As Darwin quickly recognised, however, Malthus’s checks and Quetelet’s statistics of normal tendencies unfortunately left out the critical explicandum of the proximate mechanisms of variation.2 There is, put very simply, much more going on in the lives of species members, or individuals and groups in society, than competition for survival and the average outcomes of such a process. Not everything that heredity and environment-organism interaction generates is telling for the divergence of demes and species, and even if significant for divergence the effects may only become important later in history. Darwin therefore turned his attention concertedly to the problem of how to formulate a cohesive theory of the creative process of variation.

The logic of the division of labour, which already existed as a model embracing population heterogeneity and openness, and had been remarked by natural historians (Kreager 2015: 76–77), became the focus of his attention. His familiarity with this logic as applied to biological processes emerged by the 1840s in his detailed notes on Milne-Edwards’ Introduction á la zoologie générale (1851 [1834]), and other writings to which he had access (Limoges 1968, 1970; Schweber 1980: 249–57). Milne-Edwards worked in an established natural historical approach known as “animal economy”, and employed the phrase “division of labour” to explain how organs in the body become progressively specialised. His development of this analogy closely followed the line of reasoning in Smith’s Wealth of Nations (1976 [1776]). Just as Smith describes how society and economy evolve from hunter-gatherer groups in which all individuals carry out the same productive, military and other functions, Milne-Edwards describes how, in simple organisms like polyps, bodily functions are not differentiated; just as agricultural and commercial societies advance beyond the simplest level of social organisation by developing specialised personnel for agriculture, defence, manufactures, transport and so forth, so species become more complex by developing specialised organs for respiration, digestion and reproduction (cf. Milne-Edwards 1827 and Limoges 1968 to Smith 1976 vol. I: 689 et seq. and Kreager 2017).

Darwin, like Smith, readily came to view the idea of the division of labour as of major importance at the population level. Both authors considered the renewal of the many and heterogeneous groups, and the emergence of new populations with specialisations productive in changing environments, as key motors of historical and evolutionary change. Darwin’s elaborate development of the analogy between the creative force of variation and the division of labour in human society is extensive and detailed, and a few examples will have to suffice here to give the reader an idea.3

Transferred to the population level, Milne-Edwards’ account of the development of specialised organic characteristics becomes an account not only of physiological development in individual members of a group, but of how such greater or lesser divergence characterising species sub-populations translates into their greater or lesser adaptive capacities for expanding into environments available to them, and the heterogeneity of groups that comes to characterise such sites. As these capacities become manifest, accompanying changes in population composition, size and growth follow suit. Darwin, citing Milne-Edwards (1996: 92–98), illustrates his argument by many examples drawn from competition amongst flora and fauna, leading to his famous diagram of species divergence.4 Such specialisation, as in Adam Smith’s account of the division of labour, is closely bound up with the interaction or interdependence of sub-populations in a given productive environment. For Smith, the specialisation of tasks in the division of labour both develops individual capacities and characteristics, and requires many productive groups to work in close interdependence; expanded capacities for individual agency and production enhance general living conditions for the several sub-populations involved in a given productive niche, affording them competitive collective advantages in their wider environment; this entails not only enhanced economic but social agency. Specialisation and interdependence of constituent populations making up a society are thus a principal motor of their own and general social change, and the integral role of population composition, size and growth in the evolution of economy and society is explained by Smith in these terms. In essence: “the number of workmen in every branch of business generally increases with the division of labour in that branch or, rather, it is the increase of their number which enables them to class and subdivide themselves in this manner” (1976 vol. II, Introduction, p. 277). Population, in other words, tends to increase in sub-populations working in tandem in a given economic sector or sectors, and this becomes a motor of population growth in society more generally. By analogy, Darwin “chose the principle of optimalisation of the amount of life per unit area as the overall explanatory principle” (Schweber 1980: 288).

Thus, both Smith and Darwin considered (contra Malthus) that the growth of a population was not only key evidence of its competitive success, but that such growth was itself a principal mechanism of improvement. Competition at the individual level may ultimately be decisive, but is conditioned by the structure of interdependence between populations, which conditions the circumstances in which an individual acts. Darwin therefore, like Smith, considered the positive check as functioning in proximate terms, that is, as conditional on environment-organism interactions and on the nature of relationships within and between local populations — rather than, as in Malthus, an ultimate or universal mechanism to which all populations and all members must sooner or later answer in a particular way. Rather than fundamentally and ultimately closed, population dynamics are by nature open, as groups exist in manifold relationships and interdependencies with other groups. These interdependencies, as in Smith’s analysis, give Darwin’s account a much more extensive set of organism-environment feedbacks than Malthus’s singular stress on the positive and preventive checks in an ultimately closed environment. As Schweber remarks, Darwin’s whole approach reflects a critical difference between Smith’s account and Malthus’s: individual species members have much more agency in dealing with proximate causes than is possible under Malthus’s emphasis on the ultimate necessity of his two checks on population (1977: 283; Kreager 2017: 531).

This emphasis on the agency that diverse group members exercise in producing variations followed directly from the much more extensive body of direct observation of adaptive processes that characterised Darwin’s natural history, in contrast to Malthus’s political economy. For Darwin, explaining processes of population change rests first on empirical identification of proximate causes, as these arbitrate the possible operation of ultimate positive checks. Put another way, the inter-relationships between groups in a given environment requires a bottom-up perspective: explaining population dynamics begins in observation at lower levels of aggregation, since changing group compositions and interrelationships carry implications for higher levels of aggregation, both in the short and long term.

Two Concepts of Population

Darwin’s quantitative skills remained those of a botanical arithmetician, employing methods similar to those of seventeenth- and eighteenth-century population arithmetic; his notebooks make clear that he was not adept at higher mathematics.5 Yet, as we have seen, his population thinking was prescient in understanding that the different conceptual approaches to population underlying Smith’s and Malthus’s works are both necessary to explaining how populations evolve. From the former Darwin took the idea that populations are by nature open and heterogeneous, variation arising in them from the interdependence of groups and their members, which he saw as analogous to the way specialisation functions in the division of labour. Such open population thinking was a breakthrough in showing how the vast body of his natural historical evidence could be generalised at the population level.6 It did not, however, satisfy the scientific criteria expected of theory in the milieu in which he wrote. As remarked earlier, the middle decades of the nineteenth century were an era in which the rise of population statistics led to its proposed formalisation as a social physics (Porter 1986).

Lacking close familiarity with the new methods, Darwin nonetheless responded to this second idea of population by drawing on contemporary views of Malthus’s Essay, in which the impact of the positive check was understood as imposing absolute limits on population suitable to developing methods of social physics. The mortality of the positive check could be used to define limits to growth for any population given the particular environment in which it is found. Darwin hoped such an approach would enable statistics to demonstrate changes in the frequencies of specific evolutionary traits.

