Expected intervention cost (from model coefficients) plotted by intervener rank for several intervention types.

<p>Expected intervention cost (from model coefficients) plotted by intervener rank for several intervention types.</p

Observed frequency of targeting each sex-dyad combination across intervention types.

a<p>Values highlighted in <b>bold</b> differed significantly from expected in Chi-square tests.</p>b<p>Expected values are given in parentheses.</p

Expected frequency of SNP support plotted by intervener-beneficiary groom frequency for beneficiaries of high and low rank.

<p>Expected frequency of SNP support plotted by intervener-beneficiary groom frequency for beneficiaries of high and low rank.</p

Expected frequency of SND support plotted by intervener-beneficiary groom frequency for beneficiaries of high and low rank.

<p>Expected frequency of SND support plotted by intervener-beneficiary groom frequency for beneficiaries of high and low rank.</p

Proposed hypotheses regarding the function of impartial interventions in rhesus macaques.

<p>Proposed hypotheses regarding the function of impartial interventions in rhesus macaques.</p

Expected mating between intervener and beneficiary (from model coefficients) plotted by intervener rank for several intervention types.

<p>Expected mating between intervener and beneficiary (from model coefficients) plotted by intervener rank for several intervention types.</p

Group-level characteristics.

<p>Group-level characteristics.</p

Summary of results across intervention types.

<p>Summary of results across intervention types.</p

Proposed hypotheses regarding the function of support of subordinate non-kin in rhesus macaques.

<p>Proposed hypotheses regarding the function of support of subordinate non-kin in rhesus macaques.</p

Systemic Testing on Bradley-Terry Model against Nonlinear Ranking Hierarchy

<div><p>We take a system point of view toward constructing any power or ranking hierarchy onto a society of human or animal players. The most common hierarchy is the linear ranking, which is habitually used in nearly all real-world problems. A stronger version of linear ranking via increasing and unvarying winning potentials, known as Bradley-Terry model, is particularly popular. Only recently non-linear ranking hierarchy is discussed and developed through recognition of dominance information contents beyond direct dyadic win-and-loss. We take this development further by rigorously arguing for the necessity of accommodating system's global pattern information contents, and then introducing a systemic testing on Bradley-Terry model. Our test statistic with an ensemble based empirical distribution favorably compares with the Deviance test equipped with a Chi-squared asymptotic approximation. Several simulated and real data sets are analyzed throughout our development.</p></div