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In polygynous and polygynandrous species, there is often intense male-male competition over access to females, high male reproductive skew, and more male investment in mating effort than parenting effort [1]. However, the benefits derived from mating effort and parenting effort may change over the course of males' lives. In many mammalian species, there is a ∩-shaped relationship between age, condition, and resource holding power as middle-aged males that are in prime physical condition outcompete older males [2-8] and sire more infants [9-12]. Thus, males might derive more benefits from parenting effort than mating effort as they age and their competitive abilities decline [13]. Alternatively, older males may invest more effort in making themselves attractive to females as mates [14]. One way that older males might do so is by developing relationships with females and providing care for their offspring [14, 15]. Savannah baboons provide an excellent opportunity to test these hypotheses. They form stable multi-male, multi-female groups, and males compete for high ranking positions. In yellow and chacma baboons (Papio cynocephalus and P. ursinus), there is a ∩-shaped relationship between male age and dominance rank [12], and high rank enhances paternity success [12, 16]. Lactating female baboons form close ties ("primary associations" hereafter) with particular males [15-20], who support them and their infants in conflicts [15, 19] and buffer their infants from rough handling [20]. Females' primary associates are often, but not always, the sires of their current infants [16, 20-22]., Competing Interests: Declaration of Interests The authors declare no competing interests., (Copyright © 2020. Published by Elsevier Inc.)

Long-term male-female bonds and bi-parental investment in offspring are hallmarks of human society. A key question is how these traits evolved from the polygynandrously mating multimale multifemale society that likely characterized the Pan-Homo ancestor. In all three species of savanna baboons, lactating females form strong ties (sometimes called "friendships") with one or more adult males. For yellow baboons (Papio cynocephalus) and chacma baboons (Papio ursinus), several lines of evidence suggest that these relationships are a form of male parenting effort. In olive baboons (Papio anubis), females are thought to preferentially mate with their "friends", and male-female bonds may thus function as a form of mating effort. Here, we draw on behavioral and genetic data to evaluate the factors that shape male-female relationships in a well-studied population of olive baboons. We find support for the parenting effort hypothesis in that sires have stronger bonds with their infants' mothers than do other males. These bonds sometimes persist past weaning age and, in many cases, the sire of the previous infant is still a close partner of the female when she nurses her subsequent offspring. We find that males who have the strongest bonds with females that have resumed cycling, but are not currently sexually receptive, are more likely to sire the female's next offspring but the estimate is associated with large statistical uncertainty. We also find that in over one third of the cases, a female's successive infants were sired by the same male. Thus, in olive baboons, the development of stable breeding bonds and paternal investment seem to be grounded in the formation of close ties between males and anestrous females. However, other factors such as male dominance rank also influence paternity success and may preclude stability of these bonds to the extent found in human societies., (Copyright © 2018 Elsevier Ltd. All rights reserved.)