- Professor, Ecology and Evolutionary Biology
- Adjunct Professor, Animal and Comparative Biomedical Sciences
- Professor, Public Health
- Adjunct Professor, Molecular and Cellular Biology
- Professor, BIO5 Institute
- Professor, Plant Sciences
- Professor, Applied Mathematics - GIDP
- Professor, Entomology / Insect Science - GIDP
- Professor, Genetics - GIDP
- Professor, Statistics-GIDP
- Chapman Lecture in Animal Breeding
- University of Wisconsin, Spring 2019
- College of Science Career Teaching Award
- Fall 2013
No activities entered.
Fundament Of EvolutionECOL 600A (Spring 2021)
Introductory Biology IIECOL 182R (Spring 2021)
GeneticsECOL 320 (Fall 2020)
GeneticsECOL 320H (Fall 2020)
Introductory Biology IIECOL 182R (Fall 2020)
GeneticsECOL 320 (Summer I 2020)
Fundament Of EvolutionECOL 600A (Spring 2020)
Introductory Biology IIECOL 182R (Spring 2020)
GeneticsECOL 320 (Fall 2019)
GeneticsECOL 320H (Fall 2019)
Introductory Biology IIECOL 182R (Fall 2019)
Fundament Of EvolutionECOL 600A (Spring 2019)
Introductory Biology IIECOL 182R (Spring 2019)
GeneticsECOL 320 (Fall 2018)
GeneticsECOL 320H (Fall 2018)
Introductory Biology IIECOL 182R (Fall 2018)
Fundament Of EvolutionECOL 600A (Spring 2018)
Introductory Biology IIECOL 182R (Spring 2018)
GeneticsECOL 320 (Fall 2017)
GeneticsECOL 320H (Fall 2017)
Introductory Biology IIECOL 182R (Fall 2017)
Introductory Biology IIECOL 182R (Spring 2017)
Introductory Biology IIECOL 182R (Spring 2016)
- Walsh, J. B. (2017). Commentary: Fisher 1918: the foundation of the genetics and analysis of complex traits.. International Journal of Epidemiology:, dyx12, dyx12.
- Walsh, J. B. (2017). Crops can be strong and sensitive. Nature Plants, 3, 694.
- Walsh, B. (2014). Special issues on advances in quantitative genetics: Introduction. Heredity, 112(1), 1-3.
- Xie, S., Chen, J., & Walsh, B. (2014). Genetic mapping of sterile genes with epistasis in backcross designs. Heredity, 112(2), 165-171.More infoAbstract: The mapping of sterile genes is an essential issue, which should be solved for the investigation of sterility mechanism in wide hybridization of plants. However, the methods formerly developed cannot address the problem of mapping sterile loci with epistasis. In this study, we developed a new method to map sterile genes with epistasis in wide hybridizations of plants using a backcross design. The maximum likelihood method was used to estimate the parameters of recombination fractions and effects of sterile genes, and the convergent results of these parameters were obtained using the expectation maximization (EM) algorithm. The application and efficiency of this method were tested and demonstrated by a set of simulated data and real data analysis. Results from the simulation experiments showed that the method works well for simultaneously estimating the positions and effects of sterile genes, as well as the epistasis between sterile genes. A real data set of a backcross (BC) population from an interspecific hybrid between cultivated rice, Oryza sativa, and its wild African relative, Oryza longistaminata, was analyzed using the new method. Five sterile genes were detected on the chromosomes of 1, 3, 6, 8 and 10, and significant epistatic effects were found among the four pairs of sterile genes. © 2014 Macmillan Publishers Limited.
- Lafontaine, J. D., & Walsh, J. B. (2013). A revision of the genus Ufeus Grote with the description of a new species from Arizona (Lepidoptera, Noctuidae, Noctuinae, Xylenini, Ufeina). ZooKeys, 264(SPL.ISS), 193-207.More infoPMID: 23730181;PMCID: PMC3668379;Abstract: The genus Ufeus Grote is revised to include five species including U. felsensteini, sp. n. in southern Arizona. A key to species, descriptions, illustrations of adults and genitalia are included. © Authors.
- Lafontaine, J. D., & Walsh, J. B. (2010). A review of the subfamily Anobinae with the description of a new species of Baniana Walker from North and Central America (Lepidoptera, Erebidae, Anobinae). ZooKeys, 39(SPEC. ISSUE 5), 3-11.More infoAbstract: A new species of Baniana Walker related to B. gobar Druce is described from Arizona and Costa Rica and the status of Baniana, Anoba Walker, and the Anobinae are discussed. Adults and/or genitalia of Anoba trigonoides Walker, Anoba sp. trigonoides group, Baniana significans Walker, B. minor sp. n., B. gobar, and Deinopa delinquens (Walker) are illustrated. © J.D. Lafontaine, J.B. Walsh.