As we shall see, this proposition proved very difficult for Darwin’s followers to develop in the late nineteenth and early twentieth century. Before turning to their several formulations — some brilliant and of enduring importance, whilst others have come to be recognised as not only dubious but dangerous — we can at least try to state succinctly the fundamental problem posed by Darwin’s dual approach to population: his open population thinking, grounded in natural history and the role of environmental constraints in shaping evolution, is analytically distinct from, and may even seem opposed to the closed populations on which formal modelling depends. The extent to which Darwin was himself aware of this difference remains uncertain. It was brought out at least as early as the 1920s by the doyen of twentieth-century formal demography, Alfred Lotka, whose mathematics of population ecology (1925) was one of the earliest evolutionary formalisms to be established, and then extended to human fertility and mortality (1934; 1939). What Darwin appears to have been the first to recognise, at least implicitly, is that the two concepts, even if radically different, are nonetheless complementary. How, then, did he bring open and closed population thinking together? What problems then remained, that generated such variously seminal and flawed approaches amongst his followers?

The closed character of formal population analysis and data systems needs, of course, no introduction to a twenty-first-century audience of demographers and population geneticists. Lotka used his training in physical chemistry to argue the generality of this scientific methodology.7 Whether in thermodynamics, census-taking, life table construction or the theory of population renewal which was Lotka’s own contribution — the individuals making up a population are treated as identical subject to the system of classification employed. Just as the behaviour of atoms and molecules conforms to the rules of the periodic table, so the population movements of human beings conform to the fixed set of statuses given, for example, in a census schedule. Censuses, like the periodic table, have the considerable advantage of being effectively comprehensive, thus enabling exhaustive and purely formal analysis of all changes of state between recognised categories. Once born, an individual can only move between classificatory statuses: he or she gets older, marries, establishes a household, has children, changes occupations […] and eventually dies. Closed units, whether of the total population under analysis, or of any of its component sub-populations, enable aggregate states of population change to be calculated precisely: age and sex structures, gene frequencies, life expectation, trends in fertility, mortality, labour force participation and so forth. This approach, which Mayr and other contributors to Evolutionary Synthesis referred to as “typological” or “essentialist” (1982: 47), is immensely powerful once species and demic populations have been identified.

Darwin’s Origin was, however, concerned not only with the renewal of existing populations but the renewal of population heterogeneity, since evolution proceeds by continuing adaptation and consequent variation in and between populations. To begin by treating populations in nature as closed is artificial. As natural historians had long recognised, species rarely present themselves as discrete groups in nature. Sustained observation is a first necessary step, to identify the role of environmental factors in shaping variation at local levels. Such open inquiry decides which characteristics should be tracked, and in which environments. Identifying the relationships between individuals that appear to constitute membership of a species involves repeated hypotheses and continuing observation to test them, until the unity of a proposed species can be considered established. Of course, the rise of genetics since Darwin’s time has provided further laboratory methods of observation that greatly assist identification. Nonetheless, the primary questions necessary to track variation and possible divergence remain: “What is a population (i.e. for the purpose of differentiating organisms in the process of variation)?”; “What set of sub-population units comprise a species?”; and “What relationships account for their differences?”

Natural historians up until the late nineteenth century employed enumeration as part of open population thinking, i.e. accepting that an exhaustive or complete counting was only exceptionally realisable. Similar to Graunt and other early modern population arithmeticians, totals could be compared without formal mathematics and without comprehensive census inventories. Where characteristics appeared to clearly differentiate groups, they were accepted as indicating the presence of distinct phenomena whether the entity was a plant or animal in the wild, a human being recorded as dying of a specific disease in the “mortality bills” that were the only record of causes of death before the modern census era. Darwin, in effect, moved on from his predecessors by the simple step of accepting that a carefully observed body of numerical evidence at the population level — however provisional — was effectively complete. This appeared to be a substantial improvement on previous practice that was not population-based, in which whole species and higher types might be proposed from merely a few specimens.

Darwin’s reasoning, as we have seen, addressed variation and the divergence of species in terms of optimalisation: the amount of life that could be supported in any setting would become greater, more diverse and complex as competition intensified; larger genera, species and demes would tend to produce more hereditary variation, in which those offspring with more diverse characteristics would have additional advantages to adapt and increase their numbers. Such a local “division of labour” in this way provided a plausible account of how particular adaptive advantages could accumulate at higher levels of aggregation, further encouraging Darwin to think at the level of populations. As Schweber remarks (1980: 288), Darwin’s premise that the quantity of life is gradually optimised in local environments effectively bypassed the difficulties of integrating different levels of description: local observation of open populations, in which characteristics are gradually differentiated as inquiry proceeds, seems to flow seamlessly into later analysis in which units of population might be defined formally as distinctive demic and species populations, i.e. treated as closed for purposes of statistical analysis. Indeed, as an empirical procedure for generating and testing hypotheses, this logic appears straightforward. Hence Darwin could hope that emerging emerging statistical techniques could be applied to variation and divergence, even if his own understanding did not extend to how formal models and data systems are actually constructed.

What this way of thinking assumes, however, is that the role of open population thinking — sustained local observation of proximate relationships in order to differentiate units of population — has been carried out prior to statistical modelling. With the benefit of hindsight, we can see that, for a scientist of long natural historical experience like Darwin, this “bottom up” approach was so elemental it could not ever be questioned. Formal analysis, however, can take place whether or not sustained observation has given an empirical ground to hypotheses, and whether or not local processes are translated accurately into specifications of closed population units entailed in large datasets. We turn now to subsequent developments in evolutionary theory, which proved to be fraught with controversy. Apparently powerful arguments claiming to establish ultimate causes were built on the basis of classifications and units of measurement not grounded in observation of proximate causes. Arguably, one of the critical lessons from the emergence of evolution as a population theory is that confusion and ambiguity proliferate where the different roles of the two concepts of population, and their engagement at different stages of analysis, are not recognised.

The Early Struggle to Incorporate Population Genetics and Demography into Evolution

In this short account, we will consider two contrasting approaches of the late nineteenth and early twentieth centuries which illustrate this issue: Galton’s attempt to use evolution to build a science of eugenics; and the several contemporaneous movements in early-twentieth-century population thinking that led to the consolidation of demography as a discipline, and gave its methods a fundamental role in population genetics as a core component of the Evolutionary Synthesis. This period stands as something of a paradox for demography: as the discipline gradually took its contemporary shape, its formal methodologies made significant contributions to population ecology, to the critique of eugenics and to the formulation of the Synthesis — yet its professional stance became increasingly separate from evolutionary biology.

