.76). These results strongly contradict the idea that prosocial choices were just a training effect that decayed in a linear or nonlinear fashion.

1. Burnham KP, Anderson DR (2002) Model Selection and Multi-Model Inference: A Practical Information Theoretic Approach (Springer, New York), 2nd Ed.

2. Akaike H (1973) in Second International Symposium on Information Theory, eds Petrov BN, Csaki F (Akademiai Kiado, Budapest), pp 267-281.

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