Kyushu University Academic Staff Educational and Research Activities Database
List of Papers
Kosuke Teshima Last modified date:2019.06.20

Assistant Professor / Dynamic biology / Department of Biology / Faculty of Sciences

1. Akiko Satake, Kazutaka Kawatsu, Kosuke Teshima, Daisuke Kabeya, Qingmin Han, Field transcriptome revealed a novel relationship between nitrate transport and flowering in Japanese beech, Scientific reports, 10.1038/s41598-019-39608-1, 9, 1, 2019.12, Recent advances in molecular and genetic studies about flowering time control have been increasingly available to elucidate the physiological mechanism underlying masting, the intermittent and synchronized production of a large amount of flowers and seeds in plant populations. To identify unexplored developmental and physiological processes associated with masting, genome-wide transcriptome analysis is a promising tool, but such analyses have yet to be performed. We established a field transcriptome using a typical masting species, Japanese beech (Fagus crenata Blume), over two years, and analyzed the data using a nonlinear time-series analysis called convergent cross mapping. Our field transcriptome was found to undergo numerous changes depending on the status of floral induction and season. An integrated approach of high-throughput transcriptomics and causal inference was successful at detecting novel causal regulatory relationships between nitrate transport and florigen synthesis/transport in a forest tree species. The synergistic activation of nitrate transport and floral transition could be adaptive to simultaneously satisfy floral transition at the appropriate timing and the nitrogen demand needed for flower formation..
2. Aki Nakabayashi, Takehisa Yamakita, Takashi Nakamura, Hiroaki Aizawa, Yuko F. Kitano, Akira Iguchi, Hiroya Yamano, Satoshi Nagai, Sylvain Agostini, Kosuke Teshima, Nina Yasuda, The potential role of temperate Japanese regions as refugia for the coral Acropora hyacinthus in the face of climate change, Scientific reports, 10.1038/s41598-018-38333-5, 9, 1, 2019.12, As corals in tropical regions are threatened by increasing water temperatures, poleward range expansion of reef-building corals has been observed, and temperate regions are expected to serve as refugia in the face of climate change. To elucidate the important indicators of the sustainability of coral populations, we examined the genetic diversity and connectivity of the common reef-building coral Acropora hyacinthus along the Kuroshio Current, including recently expanded (<50 years) populations. Among the three cryptic lineages found, only one was distributed in temperate regions, which could indicate the presence of Kuroshio-associated larval dispersal barriers between temperate and subtropical regions, as shown by oceanographic simulations as well as differences in environmental factors. The level of genetic diversity gradually decreased towards the edge of the species distribution. This study provides an example of the reduced genetic diversity in recently expanded marginal populations, thus indicating the possible vulnerability of these populations to environmental changes. This finding underpins the importance of assessing the genetic diversity of newly colonized populations associated with climate change for conservation purposes. In addition, this study highlights the importance of pre-existing temperate regions as coral refugia, which has been rather underappreciated in local coastal management..
3. Natsuki Moriguchi, Kentaro Uchiyama, Ryutaro Miyagi, Etsuko Moritsuka, Aya Takahashi, Koichiro Tamura, Yoshihiko Tsumura, Kosuke M. Teshima, Hidenori Tachida, Junko Kusumi, Inferring the demographic history of Japanese cedar, Cryptomeria japonica, using amplicon sequencing, Heredity, 10.1038/s41437-019-0198-y, 2019.01, The evolution of a species depends on multiple forces, such as demography and natural selection. To understand the trajectory and driving forces of evolution of a target species, it is first necessary to uncover that species’ population history, such as past and present population sizes, subdivision and gene flow, by using appropriate genetic markers. Cryptomeria japonica is a long-lived monoecious conifer species that is distributed in Japan. There are two main lines (omote-sugi and ura-sugi), which are distinguished by apparent differences in morphological traits that may have contributed to their local adaptation. The evolution of these morphological traits seems to be related to past climatic changes in East Asia, but no precise estimate is available for the divergence time of these two lines and the subsequent population dynamics in this species. Here, we analyzed the nucleotide variations at 120 nuclear genes in 94 individuals by using amplicon sequencing in combination with high-throughput sequencing technologies. Our analysis indicated that the population on Yakushima Island, the southern distribution limit of C. japonica in Japan, diverged from the other populations 0.85 million years ago (MYA). The divergence time of the other populations on mainland Japan was estimated to be 0.32 MYA suggesting that the divergence of omote-sugi and ura-sugi might have occurred before the last glacial maximum. Although we found modest levels of gene flow between the present populations, the long-term isolation and environmental heterogeneity caused by climatic changes might have contributed to the differentiation of the lines and their local adaptation..
