Conventional approaches to population biology emphasise the roles of climatic conditions, nutrient flow and predation as constraints on population dynamics. We argue here that this focus has obscured the role of time as a crucial constraint on species' abilities to survive in some habitats. Time constraints may be particularly intrusive both for species that live in intensely bonded groups (where the need to devote time to social interaction may ultimately limit the size of group that a species can maintain in a particular habitat) and for taxa that face constraints on the length of the active day. We use a linear programming approach that allows us to specify both how time allocations to different activities are influenced by local environmental and climatic variables and how these in turn limit group size and population density. The linear programming approach identifies the realizable niche space within which a species can maintain coherent groups that are larger than the minimum viable group size (or density). This approach thus allow us to understand better why a given taxon can survive in some habitats but not others, as well as the demographic stress that a population may face. In addition, they also allow us to evaluate the implications of both past and future climate change for a taxon's ability to cope with particular habitats.

Most primates live in social groups in which affiliative bonds exist between individuals. Because these bonds need to be maintained through social interactions (grooming in most primates), sociality will be limited by time constraints. It has previously been shown that the time primates invest in grooming increases with group size. However, when groups become too large, individuals will not have enough time available to service all possible social relationships and group cohesion is expected to decrease. In this study, we use data from previously published studies to determine how large groups compromise on their grooming time and how ecological, phylogenetic and lifehistory variables affect time invested in grooming (across species as well as within taxa). We use path analysis to analyse direct and indirect (via group size) effects on grooming. We show that not only is grooming time determined by group size, but it is also affected by dispersal patterns and sex ratio. Furthermore, we found that grooming time is asymptotic when group size exceeds 40 individuals, indicating that time constraints resulting from ecological pressure force individuals to compromise on their grooming time. This was true across species, but a similar effect was also found within taxa. Cognitive constraints and predation pressure strongly affect group sizes and thereby have an indirect effect on primate grooming time.Primates that were found to live in groups larger than predicted by their neocortex size usually suffered from greater predation risk. However, most populations in our analysis were placed well within what we define as their eco-cognitive niche. A number of factors are known to influence social group size in mammals (Caraco & Wolf, 1975;Pulliam & Caraco, 1984;Hass & Valenzuela, 2002). Among these, food distribution and predation pressure are the two best studied factors (Chapman et al., 1995;Janson & Goldsmith, 1995;Hass & Valenzuela, 2002;Downes & Hoefer, 2004). In addition to these, the social brain hypothesis suggests that, in species that live in socially bonded groups (such as many primates and carnivores), group size can be constrained by cognitive abilities (Dunbar, 1992a). This hypothesis is based on the finding that group size is strongly correlated with brain size (and specifically neocortex size in relation to the rest of the brain). The size of the neocortex is assumed to limit the number of social relationships an individual can keep track of. If group size becomes too large, it becomes impossible for an individual to maintain close social bonds with all group members. As a consequence, group cohesion will decrease and the group will eventually split (see (Henzi et al., 1997a;Henzi et al., 1997b).In support of this, Kudo and Dunbar (Kudo & Dunbar, 2001) have shown that social network size in primates is correlated with neocortex ratio, indicating that the number of grooming partners that primates can maintain as a coherent set is also related to the size of their neocortex. However, maintaining rela...

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