Sam Karlin and multi-locus population genetics

Between 1967 and 1982, Sam Karlin made fundamental contributions to many areas of deterministic population genetic theory. This remembrance focuses on his work in multi-locus population genetics, primarily on the interaction between genotypic selection and the rate of recombination.     

Sam Karlin and the stochastic theory of evolutionary population genetics

Sam Karlin’s role in the development of the stochastic theory of evolutionary population genetics is outlined, together with his work in developing BLAST theory.     

On a simple epidemic model with a heterogeneous infective population

This paper is concerned with a generalization of the simple epidemic model in which the infective population is partitioned intom classes, each of specific infectiousness. Attention is restricted, however, to the case where all the meeting rates between two individuals are equal to each other. Both deterministic and stochastic versions are examined. In either case the development in time of the epidemic process is investigated by exploiting a connection with the standard simple epidemic model. Finally, it is shown that the technique used also applies to a similar model for the spread of information.     

Inference of population structure using genetic markers and a Bayesian model averaging approach for clustering.

The analysis of the structure of populations on the basis of genetic data is essential in population genetics. It is used, for instance, to study the evolution of species or to correct for population stratification in association studies. These genetic data, normally based on DNA polymorphisms, may contain irrelevant information that biases the inference of population structure. In this paper we adapt a recently proposed algorithm, named multistart EMA, to be used in the inference of population structure. This algorithm is able to deal with irrelevant information when obtaining the (probabilistic) population partition. Additionally, we present a maker selection test able to obtain the most relevant markers to retrieve that population partition. The proposed algorithm is compared with the widely used STRUCTURE software on the basis of the F(ST) metric and the log-likelihood score. It is shown that the proposed algorithm improves the obtention of the population structure. Moreover, information about relevant markers obtained by the multi-start EMA can be used to improve the results obtained by other methods, correct for population stratification or even also reduce the economical cost of sequencing new samples. The software presented in this paper is available online at http://www.sc.ehu.es/ccwbayes/members/guzman.     

On periodic cohort solutions of a size-structured population model

 We consider a size-structured population model with discontinuous reproduction and feedback through the environmental variable ‘substrate’. The model admits solutions with finitely many cohorts and in that case the problem is described by a system of ODEs involving a bifurcation parameter β. Existence of nontrivial periodic n-cohort solutions is investigated. Moreover, we discuss the question whether n cohorts (n≧2) with small size differences will tend to a periodic one-cohort solution as t→∞. Received 16 March 1995; received in revised form 7 January 1997     

Functional repurposing revealed by comparing S. pombe and S. cerevisiae genetic interactions

We present a genetic interaction map of pairwise measures including ～40% of nonessential S. pombe genes. By comparing interaction maps for fission and budding yeast, we confirmed widespread conservation of genetic relationships within and between complexes and pathways. However, we identified an important subset of orthologous complexes that have undergone functional "repurposing": the evolution of divergent functions and partnerships. We validated three functional repurposing events in S. pombe and mammalian cells and discovered that (1) two lumenal sensors of misfolded ER proteins, the kinase/nuclease Ire1 and the glucosyltransferase Gpt1, act together to mount an ER stress response; (2) ESCRT factors regulate spindle-pole-body duplication; and (3) a membrane-protein phosphatase and kinase complex, the STRIPAK complex, bridges the cis-Golgi, the centrosome, and the outer nuclear membrane to direct mitotic progression. Each discovery opens new areas of inquiry and-together-have implications for model organism-based research and the evolution of genetic systems.     