4. Haruna Nakamura, Kosuke Teshima, Hidenori Tachida, Effects of cyclic changes in population size on neutral genetic diversity, Ecology and Evolution, 10.1002/ece3.4436, 8, 18, 9362-9371, 2018.09, Recurrent changes in population size are often observed in nature, influencing the efficiency of selection and consequently affecting organismal evolution. Thus, it is important to know whether such changes occurred in the past history of a focal population of evolutionary interests. Here, we focused on cyclic changes in population size and investigated the distributional properties of Tajima's D and its power to distinguish a cyclic change model compared with the standard neutral model, changing the frequency and magnitude of the cyclic change. With very low or very high frequencies of the cycle, the distribution of Tajima's D was similar to that in a constant size population, as demonstrated by previous theoretical works. Otherwise, its mean was negative or positive, and its variance was smaller or larger depending on the time of sampling. The detection rate of the cyclic change against the constancy in size by Tajima's D depended on the sample size, the number of loci, and the time of sampling in addition to the frequency and amplitude of the cycle. Using sequence data of several tens of loci, the detection rate was fairly high if the frequency was intermediate and the sampling was made when population size was large; otherwise, the detection rate was not high. We also found that cyclic change could be discriminated from simple expansion or shrinkage of a population by Tajima's D only if the frequency was in a limited range and the sampling was made when the population was large..
5. Yuichiro Hiraoka, Eitaro Fukatsu, Kentaro Mishima, Tomonori Hirao, Kosuke Teshima, Miho Tamura, Miyoko Tsubomura, Taiichi Iki, Manabu Kurita, Makoto Takahashi, Atsushi Watanabe, Potential of genome-wide studies in unrelated plus trees of a coniferous species, cryptomeria japonica (japanese cedar), Frontiers in Plant Science, 10.3389/fpls.2018.01322, 9, 2018.09, A genome-wide association study (GWAS) was conducted on more than 30,000 single nucleotide polymorphisms (SNPs) in unrelated first-generation plus tree genotypes from three populations of Japanese cedar Cryptomeria japonica D. Don with genomic prediction for traits of growth, wood properties and male fecundity. Among the assessed populations, genetic characteristics including the extent of linkage disequilibrium (LD) and genetic structure differed and these differences are considered to be due to differences in genetic background. Through population-independent GWAS, several significant SNPs found close to the regions associated with each of these traits and shared in common across the populations were identified. The accuracies of genomic predictions were dependent on the traits and populations and reflected the genetic architecture of traits and genetic characteristics. Prediction accuracies using SNPs selected based on GWAS results were similar to those using all SNPs for several combinations of traits and populations. We discussed the application of genome-wide studies for C. japonica improvement..
6. Yuka Ikezaki, Yoshihisa Suyama, Beth A. Middleton, Yoshihiko Tsumura, Kosuke Teshima, Hidenori Tachida, Junko Kusumi, Inferences of population structure and demographic history for Taxodium Distichum, a coniferous tree in North America, based on Amplicon sequencing analysis, American Journal of Botany, 10.3732/ajb.1600046, 103, 11, 1937-1949, 2016.11, PREMISE OF THE STUDY: Studies of natural genetic variation can elucidate the genetic basis of phenotypic variation and the past population structure of species. Our study species, Taxodium distichum, is a unique conifer that inhabits the flood plains and swamps of North America. Morphological and ecological differences in two varieties, T. distichum var. distichum (bald cypress) and T. distichum var. imbricarium (pond cypress), are well known, but little is known about the level of genetic differentiation between the varieties and the demographic history of local populations. METHODS: We analyzed nucleotide polymorphisms at 47 nuclear loci from 96 individuals collected from the Mississippi River Alluvial Valley (MRAV), and Gulf Coastal populations in Texas, Louisiana, and Florida using high-throughput DNA sequencing. Standard population genetic statistics were calculated, and demographic parameters were estimated using a composite-likelihood approach. KEY RESULTS: Taxodium distichum in North America can be divided into at least three genetic groups, bald cypress in the MRAV and Texas, bald cypress in Florida, and pond cypress in Florida. The levels of genetic differentiation among the groups were low but significant. Several loci showed the signatures of positive selection, which might be responsible for local adaptation or varietal differentiation. CONCLUSIONS: Bald cypress was genetically differentiated into two geographical groups, and the boundary was located between the MRAV and Florida. This differentiation could be explained by population expansion from east to west. Despite the overlap of the two varieties’ ranges, they were genetically differentiated in Florida. The estimated demographic parameters suggested that pond cypress split from bald cypress during the late Miocene..