- Lafontaine, J. D., Ferris, C. D., & Walsh, J. B. (2010). A revision of the genus Hypotrix Guenée in North America with descriptions of four new species and a new genus (Lepidoptera, Noctuidae, Noctuinae, Eriopygini). ZooKeys, 39(SPEC. ISSUE 5), 225-253.More infoAbstract: The genus Hypotrix Guenée, 1852 is synonymized with Trichorthosia Grote, 1883, Proteinania Hampson, 1905, Ursogastra Smith, 1906, and Trichagrotis McDunnough, . Four species are transferred from the genus Hexorthodes McDunnough [Hypotrix trifascia (Smith, 1891), comb. n., H. alamosa (Barnes, 1904), comb. n., T. hueco (Barnes, 1904), comb. n., and T. optima (Dyar, 1920), comb. n.]. Four new species are described (T. basistriga Lafontaine, Ferris & Walsh; T. naglei Lafontaine, Ferris & Walsh; T. ocularis Lafontaine, Ferris & Walsh; and T. rubra Lafontaine, Ferris & Walsh). A new genus, Anhypotrix Lafontaine, Ferris & Walsh, is proposed for Polia tristis Barnes & McDunnough, 1910, currently misplaced in Trichorthosia. A key to species, descriptions, illustrations of adults and genitalia are included. © J.D. Lafontaine, C.D. Ferris, J.B. Walsh.
- Lafontaine, J. D., Walsh, J. B., & Holland, R. W. (2010). A revision of the genus Bryolymnia Hampson in North America with descriptions of three new species (Lepidoptera, Noctuidae, Noctuinae, Elaphriini). ZooKeys, 39(SPEC. ISSUE 5), 187-204.More infoAbstract: The three known North American species of Bryolymnia Hampson, 1908 are reviewed and three additional species are described as new. Two additional species, Elaphria ensina (Barnes, 1907) and Cryphia viridata (Harvey, 1876) are transferred to Bryolymnia as new combinations. The North American species are compared with related species in Central America. Adults of 11 species and male and female genitalia, where available, are illustrated. © J.D. Lafontaine, J.B. Walsh, R.W. Holland.
- Valenzuela, R. K., Henderson, M. S., Walsh, M. H., Garrison, N. A., Kelch, J. T., Cohen-Barak, O., Erickson, D. T., Meaney, F. J., Walsh, J. B., Cheng, K. C., Ito, S., Wakamatsu, K., Frudakis, T., Thomas, M., & Brilliant, M. H. (2010). Predicting phenotype from genotype: Normal pigmentation. Journal of Forensic Sciences, 55(2), 315-322.More infoPMID: 20158590;PMCID: PMC3626268;Abstract: Genetic information in forensic studies is largely limited to CODIS data and the ability to match samples and assign them to an individual. However, there are circumstances, in which a given DNA sample does not match anyone in the CODIS database, and no other information about the donor is available. In this study, we determined 75 SNPs in 24 genes (previously implicated in human or animal pigmentation studies) for the analysis of single- and multi-locus associations with hair, skin, and eye color in 789 individuals of various ethnic backgrounds. Using multiple linear regression modeling, five SNPs in five genes were found to account for large proportions of pigmentation variation in hair, skin, and eyes in our across-population analyses. Thus, these models may be of predictive value to determine an individual's pigmentation type from a forensic sample, independent of ethnic origin. © 2010 American Academy of Forensic Sciences.
- Chen, J., & Walsh, B. (2009). Method for the mapping of a female partial-sterile locus on a molecular marker linkage map. Theoretical and Applied Genetics, 119(6), 1085-1091.More infoPMID: 19621212;Abstract: The female gametophyte is an absolutely essential structure for angiosperm reproduction, and female sterility has been reported in a number of crops. In this paper, a maximum-likelihood method is presented for estimating the position and effect of a female partial-sterile locus in a backcross population using the observed data of dominant or codominant markers. The ML solutions are obtained via Bailey's method. The process for the estimating of the recombination fractions and the viabilities of female gametes are described, and the variances of the estimates of the parameters are also presented. Application of the method is demonstrated using a set of simulated data. This method circumvents the problems of the traditional mapping methods for female sterile genes which were based on data from seed set or embryo-sac morphology and anatomy. © 2009 Springer-Verlag.