Galtonian Eugenics

Darwin’s need to treat heredity as a “black box” in his theory led to an immense amount of speculation and exploratory research (Provine 1971). As Porter (1986:280) remarks, Darwin’s own later ruminations on this problem were “virtually a complete failure amongst biologists”, although they attracted the attention of the biometric school developed from the 1870s by Galton and Pearson. Both men were remarkable polymaths whose life work focussed on developing advanced statistical techniques to track the evolution of hereditary and racial differences, which they then put forward to legitimise highly controversial public policies. Darwin had speculated that hereditary took the form of particles or “gemmules” that circulate in all parts of the body, transmitting specific traits particularly in the course of embryo formation (1868). He was led to this in part by questions concerning the role of evolution in shaping human society. Galton, for whom the latter concern was paramount, redeveloped the gemmule hypothesis not as a matter of embryology, but as a demographic phenomenon. For this purpose, he prioritised the Malthusian component of Darwin’s theory — superfecundity — as the primary force in evolution. Reproduction, Galton argued, arbitrates the role of heredity in human and social development, since varying levels of fertility within and between groups in a population determine which, and how widely, certain hereditary characteristics rather than others come to predominate; fertility differentials constitute “reproductive selection”, the importance of which is vastly greater as a factor in natural selection than environment-organism interaction. He coined the term “eugenics” to refer to an ostensibly scientific and statistical practice that would ensure that only the best babies could be born. Not only should those judged the most fit members of a society be encouraged to reproduce, steps should be taken actively to restrict the fertility of less desirable groups. As Galton repeatedly emphasized, the majority of offspring were being produced by only certain (lower-class) groups in society. Eugenics rapidly became highly topical in an era in which European reproductive levels had for the first time begun to decline radically.

To understand the impact of reproductive differentials on the quality of human populations, Galton needed a statistical method that could discriminate between more and less powerful influences on genetic transmission. This led to his famous conceptualisation of statistical correlation and regression, and their formal mathematical development by his associate, Karl Pearson. Both concepts, of course, have come subsequently to play a widespread role in population research. Their use in eugenic argument, however, relied on institutional and popular definitions of social class differences, ascribing ultimate causes to them without examination of their empirical basis.

While insisting on their allegiance to Darwin’s and Malthus’s theories, Galton and Pearson argued that there were crucial flaws in their reasoning. Darwin, as noted above, did not give sufficient attention to reproductive selection. Malthus did not go far enough in his criticism of a supposed lack of sexual restraint among the poorer classes; while recognising that their superfecundity leads necessarily to the action of the positive check, he did not ask whether that check would actually be sufficient, i.e. whether there would still be a great majority of lower-class children relative to those of higher classes. The normal function of mortality Galton and Pearson termed “the selective death rate”, i.e. the ultimate mechanism of natural selection in weeding out the less fit. Average family size had, nonetheless, remained higher in lower-class “degenerate and pathological stocks” (Pearson 1912: 27). Hence the dire prospect, if the positive check did not remove the greater majority of lower-class children, of their superfecundity of surviving children to greatly outnumber those of “the cultured and highly sensitive upper and middle classes”; the outcome would be “race suicide” which, “in the inmost recesses of history […] explains the fall of great world-civilisations” (Pearson 1912: 10, 39).

The central issue, for eugenic argument, was thus how to demonstrate this calculus. Correlation, Galton remarked, provided the method demonstrating “the closeness of the relation between any two systems whose variations are due partly to causes common to both, and partly to causes special to each” (1907: 174). Pearson’s mathematical development, appearing in his note on reproductive selection to the Royal Statistical Society (1896), begins with statistical demonstration of the correlation between fertility and organic characteristics across generations. For this purpose, he employed a classic measure in social physics — height — in this case of mothers, daughters and wives in “1,842 families of Danish race”. Pearson showed a regular percentage change in height across generations; he would later describe such variation as an instance of “the law of ancestral heredity”, i.e. the change of any organ or physical or mental characteristic that typifies its spread in a large population over time (e.g. Pearson 1912). The question, then, was what part of the Danish population was contributing most to such changes. Analysing net fertility (i.e. allowing for infant and child mortality, and for non-marriage) in artisan and professional classes, Pearson concluded that while the former represented only 27 per cent of the population, its greater fertility produced over half of the younger generation. In short, on this account reproductive selection is the much greater factor than natural selection (i.e. as defined only in terms of the selective death rate) in population replacement and change.

Pearson’s “The Problem of Practical Eugenics” (1912), is one of many articles in which he developed this mathematics of correlation as a basis of demographic policy, particularly in the context of the fertility declines now commonly known as demographic transition. Anticipating later demographic interests, he was particularly concerned with the economic value of children, notably the impact of factory legislation which had removed the value of child labour as a component of working-class family incomes. His analysis assumes the “law of ancestral heredity”, and is directed particularly to showing that well-intentioned government policies supposed to improve the environmental conditions of factory populations are much less important to national development than their impacts on heredity. He traces fertility declines in the Registrar General’s data for a number of manufacturing towns and rural areas, particularly in the period 1870–1905, in relation to the several Acts that prohibited child labour. He notes not only the steep decline in birth rates, coupled with the still relatively larger family sizes of the working classes, but levels of tuberculosis, insanity, deafness and other conditions he considers pathological, calling attention to their incidence by birth order. As these conditions are markedly more common in the first, second or third child a woman bears, Pearson concludes that not only are working classes producing a higher percentage of the population, their reproduction ensures a higher percentage of “cacogenic” stock overall. Meanwhile, the upper and middle classes have come to have an “artificial birth rate” in consequence of their inclination to lower fertility in the context of changing economic conditions. Pearson then traces the implications of these several developments in relation to demographic topics that have proven of long-term interest, notably contraception and ageing. More immediately, Pearson advocated major changes to taxation, (raising rates on income, estate and inheritance for the childless); while factory legislation should not simply be repealed, its continuing impact on the “racial efficiency” of the population could only be countered by amplifying the numbers of “well-born children”.

Both Galton and Pearson played major and respected roles in scientific organisations of the time, and both were offered knighthoods.8 Their eugenics is a reminder that distinguished authors claiming to be followers of Malthus and Darwin may, in fact, be promoting theories that are hardly consistent with such claims (cf. Kreager 2014). On the statistical side of population thinking, there can be no doubt that their work constituted a serious and imaginative attempt to address fundamental problems of conceptualising and measuring structural changes in frequencies across generations, of the logic of population stabilisation given incomplete genetic data, and of the incremental or “small steps” by which genetic variation influences population change. Their technical insights, however, were vitiated by two radical departures from the evolutionary structure of population thinking that Darwin had carefully developed: their predilection for arguments based exclusively on ultimate causes; and their sole reliance on closed or typological population thinking.

