There is abundant evidence that amongst cooperative species group size is an important variable [43, 44]. Furthermore, in many cases, including Lycaon, optimal group sizes have been identified [26, 27, 40, 45]. However, the role of demographic Allee effects in this context has been neglected. Our consideration of Allee effects leads to the proposition that they operate at three different levels: the individual, the group and the population (component, group and demographic Allee effects). We thus introduce the concept of a group Allee effect, and its relevance for population dynamics and persistence.
We reveal how highly social species, suggested to be very susceptible to component Allee effects, can avoid the population extinction that is predicted to follow from Allee effects. In obligate cooperate breeders, individual fitness and group fate are highly dependent on each other, because individuals generally cannot survive outside groups. We propose that the organization of the population into a mix of large and small groups is indeed buffering (through the dispersal of large groups) the Allee effects occurring in small groups (at the individual and group levels). Furthermore, we highlight that it is indeed the evolution of eusociality and subsequent individual behavioural strategies (e.g. passive territoriality) that is facilitating the independence of groups and thus the co-existence of large and small groups in the populations, that compensates for the higher extinction risks of smaller packs caused by component and group Allee effects (we found 80% of groups went extinct in our Lycaon population, but the population persisted). If groups are independent, their sizes will also be independent of population size, so that the extinction of small groups will not be linked to the extinction of the population. We also hypothesized that, under these circumstances, density dependent effects at the levels of both individuals and groups will be determined by group size and not by population size. Our empirical analysis confirmed our hypotheses, demonstrating the existence of multiple component and group Allee effects in various life history traits in Lycaon, with frequent group extinctions, but no detectable consequences at the population level. We also found that Allee effect was caused by group sizes and not by population size, and that group size was independent of population size. This explains the seemingly contradictory results of previous studies on Lycaon, where both defendants and sceptics of Allee effects in this species had solid cases (see Table 1 and 2).
Individual performance and the importance of group size
At the individual level, we found Allee effects in the breeding and survival of pups and dispersers, but the absence of an Allee effect related to the survival of either adults or yearlings was unexpected, although similar results have been found in other populations (Table 1 and 2). The component Allee effect affecting breeding could be explained by the scarcity of helpers in small packs. This is not a surprising result as the importance of helpers in this species has already been emphasized [26, 40, 45] and relationship between pack size and breeding success has also been shown in other populations [22, 46] and see Table 1. The component Allee effect affecting the survival of pups could also be explained by its high dependence on the presence and abundance of helpers [22, 27, 33, 47].
The dynamics of groups have significant bearing on the production of dispersers and success of colonization events . We showed, for the first time, Allee effect in the survival of dispersers. Somers et al.  did not find such a relationship in the HiP population (which had been reintroduced after an absence of 50 years); they explained the lack of component Allee effects in terms of low interspecific competition and high prey availability. Here it is important to note that HiP was fenced which will unnaturally increase prey capture by reducing chase distances . Consequently, unnaturally high energetic return from these factors and subsequent increased births  and survival could well negate Allee effects. Survival in our study was higher when dispersers came from a large pack and maximal when the packs from which they dispersed comprised more than 12 individuals. Higher survival of dispersers coming from larger packs probably resulted from a better body condition at dispersal than those dispersers coming from smaller packs, as individuals in larger packs bank more energy per day . This was not mediated by the collective prowess of dispersers, as smaller packs did not produce smaller groups of dispersers in this population. There is a minimum quorum for dispersal so members of smaller packs delay dispersal until they can meet the minimum strength of numbers. However, perhaps because they were fitter as they would have banked more energy , dispersers from larger packs fared better, as has been suggested elsewhere [40, 45].