7. Wei Lun Ng, Yoshitaka Onishi, Nobuyuki Inomata, Kosuke M. Teshima, Hung Tuck Chan, Shigeyuki Baba, Suchitra Changtragoon, Iskandar Z. Siregar, SZMIDT ALFRED EDWARD, Closely related and sympatric but not all the same: genetic variation of Indo-West Pacific Rhizophora mangroves across the Malay Peninsula, 16, 137-150, 2015.02.
8. Wei Lun Ng, Yoshitaka Onishi, Nobuyuki Inomata, Kosuke Teshima, Hung Tuck Chan, Shigeyuki Baba, Suchitra Changtragoon, Iskandar Z. Siregar, Alfred Szmidt, Closely related and sympatric but not all the same
genetic variation of Indo-West Pacific Rhizophora mangroves across the Malay Peninsula, Conservation Genetics, 10.1007/s10592-014-0647-3, 16, 1, 137-150, 2014.01, Members of the mangrove genus Rhizophora represent the most commonly occurring and highly valued species in the Indo-West Pacific region. However, to date, few studies have been directed towards the understanding of their genetic variation. The levels and patterns of genetic variation at chloroplast and nuclear gene regions were studied in R. apiculata, R. mucronata, and R. stylosa sampled from Southeast Asia and Japan. All three species were characterized by low intraspecific genetic variation and a deficiency of heterozygotes in populations within the region, consistent with findings in studies on other mangrove species. Rhizophora mucronata and R. stylosa were also found to be more closely related than any of them with R. apiculata. During the Last Glacial Maximum, sea levels dropped to 120 m below the current levels, exposing part of the Sunda Shelf that became a barrier that limited gene flow between marine species living in the Pacific and Indian Oceans. Today, the Malay Peninsula is thought to still serve as a barrier to gene flow between populations occurring on its coasts. The pattern of genetic differentiation of R. apiculata supports the hypothesis of the land barrier effect of the Malay Peninsula, but such patterns were not found in R. mucronata and R. stylosa. Our findings suggest that R. apiculata, R. mucronata, and R. stylosa have different demographic histories despite being closely related and having sympatric distributions today. Furthermore, all three species appear to have high levels of inbreeding due to limited pollen and propagule dispersal, and that both these factors contributed to population differentiation..
9. Chie Urashi, Kosuke Teshima, Sumiko Minobe, Osamu Koizumi, Nobuyuki Inomata, Inferences of evolutionary history of a widely distributed mangrove species, Bruguiera gymnorrhiza, in the Indo-West Pacific region, Ecology and Evolution, 10.1002/ece3.624, 3, 7, 2251-2261, 2013.07, Inference of genetic structure and demographic history is fundamental issue in evolutionary biology. We examined the levels and patterns of genetic variation of a widespread mangrove species in the Indo-West Pacific region, Bruguiera gymnorrhiza, using ten nuclear gene regions. Genetic variation of individual populations covering its distribution range was low, but as the entire species it was comparable to other plant species. Genetic differentiation among the investigated populations was high. They could be divided into two genetic clusters: the West and East clusters of the Malay Peninsula. Our results indicated that these two genetic clusters derived from their ancestral population whose effective size of which was much larger compared to the two extant clusters. The point estimate of speciation time between B. gymnorrhiza and Bruguiera sexangula was two times older than that of divergence time between the two clusters. Migration from the West cluster to the East cluster was much higher than the opposite direction but both estimated migration rates were low. The past Sundaland and/or the present Malay Peninsula are likely to prevent gene flow between the West and East clusters and function as a geographical or land barrier..
