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Joint modeling of multiple social networks to elucidate primate social dynamics: I. maximum entropy principle and network-based interactions.

Chan S, Fushing H, Beisner BA, McCowan B - PLoS ONE (2013)

Bottom Line: Here we develop a bottom-up, iterative modeling approach based upon the maximum entropy principle.Using a rhesus macaque group as a model system, we jointly modeled and analyzed four different social behavioral networks at two different time points (one stable and one unstable) from a rhesus macaque group housed at the California National Primate Research Center (CNPRC).We report and discuss the inter-behavioral dynamics uncovered by our joint modeling approach with respect to social stability.

View Article: PubMed Central - PubMed

Affiliation: Department of Statistics, University of California Davis, Davis, California, USA.

ABSTRACT
In a complex behavioral system, such as an animal society, the dynamics of the system as a whole represent the synergistic interaction among multiple aspects of the society. We constructed multiple single-behavior social networks for the purpose of approximating from multiple aspects a single complex behavioral system of interest: rhesus macaque society. Instead of analyzing these networks individually, we describe a new method for jointly analyzing them in order to gain comprehensive understanding about the system dynamics as a whole. This method of jointly modeling multiple networks becomes valuable analytical tool for studying the complex nature of the interaction among multiple aspects of any system. Here we develop a bottom-up, iterative modeling approach based upon the maximum entropy principle. This principle is applied to a multi-dimensional link-based distributional framework, which is derived by jointly transforming the multiple directed behavioral social network data, for extracting patterns of synergistic inter-behavioral relationships. Using a rhesus macaque group as a model system, we jointly modeled and analyzed four different social behavioral networks at two different time points (one stable and one unstable) from a rhesus macaque group housed at the California National Primate Research Center (CNPRC). We report and discuss the inter-behavioral dynamics uncovered by our joint modeling approach with respect to social stability.

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Related in: MedlinePlus

Histograms of the expected frequency of each linkage vector category under the  model of independence and after the cumulative application of the four constraint functions.
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pone-0051903-g003: Histograms of the expected frequency of each linkage vector category under the model of independence and after the cumulative application of the four constraint functions.

Mentions: In Figure 3, we can see the differences between the computed expected number for each type of link and the observed number. The expected distribution is under the assumption that each link is independent for the rest, which is clearly not true. The first function () adjusts for the covariance association in the first network (grooming), and this adjustment is most apparent in the first two linkage vectors and, as these bars approach zero. The second function () adjusts for the covariance in the second network (aggression), and this is most evident in the two linkage vectors corresponding to aggression and , as these bars approach zero. These covariance adjustments generate an expected probability that is closer to the observed value. The third function () adjusts for the opposite directions between and, in order to pull these discrepancies toward zero. This can be seen as the fifth and sixth bars approach zero in . Looking at the differences we still see that the first four bars (where only one of the networks has an occurrence) have lower observed than expected values, and the last six bars (where either both or neither networks have an occurrence) have higher observed than expected value. The fourth function () aims to adjust for the covariance between the two networks, which decreases the expected value for the first four vectors and increases the expected value for the other six vectors. This function brings all of the discrepancies closer to zero. There appear to be more links of than expected over all four functions. However, the Chi-squared value for is considerably low, because the difference is low compared to the relatively high number (4575) of non-connected links.


Joint modeling of multiple social networks to elucidate primate social dynamics: I. maximum entropy principle and network-based interactions.

Chan S, Fushing H, Beisner BA, McCowan B - PLoS ONE (2013)

Histograms of the expected frequency of each linkage vector category under the  model of independence and after the cumulative application of the four constraint functions.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3585323&req=5

pone-0051903-g003: Histograms of the expected frequency of each linkage vector category under the model of independence and after the cumulative application of the four constraint functions.
Mentions: In Figure 3, we can see the differences between the computed expected number for each type of link and the observed number. The expected distribution is under the assumption that each link is independent for the rest, which is clearly not true. The first function () adjusts for the covariance association in the first network (grooming), and this adjustment is most apparent in the first two linkage vectors and, as these bars approach zero. The second function () adjusts for the covariance in the second network (aggression), and this is most evident in the two linkage vectors corresponding to aggression and , as these bars approach zero. These covariance adjustments generate an expected probability that is closer to the observed value. The third function () adjusts for the opposite directions between and, in order to pull these discrepancies toward zero. This can be seen as the fifth and sixth bars approach zero in . Looking at the differences we still see that the first four bars (where only one of the networks has an occurrence) have lower observed than expected values, and the last six bars (where either both or neither networks have an occurrence) have higher observed than expected value. The fourth function () aims to adjust for the covariance between the two networks, which decreases the expected value for the first four vectors and increases the expected value for the other six vectors. This function brings all of the discrepancies closer to zero. There appear to be more links of than expected over all four functions. However, the Chi-squared value for is considerably low, because the difference is low compared to the relatively high number (4575) of non-connected links.

Bottom Line: Here we develop a bottom-up, iterative modeling approach based upon the maximum entropy principle.Using a rhesus macaque group as a model system, we jointly modeled and analyzed four different social behavioral networks at two different time points (one stable and one unstable) from a rhesus macaque group housed at the California National Primate Research Center (CNPRC).We report and discuss the inter-behavioral dynamics uncovered by our joint modeling approach with respect to social stability.

View Article: PubMed Central - PubMed

Affiliation: Department of Statistics, University of California Davis, Davis, California, USA.

ABSTRACT
In a complex behavioral system, such as an animal society, the dynamics of the system as a whole represent the synergistic interaction among multiple aspects of the society. We constructed multiple single-behavior social networks for the purpose of approximating from multiple aspects a single complex behavioral system of interest: rhesus macaque society. Instead of analyzing these networks individually, we describe a new method for jointly analyzing them in order to gain comprehensive understanding about the system dynamics as a whole. This method of jointly modeling multiple networks becomes valuable analytical tool for studying the complex nature of the interaction among multiple aspects of any system. Here we develop a bottom-up, iterative modeling approach based upon the maximum entropy principle. This principle is applied to a multi-dimensional link-based distributional framework, which is derived by jointly transforming the multiple directed behavioral social network data, for extracting patterns of synergistic inter-behavioral relationships. Using a rhesus macaque group as a model system, we jointly modeled and analyzed four different social behavioral networks at two different time points (one stable and one unstable) from a rhesus macaque group housed at the California National Primate Research Center (CNPRC). We report and discuss the inter-behavioral dynamics uncovered by our joint modeling approach with respect to social stability.

Show MeSH
Related in: MedlinePlus