In eugenics, heredity displaced Darwin’s emphasis on environment-organism interaction in the study of variation. Pearson considered heredity “more potent”, adding acerbically that population policy makers should know that a stud productive of Derby winners does not rely chiefly on improved stables (Pearson 1912: 36, 38). Eugenicists’ pursuit of heredity as the seat of ultimate causes was, moreover, built upon incomplete and ambiguous definitions of the human sub-populations treated in published statistics, and the more or less complete exclusion of sub-population interactions that, as proximate causes, were crucial to Darwin’s view of evolution. The populations Pearson employed were drawn from standard institutional sources in which classification rested on criteria not informed by observation of how groups are formed, sustained and related over time. Given Pearson’s “cacogenic” arguments, it is also evident that the classifications selected were in consequence all the more susceptible to powerful class and other biases. Pearson in effect extended closed population thinking to human heredity in ways that run counter to Darwin and Mendel: all genetic and physiological characteristics other than those mentioned above were taken to be identical for all individuals in each given population type; all genealogical or other links that show members’ involvement with other populations were not considered; and change over time was always directed, i.e. not isotropic.9 In the end, the eugenic exercise excluded a vast array of sources of variation, and was strongly tautological: those groups with higher birth and death rates were categorised from the start in closed classifications as “cacogenic” or “degenerate”.

Vital Statistics, Population Ecology and Genetics: Some First Steps toward an Evolutionary Demography

As we have seen, Darwin’s conviction that statistical evidence is essential to understanding evolution as a process of population interaction embraced both numerical observation at the local level and the potential for modelling aggregate frequencies at higher levels of analysis. In evolutionary biology, the famous breakthrough that swept away eugenic and many other arguments came at the local level: the rediscovery in 1900 of Mendel’s experiments on genetic variation in peas. Mendel’s work differed sharply from the eugenicists in the careful observational method used to establish sub-populations and the nature and structure of their relationships.10

With the benefit of hindsight, the early biometricians’ eugenic project may be said to have occupied a kind of median position between the continuing research of evolutionary biologists and the much wider period concerns about the potential impact of declining birth and mortality rates, race, and migration on national population composition and replacement. Controversy over the role of reproductive selection embraced vital statistics, public health, biological anthropology, sociology and a great many essays (variously of socialist, conservative, feminist and other persuasions) written for general audiences (Soloway 1982). The issue was one of general public concern. Eugenics, with its technical claims and dramatic highlighting of demographic differentials as simultaneously social and genetic determinants, attracted widespread attention, and was without doubt a major stimulus both to controversy and to recognition of the need for more critical, observation-based approaches. Developments in social and vital statistics were, of course, for the most part of a fundamentally different kind from Mendel’s work, since they relied on closed-population datasets established during the nineteenth century with the founding of national statistical offices and professional statistical societies, and the dream of a social physics.

These data provided the foundation for several environmental reforms, including those Pearson attacked, and for declines in mortality related to these reforms at all but the youngest age over the later nineteenth century. They also, as we have seen, provided primary evidence of fertility declines. Vital and social statisticians thus felt a strong need to respond to the eugenicists’ arguments, but they also faced uncertainty regarding the specific mechanisms underlying differentials in fertility and mortality between social groups. Their response was to tighten and extend the actuarial approach on which demography rests. This response was characteristic of three major innovations in which demographic methods became fundamental to addressing problems in population biology in the early decades of the twentieth century. The first emerged in part as a response to eugenics, while the second two were driven by problems in evolutionary biology.

The first development, reflecting concerns over differentials in declining fertility, led the General Registry Office (GRO) in England and Wales to put the need for a comprehensive social classification scheme on its agenda. As Szreter’s (1986) study of the GRO’s programme has shown, its class schema was designed to refute eugenic arguments, although the alternative mechanism put forward to explain fertility declines (the rise of contraception) remained inadequately documented. In addition, a detailed family census was conducted, in 1911, which included more variables, such as parity, than existing censuses. As Szreter (1986: 538–40) remarks, the GRO social class scheme, which remained largely unchanged until the 1970s, continued to reflect several problematic eugenic assumptions which reduced the forms of variation that could be tracked. In short, the immense improvement in data and measurement techniques remained dependent on statistics that track sub-populations defined by occupational, provincial and other conventionally pre-determined, closed administrative units. Relations within and between such groups that involve, for example, gender, labour sectors that combine several occupations, and regional cultures and economies, may not be captured accurately in standard administrative units. Subsequent research reanalysing closed data to reflect non-standard units has revealed major fertility differentials and patterns of variation that conventional classifications missed (Szreter 1996; Garrett et al. 2001; Pooley 2013). As evolutionary biologists would expect, population heterogeneity remains strongly characteristic of modern fertility and mortality trends, including the great diversity in patterns of decline. An approach based on a priori closed classifications and units has, by itself, not succeeded in establishing the several theories put forward to explain demographic transition, and this problem continues to this day (Cleland and Wilson 1987; Pollak and Watkins 1993; Demeny and McNicoll 2006).

A second major demographic development of the early twentieth century, Lotka’s stable population theory, was conceived as a new foundation for the mathematics of evolution. Lotka carried social physics a step further, reasoning that stabilisation in human and molecular populations is analogous, so that the second law of thermodynamics can be used as a model for formal demography. In the Elements of Physical Biology (1925), Lotka successfully applied his approach to relations between species, leading to what are now called the Lotka-Volterra equations which provide the basis for studying predator-prey relations. While providing a central and fruitful framework for population ecology, such models address species-level phenomena without attention to intra-species variation, leading Lewontin to remark that they “are both overly specific and arbitrary in their mathematical form so that they may not catch the important reality of interactions” (2004: 15).

More generally, the approach shared some important limitations with Galton and Pearson’s work, which have kept it from becoming the general mathematics of evolution that Lotka had hoped to provide. First, because Lotka sets aside the role of intra-species divergence in the renewal of population heterogeneity, his work remained marginal to central debates in evolutionary theory after Mendel, i.e. the problem of how to integrate genetic variation into population thinking, in which heterogeneity arising from environment-organism interactions remained fundamental. Second, Lotka largely ignored actual processes and variation in organism-environment interaction. Biologists have more recently remarked that the assumption in which the environment acts on the organism as an autonomous force is simply unrealistic: such a view implies that fully formed niches exist waiting for organisms to come to live in them. This assumption is conducive to closed population thinking, since nothing beyond the premise that self-contained environmental units exist in nature is required. Such a view is, however, deeply troubled by evidence that organisms play an active role in constructing niches, so that organisms and environments co-evolve (Lewontin 2001; 2004: 13–16). The same lack of realism arises in human populations if considered in conventional Malthusian terms in which there is a fixed carrying capacity for any environment (Odling-Smee 2015). Reconciling these more recent criticisms with the continuing utitlity of Lotka’s work for population ecology appears to be an ongoing subject of debate.

