SYSTEMS OF MATING. I. THE BIOMETRIC RELATIONS BETWEEN PARENT AND OFFSPRING

Viability selection at three early life stages of the tropical tree, Platypodium elegans (Fabaceae, Papilionoideae)

Given the enormous number and high mortality of fertilized ovules in plants, it is possible that selection during the earliest stages of the life cycle plays an important role in shaping the genetic composition of plant populations. Previous research involving selection component analyses found strong evidence for viability selection in annual plant species. Yet despite this evidence, few attempts have been made to identify the magnitude and timing of viability selection as well as the mechanisms responsible for mortality among genotypes. Platypodium elegans, a Neotropical tree with high rates of early fruit mortality, represents an opportunity to study viability selection at a level of discernment not previously possible. Microsatellite markers were used to analyze the genetic composition of aborted embryos, as well as mature seeds and seedlings of the same cohort. While selection resulted in an overall decrease in self-fertilized progeny across each life stage, the greatest change in the genetic composition of progeny occurred between mature seeds and established seedlings. This suggested that inbreeding depression, and not late-acting self-incompatibility, was responsible for early selection. An investigation of the mature seed stage revealed that self-fertilized seeds weigh significantly less than outcrossed seeds. The result of this early selection conceals the mixed-mating system and high levels of inbreeding depression in Platypodium elegans, resulting in an apparently outcrossed adult population that does not differ significantly from Hardy-Weinberg expectations.

Hitchhiking mapping--functional genomics from the population genetics perspective

Several statistical tests based on population genetic theory are used to identify genes that have recently acquired a beneficial mutation. Here, I describe the extension of these tests to a multilocus approach for a genome-wide survey for genes that have been under recent positive selection. As this strategy could potentially identify genes with weak phenotypic effects, it will be very useful in population genetic approaches aimed at understanding adaptation processes in natural populations. Furthermore, this 'hitchhiking mapping' could also help in the functional characterization of genomes.

Extensive linkage disequilibrium in small human populations in Eurasia

The extent of linkage disequilibrium (LD) was studied in two small food-gathering populations-Evenki and Saami-and two larger food-producing populations-Finns and Swedes-in northern Eurasia. In total, 50 single-nucleotide polymorphisms (SNPs) from five genes were genotyped using real-time pyrophosphate DNA sequencing, whereas 14 microsatellites were genotyped in two X-chromosomal regions. In addition, hypervariable region I of the mtDNA was sequenced to shed light on the demographic history of the populations. The SNP data, as well as the microsatellite data, reveal extensive levels of LD in Evenki and Saami when compared to Finns and Swedes. mtDNA-sequence variation is compatible with constant population size over time in Evenki and Saami but indicates population expansion in Finns and Swedes. Furthermore, the similarity between Finns and Swedes in SNP allele- and haplotype-frequency distributions indicate that these two populations may share a recent common origin. These findings suggest that populations such as the Evenki and the Saami, rather than the Finns, may be particularly suited for the initial coarse mapping of common complex diseases.

The estimation of population differentiation with microsatellite markers

Microsatellite markers are routinely used to investigate the genetic structuring of natural populations. The knowledge of how genetic variation is partitioned among populations may have important implications not only in evolutionary biology and ecology, but also in conservation biology. Hence, reliable estimates of population differentiation are crucial to understand the connectivity among populations and represent important tools to develop conservation strategies. The estimation of differentiation is c from Wright's FST and/or Slatkin's RST, an FST -analogue assuming a stepwise mutation model. Both these statistics have their drawbacks. Furthermore, there is no clear consensus over their relative accuracy. In this review, we first discuss the consequences of different temporal and spatial sampling strategies on differentiation estimation. Then, we move to statistical problems directly associated with the estimation of population structuring itself, with particular emphasis on the effects of high mutation rates and mutation patterns of microsatellite loci. Finally, we discuss the biological interpretation of population structuring estimates.