10. Iwanaga, Hiroko, Kosuke Teshima, Khatab, Ismael A., Inomata, Nobuyuki, Finkeldey, Reiner, Siregar, Iskandar Z., Siregar, Ulfah J., ALFRED EDWARD SZMIDT, Population structure and demographic history of a tropical lowland rainforest tree species Shorea parvifolia (Dipterocarpaceae) from Southeastern Asia, ECOLOGY AND EVOLUTION, 10.1002/ece3.284, 2, 7, 1663-1675, 2012.07, Distribution of tropical rainforests in Southeastern Asia has changed over geo-logical time scale, due to movement of tectonic plates and/or global climatic changes. Shorea parvifolia is one of the most common tropical lowland rainforest tree species in Southeastern Asia. To infer population structure and demographic history of S. parvifolia, as indicators of temporal changes in the distribution and extent of tropical rainforest in this region, we studied levels and patterns of nucleotide polymorphism in the following five nuclear gene regions: GapC, GBSSI, PgiC, SBE2, and SODH. Seven populations from peninsular Malaysia, Sumatra, and eastern Borneo were included in the analyses. STRUCTURE analysis revealed that the investigated populations are divided into two groups: Sumatra-Malay and Borneo. Furthermore, each group contained one admixed population. Under isolation with migration model, divergence of the two groups was estimated to occur between late Pliocene (2.6 MYA) and middle Pleistocene (0.7 MYA). The log-likelihood ratio tests of several demographic models strongly supported model with population expansion and low level of migration after divergence of the Sumatra-Malay and Borneo groups. The inferred demographic history of S. parvifolia suggested the presence of a scarcely forested land bridge on the Sunda Shelf during glacial periods in the Pleistocene and predominance of tropical lowland rainforest at least in Sumatra and eastern Borneo.
11. Teshima KM, Innan H, The coalescent with selection on copy number variants, Genetics, 190, 3, 1077-86, 2012.05, We develop a coalescent-based simulation tool to generate patterns of single nucleotide polymorphisms (SNPs) in a wide region encompassing both the original and duplicated genes. Selection on the new duplicated copy and interlocus gene conversion between the two copies are incorporated. This simulation enables us to explore how selection on duplicated copies affects the pattern of SNPs. The fixation of an advantageous duplicated copy causes a strong reduction in polymorphism not only in the duplicated copy but also in its flanking regions, which is a typical signature of a selective sweep by positive selection. After fixation, polymorphism gradually increases by accumulating neutral mutations and eventually reaches the equilibrium value if there is no gene conversion. When gene conversion is active, the number of SNPs in the duplicated copy quickly increases by transferring SNPs from the original copy; therefore, the time when we can recognize the signature of selection is decreased. Because this effect of gene conversion is restricted only to the duplicated region, more power to detect selection is expected if a flanking region to the duplicated copy is used..
12. Kosuke Teshima, Hideki Innan, The coalescent with selection on copy number variants, Genetics, 10.1534/genetics.111.135343, 190, 3, 1077-1086, 2012.03, We develop a coalescent-based simulation tool to generate patterns of single nucleotide polymorphisms (SNPs) in a wide region encompassing both the original and duplicated genes. Selection on the new duplicated copy and interlocus gene conversion between the two copies are incorporated. This simulation enables us to explore how selection on duplicated copies affects the pattern of SNPs. The fixation of an advantageous duplicated copy causes a strong reduction in polymorphism not only in the duplicated copy but also in its flanking regions, which is a typical signature of a selective sweep by positive selection. After fixation, polymorphism gradually increases by accumulating neutral mutations and eventually reaches the equilibrium value if there is no gene conversion. When gene conversion is active, the number of SNPs in the duplicated copy quickly increases by transferring SNPs from the original copy; therefore, the time when we can recognize the signature of selection is decreased. Because this effect of gene conversion is restricted only to the duplicated region, more power to detect selection is expected if a flanking region to the duplicated copy is used..
13. Kosuke Teshima, Hideki Innan, Mbs
Modifying Hudson's ms software to generate samples of DNA sequences with a biallelic site under selection, BMC Bioinformatics, 10.1186/1471-2105-10-166, 10, 2009.05, Background: The pattern of single nucleotide polymorphisms, or SNPs, contains a tremendous amount of information with respect to the mechanisms of the micro-evolutionary process of a species. The inference of the roles of these mechanisms, including natural selection, relies heavily on computer simulations. A coalescent simulation is extremely powerful in generating a large number of samples of DNA sequences from a population (species) when all mutations are neutral, and Hudson's ms software is frequently used for this purpose. However, it has been difficult to incorporate natural selection into the coalescent framework. Results: We herein present a software applicationto generate samples of DNA sequences when there is a biallelic site targeted by selection. This software application, referred to as mbs, is developed by modifying Hudson's ms. The mbs software is so flexible that it can incorporate any arbitrary histories of population size changes and any mode of selection as long as selection is operating on a biallelic site. Conclusion: mbs provides opportunities to investigate the effect of any mode of selection on the pattern of SNPs under various demography..