In the first volume of his principal demographic work, the Théorie analytique des associations biologiques (1934), Lotka reiterated the biological foundation of his approach as stated in the Elements, together with his careful emphasis, noted earlier, on the purely formal nature of closed analysis. The second volume of the Théorie (1939) then developed an extensive application to human populations without reference to other species. Lotka showed how his theory enabled demographers to integrate fertility into the style of analysis used in stationary, or life table, methods, yielding intrinsic growth rates in which purely formal population units, regardless of variation in their initial age/sex structures and vital rates, tend inevitably to stabilise over different time periods. Lotka’s later work remained subject to the limitations consequent on exclusively closed population units, just noted.11 Although post-war social demographers (e.g. Ryder 1964) expressed considerable interest in the possibility of developing Lotka’s method as a basis for a general sociological theory of population, its limited focus on population renewal, rather than the renewal of population heterogeneity, and its insensitivity to environment- organism interaction, have meant that many sources of variation cannot be integrated into his formal analysis. These commonly remain “independent” economic, cultural and other variables, often analysed via correlation and regression techniques. Thus, although Lotka greatly clarified and subtilized the formal nature of demographic analysis, and did not reduce variation solely to Queteletian normality, the problem of explaining diverse mechanisms of variation and integrating them into models of population stabilisation has remained.

The third major development combining demography and population biology arose in central evolutionary debates over the implications of Mendel’s genetic research for Darwinian population thinking. Demographic models were integrated into genetics in Fisher’s Genetical Theory of Natural Selection (1930), in which he postulated a species in which reproduction occurs continuously in stable age distributions so that, as in (but independently of) Lotka’s formulation, life table probabilities and probabilities of birth in a given interval can be combined in a single equilibrium model. Parallel contributions by Wright (1930) and others (see Provine 1971; Lewontin et al. 2003)) moved this approach toward later population genetics by demonstrating the importance of gene or allelic interactions in local populations, encouraging a return to the Darwinian view of species as aggregates of sub-populations (i.e. effective breeding populations, or demes), and of hereditary influence as a consequence of complex interactions or combinations of genetic material. This research put a final end to the eugenic quest for simple demographic laws of fitness; rather, while many demographic parameters may combine to shape fitness (e.g. population density; the relative frequency of genotypes, or the mixing of genotypes, in a population) they do so in many different, shifting combinations with other adaptive factors.12

Hiatus: the “Separatism” of Demography from Evolutionary Population Biology

All four of the above developments marked an increasing focus of research on fertility and its place in the transmission of characteristics — whether social or genetic — across generations. Without doubt, there was a growing intellectual convergence that brought early twentieth-century demography into closer alignment with evolutionary biology. Yet only the latter participated in the Evolutionary Synthesis that emerged in the 1930s and 1940s, the culmination of half a century of research that brought mathematical modelling of demographic, genetic, cellular and ecological processes into alignment with Darwin’s theory (Mayr and Provine 1998). As the 1950s and 1960s proceeded, no comparable synthesis emerged in the demographic study of human populations, and even demographic followers of Lotka eschewed his evolutionary arguments and applications. Instead, demographers’ growing preoccupation, as is well known, was with theories of demographic transition, in which population biology attained only a secondary role in the biomedicine of mortality and fertility control, and related “proximate determinants”. Evolutionary biology as a major conceptual source of theory and method was strikingly absent when demography’s central post-war concerns came to be established, a neglect that largely continued up to the 1980s (Sear 2015a). The irony, as Lewontin (2004:10) observed, is that once Fisher had put demography at the centre of the genetics of natural selection, evolutionary biology and demography went their separate ways.

Historical accounts have attributed the emergence and powerful influence of separatism to demographers’ aversion to eugenics in the aftermath of national socialism, together with the pressing agenda of post-war reconstruction and fears of rapid population growth. These were indeed important factors, and have been discussed elsewhere.13 A more important consideration, however, is that the long struggle to construct population genetics and integrate it into Darwin’s concept of natural selection had a major impact on how ultimate and proximate causation in evolution are understood. This, in turn, changed the role of mathematical modelling in evolutionary theory in ways consistent with Darwin’s work on the divergence of character, but counter to the old Newtonian ideal of theory as a mathematical formalism of ultimate physical relationships. Demographers’ non-involvement in the Synthesis meant that few were cognizant of these developments, and that mainstream approaches to population theory and methodology remained, as Hauser and Duncan noted, aligned to physics (1959: 15).

As we have seen, ideas about scientific theory, from Malthus through to Quetelet and Lotka, gave pride of place to the goal inspired by physical sciences of mathematically formulated, general-law-like systems. Darwin was from the beginning sympathetic to this view, and continued to leave open the possibility that statistics could provide methods for modelling the frequency of intra- and inter-species variation. The complexity of open population dynamics, and the “black box” of heredity, however, meant that no formal statistical laws could be put forward in his account of speciation in the Origin. In the period from the rediscovery of Mendel to the Synthesis, population genetics employing mathematical methods and closed populations became mainstream in evolutionary thinking, even while commonly seen as opposed to natural historical approaches and the more traditional, predominantly open, Darwinian logic of population thinking. Increasingly, however, the methods developed by Fisher, Wright and others were brought into closer alignment with the observational approaches of natural history and physiology via laboratory research. Species selected for experimentation, like Drosophila and small mammals, were chosen because they appeared to open up comparative research on promising hypotheses arising from natural observations (Kohler 1994). Once Mendelian features were established, demes and species populations could then be raised in lab conditions as closed populations for testing purposes, many trials becoming possible because such populations could be reproduced quickly. The role of mathematics in tracking the changing frequencies of genetic characteristics under different mating patterns was to build local models that indicated further hypotheses and tests in which genetic traits and changes could be isolated. The results increasingly moved natural historians and mathematical genetics closer together. On one hand, models such as Fisher’s and Wright’s established key natural historical arguments, notably that Mendel’s results were consistent with Darwinian population thinking. Experiments in natural, as well as laboratory conditions became possible. On the other, mathematical approaches were freed from the nineteenth-century dogma that biological theory should be built primarily along the lines of a physics of ultimate causes. Population genetics could be modelled once mathematics was applied to proximate mechanisms, further removing the dangers that eugenics had exposed in trying to postulate ultimate demographic and genetic laws of evolution. The convergence of approaches also removed, at least for a time, any suggestion of genetic transmission of environmental characteristics, thus helping to focus attention on molecular structure as key to the chemistry of genetic transmission. Watson and Crick’s DNA model followed in 1953, and with the rise of genomics, the mathematics of gene sequences can be used to hypothesize and model combinations of genetic chemistry in local parts of the genome that enable laboratory observation and exploration of proximate causes of gene expression.