Spatial population structure in a patchily distributed beetle

The dynamics and evolution of populations will critically depend on their spatial structure. Hence, a recent emphasis on one particular type of structure--the metapopulation concept of Levins--can only be justified by empirical assessment of spatial population structures in a wide range of organisms. This paper focuses on Aphodius fossor, a dung beetle specialized on cattle pastures. An agricultural database was used to locate nearly 50 000 local populations of A. fossor in Finland. Several independent methods were then used to quantify key processes in this vast population system. Allozyme markers and mitochondrial DNA (mtDNA) sequences were applied to examine genetic differentiation of local populations and to derive indirect estimates of gene flow. These estimates were compared to values expected on the basis of direct observations of dispersing individuals and assessments of local effective population size. Molecular markers revealed striking genetic homogeneity in A. fossor. Differentiation was only evident in mtDNA haplotype frequencies between the isolated Aland islands and the Finnish mainland. Thus, indirect estimates of gene flow agreed with direct observations that local effective population size in A. fossor is large (hundreds of individuals), and that in each generation, a substantial fraction (approximately one-fifth) of the individuals move between populations. Large local population size, extreme haplotype diversity and a high regional incidence of A. fossor all testify against recurrent population turnover. Taken together, these results provide strong evidence that the whole mainland population of A. fossor is better described as one large 'patchy population', with substantial movement between relatively persistent local populations, than as a classical metapopulation.

Nucleotide diversity of the TNF gene region in an African village

The wide variety of disease associations reported at the TNF locus raises the question of how much variation exists within a single population. To address this question, we sequenced the entire TNF gene in 72 chromosomes from healthy residents of a village in The Gambia, West Africa. We found 12 polymorphisms in 4393 nucleotides, of which five have not been previously described, giving an estimated nucleotide diversity (theta) of 5.6 x 10(-4). A significantly higher frequency of polymorphisms was found in the promoter region than in the coding region (8/1256 vs 0/882 nucleotides, P = 0.02). All polymorphisms with the exception of one rare allele were found to be present in Malawi, which is both geographically and genetically distant from The Gambia. Genotyping of 424 Gambian and 121 Malawian adults showed a significant frequency difference between the two populations for eight of the 12 polymorphisms, but the average fixation index across the variable sites was relatively low (F(ST) = 0.007). We conclude that, at the TNF locus, the nucleotide diversity found within a single African village is similar to the global value for human autosomal genes sampled across different continents.

Isonymy structure of USA population

The isonymy structure of the 48 states of the continental United States of America was studied using the surname distributions of 18 million telephone users, distributed in 247 towns. The shortest linear distance between nearest neighbor towns included in the sample was 12.0 km. The largest distance was 4,577 km. The number of different surnames found in the whole analysis was 899,585. Lasker's distance was found to be significantly but weakly correlated with the geographic distance, with r = 0.21 +/- 0.01. A dendrogram of the 48 states was built from the matrix of isonymy distances: it divides the US into several clusters, in general correlated with geography. A notable exception is California and New Jersey, which cluster together. Wisconsin is separated from all other states. An important cluster is formed by Texas, Colorado, New Mexico, Nevada, and Arizona, together with Illinois and Florida. It was observed that Hispanic surnames are among the most frequent in Illinois, as they are in New Jersey and California. No main distinction among the states clearly attributable to surnames of French origin was detected; however, New Hampshire, Vermont, and Maine which have a considerable number of these surnames belong to the same northeastern cluster. From the present analysis, the great mobility of the US population emerges clearly, and it seems relevant that the practical absence of isolation by distance is seen also considering only small towns. It appears that groups of different origin are well-mixed over the whole area of the United States. The values of isonymy indicate that the south-central area of the USA has the highest level of inbreeding. In fact, the heterogeneity in surname composition is greater in the coastal areas, particularly on the East Coast, than anywhere else in the USA.

Genealogical Analysis of a Closed Herd of Black Hairless Iberian Pigs

Livestock breeds are recognized as important components of world biodiversity. The Iberian pig is a swine breed well adapted to the Mediterranean forest ecosystem and provides cured products of high quality. The ancient population of Iberian pigs ( Sus scrofa meridionalis) was differentiated in several local types, the black hairless pigs representing the fattest genetic type. The conservation program of the Guadyerbas strain has maintained this germplasm isolated since 1945 as a closed population in an experimental herd. The complete pedigree, with 1000 breeding animals descending from 24 founders, has been used to measure along the successive cohorts of breeding animals the effective number of founders, effective number of nonfounders, founder genome equivalents, and expected number of founders' surviving alleles. For the last cohort, the values were 10.34, 1.42, 1.25, and 4.06, respectively. The evolution of inbreeding and coancestry and its components attributable to each founder were also studied. The rate of increase in inbreeding and coancestry was 2.21% per cohort, or 0.906% per year. Finally, the effect of family structure and mating tactics on the evolution of coancestry was also analyzed. The greatest rates of coancestry per cohort were attributable to unbalanced family sizes, and the use of minimum coancestry matings effectively delayed the increase in inbreeding.