14. Yasuyuki Takahashi, Kosuke Teshima, Shuji Yokoi, Hideki Innan, Ko Shimamoto, Variations in Hd1 proteins, Hd3a promoters, and Ehd1 expression levels contribute to diversity of flowering time in cultivated rice, Proceedings of the National Academy of Sciences of the United States of America, 10.1073/pnas.0812092106, 106, 11, 4555-4560, 2009.03, Rice is a facultative short-day plant, and molecular genetic studies have identified the major genes involved in short-day flowering. However, the molecular mechanisms promoting the diversity of flowering time in cultivated rice are not known. We used a core collection of 64 rice cultivars that represent the genetic diversity of 332 accessions from around the world and studied the expression levels and polymorphisms of 6 genes in the short-day flowering pathway. The RNA levels of Heading date 3a (Hd3a), encoding a floral activator, are highly correlated with flowering time, and there is a high degree of polymorphism in the Heading date 1 (Hd1) protein, which is a major regulator of Hd3a expression. Functional and nonfunctional alleles of Hd1 are associated with early and late flowering, respectively, suggesting that Hd1 is a major determi- nantof variation in flowering time of cultivated rice. We also found that the type of Hd3a promoter and the level of Ehd1 expression contribute to the diversity in flowering time and Hd3a expression level. We evaluated the contributions of these 3 factors by a statistical analysis using a simple linear model, and the results supported our experimental observations..
15. Ran Blekhman, Orna Man, Leslie Herrmann, Adam R. Boyko, Amit Indap, Carolin Kosiol, Carlos D. Bustamante, Kosuke Teshima, Molly Przeworski, Natural Selection on Genes that Underlie Human Disease Susceptibility, Current Biology, 10.1016/j.cub.2008.04.074, 18, 12, 883-889, 2008.06, What evolutionary forces shape genes that contribute to the risk of human disease? Do similar selective pressures act on alleles that underlie simple versus complex disorders [1-3]? Answers to these questions will shed light onto the origin of human disorders (e.g., [4]) and help to predict the population frequencies of alleles that contribute to disease risk, with important implications for the efficient design of mapping studies [5-7]. As a first step toward addressing these questions, we created a hand-curated version of the Mendelian Inheritance in Man database (OMIM). We then examined selective pressures on Mendelian-disease genes, genes that contribute to complex-disease risk, and genes known to be essential in mouse by analyzing patterns of human polymorphism and of divergence between human and rhesus macaque. We found that Mendelian-disease genes appear to be under widespread purifying selection, especially when the disease mutations are dominant (rather than recessive). In contrast, the class of genes that influence complex-disease risk shows little signs of evolutionary conservation, possibly because this category includes targets of both purifying and positive selection..
16. Kosuke Teshima, Hideki Innan, Neofunctionalization of duplicated genes under the pressure of gene conversion, Genetics, 10.1534/genetics.107.082933, 178, 3, 1385-1398, 2008.03, Neofunctionalization occurs when a neofunctionalized allele is fixed in one of duplicated genes. This is a simple fixation process if duplicated genes accumulate mutations independently. However, the process is very complicated when duplicated genes undergo concerted evolution by gene conversion. Our simulations demonstrate that the process could be described with three distinct stages. First, a newly arisen neofunctionalized allele increases in frequency by selection, but gene conversion prevents its complete fixation. These two factors (selection and gene conversion) that work in opposite directions create an equilibrium, and the time during which the frequency of the neofunctionalized allele drifts around the equilibrium value is called the temporal equilibrium stage. During this temporal equilibrium stage, it is possible that gene conversion is inactivated by mutations, which allow the complete fixation of the neofunctionalized allele. And then, permanent neofunctionalization is achieved. This article develops basic population genetics theories on the process to permanent neofunctionalization under the pressure of gene conversion. We obtain the probability and time that the frequency of a newly arisen neofunctionalized allele reaches the equilibrium value. It is also found that during the temporal equilibrium stage, selection exhibits strong signature in the divergence in the DNA sequences between the duplicated genes. The spatial distribution of the divergence likely has a peak around the site targeted by selection. We provide an analytical expression of the pattern of divergence and apply it to the human red- and greenopsin genes. The theoretical prediction well fits the data when we assume that selection is operating for the two amino acid differences in exon 5, which are believed to account for the major part of the functional difference between the red and green opsins..