- Shen, X., Walsh, B., Li, J. J., Pang, H. X., Wang, W. J., & Tao, S. H. (2009). The correlations of the function and positional distribution of the cis-elements CArG around the TSS in the genes of Mus musculus. Genome, 52(3), 217-221.More infoPMID: 19234549;Abstract: While many studies of cis-elements CArG bound by serum response factor (SRF) are in progress, little is known about the positional distribution of the functional CArG elements around the transcription start site (TSS) of genes that they influence. We use a validated CArG data set to calculate the distance distribution of functional CArG elements around the TSS. Distances between adjacent CArGs were also analyzed. We compare these distributions with those derived using a control set of randomly selected CArGs (that were not experimentally validated for function). Our results show that most functional CArG elements (108 of 152, 71%) exist upstream of the annotated TSS, with copy number increasing as one moves closer to the TSS. Moreover, the average number of the CArG elements in the CArG-containing genes is significantly more than that in the control genes. Our study extends earlier bioinformatic analyses of functional CArG elements and provides an application of comparative sequence data to the identification of transcription factor binding sites.
- Walsh, B. (2009). Quantitative genetics, version 3.0: Where have we gone since 1987 and where are we headed?. Genetica, 136(2), 213-223.More infoPMID: 18791866;Abstract: The last 20 years since the previous World Congress have seen tremendous advancements in quantitative genetics, in large part due to the advancements in genomics, computation, and statistics. One central theme of this last 20 years has been the exploitation of the vast harvest of molecular markers-examples include QTL and association mapping, marker-assisted selection and introgression, scans for loci under selection, and methods to infer degree of coancestry, population membership, and past demographic history. One consequence of this harvest is that phenotyping, rather than genotyping, is now the bottleneck in molecular quantitative genetics studies. Equally important have been advances in statistics, many developed to effectively use this treasure trove of markers. Computational improvements in statistics, and in particular Markov Chain Monte Carlo (MCMC) methods, have facilitated many of these methods, as have significantly improved computational abilities for mixed models. Indeed, one could argue that mixed models have had at least as great an impact in quantitative genetics as have molecular markers. A final important theme over the past 20 years has been the fusion of population and quantitative genetics, in particular the importance of coalescence theory with its applications for association mapping, scans for loci under selection, and estimation of the demography history of a population. What are the future directions of the field? While obviously important surprises await us, the general trend seems to be moving into higher and higher dimensional traits and, in general, dimensional considerations. We have methods to deal with infinite-dimensional traits indexed by a single variable (such as a trait varying over time), but the future will require us to treat much more complex objects, such as infinite-dimensional traits indexed over several variables and with graphs and dynamical networks. A second important direction is the interfacing of quantitative genetics with physiological and developmental models as a step towards both the gene-phenotype map as well as predicting the effects of environmental changes. The high-dimensional objects we will need to consider almost certainly have most of their variation residing on a lower (likely much lower) dimensional subspace, and how to treat these constraints will be an important area of future research. Conversely, the univariate traits we currently deal with are themselves projections of more complex structures onto a lower dimensional space, and simply treating these as univariate traits can result in serious errors in understanding their selection and biology. As a field, our future is quite bright. We have new tools and techniques, and (most importantly) new talent with an exciting international group of vibrant young investigators who have received their degrees since the last Congress. One cloud for concern, however, has been the replacement at many universities of plant and animal breeders with plant and animal molecular biologists. Molecular tools are now an integral part of breeding, but breeding is not an integral part of molecular biology. © 2008 Springer Science+Business Media B.V.
- Walsh, B. (2008). Evolutionary Quantitative Genetics. Handbook of Statistical Genetics: Third Edition, 1, 533-586.More infoAbstract: Evolutionary quantitative genetics is the study of how complex traits evolve over time. While this field builds on traditional concepts from quantitative genetics widely used by applied breeders and human geneticists (in particular, the inheritance of complex traits), its unique feature is in examining the role of natural selection in changing the population distribution of a complex trait over time. Our review focuses on this role of selection, starting with response under the standard infinitesimal model, in which trait variation is determined by a very large number of loci, each of small effect. We then turn to issues of measuring fitness (and hence natural selection) on both univariate and multivariate traits. We conclude by examining models that treat fitness itself as a complex trait. © 2007 John Wiley & Sons, Ltd.