Quantitative genetics of allogamous F2: an origin of randomly fertilized populations

The quantitative genetic properties are derived for the bulk F2 originating from random fertilization (RF) amongst hybrid (F1) individuals. Only its mean appears to have been derived previously, and that definition is confirmed (by another method). New general equations are found also for all genotype frequencies, allele frequencies, inbreeding coefficient, the genotypic, additive-genetic and dominance variances, and broad-sense and narrow-sense heritabilities. The assumption that such an F2 is a classical RF population is shown to be correct. Indeed, the allogamous F2 is a natural origin for the RF population. The relationships are given between precedent RF populations (parents) and subsequent RF populations following hybridization (allogamous F2). The allogamous F2 is generally inbred with respect to its parental F1, the degree depending on the hybrid's parents' allele frequencies. At the same time, it is outbred with respect to those original parents, and not inbred at all with respect to the equivalent RF population. The genotypic variance is generally more than in the F1, and likewise for heritabilities. These findings make it possible to evaluate the genetic advance from selection and hybridization. The results depend on the allele frequencies of the original parents and the degree of overdominance, but generally, selection is more advantageous than hybrid vigour.

Investigations into the Genetic Variation, Population Structure, and Breeding Systems of the Fern Asplenium trichomanes subsp. quadrivalens

The genetic structure of five populations of the tetraploid fern Asplenium trichomanes subsp. quadrivalens in northern Switzerland was analyzed. Asplenium trichomanes subsp. quadrivalens is one of the most common and most widespread ferns in Europe. In this study we have combined genetic investigations, spatial autocorrelation, and breeding experiments to investigate in detail five populations from natural rock faces. Enzyme electrophoresis revealed very low genetic variability within and among the populations. The small amount of variation was partitioned mainly among the localities, indicated by high Fst values up to 0.764. Overall means of the proportion of polymorphic loci (P=0.076), the mean number of alleles per locus (A=1.086), and the mean expected heterozygosity (H=0.018) were low compared with other ferns (e.g., Kirkpatrick et al. 1990). Very few heterozygous individuals were found. Values of the fixation index (F) were high, ranging between 0.732 and 1.000 and indicating substantial inbreeding. Spatial autocorrelation showed different patterns of substructure in populations of A. trichomanes subsp. quadrivalens with a tendency for patches in short distances (up to 1.5 m). The breeding experiments with isolated prothalli and prothalli pairs showed that a mean of 56.4% of the isolated prothalli were successful in sporophyte formation. The highest rate in one population was 83.3%. We conclude that genetic load must be low in A. trichomanes subsp. quadrivalens. Sporophyte formation was statistically more successful in the experiments with gametophyte pairs than in isolates, indicating that additional cross-fertilization occurred. The latter agreed with the occurrence of few heterozygote samples and the small number of multilocus phenotypes found in natural habitats. Asplenium trichomanes subsp. quadrivalens is shown to be a highly inbreeding taxon with the capability of single spore colonization and subsequent founding of new populations. Such features can be hypothesized to have contributed to the postglacial colonization and the widespread distribution of this taxon in Europe.