17. Kosuke Teshima, Graham Coop, Molly Przeworski, How reliable are empirical genomic scans for selective sweeps?, Genome Research, 10.1101/gr.5105206, 16, 6, 702-712, 2006.06, The beneficial substitution of an allele shapes patterns of genetic variation at linked sites. Thus, in principle, adaptations can be mapped by looking for the signature of directional selection in polymorphism data. In practice, such efforts are hampered by the need for an accurate characterization of the demographic history of the species and of the effects of positive selection. In an attempt to circumvent these difficulties, researchers are increasingly taking a purely empirical approach, in which a large number of genomic regions are ordered by summaries of the polymorphism data, and loci with extreme values are considered to be likely targets of positive selection. We evaluated the reliability of the "empirical" approach, focusing on applications to human data and to maize. To do so, we considered a coalescent model of directional selection in a sensible demographic setting, allowing for selection on standing variation as well as on a new mutation. Our simulations suggest that while empirical approaches will identify several interesting candidates, they will also miss many - in some cases, most - loci of interest. The extent of the trade-off depends on the mode of positive selection and the demographic history of the population. Specifically, the false-discovery rate is higher when directional selection involves a recessive rather than a co-dominant allele, when it acts on a previously neutral rather than a new allele, and when the population has experienced a population bottleneck rather than maintained a constant size. One implication of these results is that, insofar as attributes of the beneficial mutation (e.g., the dominance coefficient) affect the power to detect targets of selection, genomic scans will yield an unrepresentative subset of loci that contribute to adaptations..
18. Kosuke Teshima, Molly Przeworski, Directional positive selection on an allele of arbitrary dominance, Genetics, 10.1534/genetics.105.044065, 172, 1, 713-718, 2006.01, Most models of positive directional selection assume codominance of the beneficial allele. We examine the importance of this assumption by implementing a coalescent model of positive directional selection with arbitrary dominance. We find that, for a given mean fixation time, a beneficial allele has a much weaker effect on diversity at linked neutral sites when the allele is recessive..
19. Kosuke Teshima, Hideki Innan, The Effect of Gene Conversion on the Divergence between Duplicated Genes, Genetics, 10.1534/genetics.166.3.1553, 166, 3, 1553-1560, 2004.03, Nonindependent evolution of duplicated genes is called concerted evolution. In this article, we study the evolutionary process of duplicated regions that involves concerted evolution. The model incorporates mutation and gene conversion: the former increases d, the divergence between two duplicated regions, while the latter decreases d. It is demonstrated that the process consists of three phases. Phase I is the time until d reaches its equilibrium value, d6. In phase II d fluctuates around d0, and d increases again in phase III. Our simulation results demonstrate that the length of concerted evolution (i.e., phase II) is highly variable, while the lengths of the other two phases are relatively constant. It is also demonstrated that the length of phase II approximately follows an exponential distribution with mean τ, which is a function of many parameters including gene conversion rate and the length of gene conversion tract. On the basis of these findings, we obtain the probability distribution of the level of divergence between a pair of duplicated regions as a function of time, mutation rate, and T. Finally, we discuss potential problems in genomic data analysis of duplicated genes when it is based on the molecular clock but concerted evolution is common..
20. Kosuke Teshima, Fumio Tajima, The Effect of Migration during the Divergence, Theoretical Population Biology, 10.1006/tpbi.2002.1580, 62, 1, 81-95, 2002, The mean and variance of the number of nucleotide differences were obtained when the ancestral population diverged with migration. The number of nucleotide differences obtained indicates that not only the migration rate but also the period of migration has influence on a population structure. According to the migration rate and the period of migration, populations behave approximately as a single unit, diverged and isolated populations, two populations under equilibrium, or none of them. When Σm(t) is about one, the variance of the number of nucleotide differences becomes large, where Σm(t) is the sum of the migration rate for the period of migration. The distribution of the estimated divergence time was also obtained using computer simulations. It was found that the divergence time can be explained by Σm(t). That is, the divergence time is mostly estimated as the time when Σm(t) is less than 1..