Effect of Infant Presence on Social Networks of Sterilized and Intact Wild Female Balinese Macaques (Macaca fascicularis)

Contraception is increasingly used to control wild animal populations. However, as reproductive condition influences social interactions in primates, the absence of new offspring could influence the females’ social integration. We studied two groups of wild macaques (Macaca fascicularis) including females recently sterilized in the Ubud Monkey Forest, Indonesia. We used social network analysis to examine female grooming and proximity networks and investigated the role of infant presence on social centrality and group connectivity, while controlling for the fertility status (sterilized N = 14, intact N = 34). We compared the ego networks of females experiencing different nursing conditions (young infant (YI) vs old infant (OI) vs non-nursing (NN) females). YI females were less central in the grooming network than other females while being more central in proximity networks, suggesting they could keep proximity within the group to protect their infant from hazards, while decreasing direct grooming interactions, involving potential risks such as kidnapping. The centrality of sterilized and intact females was similar, except for the proximity network where sterilized females had more partners and a better group connectivity. These results confirm the influence of nursing condition in female macaque social networks and did not show any negative short-term effects of sterilization on social integration.

Group Connectivity and Group Coloring: Small Groups versus Large Groups

A well-known result of Tutte says that if $\Gamma$ is an Abelian group and $G$ is a graph having a nowhere-zero $\Gamma$-flow, then $G$ has a nowhere-zero $\Gamma'$-flow for each Abelian group $\Gamma'$ whose order is at least the order of $\Gamma$. Jaeger, Linial, Payan, and Tarsi observed that this does not extend to their more general concept of group connectivity. Motivated by this we define $g(k)$ as the least number such that, if $G$ is $\Gamma$-connected for some Abelian group $\Gamma$ of order $k$, then $G$ is also $\Gamma'$-connected for every Abelian group $\Gamma'$ of order $|\Gamma'| \geqslant g(k)$. We prove that $g(k)$ exists and satisfies for infinitely many $k$, \begin{align*}(2-o(1)) k < g(k) \leqslant 8k^3+1.\end{align*} The upper bound holds for all $k$. Analogously, we define $h(k)$ as the least number such that, if $G$ is $\Gamma$-colorable for some Abelian group $\Gamma$ of order $k$, then $G$ is also $\Gamma'$-colorable for every Abelian group $\Gamma'$ of order $|\Gamma'| \geq h(k)$. Then $h(k)$ exists and satisfies for infinitely many $k$, \begin{align*}(2-o(1)) k < h(k) < (2+o(1))k \ln(k).\end{align*} The upper bound (for all $k$) follows from a result of Král', Pangrác, and Voss. The lower bound follows by duality from our lower bound on $g(k)$ as that bound is demonstrated by planar graphs.