Complexities in the genetic structure of Anopheles gambiae populations in west Africa as revealed by microsatellite DNA analysis

Chromosomal forms of Anopheles gambiae, given the informal designations Bamako, Mopti, and Savannah, have been recognized by the presence or absence of four paracentric inversions on chromosome 2. Studies of karyotype frequencies at sites where the forms occur in sympatry have led to the suggestion that these forms represent species. We conducted a study of the genetic structure of populations of An. gambiae from two villages in Mali, west Africa. Populations at each site were composed of the Bamako and Mopti forms and the sibling species, Anopheles arabiensis. Karyotypes were determined for each individual mosquito and genotypes at 21 microsatellite loci determined. A number of the microsatellites have been physically mapped to polytene chromosomes, making it possible to select loci based on their position relative to the inversions used to define forms. We found that the chromosomal forms differ at all loci on chromosome 2, but there were few differences for loci on other chromosomes. Geographic variation was small. Gene flow appears to vary among different regions within the genome, being lowest on chromosome 2, probably due to hitchhiking with the inversions. We conclude that the majority of observed genetic divergence between chromosomal forms can be explained by forces that need not involve reproductive isolation, although reproductive isolation is not ruled out. We found low levels of gene flow between the sibling species Anopheles gambiae and Anopheles arabiensis, similar to estimates based on observed frequencies of hybrid karyotypes in natural populations.

Essential role of mouse telomerase in highly proliferative organs

We have investigated the role of the enzyme telomerase in highly proliferative organs in successive generations of mice lacking telomerase RNA. Late-generation animals exhibited defective spermatogenesis, with increased programmed cell death (apoptosis) and decreased proliferation in the testis. The proliferative capacity of haematopoietic cells in the bone marrow and spleen was also compromised. These progressively adverse effects coincided with substantial erosion of telomeres (the termini of eukaryotic chromosomes) and fusion and loss of chromosomes. These findings indicate an essential role for telomerase, and hence telomeres, in the maintenance of genomic integrity and in the long-term viability of high-renewal organ systems.

The exact description of living organization

The papers contributed to the discussion give an idea of the large amount of work that has been devoted to the study of the relative growth of parts and the deter­mination of the shape of the body. There is a danger that the fascination of such investigation may lead to the prosecution of studies of this sort without sufficient consideration of their objective. Why do we want to study the shapes of living organisms? Several replies no doubt spring to mind, for instance, that we make such studies in order to facilitate comparisons between organisms. This, however, presupposes that the sort of comparison that can most usefully be made is essen­tially a visual one, involving the geometric outlines of the parts, a view that can only be accepted with reservations and if its implications are understood. For some centuries the science of anatomy has grown up by the study of the visible outlines of the parts of the body. In the case of the anatomy of man, the obvious value of such studies, especially for the surgeon, has encouraged their pursuit into the most minute details. Valuable as such work undoubtedly is, biologists have long realized that it has severe disadvantages. However important it may be to know the details of the shape of any organ or part, we are not, as biologists, ultimately interested in these shapes but in the life of the organism. In the last resort any biological study must deal with the organism as a self­-preserving system—we are interested in whether and how each individual or population will continue to live. Study of the visible shape is an essential part of almost every biological study, but it is only a part. The anatomist has long ago discovered that if he is to make his science useful he must treat the shape of each structure as a reflexion of the processes going on within it. The anatomist, microscopist and biochemist can thus pursue together the study of the organism as a steady-state system, discovering the genetic, internal and external factors that maintain its balance.

Time-series analysis of seasonal changes of the O inversion polymorphism of Drosophila subobscura

We have studied seasonal variation (spring, early summer, last summer and autumn) of inversion polymorphisms of the O chromosome of Drosophila subobscura in a natural population over 15 years. The length of the study allowed us to investigate the temporal behavior (short-term seasonal changes and long-term directional trends) of the O arrangements by the powerful statistical method of time series analysis. It is shown that the O inversion polymorphisms varied on two different time scales: short-term seasonal changes repeated over the years superimposed on long-term directional trends. All the common arrangements (O3+4+7, Osr, O3+4+8) showed significant cyclic seasonal changes, and all but one of these arrangements (O3+4+7) showed significant long-term trends. Moreover, the degree of seasonality was different for different arrangements. Thus, O3+4+7 and OST showed the highest seasonality, which accounted for approximately 61 and 47% of their total variances, respectively. The seasonal changes in the frequencies of chromosome arrangements were significantly associated with the seasonal variation of the climate (temperature, rainfall, humidity and insolation). In particular, O3+4+7 and OST, the arrangements with the greatest seasonal component, showed the strongest association with all climatic factors investigated, especially to the seasonal changes of extreme temperature and humidity.