Emergent Evolutionary Demography

The approach to general theory in population biology that has emerged from the Synthesis thus remains a methodology that combines insights from closed and open population thinking, not a quest for a universal formalism of evolution. The fundamental open population question, “What is a population?”, still has to be answered whenever the quest is to identify mechanisms of genetic, environmental and phenotypical variation, and this usually requires observation or laboratory construction of local populations (Kreager et al. 2015). The role of formal mathematical approaches, however, has greatly expanded, for example via models that simulate the implications of particular genetic or environmental variations for population composition, structure and change. This is most obviously necessary in the context of genomics: with billions of base pairs, and even more possibly significant combinations of them than persons to which they can belong, the “What is a population?” question becomes “Which population?”, i.e. which set of genetic and other parameters, out of the many possible combinations, can be observed to function as proximate causes leading to expression of characteristics that define a population?14

As Wachter (2015) observes, the route to defining actual populations increasingly proceeds via hypothesized populations. Thus: hypotheses arising from incomplete evidence at higher levels of aggregation in the genome are used to model “local population spaces” in which tests may be carried out, and this activity is likely to precede and accompany successive hypotheses/empirical trials in which key sub-population characteristics are gradually isolated (Lewontin 2004: 17–18). Specifying the population is a critical step in research, and the approach as a whole combines top-down and bottom-up research strategies, as models specifying population characteristics are revised on the basis of each round of evidence.¹⁵ The Synthesis, in short, is not a static paradigm, but has continued to evolve. Evidence, for example, questioning the idea that environmental niches can be modelled simply as closed entities given in nature, has led to reconsideration of Mayr’s ultimate/proximate distinction so that it may better allow for feedback processes (Laland et al. 2010, 2011; Huneman et al. 2017). Such developments are of obvious interest to demography, as they encourage study of how social and cultural relationships are integral to natural selection as part of feedbacks with the genome and the environment.

The recent renewal of demographic interest in evolutionary biology as a source of concepts and models has grown up in this dynamic situation, where the critical role of collaborative research is once again recognised as necessary. On the demographic side, an impetus has also undoubtedly come from the huge problem, noted earlier, of the unexplained heterogeneity of demographic transitions. The “Which population?” question here is broadly analogous to that described for genomics, above. A theory of transition was initially assumed to be universal: modernisation would explain how social, cultural, economic and other proximate causes combine consistently to produce one sequence of reproductive and mortality declines everywhere (allowing, of course, for secondary variations). Instead, an immense heterogeneity of trends within and between societies has been documented, the diversity of which is not consistently explained by the matrix of modernisation variables (see references given in the sub-section on vital statistics, above). In demographers’ exploration of alternative approaches, two remarkable parallels to evolutionary biology may be noted.

One is the much greater interest in open population processes, that is, functional links between individuals and between sub-population memberships that are unobserved in standard demographic classifications and closed population units. These include: the impact of hierarchical relations on inequalities in demographic outcomes; inter-generational relationships and variation of generational roles across the life course as they affect reproduction, family formation and longevity; migration and changing cultural identities as adaptive strategies; and network transmission of ideas and practices between sub-populations as they shape varying reproductive choice and health outcomes within and between groups. The second and related development is increasing attention to sub-population variation at levels below, or that cut across, conventional national and provincial administrative population units. Current problems of demographic explanation, in other words, have drawn the field toward the kinds of issues that long ago, in Classical population thinking, gave relationships between sub-populations and their members a determinant role, and which likewise shaped Darwin’s account of how demes and species are formed and change.

By way of conclusion, two brief examples drawn from recent evolutionary demography can be used to illustrate how the methodology of local population spaces described above is now being used to address central problems of demographic explanation. As Kaplan and Gurven (2008) reiterate, combined top-down and bottom-up population thinking is necessary. Bottom-up approaches may, for example, relate physiological variables (e.g. mothers’ energy reserves as indicated by body mass index (BMI); dietary constraints; local environmental disease risks to infants) to demographic measures (mothers’ age at first birth, parity progression, infant mortality) in order to identify proximate causes as they vary health conditions and changing vital rates in different sub-populations. The top-down element is provided by life history theory: reproduction entails trade-offs in which available parental energy and resources for childrearing must be balanced against the increasing demands that a succession of children inevitably makes; natural selection occurs as interactions between physiological constraints and the incidence of births and infant deaths alter this balance in ways that regulate continuing parental investments and the survival of certain children. Note that this approach, rather than treating fertility and mortality separately, focusses on feedback mechanisms between them in specific environments. Modernisation variables act not as external forces that sweep away traditional arrangements, but through this proximate process, and they may be more or less important depending on which aspects of environment-organism-genetic interaction they influence.

Longitudinal research on Tsimane communities in Bolivia provides an example of a “bottom-up” study, addressed to lowland, subsistence farming and foraging communities whose way of life and demography remain substantially traditional (Kaplan et al. 2015). A combined ethnographic methodology incorporates continuing comprehensive census data collection, reproductive history interviewing and annual medical examination of a wide range of physiological characteristics. This combination provides local population data from several observational techniques which can be compared and analysed as an effectively closed population. Total fertility is at very high pre-transition levels (8.8 births per woman), with modestly lower rates in communities somewhat more exposed to Bolivian towns. Although the latter communities now have greater access to public health facilities, infant mortality levels have risen, even while women’s BMI has improved. The authors show how this rather counter-intuitive pattern can be accounted for by linking reproductive histories to women’s improved energy circumstances: births have come at earlier ages in marriage, and closer together, both of which are facilitated by higher energy resources, but which normally carry added health risks. Variables that might be expected indicate modern impacts, like education and greater facility in speaking Spanish, appear to have at most minor influence. In the authors’ view, this finding shows the operation of natural selection as maximising the production of surviving offspring (i.e. not maximised fertility) in balance with the realities of parental investment.

The study is prospective in the sense that the Tsimane communities are at a pre- or initial stage of demographic transition: the authors, expecting fertility declines to ensue, have established a baseline of current proximate mechanisms and their relationships on which subsequent variations in familial, physiological and community-level factors and their interactions can be assessed. Such baselines have been notably absent in most transition research. Their finding that mothers’ age declines at first birth, associated with higher overall levels of fertility, is already indicative of a central mechanism of “pre-decline rise” in the region, and is one of the main lacunae to have been found in transition theory (Dyson and Murphy 1985). Their approach, in considering feedbacks between fertility and mortality via physiological factors, also runs counter to conventional transition and Malthusian arguments that higher fertility is a homeostatic response to higher mortality. While community variables like education and bilingualism are not yet important influences, as components of social learning they are likely to become a potentially major environmental force in social and genetic change (Sears 2015b). The authors underline the importance of ethnography at sub-population levels in evolutionary demography, noting that subsequent research will need to identify the social networks in which health information associated with these variables may spread more widely.

The second example takes up the question of how such social relationships can be integrated into formal modelling of evolutionary change. As noted earlier, one of the problems demography has faced is how to bring variation in social and economic relationships, or “independent” variables, into core demographic analysis. The issue is thus one of preparing new top-down approaches. Lee (2003, 2008), for example, has addressed the role of inter-generational transfers as a mechanism of evolutionary demography, with particular reference to ageing and juvenile mortality. Conventional evolutionary models, following Hamilton (1966), rest on a purely demographic analysis in which, under a stable population growth rate, mortality increases at older ages in inverse relation to expected fertility by age. Put very simply: as older people do not have babies, their contribution to group fitness may appear to be marginal; further, if they have no proximate functions supporting fertility, and are susceptible to the complications of age-specific deleterious mutations as they reach later life, there would seem to be no serious evolutionary advantage to their increased longevity.