Identification of genetic polymorphisms of CYP2S1 in a Finnish Caucasian population

CYP2S1 is a recently discovered member of the cytochrome P450 (CYP) gene superfamily. Interestingly, even though the DNA sequence identifies it as the sole member of the new CYP2S family, CYP2S1 exhibits many features typical to CYP1 family members, e.g. dioxin-inducibility mediated by the aryl hydrocarbon receptor (AHR) and the aryl hydrocarbon receptor nuclear translocator (ARNT). In addition, CYP2S1 metabolises some aromatic hydrocarbons as well as cellular substances. These characteristics, together with a wide extrahepatic tissue distribution, suggest that CYP2S1 may have an important role in both exogenous and endogenous metabolism. This is the first study characterising CYP2S1 alleles and naming them with the recommended CYP allele nomenclature. We used denaturing gradient gel electrophoresis (DGGE) and direct sequencing to investigate genetic variation of CYP2S1 in 100 male Finnish Caucasians. Those exons in which variation was found were examined in subsequent 100 subjects. The coding region of all of the nine exons, as well as a 449 bp fragment of the proximal promoter region, was analysed. This systematic investigation revealed eight single nucleotide polymorphisms (SNPs), which comprise nine different variant alleles (haplotypes), in addition to the wild-type allele. Seven of the SNPs occurred in the protein-coding areas and one in the proximal 3' untranslated region (3'UTR). Two of these sequence variations (10347C > T and 13106C > T) result in non-conservative amino acid substitutions, i.e. Arg380Cys and Pro466Leu, respectively. The respective allelic variants, CYP2S1*2 ([10347C > T]) and CYP2S1*3 (13106C > T; 13255A > G]), occurred in our study population at frequencies of 0.50 and 3.75%, respectively. The most common of the variant alleles was CYP2S1*1H (23.8%), harbouring a 13255A > G substitution located in the 3'UTR.     

Identification of spatial genetic boundaries using a multifractal model in human population genetics

There are two purposes in displaying spatial genetic structure. One is that a visual representation of the variation of the genetic variable should be provided in the contour map. The other is that spatial genetic structure should be reflected by the patterns or the gradients with genetic boundaries in the map. Nevertheless, most conventional interpolation methods, such as Cavalli-Sforza's method in genography, inverse distance-weighted methods, and the Kriging technique, focus only on the first primary purpose because of their arbitrary thresholds marked on the maps. In this paper we present an application of the contour area multifractal model (CAMM) to human population genetics. The method enables the analysis of the geographic distribution of a genetic marker and provides an insight into the spatial and geometric properties of obtained patterns. Furthermore, the CAMM may overcome some of the limitations of other interpolation techniques because no arbitrary thresholds are necessary in the computation of genetic boundaries. The CAMM is built by establishing power law relationships between the area A (> or =rho) in the contour map and the value p itself after plotting these values on a log-log graph. A series of straight-line segments can be fitted to the points on the log-log graph, each representing a power law relationship between the area A (> or =rho) and the cutoff genetic variable value for rho in a particular range. These straight-line segments can yield a group of cutoff values, which can be identified as the genetic boundaries that can classify the map of genetic variable into discrete genetic zones. These genetic zones usually correspond to spatial genetic structure on the landscape. To provide a better understanding of the interest in the CAMM approach, we analyze the spatial genetic structures of three loci (ABO, HLA-A, and TPOX) in China using the CAMM. Each synthetic principal component (SPC) contour map of the three loci is created by using both Han and minority groups data together. These contour maps all present an obvious geographic diversity, which gradually increases from north to south, and show that the genetic differences among populations in different districts of the same nationality are greater than those among different nationalities of the same district. It is surprising to find that both the value of p and the fractal dimension alpha have a clear north to south gradient for each locus, and the same clear boundary between southern and northern Asians in each contour map is still seen in the zone of the Yangtze River, although substantial population migrations have occurred because of war or famine in the last 2,000 or 3,000 years. A clear genetic boundary between Europeans and Asians in each contour map is still seen in northwestern China with a small value of alpha, although the genetic gradient caused by gene flow between Europeans and Asians has tended to show expansion from northwestern China. From the three contour maps another interesting result can be found: The values of alpha north of the Yangtze River are generally less than those south of the Yangtze River. This indicates that the genetic differences among the populations north of the Yangtze River are generally smaller than those in populations south of the Yangtze River.     

The genetic epidemiology of leprosy in a Brazilian population.

