Multiple-Locus Departures from Panmictic Equilibrium within and between Village Gene Pools of Amerindian Tribes at Different Stages of Agglomeration

A comparative analysis of departures from multiple-locus Hardy-Weinberg equilibrium is presented for a set of four tribal Indian groups (the Yanomama, Makiritare, Wapishana and Ticuna) from the lowlands of South America. These tribes span a range of agglomeration and acculturation from the most traditional, swidden horticulturalists to frontier townspeople. The small-group social organization typical of traditional horticulturalists leads to substantial departures from tribal panmixia, as manifested by the distribution of multiple-locus genotypes both within and between villages. Within villages, the departures from single-locus Hardy-Weinberg equilibrium are small and nonsignificant, but the departures from gametic equilibrium (independence of loci) are substantial, even for the unlinked loci we have used to characterize these populations. The departures from single-locus homogeneity across villages are also substantial. One of the normal concomitants of increasing acculturation in this setting is an increase in agglomeration. As agglomeration increases, the departures from multiple-locus panmixia decrease, a process that can be very rapid. We discuss both the shifting balance theory of evolution and punctuated evolutionary rates in light of the small group social organization that must have obtained throughout most of human evolution.     

Intertribal gene flow between the Ye'cuana and Yanomama: genetic analysis of an admixed village

Genetic exchange with a neighboring village of Ye'cuana Indians had introduced two alleles, Dia and ACPa, into the Yanomama Indian Village of Borabuk. After several generations, these alleles had reached frequencies of 0.08 and 0.10, respectively. These frequencies are puzzling because they are higher in Borabuk than in the Ye'cuana village from which they were derived. Single allele estimates of ancestral proportions obtained from either of these traits are biologically unrealistic and suggest that admixture is not a good explanation for genetic variation in Borabuk. Nevertheless, multiallelic admixture models are seen to produce credible estimates of ancestral proportions and to explain a large amount of allele frequency variation in Borabuk. When these results are compared with expectations derived froma formal pedigree analysis, good agreement is seen. Comparison of single allele estimates of ancestral proportions obtained from alleles at 11 loci, with multiallelic estimates obtained from the same 11 loci and with the pedigree-derived estimates, demonstrates the superiority of the multiallelic approach.     

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.Supported by NSF Grant 22770, AEC Contract AT-(40-1)-4023, and NIH Career Development Award GM 47350-05 to R.H.R.     

Patterns of Molecular Variation. II. Associations of Electrophoretic Mobility and Larval Substrate within Species of the DROSOPHILA MULLERI Complex

Electromorphic variation among populations of Drosophila mojavensis, D. arizonensis and D. longicornis was examined for seven genetic loci. The average electrophoretic mobility for a population was used as the metric. D. mojavensis and D. arizonensis use larval substrates in different parts of their geographic ranges, while D. longicornis is more narrowly restricted to different species of the cactus Opuntia in different localities. There is marked electromorphic variation among populations of either D. mojavensis or D. arizonensis, and the bulk of this variation is accounted for by differences in laval substrate. There is somewhat less variation among populations of D. longicornis, and only a moderate portion of this is accounted for by larval substrate differences. There appears to be an association between the taxonomic diversity of the larval substrates and the electromorphic diversity of the Drosophila populations utilizing those substrates. Evidence is reviewed that suggests physiological mechanisms for these possibly adaptive associations.     

Mathematical models for continuous culture growth dynamics of mixed populations subsisting on a heterogeneous resource base. II. Predation and trophic structure

Models are presented for the joint dynamics of predators and prey, maintained in continuous flow chemostat culture. The predators are visualized as subsisting on one or more prey organisms, which in turn are visualized as subsisting on one or more substrate resources supplied by the investigator. The dynamic equations are translated into an analogous Lotka-Volterra predation model, and the criteria for the existence and stability of various equilibria are indicated. Denoting the number of different predator organisms as N_H, the number of different prey organisms by N_I and the number of different substrates as N_J, it is shown that the joint coexistence of all components requires 0 ? N_I ? N_H ? N_J. The model is extended to more complex situations by including additional trophic layers and by allowing trophic layer “leap-frogging.” The model may always be translated into an approximately quadratic differential equation of the Lotka-Volterra type. The α- and β-coefficients of these latter are really variables, and become quite complex for some of the multi-layered models.     

Mathematical models for continuous culture growth dynamics of mixed populations subsisting on a heterogeneous resource Base: I. Simple competition

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.     

Resolving UV Bioactinometric Results with Intensity and Time Distributions

A UV reactor with an annular design, a total liquid volume of 460[emsp4 ]ml, and outfitted with a single lamp with 1690[emsp4 ]mW of germicidal power was tested. Coliphage MS2 was used as a bioactinometer to measure the UV dose at a flow rate of 56.7[emsp4 ]ml/sec in water with a very low absorbance. The Beers Law coefficient was A₁₀0.003. The measured dose (MS2 bioactinometry) was 35.2±1.1[emsp4 ]mW-sec/cm².A retention time distribution was generated with a dye tracer study. The reactor was modeled as if flow was confined to ten equal volume paths existing as concentric rings around the lamp. The UV intensity along each path (ith intensity) was calculated to generate a simulated distribution of UV intensity in the reactor. The retention time distribution was subdivided to estimate the retention time associated with each decile jth time) of the total flow.Seven methods of associating the ith intensity with the jth retention time were used to produce simulated dose distributions for the reactor. The average UV dose for each distribution was calculated as the average of the products of I and t (AP protocol) and by the apparent survival (AS protocol), in which the predicted survival along each path was averaged to back-calculate dose from the reference batch inactivation curve. The average dose predicted assuming that time and intensity were independent was 51.5[emsp4 ]mW-sec/cm² based on the arithmetic average (AP protocol). Using the apparent survival method, the predicted dose for the independent distribution (I independent of t) was 36.4[emsp4 ]mW-sec/cm². Three methods of developing dependent structure between time and intensity were tested. In the best possible case for stratified flow (I negatively correlated with t) the calculated (AS) intensity was 46.3[emsp4 ]mW-sec/cm^2. In the worst case for stratified flow (I positively correlated with t) the AS intensity was 32.0[emsp4 ]mW-sec/cm². In a rational case where flows were assumed to be distributed parabolically (low flow at the wall and at the lamp) produced an AS intensity of 37.7[emsp4 ]mW-sec/cm². When either time or intensity was averaged, while the other variable was allowed to keep its distribution, the (AS) dose (time averaged 43.3[emsp4 ]mW-sec/cm², intensity averaged 41.0[emsp4 ]mW-sec/cm²), yielded a poor prediction compared to the measured value.The errors associated with averaging time, intensity, or both, far outweigh the errors associated with choosing a rational distribution or an independent distribution of time and intensity in the prediction. This observation is generally true whenever an organism is exposed to UV light in a flow through reactor such that the range of doses is within the portion of the inactivation curve exhibiting strong exponential decay.