Visualization of inheritance patterns from graphic representation of additive and dominance relationships between animals

Evaluation of pedigrees of normal and affected individuals help to suggest possible patterns of inheritance. Because large numbers of individuals are involved in studies of genetic disease, classic two-dimensional family tree charts are difficult to draw. Instead, DFA plots of graduated circles, weighted by dominance relationships, inbreeding, and additive relationships between individuals can be plotted above, on, and below the diagonal. Base animals without phenotypic measurements contribute information for computation of approximate dominance relationship, inbreeding, and additive relationships, but are not explicitly in the graph. Plotting only a set of randomly selected animals for each combination of phenotypes improves the visualization effect, especially when pedigrees are large or when computer resources are limited. For deficiency of uridine monophosphate synthase and interdigital hyperplasia, DFA plots showed higher densities of additive and dominance relationships among affected animals. However, DFA plots did not show clear patterns of inheritance for heel erosion, laminitis, or sole ulcers because environmental effects were important for those traits. Grouped graduated circles also improved visualization. The function of DFA plots is comparable with statistical scatter plots that display data to help examine statistical approaches. The DFA plots serve as a first approach to evaluate genetic hypotheses before a more complex model is fit.

The Long-Term Effects of Tiger Poaching on Population Viability

Poaching tigers, primarily for their bones, has become the latest threat to the persistence of wild tiger populations throughout the world. Anecdotal information indicates the seriousness of this new threat. It is important, however, to provide a quantitative analysis of poaching as a basis for strong policy action. We therefore created a tiger simulation model to explore the effects of realistic levels of poaching on population viability. The model is an individually based, stochastic spatial model that is based on the extensive data set from Royal Chitwan National Park, Nepal. We found that as poaching continues over time, the probability of population extinction increases sigmoidally; a critical zone exists in which a small, incremental increase in poaching greatly increases the probability of extinction. The implication is that poaching may not at first be seen as a threat but could suddenly become one. Moreover, even if poaching is effectively stopped, tiger populations will still be vulnerable and could go extinct due to demographic and environmental stochasticity. Our model also shows that poaching reduces genetic variability, which could further reduce population viability due to inbreeding depression. The longer poaching is allowed to continue, the more vulnerable a population will be to these stochastic events. At currently reported rates of poaching our analysis indicates that many wild tiger populations will be extirpated during the latter half of the 1990s. Los efectos a largo plazo de la caza furtiva de tigres sobre la viabilidad poblacional.

Alternative approaches to population structure

There are three approaches to DNA identification: tectonic, halieutic and icarian, of which the tectonic is sensible, the halieutic impractical, and the icarian idiotic. The rationale and consequences of these approaches are detailed.

Estimation of inbreeding coefficients from genotypic data on multiple alleles, and application to estimation of clonality in malaria parasites

Methods for estimating probability of identity by descent (f) are derived for data on numbers of genotypes at single loci and at pairs of loci with many alleles at each locus. The methods are general, but are specifically applied to data on genotype frequencies in zygotes of the malaria parasite sampled from its mosquito host in order to find the extent of outcrossing in the parasite and the degree of clonality in populations. It is assumed that zygotes are the outcome either of gametes of the same clone, in which they are identical at all loci, or are products of two random, unrelated clones. From the estimate of f an effective number of clones per human host can also be derived. For Plasmodium falciparum from a Tanzanian village, estimates of f are 0.33 from data on zygote frequencies at two multiallelic loci, indicating that two-thirds of zygotes produce recombinant type.

Effects of various breeding strategies on diploid drone frequency and quantitative traits in a honey bee population