- Walsh, B. (2008). Using molecular markers for detecting domestication, improvement, and adaptation genes. Euphytica, 161(1-2), 1-17.More infoAbstract: Development of statistical tests to detect selection (strictly speaking, departures from the neutral equilibrium model) has been an active area of research in population genetics over the last 15 years. With the advent of dense genome sequencing of many domesticated crops, some of this machinery (which heretofore has been largely restricted to human genetics and evolutionary biology) is starting to be applied in the search for genes under recent selection in crop species. We review the population genetics of signatures of selection and formal tests of selection, with discussions as to how these apply in the search for domestication and improvement genes in crops and for adaptation genes in their wild relatives. Plant domestication has specific features, such as complex demography, selfing, and selection of alleles starting at intermediate frequencies, that compromise many of the standard tests, and hence the full power of tests for selection has yet to be realized. © 2007 Springer Science+Business Media B.V.
- Walsh, B., Redd, A. J., & Hammer, M. F. (2008). Joint match probabilities for Y chromosomal and autosomal markers. Forensic Science International, 174(2-3), 234-238.More infoPMID: 17449208;Abstract: Empirical tests of association between Y chromosome and autosomal markers are presented and a theoretical framework for determining a joint match probability is recommended. Statistical analyses of association were performed in 16 US populations between the autosomal genotypes from loci CSF1PO, FGA, THO1, TPOX, vWA, D3S1358, D5S818, D7S820, D8S1179, D13S317, D16S539, D18S512, D21S11 and Y chromosome haplotypes from loci DYS19, DYS385ab, DYS389I, DYS389II, DYS390, DYS391, DYS392, DYS393, DYS438, and DYS439. The sample populations include individuals of European-, African-, Hispanic-, Native-, and Asian-American ancestry. The results are consistent with independence of Y and autosomal markers, although small amounts of dependence would likely have escaped our tests. Given the data in hand, we suggest it is appropriate to compute joint match probabilities by multiplying the Y haplotype frequency with the appropriately corrected autosomal frequency. In addition to correcting for autosomal frequency differences between groups, a further correction may be required. Since two individuals sharing the same Y haplotype are likely to be more recently related than two randomly chosen individuals, the autosomal frequencies have to be adjusted to account for this, akin to the θ correction used to account for population substructure. The structure imposed on the autosomal frequencies conditioned in a Y match is a function of the number of markers scored and their mutation rate. However, in most settings θ < 0.01. When population structure is already present in the autosomes, the additional effect due to conditioning on the Y is small. For example, if the amount of structure in the population is θ = 0.01 or 0.03 (the NRCII range), then the effect of conditioning on the Y results in only a trivial increase in θ to 0.02-0.04, respectively. © 2007 Elsevier Ireland Ltd. All rights reserved.
- Ray, D. T., Veatch-Blohm, M. E., Teetor, V. H., & Walsh, B. (2007). Upper and lower heritability estimates in guayule based on mode of reproduction. Journal of the American Society for Horticultural Science, 132(2), 213-218.More infoAbstract: Guayule (Parthenium argentatum Gray) has been difficult to improve through classical plant breeding because of its facultative apomictic reproductive system and long growth period to harvest (2-5 years). Attempts have been made to increase rubber concentration and yield by selecting for traits correlated with rubber production. The objective of this study was to estimate heritability values in guayule that more accurately account for the contributions of apomictic and sexual reproduction occurring among populations, using a modified parent-progeny regression. Heritability was calculated using a modified version of the formula for single parent-progeny regression (h2 = 2b): that is, h2 = (2 - p)b, where p = proportion of apomixis and b = regression coefficient. Therefore, heritability was estimated as a range of values between the midparent and single parent regression, which correspond to complete apomixis and complete sexuality, respectively. At 2 years of growth, there was a significant regression between each parent trait and the corresponding progeny trait except rubber and guayulin B concentrations, with heritability estimates ranging from moderate to high for most parameters measured. Because apomixis occurs more frequently than sexual reproduction, most heritability estimates should fall closer to the midparent value, resulting in lower heritability. To increase resin and rubber yield in the progeny, selection should focus on plant height and width because these two traits are highly correlated with resin and rubber yield and have the highest heritability of the traits measured.