Data on leprosy patients have been obtained from the Dispensary of Leprosy of Campinas, São Paulo, where records on practically all cases of leprosy in the Campinas area during the period 1960-70 are filed. The whole sample comprises 10,886 individuals, distributed among 1,568 families. Complex segregation analysis was utilized to determine the nature of the genetic factors that may operate on leprosy and its subtypes. The results suggest the presence of a recessive major gene controlling susceptibility to leprosy per se, with frequency of approximately .05, although there are deviations from the expected Mendelian segregation proportions. Possible etiologic heterogeneity was examined by considering two subtypes separately: for lepromatous leprosy and tuberculoid leprosy there are suggestions for a segregating major effect; however, Mendelian transmission could not be demonstrated in either case. Therefore, there is no evidence to suggest unique genetic determinants for leprosy subtypes.     

The probability distribution under a population divergence model of the number of genetic founding lineages of a population or species

The composition of genetic variation in a population or species is shaped by the number of events that led to the founding of the group. We consider a neutral coalescent model of two populations, where a derived population is founded as an offshoot of an ancestral population. For a given locus, using both recursive and nonrecursive approaches, we compute the probability distribution of the number of genetic founding lineages that have given rise to the derived population. This number of genetic founding lineages is defined as the number of ancestral individuals that contributed at the locus to the present-day derived population, and is formulated in terms of interspecific coalescence events. The effects of sample size and divergence time on the probability distribution of the number of founding lineages are studied in detail. For 99.99% of the loci in the derived population to each have one founding lineage, the two populations must be separated for 9.9N generations. However, only approximately 0.87N generations must pass since divergence for 99.99% of the loci to have <6 founding lineages. Our results are useful as a prior expectation on the number of founding lineages in scenarios that involve the evolution of one population from the splitting of an ancestral group, such as in the colonization of islands, the formation of polyploid species, and the domestication of crops and livestock from wild ancestors.     

Transposable element-medicated evolution of sex: A population genetic model

For a population made up of individuals capable of sexual as well as asexual modes of reproduction, conditions for the spread of a transposable element are explored using a one-locus, two-haplotype model. The analysis is then extended to include the possibility that the transposable element can modulate the probability of sexual reproduction, thus casting Hickey’s (1982,Genetics 101: 519–531) suggestion in a population genetics framework. The model explicitly includes the cost of sexual reproduction, fitness disadvantage to the transposable element, probability of transposition, and the predisposition for sexual reproduction in the presence and absence of the transposable element. The model predicts several kinds of outcome, including initial frequency dependence and stable polymorphism. More importantly, it is seen that for a wide range of parameter values, the transposable element can go to fixation. Therefore it is able to convert the population from a predominantly asexual to a predominantly sexual mode of reproduction. Viewed in conjunction with recent results implicating short stretches of apparently non-coding DNA in sex determination (McCoubreyet al. 1988,Science 242: 1146–1151), the model hints at the important role this mechanism could have played in the evolution of sexuality.     

A population genetic model of selection that maintains specific trinucleotides at a specific location

Summary Periodic appearances of specific trinucleotides along the DNA sequence have been reported in the chicken core DNA and the phenomenon has been suggested to be related to the supercoiling of DNA around nucleosomes. A population genetic model is constructed in which selection is operating to maintain specific trinucleotides at a specific location on the DNA sequence. Assuming low mutation rates, equilibrium probabilities of the appearances of respective trinucleotides were computed. Vague patterns appeared if the product of the effective size and the selection coefficient was 0.1–2.0. The genetic load and substitution rates in the equilibrium state were also computed. When the model was applied to the chicken DNA data, the product of the effective size and the selection coefficient was estimated to be 0.1–0.2. With this intensity of selection, the substitution rate was hardly different from that in the case without selection. However, the genetic load became fairly large. Considering the large number of times that DNA coils about nucleosomes, the number of trinucleotide sites must be very large, and thus the total load might be too large. Epistasis among these sites to reduce the total load is suggested to exist if selection is responsible for this periodic pattern observed in the chicken core DNA.     