When selecting in a finite population of honeybees there is a conflict between gain in a quantitative trait and increasing homozygosity, and therefore the frequency of inviable diploid drones. The consequences when using different mating, import, and selection strategies on diploid drone frequency and genetic gain, was explored with Monte Carlo computer simulations.Within a closed population breeding structure, mass selection gave the highest genetic gain in the quantitative trait, but also the largest increase in percentage diploid drones and queens with unacceptably-low brood viability. Mass selection combined with truncation selection against queens having more than 15% diploid drones gave a comparable genetic gain and was the best strategy of the ones studied to avoid diploid drones. Within-family selection (one replacement per sib group) gave the least genetic gain, and a frequency of diploid drones comparable to random (no) selection. It was intermediate between mass selection and mass selection combined with viability selection concerning the frequency of diploid drones.Insemination with pooled and homogenized semen originating from all breeder queens (30), as compared to natural mating with 12 randomly-selected drones, had little effect on the genetic gain and on the overall frequency of diploid drones (10 to 15% by generation 20).The effect of opening the closed breeding population for the import of external queens every generation, by exchanging breeder queens of lowest performance with a corresponding number of new queens (5, 10and 15 out of 30), was also investigated. Under mass selection (natural mating as well as artificial insemination) the frequency of diploid drones and the proportion of queens discarded were reduced because of low brood viability. However, artificial insemination was superior to natural mating considering the latter criterion. If the imported queens were at the same genetic level for the quantitative trait under selection as the whole breeding population at that generation, or 10% better, the genetic gain was respectively slightly reduced and approximately maintained. If the imported queens were of inferior quality (equal to the initial population) the import of queens slowed genetic progress considerably.

The selection index--then, now, and for the future

When improvement is desired for several traits that may differ in variability, heritability, economic importance, and in the correlation among their phenotypes and genotypes, simultaneous multiple-trait index selection was more effective than independent culling levels or sequential selection. Such comparisons required definition of aggregate breeding value determined jointly by breeding values and economic importance of the component traits. The economic weight should approximate the partial regression of cost per unit of enterprise output value on breeding value for each trait. These can vary with production and marketing system, with performance of traits, and with breed role (i.e., paternal, maternal, or general) in crossbreeding systems. Genetic gains desired to maintain competitive ranking also may define the relative importance of traits. Because information available to estimate breeding values varies among the ages and categories of individuals under selection and because means are unknown, regressed (BLUP) predictions of trait breeding values are useful. They allow appropriate economic weights to be applied as the last step for predicting aggregate breeding values for individuals of different age classes, and they simplify choosing the proportions of selected breeders from each age class that maximize rate of change in aggregate breeding values. Inappropriate economic weights or errors in the parameters used to predict trait breeding values overestimate realized response in true aggregate breeding value.

Variance components for statistical genetics: applications in medical research to characteristics related to human diseases and health

RA Fisher introduced variance components in 1918. He synthesized Mendelian inheritance with Darwin's theory of evolution by showing that the genetic variance of a continuous trait could be decomposed into additive and non-additive components. The model can be extended to include environmental factors, interactions, covariation, and non-random mating. Identifiability depends critically on design. Methods of analysis include modelling the mean squares from a fixed effects analysis of variance, and covariance structure modelling, which can be extended to multivariate traits and has been used to study ordinal traits by reference to postulated, unmeasured, latent 'liabilities'. These methods operate on dependent observations within independent groups of the same size and structure, and therefore require balanced designs ('regular' pedigrees). A multivariate normal model handles data in its generic form, utilizes data efficiently from all members of pedigrees of unequal size or varying structure, accommodates individuals missing at random, and allows flexible modelling with tests of distributional assumptions and fit. Most analytical methods use least squares or maximum likelihood under normal theory. Robust methods, scale transformation, ascertainment, path diagrams and correlational path models (popular in behavioural genetics through addressing nonrandom mating and social interactions), 'heritability', and the contribution and limitations of statistical modelling to the 'nature-nurture' debate, are discussed.

Genetic evaluation methods for populations with dominance and inbreeding

The effect of inbreeding on mean and genetic covariance matrix for a quantitative trait in a population with additive and dominance effects is shown. This genetic covariance matrix is a function of five relationship matrices and five genetic parameters describing the population. Elements of the relationship matrices are functions of Gillois (1964) identity coefficients for the four genes at a locus in two individuals. The equivalence of the path coefficient method (Jacquard 1966) and the tabular method (Smith and Mäki-Tanila 1990) to compute the covariance matrix of additive and dominance effects in a population with inbreeding is shown. The tabular method is modified to compute relationship matrices rather than the covariance matrix, which is trait dependent. Finally, approximate and exact Best Linear Unbiased Predictions (BLUP) of additive and dominance effects are compared using simulated data with inbreeding but no directional selection. The trait simulated was affected by 64 unlinked biallelic loci with equal effect and complete dominance. Simulated average inbreeding levels ranged from zero in generation one to 0.35 in generation five. The approximate method only accounted for the effect of inbreeding on mean and additive genetic covariance matrix, whereas the exact accounted for all of the changes in mean and genetic covariance matrix due to inbreeding. Approximate BLUP, which is computable for large populations where exact BLUP is not feasible, yielded unbiased predictions of additive and dominance effects in each generation with only slightly reduced accuracies relative to exact BLUP.

