Peter E. Smouse

Problems in the assessment of relative risk of chronic disease among biological relatives of affected individuals

A question often asked in regard to a chronic disease is whether the risk to a biological relative of a case is evaluated, and if so by how much the risk is altered. To answer this question, data may be collected directly with genetic objectives in mind by ascertaining population of pedigrees. More often, the initial assessment of the question comes from family history data collected in an incidental manner in the course of a case-control or similar type of study. This paper discusses some limitations to the inferences which can be derived from such casual family history data. These include (i) poor statistical properties of standard relative risk measures, (ii) interpretational problems of observed relative risks when affected cases arise from genetic as well as nongenetic causes and when genes may not always be expressed in individuals in whom they are present, and (iii) confounding effects which may occur when a high risk allele alters the age of onset pattern of the disease. These problems result largely from a loss of design control over the degree of exposure of individuals ascertained and can lead to a small observed relative risk value even when genetic factors are important. Suggestions for handling such casual family history data are offered.

Multiple-Locus Allocation of Individuals to Groups as a Function of the Genetic Variation Within and Differences Among Human Populations

Multivariate (multiple-locus) analytic procedures are used to show that the amount of genetic overlap of two or more populations, as measured by the difficulty of correctly allocating individuals, may be formally related to the average genetic distance between pairs of populations. On theoretical grounds, we argue that the probability of correct allocation for individuals should: (1) increase with the number of segregating loci; (2) increase with increasing taxonomic disparity of the populations considered; and (3) decrease with an increase in the number of candidate populations. Genetic data on 5,214 individuals from seven South American Indian tribes are used to evaluate these theoretical predictions. We have analyzed genetic distance and classification with the seven tribes, as well as with seven village clusters within one tribe and seven villages within one cluster. At all three levels of taxonomic organization (tribal, cluster, village), the probability of correct allocation did increase with the number of loci, as predicted. This pattern was consistent with the computed average distances between populations, also as predicted. Some loci were more useful for allocation than others. In general, high-frequency polymorphic markers were the most useful, while tribally restricted (but low-frequency) markers were not helpful. There was consistent evidence that the genetic overlap for tribes was less than that for clusters and that the overlap for clusters was less than that for villages. As a consequence, tribal allocation was more accurate than cluster allocation and cluster allocation was more accurate than village allocation. To place these differences in wider perspective, we computed the genetic distance measure for a set of seven racial groups. The predicted overlap for races was substantially less than that for tribes. Finally, we compared our results with those of others, and showed that the differences result from our use of a multiple-locus rather than a single-locus analysis. The two types of results are strictly compatible, however, once this technical gap is bridged. The conclusion is inescapable that some human populations show substantial genetic differences, measured relative to the variation within populations. For populations as similar as nearby villages, genetic overlap is substantial; for populations as different as racial groups, genetic overlap is small.

Genetic studies on the Ticuna, an eniǵmatic tribe of Central Amazonas

The Ticuna are an Amerindian tribe of Central Amazonas, a key location in theories of the peopling of eastern South America. The results of typing some 1760 members of the tribe with respect to 37 different genetic systems are reported, as are the results of HLA typings on a subsample of 129 persons. Salient findings include the following. (1) Except for a high frequency of the LMsallele and an unusual combination of HLA allele frequencies, there are no notable findings with respect to the commonly studied polymorphic systems. A multivariate treatment of six of the most commonly studied genetic polymorphisms accords the Ticuna an ‘average’ position among Amerindian tribes. (2) There is much less intervillage heterogeneity than usually encountered in Amerindian tribes; this is attributed to recent high rates of intervillage migration due to religious developments. (3) A thus‐far unique polymorphism of ACP1was identified, the responsible allele having a frequency of 0.111. (4) In proportion to the size of the tribe, there was a relative paucity of ‘private’ genetic variants, the ACP1 allele being the only one. This discrepancy is attributed to a relatively recent numerical expansion of the tribe; effective population size over the past several thousand years is thought to have been well below what present numbers would suggest. (5) The thesis is again advanced that ‘private variants’ (alleles not occurring as polymorphisms of wide distribution) are more common in Amerindian than in Caucasian or Japanese populations.

The genetic implications of age-dependent penetrance in manic-depressive illness

Abstract An age dependent penetrance function was derived for manic-depressive illness, using age-of-onset data from sixty-one affected probands. The function used was a one-hit model, with earliest age-of-onset at about 14 yr, and a steadily increasing probability of manifesting the illness thereafter. The utility of the penetrance function for pedigree analysis was illustrated, using the families of the sixty-one probands. A sex-linked dominant model of inheritance was about eighty-nine times more likely than an autosomal dominant model, and both were far more likely than autosomal recessive or sex-linked recessive models. The more general single major locus model and the polygenic model cannot be ruled out, but would seem to be unnecessarily over-parameterized for the data at hand. The sex-linked dominant and autosomal dominant models were also compared, by means of the age specific morbidity risks and sibs and children. Both models provided a fairly close fit of expectation and observation, but the sex-linked model was preferable. Although the genetic conclusions cannot automatically be applied to other material, the analytical techniques should be useful elsewhere. Other uses of the penetrance function were indicated.

