What Is The Minimum Size Of A Hunter-Gatherer Society's Population Bottleneck?

In order to have sustainable in a hunter-gatherer population (i.e. one that is not moribund), you need a gender balanced population of 150 people, although "less restrictive marriage rules" allow for a somewhat smaller population (as low as 40-60 people) to remain viable. 

A non-spatial agent-based model is used to explore how marriage behaviors and fertility affect the minimum population size required for hunter-gatherer systems to be demographically viable. The model incorporates representations of person- and household-level constraints and behaviors affecting marriage, reproduction, and mortality. Results suggest that, under a variety of circumstances, a stable population size of about 150 persons is demographically viable in the sense that it is largely immune from extinction through normal stochastic perturbations in mortality, fertility, and sex ratio. Less restrictive marriage rules enhance the viability of small populations by making it possible to capitalize on a greater proportion of the finite female reproductive span and compensate for random fluctuations in the balance of males and females.

Andrew White, "A Model-Based Analysis of the Minimum Size of Demographically-Viable Hunter-Gatherer Populations" 20(4) Journal of Artificial Societies and Social Simulation 9 (published online September 20, 2017 in advance of October 31, 2017 print publication) (open access). DOI: 10.18564/jasss.3393

The study does not look carefully at inbreeding concerns other than assuming a basic incest taboo.

This is order of magnitude compatible for known extreme founder events such as the founding populations of Madagascar, the Americas, Australia, and New Zealand, and the paper notes that colonizing populations such as these could actually be considerably smaller and still be viable, although at that point, a serious look at inbreeding depression issues would be necessary. This is particularly an issue since the available data suggest that colonizing populations often involve a small number of extended families.

Ethnographically, widespread (but not universal) cousin marriage appears to be sustainable, but starts to become problematic over multiple generations as cousins become increasingly more closely related than two cousins from otherwise non-inbred populations over time. If more closely related couples are allowed, e.g. sibling marriage (e.g. in Egyptian royal dynasties) or aunt-nephew marriage (seen in a number of contexts), the available ethnographic evidence suggests that this is not sustainable as congenital defects rise to problematically high levels.

It isn't entirely clear what impact the founding population means of food production has on the total. Would the minimum size of a population of herders or farmers or fishermen be higher or lower respectively? What about a technologically advanced civilization?

More material from the body of the paper:

In this paper, a "viable" population is defined as one that survives over a span of 400 years. . . . Many ethnographically-documented hunter-gatherer populations spend at least part of the year in dispersed, autonomous foraging groups generally containing less than 35 persons (Binford 2001; Kelly 1995). The size and mobility behaviors of these foraging groups are strongly conditioned by subsistence ecology, which often makes it impossible to support larger aggregations of persons for extended periods of time (Binford 1980, 1983, 2001; Kelly 1995). While these small foraging groups constitute functional economic units for subsistence purposes, they are not presumed to be demographically self-sustaining over the course of many generations. Thus groups large enough to be demographically viable are too large to be economically viable, while groups small enough to be economically viable on a day-to-day basis are not demographically viable over the long term. Ethnographic hunter-gatherer systems "solve" this dilemma by using cultural mechanisms (e.g., kinship, exchange, and personal/group mobility) to build and maintain a social system that binds together a dispersed population, facilitating the transfer of information and persons between groups (see White 2012). . . . 

Birdsell (1953, 1958, 1968) approached the problem of determining equilibrium size by considering ethnographic data from Australia. He noted that the size of "dialectical tribes" of Australian hunter-gatherers had a central tendency of around 500 persons, and reasoned that endogamous social systems of this size were probably also typical of Paleolithic hunter-gatherers. It is worth pointing out, as Birdsell (1953, p. 197) himself did, that the number 500 was a statistical abstraction produced from disparate sources of ethnographic data: the documented size range of Australian "tribes," while varying around a central tendency of about 500 persons, commonly included groups of less than 200 (see Birdsell 1953, Figure 8, 1958, p. 186; Kelly 1995, pp. 209-210). . . .

Other settings being equal, polygynous systems in the model generally have smaller MVP sizes than monogamous ones. Polygynous systems are associated with higher mean total fertilities (the number of children born to a female over the course of her reproductive years), lower mean female ages at marriage, and lower mean inter-birth intervals (see Table 6 and Figure 3). The negative relationship between total fertility and female age at marriage is clear when the two variables are plotted against one another (Figure 10). The polygynous model systems provide more opportunities for females to marry earlier in life and potentially bear more offspring during the course of their reproductive spans, enhancing the viability of small populations by increasing fertility and compensating for imbalances in sex ratio. Imposition of marriage divisions has less effect on MVP size in polygynous systems than monogamous ones. . . .

Results from the model suggest that populations limited to as few as 40-60 people can be demographically viable over long spans of time when cultural marriage rules are no more restrictive than the imposition of a basic incest taboo. Even under the most restrictive marriage rules and most severe morality conditions imposed during model experiments, populations of at least 150 persons were demographically viable over 400 years of model time. These estimates of MVP size were calculated for populations with no logistical constraints (e.g., no impediments to information flow and no spatial component of interaction) to identifying and obtaining marriage partners. 

With regard to MVP size, my results are generally consistent with the conclusions of Wobst (1974). Forty runs of his model under varying conditions returned values of MES (minimal equilibrium size) between 79 and 332 people (Wobst 1974, pp. 162-163, 166). As discussed above, Wobst’s higher, often-quoted estimate of MES range of 175-475 persons was tied to specific assumptions about both population density and the arrangement of the population in space. Neither density nor spatial distribution of population are represented in my model. It is possible that those differences alone account for the majority of differences in the results from the two models. It is also possible that differences in the representation of marriage, mortality, fertility, and family structure are important. One way to investigate this would be to implement Wobst’s model as an ABM and make a direct comparison. 

Keeping in mind that MVP and MES are not strictly synonymous, the broad agreement between my results and those of Wobst is noteworthy. Both sets of results are consistent with the idea that, in the absence of strong cultural restrictions on marriage, populations limited to perhaps 150 people are of sufficient size to nearly ensure survival over long spans of time and populations limited to as few as 75 persons have a good chance of long-term survival under the same conditions.

Although my conclusion is at odds with the generality offered by Moore and Moseley (2001, p. 526) that "bands of such small size [175 persons, 50 persons, or 25 persons] usually do not constitute viable mating systems that would guarantee the reproductive future of the band," it is actually in broad agreement with the data that they present. Figure 11 compares the percentage of populations of a given initial size range that survive a span of 400 years in data provided by Moore (2001, Table 6) and two sets of my own data. Moore’s (2001) results are similar to mine in terms of the relationship between initial population size and survivorship. Although Moore (2001) does not provide data for initial populations larger than 60 persons, the trends in his data clearly suggest that populations of around 100 persons would have a very high survival rate over a 400-year span in his model, even under the low fertility regime he employed to produce the results in his Table 6 (i.e., a mean of 2.56 births during a full female reproductive span [see Moore 2001, Table 1]). . . .

While this analysis wasn’t aimed directly at issues of the viable size of colonizing populations, it is worth noting that the results do not necessarily conflict with the idea that successful colonizing populations of hunter-gatherers could initially be much smaller than MVP size. The experiments discussed here were performed under conditions where population sizes were stabilized through a feedback mechanism to determine at what population threshold the inherent stochastic variability in human mortality/fertility was not a threat to long-term survival. In the absence of feedbacks to constrain population size, conditions where fertility exceeds mortality could allow very small populations to grow to a point where normal stochastic perturbations no longer pose a threat of extinction. Exploration of that subject will require further experimentation.