Half-sib mating structures

All ways in which all matings in a population can be between half-sibs under a generalization of regular systems of inbreeding are characterized for both finite and infinite populations. A model of random half-sib mating is developed and analyzed, and the asymptotic configuration of populations subject to it is described. The classical model of half-sib mating which ensues from the standard definition of regular systems of inbreeding is only one of many ways a population can propagate by half-sib mating, and a wide range of genetic identity is possible dependent on which half-sib mating structure governs a population.

The emergence of biomathematics and the case of population dynamics: a revival of mechanical reductionism and Darwinism

The development of modern mathematical biology took place in the 1920s in three main directions: population dynamics, population genetics, and mathematical theory of epidemics. This paper focuses on the first trend which is considered the most significant. Modern mathematical theory of population dynamics is characterized by three aspects (the first two being in a somewhat critical relationship): the emergence of the mathematical modeling approach, the attempt at establishing it in a reductionist-mechanist conceptual framework, and the revival of Darwinism. The first section is devoted to the analysis of the concept of mathematical model and the second one presents an example of a mathematical model (Van der Pol's model of heartbeat) which is a good prototype of that concept. In section 3 the main trends of mathematization of biology and the cultural and scientific contexts in which they found their development are discussed. Sections 4 and 5 are devoted to the contributions of V. Volterra and A. J. Lotka, to the analysis of the differences of their scientific conceptions, and to a discussion of a case study: the priority dispute concerning the discovery of the Volterra-Lotka equations. The historical analysis developed in this paper is also intended to detect the roots of some recent trends of mathematization of biology.

The use of quantitative genetics for estimating the non-inherited and inherited contributions to metastasis formation

The contribution of both non-inherited (stochastic, random, environmental, and other non-inherited influences) and inherited factors (genetic and inherited epigenetic factors) to the variability of spontaneous lung metastasis formation in over 100 metastatic lines from each of three murine tumors was measured. The contribution of inherited and genetic sources of variability to metastasis formation was significantly greater than 0 in all cases, but only in the lines of sarcoma SANH was it the major influence on metastatic variability. In the sarcoma SA4020 and hepatocarcinoma HCA-1 lines, non-inherited factors accounted for the majority of the variation in spontaneous lung metastasis formation. A similar situation was also observed in the variability of the tumors with respect to the diameter doubling time. In conclusion, both non-inherited and genetic/inherited factors significantly influenced the formation of spontaneous metastases in the tumors examined. The significance of this finding for the cloning of metastatic genes is discussed.

A LISREL 8 model with constrained parameters for twin and adoptive families

Constrained optimization recently has been implemented in the LISREL software package, allowing formulation of parent-offspring transmission models in a simple and efficient manner. A reverse path model of parental transmission is described within the LISREL framework for application to twin and/or adoptive family data. The model incorporates genetic and environmental parameter constraints arising from assortative mating and cultural transmission. An illustration of the LISREL model is given using measures obtained from twins and parents involving fear of social criticism.

On the robustness of regular systems of inbreeding

Half-sib, first cousin, half nth cousin, and nth cousin mating systems are robust in that small deviations from the mating structure will not significantly alter the levels of genetic identity or effect qualitative distinctions between the models. Substitution of nearest kin in matings may either increase or decrease the level of homozygosity depending on the mating structure; the effect of a single error in the mating structure is not an accurate indicator of the equilibrium resulting from recurrent errors. Models of mixed half nth cousin or nth cousin mating show that the relative frequency of the lowest order inbred mating essentially determines the level of homozygosity. Any positive relative frequency of more distant matings will reduce the probability of identity by descent under half-sib or first cousin mating to less than 1.