The Demographic Stability of Small Human Populations

of birth and death which prevail in the population over a long time period. We have two basic kinds of data. There are aged skeletal series from large burial sites, and there are censuses from living primitive populations. The former give us direct information from past populations, and the latter give us information from living populations generally assumed to be representative of cultures during the long period of human evolution. Hence, both sources are used to reconstruct human demographic evolution. Most populations of these types are small ones which are not literate and do not keep records sufficient for demographic analysis. We generally have but a single census (or aged skeletal series) and only minor scraps of other information. There is almost never any actual data on age-specific rates of mortality, yet these rates are the fundamental parameters of demography and must be known. With standard theoretical approaches, it has been shown that the age distribution of small groups is unstable from year to year, and may be unreliable as a source from which to determine age-specific death rates (e.g., Moore, Swedlund & Armelagos, 1975; Angel, 1969). It is also known that populations are so subject to extinction, due to statistical fluctuations in births and deaths, that they are too transitory and unstable for useful study (this is based on statistical theory, which can be found in Bartlett, 1960; Pielou, 1969; Keyfitz, 1968). If this is true, then we must avoid the use of typical anthropological data, and are to a great extent prevented from gaining a reasonable knowledge of past demographic patterns. The mathematical models on which these assertions are based use fixed age-specific birth and death rates. Yet there is a wealth of biological and anthropological information to show that these vital processes of a population vary according to population size or density in a negative-feedback way. A population which becomes crowded suffers higher mortality and lowered fertility, and one which is uncrowded enjoys higher fertility and lower mortality. These facts must be incorporated into a realistic demographic model.

Patterns of molecular variation. I. Interspecific comparisons of electromorphs in the Drosophila mulleri complex.

The average mobility of electromorphs at an enzyme locus in a single population was defined as the weighted average mobility of the electromorphs in that population, where the electromorph frequencies are the weights. A derivative distance measure was defined whose taxonomic utility was determined in the Drosophila mulleri species complex. Most of the variation in this metric was at the interspecific level, primarily among clusters of sibling species. The electromorphs of some loci were equally and regularly spaced, while those of other loci were less regular in their spacing. Overall, these minor perturbations from regular spacing did not noticeably detract from the taxonomic utility of average mobility, and cluster analysis yielded the same taxonomic relationships as more conventional nonmolecular treatments. On the other hand, electromorph spacing may be related to functional constraints on the enzyme molecules. Some possible implications of the results for the modes of selection during evolution of the different enzymes are discussed.

Mathematical Models for Continuous Culture Growth Dynamics of Mixed Populations Subsisting on a Heterogeneous Resource Base: I. Simple Competition*

Abstract The classical Monod model for bacterial growth in a chemostat, based on a Michaelis-Menten kinetic analog, is restated in terms of an approximate Lotka-Volterra formulation. The parameters of these two formulations are explicitly related; the new model is easier to work with, but yields the same results as the original. The model is then extended to the case where multiple alternate substrates may be growth limiting, using the corresponding kinetic analogs for multiple-substrate enzymes. Again, one is led to a Lotka-Volterra analog. In the multiple-substrate model, however, coexistence of multiple genotypes is possible, in contrast to the single-substrate model. The usual Lotka-Volterra conditions for existence and stability of pure or mixed equilibria may all be translated into corresponding statements about the parameters of the chemostat system. Possible extensions to deal with metabolic inhibition, cross-feeding, and predation are indicated.

Discrete demographic models with density-dependent vital rates

SummaryThe standard Leslie model of population growth in an age structured population is modified so as to incorporate density-dependent feedback control on each parameter of the standard projection matrix. Under fairly general conditions, the population converges to a stable age-distribution and a constant population size. This steady-state solution is uniquely determined by the parameters of the model. In general, fertility damping results in a flatter age-distribution than yielded by the undamped Leslie model. General survival damping results in the Leslie age-distribution. Post-infant survival damping results in a very steep age-distribution. For populations with high intrinsic growth rates, these differences in stable age-distributions are pronounced. For populations of low intrinsic growth rate, the patterns are the same, but the differences in stable age-distribution are more subtle. The age-distribution usually converges rapidly to the steady-state array, although population size generally takes longer to approach a stable value. Convergence properties are described for a series of cases which show periodicity. Such cases arise from “periodic” behavior of certain fertility-damping strategies, and ultimately approach a stable steady-state, although convergence may be very slow. Although the model is very general, it can be considerably simplified in practice. Special cases, which can be constructed, are the Malthusian (Leslie) model and the Logistic model. As a generality, the model is approximately Logistic, once the age-distribution approaches the steady-state array. One may use this fact for purposes of population projection.

Genetic Architecture of Swidden Agricultural Tribes from the Lowland Rain Forests of South America

The first humans entered South America between 10,000 and 15,000 years ago (Willey, 1978). By about 10,000 years b.p., humans had reached Tierra del Fuego and had presumably occupied the whole continent. At the beginning of this continental colonization, humans were hunter-gatherers (Martin, 1973) and undoubtedly remained so for at least a few millenia more. Both their ecological setting and their social organization would have reflected this fact. The physiography, climate, and biota of the continent were so incredibly diverse, however, that any sort of long-term habitation would have inevitably entailed severe adjustments in life-style to accomodate local ecological conditions in different areas. It seems probable that sociocultural radiation would have begun even as humans began to penetrate the rain forests, scale the cordilleras, and wander the grasslands. Social adaptation was undoubtedly a slow and fitful process, but by the time the early European explorers arrived, South America already exhibited a rich variety of social and cultural adaptations, a diversity in keeping with the underpinning ecological variety.

A Simple Test for the Aggregation of Disease Occurrence in Genealogical Data

A simple test for the aggregation of occurrence of a trait in genealogical data is given; a test criterion is developed, and the power of the test to detect aggregation of risk is computed. The test utilizes pairs of individuals between whom transmission of risk factors may occur. As long as aggregation is reasonably strong and prevalence not too low, only modest amounts of data are required. It provides an easy and inexpensive first examination of data which can reveal whether the effort required to conduct more elaborate genealogical studies and analysis is warranted.