An approximate likelihood for genetic data under a model with recombination and population splitting

We describe a new approximate likelihood for population genetic data under a model in which a single ancestral population has split into two daughter populations. The approximate likelihood is based on the ‘Product of Approximate Conditionals’ likelihood and ‘copying model’ of Li and Stephens [Li, N., Stephens, M., 2003. Modeling linkage disequilibrium and identifying recombination hotspots using single-nucleotide polymorphism data. Genetics 165 (4), 2213–2233]. The approach developed here may be used for efficient approximate likelihood-based analyses of unlinked data. However our copying model also considers the effects of recombination. Hence, a more important application is to loosely-linked haplotype data, for which efficient statistical models explicitly featuring non-equilibrium population structure have so far been unavailable. Thus, in addition to the information in allele frequency differences about the timing of the population split, the method can also extract information from the lengths of haplotypes shared between the populations. There are a number of challenges posed by extracting such information, which makes parameter estimation difficult. We discuss how the approach could be extended to identify haplotypes introduced by migrants.     

Weedy adaptation in Setaria spp. II. Genetic diversity and population genetic structure in S. glauca,S. geniculata,and S. faberii (Poaceae)

Setaria glauca (yellow foxtail), S. geniculata (knotroot foxtail), and S. faberii (giant foxtail) are important cosmopolitan weeds of temperate and tropical regions. Isozyme markers were used to investigate genetic diversity and population genetic structure in 94 accessions of yellow foxtail, 24 accessions of knotroot foxtail, and 51 accessions of giant foxtail, collected mainly from North America and Eurasia. Giant foxtail populations were nearly identical genetically, with only one population exhibiting isozyme polymorphism. Yellow and knotroot foxtail populations had low genetic diversity but marked population differentiation. Although the latter species are similar morphologically, they are readily distinguished electrophoretically, with Nei's genetic identity being 0.83. In both species, genetic divergence between accessions from Eurasia and North America was minimal. Populations from the native ranges had slightly greater genetic diversity than those from the respective introduced ranges. Yellow foxtail populations genetically clustered into Asian, European, and North American groups. Within North America, yellow foxtail populations from Iowa were genetically diverse whereas populations collected from other North American locations were nearly monomorphic for the same multilocus genotype. Knotroot foxtail populations in North America were genetically differentiated into northern and southern groups on either side of a line at ≈37° N latitude. No genetic patterning was evident in knotroot foxtail populations from Eurasia. In both yellow and knotroot foxtail, patterns of population genetic structure have been influenced by several factors, including genetic bottlenecks associated with founder events, genetic drift, and natural selection.     

Construction of a genetic linkage map of the model legume Lotus japonicus using an intraspecific F2 population.

Among leguminous plants, the model legume Lotus japonicus (Regel) Larsen has many biological and genetic advantages. We have developed a genetic linkage map of L. japonicus based on amplified fragment length polymorphism (AFLP), simple sequence repeat polymorphism (SSRP) and derived cleaved amplified polymorphic sequence (dCAPS). The F2 mapping population used was derived from a cross between two L. japonicus accessions Gifu B-129 and Miyakojima MG-20. These parental accessions showed remarkable cytological differences, particularly with respect to size and morphology of chromosomes 1 and 2. Using fluorescence in situ hybridization (FISH) with BAC clones from Gifu B-129 and TAC (Transformation-competent Artificial Chromosome) clones from Miyakojima MG-20, a reciprocal translocation was found to be responsible for the cytological differences between chromosomes 1 and 2. The borders of the translocations were identified by FISH and by alignment toward the L. filicaulis x L. japonicus Gifu B-129 linkage map. The markers from the main translocated region were located on linkage groups 1 and 2 of the two accessions, Gifu B-129 and Miyakojima MG-20, respectively. The framework of the linkage map was constructed based on codominant markers, and then dominant markers were integrated separately in each linkage group of the parents. The resulting linkage groups correspond to the six pairs of chromosomes of L. japonicus and consist of 287 markers with 487.3 cM length in Gifu B-129 and 277 markers with 481.6 cM length in Miyakojima MG-20. The map and marker information is available through the World Wide Web at http://www.kazusa.or.jp/lotus/.