As Lee remarks, this formulation leaves the human capacity for long post-reproductive survival unexplained.16 A considerable body of natural historical, ethnographic and historical evidence has for some time made the conventional view untenable: elders, particularly female relatives, contribute substantial support to raising their grandchildren, and in many cases to others in younger generations that are not direct descendants. As proximate functions of support contributed by elders to the survival and growth of groups are evident in many species, selection for their greater longevity (including differences for the sex contributing most to transfers) is logically indicated. Likewise, the uniform progression of mortality with age in the conventional model, by not taking account of transfers, fails to recognise that early death, e.g. in infancy, incurs much less physiological and support cost than deaths at juvenile ages, by which time much greater investments have been made.

Life history theory, in which a balance between fertility, mortality and investments in children is fundamental to evolution, again provides the elemental logic. Lee’s model is addressed to the long period from prehistory in which the human race depended on foraging, so again a kind of baseline is being established. As the objective is to show what difference transfers make to levels of fertility, mortality and natural increase at each age across the life course, a complex set of variables is entailed. Since production varies with a group’s relative success in competition for food and resources, the capacity to make transfers depends on population density and size. Production also depends on feedbacks from consumption, since it depends on the growth, size and strength of individual members, which have been shaped by the food and resources available to them. The net transfer that becomes possible at each age can therefore be modelled as estimated production minus consumption (assuming no wastage); this will vary according to the composition of units or groups involved, and Lee’s model may be applied to a range, from individuals and mother-offspring sets to larger family groups and cooperative breeding groups. The implications for natural selection then turn on how changes in fertility and mortality, and resulting age structures, interact with intergenerational investment supported by transfers. Lower mortality at the youngest ages increases population growth, and, if coupled with lower mortality at older ages, profits from feedbacks via transfers that also optimise longevity, further stimulating population increase. Greater surviving reproduction thus increases fitness at both the top and the bottom of the age pyramid; transfers become the key to understanding longer post-reproductive longevity characterising more successful and numerically dominant competitive groups. For these groups with greater capacity to invest in children who are then more likely to survive, older adults over time will come increasingly to be selected genetically for greater longevity — this not only helps to ensure continued transfers, but opens up the possibility of reducing fertility (i.e. increasing the quality and quantity of investment per child), thus avoiding the Malthusian trap of high density groups becoming subject to too much competition. As every unit must be in transfer balance (whether successfully, or via loss of members to mortality at younger and older ages), the sum of all units, or the total population, will also be in balance.

In its early formulation, Lee’s model made a number of abstract assumptions, for example only applying to single-sex transfers of food in stable populations. Later iterations have reduced some of these, and also included more variables, but an account here would extend discussion greatly beyond the scope of this chapter. In each case the model has been developed with evidence from the ethnographic background on foraging populations in mind, and applied to population data on them. Simulations utilising the model enable a 75,000-year prehistory of foraging groups to be constructed, a picture of environment-organism-genetic interaction in the long term. This may, as further developed, serve as a baseline indicating possible ultimate evolutionary parameters within which proximate mechanisms — introduced in the relatively short and recent 2,000-year period of more complex agricultural, urban and manufacturing societies — can be understood.

Concluding Note

In view of the historical development of population thinking traced in this chapter, it is clear that research has moved on from the hunt for ostensible laws of natural selection based, for example, on Malthus’s positive check in closed populations, or the eugenics of reproductive selection. The Evolutionary Synthesis, in reasserting Darwin’s dual conceptualisation of population thinking, has facilitated a closer relation between formal modelling and local population data, whether in laboratory or field settings, and increasingly in the later twentieth century with reference to proximate processes observed in human groups. Stepping back from this long and complex history, the importance of evolutionary population biology to demography may be summarised broadly on two counts.

One, as we have seen, is to remind demographers of the substantial body of population theory on which social and biological population research jointly rest. Darwin, in building his theory of evolution on analogy between observation-based natural history and Smith’s account of the division of labour, enabled evolutionary biology to remain truer to the long tradition of open population thinking than has been the case in demography, with its overriding focus on closed methodologies of population statistics. Demography over the nineteenth and twentieth centuries remained primarily the study of population renewal, whereas evolutionary biology has addressed both renewal and structural change by explaining the dynamics that renew population heterogeneity. Yet Darwin, in also insisting on the crucial role of statistical demonstration of the variation and divergence of characteristics, opened the door to applications of actuarial methods, which early-twentieth-century analysts like Lotka, Fisher, Galton and Pearson then began to develop. Recognition of the complementarity of the two concepts of population was one of the main achievements of the Synthesis.

A second wider implication of this history follows from the fact that mid-twentieth-century social and economic demography did not undergo a comparable synthesis. Its approach to theory, notably in attempts to explain demographic transitions, remained focussed primarily on the evidence of closed population methods, often viewed in terms of stylised macro- and micro-levels. This methodology has undoubtedly proven very fruitful in tracking aggregate trends at these levels. The central finding of a vast body of research on demographic transitions has been to demonstrate the immense heterogeneity of fertility and mortality declines in the modern era, taking place in a vast array of environments — exactly as Darwinian population thinking would lead us to expect. However, in its reliance on closed units, often based on institutional compilations rather than sustained observation of groups in society, and without a primary focus on evolving interdependence and divergence amongst constituent populations, demography has encountered great difficulty in providing a scientific explanation of its central finding. Evolutionary demography, following on from population biology, recognises that heterogeneity requires explanation on several levels, from genetic and cellular processes up to the diverse ways in which social groups are distributed and redistributed in social structures over time.17 Formal population analysis remains by definition addressed to closed units, but its development is shaped necessarily by increasingly complex bottom-up configurations of observed proximate mechanisms — the “division of labour” within and amongst local populations which Darwin recognised as the locus of environment-organism-genetic evolution.

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1 For historical background to the Classical Model and its subsequent development in population arithmetic, political economy and population renewal theory see Kreager 2008, 2009 and 2017.