Group performance and the importance of group size
At the group level, we show that the number of pack formation events was positively related to the number of existing packs in the population. This agrees with results from the HiP population in South Africa , see Table 1. We also show that a pack’s growth rate depends on its size, and that it is positive when there are four or more individuals in the pack. This accords with previous studies that have demonstrated that a threshold in pack size exists; packs of more than four to six Lycaon faring better than did smaller packs [26, 27]. Throughout our analyses, our results are consistent in showing an optimal group performance of 10–12 pack members (Figures 2C,F, 3F) and these data are in striking concordance with net rate of energetic intake data  which also show rapid individual and therefore group returns. These data highlight how at a population level where foraging returns are favourable, either naturally or unnaturally as in the case of fenced reserves, obligate co-operators such as Lycaon are perhaps better fitted than their competitors to exploit favourable conditions. Consequently, it is probable that it is the group Allee level effect that protects the species in leaner times long enough for rapid recovery where foraging and prey availability conditions are optimised.
The lack of demographic Allee effect: low extinction risk at low numbers
At the population level, we found no evidence of a demographic Allee effect. This is consistent with seemingly paradoxical results from previous work in small populations of Lycaon, which not only failed to find it, but even showed negative density dependence of population growth rate [27, 29, 46]. As in previous published studies, our results on the demographic Allee effect are drawn from only one population, but this population varied greatly in size during ours long-term study. Future work might further test our hypothesis through a meta-analysis of all recently published long-term studies, profiting from their differing populations size and pack size ranges (see Table 1 and 2).
Group independence benefits sociality
Here, absence of a demographic Allee effect seems to be related to the independence, that we demonstrated here, between group sizes and population sizes, and recently suggested by Woodroffe . Previous literature reveals inconsistent results as to whether population decline is associated with a decrease in pack size or not. For example, MacLellan et al.  show that for ungulates declining populations were characterized by smaller group sizes. However, a lack of relationship between group size and population size has been seen in Serengeti lions, Panthera leo and in populations of wild dogs in Kenya and Tanzania [32, 45]. Somers et al.  showed a positive relationship between group and population sizes in Lycaon in South Africa, but the range of the population size and the number of packs analysed was smaller than in our study and than in Woodroffe ; in addition, the comparison may be inappropriate because the fences as well as the introduction of groups into the population in their study could have affected the composition of packs. Indeed, it has been shown that pre-release socialization and group fission following release is relatively frequent in wild dog reintroductions  what could have affected the size of the pack at release (as well as the corresponding estimations of yearly pack sizes) and processes such as pack formation or extinction.
The evidence of the empirical analysis suggests that relative independence amongst the dynamics of different groups has the consequence of preventing population extinctions at low numbers (thus, protecting populations from demographic Allee effects). Social groups seem to be self-contained, fluctuating in size independently of each other, in the sense that the fate of one particular group has practically no effect on the fate of other groups. This independence is strengthened by the fact that Lycaon pictus favours inter-group avoidance with large packs allowing smaller packs to utilize adjacent territories without harassment . There appears to be a non-confrontational form of space-use where even large groups avoid areas recently hunted by smaller groups by use of scent [39, 46], probably to save wasting energy attempting to capture predator-sensitized prey, or fights thus avoiding injuries that would be detrimental for both groups. This system occurs in several large carnivores that compete for territory; it is best described as “drifting territoriality” where pack ranges are sympatric over time, but parapatric at any point in time [52, 53]. These results thus support our hypothesis that group sizes and fates are largely independent of each other.
Of course, alternative hypothesis could challenge our interpretation. For example, genetic effects (including genetic Allee effects) could be involved, although the time scale of this study suggests this is not a strong argument here. Similarly, it could be argued that smaller groups might decline faster than larger ones because animals of lower fitness are restricted to marginal habitat (in terms of food availability, prevalence of competitors/predators or risk of anthropogenic mortality). Interestingly this is not the case, as larger packs in this study did not exclude smaller packs from better quality territory. Despite the impossibility to test for the multidimensional facets of habitat quality in our very large study area, we remain confident that the combination of our logical argumentation, solid long-term data and previous publications of the crucial importance of group size for Lycaon fitness (Table 1 and 2) and on the lack of demographic Allee effects and pack-population size relationships in other populations [29–32], constitute a favourable set in support of our hypothesis.