2 Schweber notes that the review of Quetelet’s book which Darwin annotated concluded with remarks on this inadequacy (1977: 293).
3 Comparison of Darwin’s and Smith’s population thinking draws on Schweber (1977, 1980) and Kreager (2017). Schweber further remarks on the status of the division of labour as a widely employed metaphor and model in the mid-nineteenth century. That said, Darwin’s debt to Smith’s account of population specialisation, interdependence and the renewal of heterogeneity as fundamental elements of the dynamics of evolution should not be overstated. As with his incorporation of Malthus’s positive check, Darwin sought analogies that would enable him to think cohesively about observed processes recorded by natural historians — not a systematic reduction of biological phenomena to principles supposed to regulate political economy. This is evident merely in the fact that most types of feedback in environment-organism interaction differ from those in the division of labour, and Darwin did not pursue analogies to Smith’s population thinking further than its general logic. As we shall see, in providing a place for formal, statistical analysis of variation in his theory, Darwin’s logic marked a major advance on Smith, which is central to the “revolution” remarked by Mayr.

4 Thus, “In an extremely small area, especially if freely open to immigration, and where the contest between individual and individual must be severe, we always find great diversity in its inhabitants. For instance, I found that a piece of turf, three feet by four in size, which had been exposed for many years to exactly the same conditions, supported twenty species of plants, and these belonged to eighteen genera and to eight orders, which shows how much these plants differed from each other. So it is with plants and insects on small and uniform islets; and so in small ponds of fresh water. Farmers find that they can raise most food by a rotation of plants belonging to the most different orders: nature follows what may be called simultaneous rotation.” (1996: 94).
5 For example, in making an estimate of relative frequency, Darwin made multiple calculations each based on different ways of proportioning a population, and then compared the results — in effect, reinventing a method Graunt had devised two centuries earlier (cf. Browne 1980; Kreager 1982).
6 Darwin adopted Classical population thinking not only because it was a model that was integral to Smith’s account of the division of labour and early quantification of human society, but because it was also established practice in natural history. Thus, in his extensive comparative study of barnacles (1851), he drew on the large body of data available in natural historians’ plant catalogues, and the established field of botanical arithmetic, in which counting and comparing physical characteristics was a standard practice (Browne 1980).
7 Lotka sets out the analogy between species populations and those of molecules carefully and elaborately, emphasizing that his analysis is confined to “isolated systems” (1925: 26) and that, as in all probabilistic models, possible events and relations are limited to those specified by classifications in advance (1925: 35; 41). When he later came to develop the model for human fertility and mortality, he was able to say more simply that analysis by definition is confined to “closed populations” (1939:11). The following very brief summary can scarcely do justice to his extended presentation.

8 Pearson refused, being a socialist.
9 Pearson admitted in a footnote (1896: 398–39, n.4) that his statistical approach via correlation puts aside Darwin’s central concern in the Origin with how variation can give rise to new demes and species. Pearson reduces fitness to progressive change in extant species defined as composed of homogeneous social classes.

10 Although outside the immediate topic of this chapter, Mendel’s method independently encapsulated the combined open and closed population reasoning that Darwin pioneered. Peas of seven seed types were selected, merely on the basis of visible distinctive characteristics (smooth, wrinkled, white, etc.). This selection amounts, in effect, to a pragmatic hypothesis that such features indicate genetic variants. The seven types were planted, and numbers of offspring consistent or variant with the original types noted in the outcomes for each planting. Self- and cross-fertilisation of offspring were then carried out in regular combinations across a succession of generations, and the outcomes enumerated. In this genetic demography of peas, the question ‘What constitutes a population or sub-population?’ is left open, and the specification of the several sub-populations emerges as a key result from observation, including the ratios that give the regular proportions of dominant and recessive forms that arise from the relationships between them. In effect, the behaviour exhibited in the experiments sorts the population into recurring groups defined by their observed qualitative and quantitative properties (of which the most famous is Mendel’s is 3:1 ratio expressing the incidence of dominant versus recessive traits); such regularities then become properties that can be tracked and modelled in wider surveys and in other populations.

11 In order to treat human populations without reference to their environment, Lotka made a number of further assumptions which have subsequently been disproven (Kreager 2009: 474n)
12 Lewontin (2004: 13) describes this as “a lack of transitivity in fitness”: “Competing genotypes can play a game of ‘scissors-paper-stone’ in which genotype A is superior in competition with B and B is superior to C but C is superior to A, because in each competitive interaction a different set of attributes is involved: A is stronger than B, B is faster moving than C and C is more aggressive than A.”

13 The view that separatism arose largely from post-war demographic aversion to eugenics and its pre-occupation with rapid population growth, for example in Kreager (2009), neglects four key factors, of which three are evident in the preceding discussion. One is that the GRO’s extensive work to refute eugenics shows that early twentieth-century demographers were already strongly critical. Secondly, eugenicists’ claims that their work was a contribution to Darwin’s theory were unfortunately not refuted adequately by Galton’s contemporaries even though, as we have seen, the fundamental premises of eugenics were a travesty of Darwinian theory. In the absence of such clarification, the confusion of evolutionary approaches with eugenics continued to influence some demographers over the whole first half of the twentieth century, e.g. Pearl (1925). Third, while demographers took Lotka’s mathematics seriously, they jettisoned its evolutionary rationale. We may wonder whether they understood clearly that his biological application concerned ecological issues marginal to central issues in evolutionary debates; again, separatism occurred on the basis of limited awareness relating to a biological sub-field, not with reference to mainstream evolutionary population thinking. In short, the separation of demography and evolutionary theory was established over the early decades of the twentieth century, and then reinforced by post-war demographic concerns.

14 For example, a population of haemophilia sufferers can be identified on the basis of a single gene, but in the study of cancer or multiple sclerosis the genetic component is much more complex, and there remain serious questions as to environmental influences across the life course which vary between individuals.
15 Spencer (2015) considers the importance of not grouping population members on a priori criteria as a concern in current genomic research. While the iterative approach to modelling just described is commonly employed, he remarks on “the unease we have with describing the continuums of diversity of organisms like humans as discrete groups” (2015: 502), and continues by pointing out that if, “in fact, genotype data are available for each individual within the sample […] why not model each individual as a ‘population’, and let the covariance in alleles between individuals capture the population structure?” (2015: 512). In such a local model space, use of an individual-level correlation matrix avoids having to define populations other than as individual genomes; the set of principal components thus established constitute clines of genetic variation, which may then be explored in a wider sample of individuals. As Spencer says, “every man is an island (or at least a population)” (2015: 512).

16 Beginning in the 1960s, two distinguished British evolutionary biologists, William Hamilton and Brian Charlesworth, developed models of ageing that relate genetic variation to life history, and which have substantially reshaped understanding of variation in longevity and its relation to fecundity. Further discussion of Hamilton can be found in Ronald Lee’s chapter, ‘Sociality, Food Sharing and the Evolution of Life Histories’, and of Charlesworth in Ken Wachter, ‘Genetic Evolutionary Demography’, both in this volume.

17 Exploration of alternative levels of analysis and their implications for explanatory models are a subject of the many contributions to Kreager et al. 2015.
18 Note this chapter has been posted on the Open Science Framework website since 13/06/2019, after it was accepted for publication, so the references will reflect when the chapter was written and not the OBP publication date.