- Walsh, B. (2007). Escape from flatland. Journal of Evolutionary Biology, 20(1), 36-38.More infoPMID: 17209996;
- Hammer, G., Cooper, M., Tardieu, F., Welch, S., Walsh, B., Eeuwijk, F. v., Chapman, S., & Podlich, D. (2006). Models for navigating biological complexity in breeding improved crop plants. Trends in Plant Science, 11(12), 587-593.More infoPMID: 17092764;Abstract: Progress in breeding higher-yielding crop plants would be greatly accelerated if the phenotypic consequences of making changes to the genetic makeup of an organism could be reliably predicted. Developing a predictive capacity that scales from genotype to phenotype is impeded by biological complexities associated with genetic controls, environmental effects and interactions among plant growth and development processes. Plant modelling can help navigate a path through this complexity. Here we profile modelling approaches for complex traits at gene network, organ and whole plant levels. Each provides a means to link phenotypic consequence to changes in genomic regions via stable associations with model coefficients. A unifying feature of the models is the relatively coarse level of granularity they use to capture system dynamics. Much of the fine detail is not directly required. Robust coarse-grained models might be the tool needed to integrate phenotypic and molecular approaches to plant breeding. © 2006 Elsevier Ltd. All rights reserved.
- Hammer, M. F., Chamberlain, V. F., Kearney, V. F., Stover, D., Zhang, G., Karafet, T., Walsh, B., & Redd, A. J. (2006). Population structure of Y chromosome SNP haplogroups in the United States and forensic implications for constructing Y chromosome STR databases. Forensic Science International, 164(1), 45-55.More infoPMID: 16337103;Abstract: A set of 61 Y chromosome single-nucleotide-polymorphisms (Y-SNPs) is typed in a sample of 2517 individuals from 38 populations to infer the geographic origins of Y chromosomes in the United States and to test for paternal admixture among African-, European-, Hispanic-, Asian-, and Native-Americans. All of the samples were previously typed with the 11 core U.S. Y chromosome short tandem repeats (Y-STRs) recommended by SWGDAM, which revealed high levels of among ethnic group variation and low levels of among-population-within-ethnic-group variation. Admixture estimates vary greatly among populations and ethnic groups. The frequencies of non-European (3.4%) and non-Asian (4.5%) Y chromosomes are generally low in European-American and Asian-American populations, respectively. The frequencies of European Y chromosomes in Native-American populations range widely (i.e., 7-89%) and follow a West to East gradient, whereas they are relatively consistent in African-American populations (26.4 ± 8.9%) from different locations. The European (77.8 ± 9.3%) and Native-American (13.7 ± 7.4%) components of the Hispanic paternal gene pool are also relatively constant among geographic regions; however, the African contribution is much higher in the Northeast (10.5 ± 6.4%) than in the Southwest (1.5 ± 0.9%) or Midwest (0%). To test for the effects of inter-ethnic admixture on the structure of Y-STR diversity in the U.S., we perform subtraction analyses in which Y chromosomes inferred to be admixed by Y-SNP analysis are removed from the database and pairwise population differentiation tests are implemented on the remaining Y-STR haplotypes. Results show that low levels of heterogeneity previously observed between pairs of Hispanic-American populations disappear when African-derived chromosomes are removed from the analysis. This is not the case for an unusual sample of European-Americans from New York City when its African-derived chromosomes are removed, or for Native-American populations when European-derived chromosomes are removed. We infer that both inter-ethnic admixture and population structure in ancestral source populations may contribute to fine scale Y-STR heterogeneity within U.S. ethnic groups. © 2005 Elsevier Ireland Ltd. All rights reserved.
- Redd, A. J., Chamberlain, V. F., Kearney, V. F., Stover, D., Karafet, T., Calderon, K., Walsh, B., & Hammer, M. F. (2006). Genetic structure among 38 populations from the United States based on 11 U.S. core Y chromosome STRs. Journal of Forensic Sciences, 51(3), 580-585.More infoPMID: 16696705;Abstract: A DNA database consisting of the 11 Y chromosome short-tandem-repeat (Y-STR) recommended by the Scientific Working Group on DNA Analysis Methods is constructed for 2517 individuals from 38 populations in the United States. The population samples derive from five ethnic groups currently living in 10 states. A multidimensional scaling (MDS) plot places the populations into four discrete clusters (African Americans (AA), European Americans (EA), Hispanic Americans (HA), and Asian Americans (SA)) and one dispersed cluster of Native Americans. An analysis of molecular variance (AMOVA) indicates that a large proportion of the total genetic variance is partitioned among ethnic groups (24.8%), whereas only a small amount (1.5%) is found among-populations within ethnic groups. Separate AMOVA analyses within each ethnic group show that only the NA sample contains statistically significant among-population variation. Pair wise population differentiation tests do uncover heterogeneity among EA and among HA populations; however, this is due to only a single sample within each group. The analyses support the creation of AA, EA, HA, and Asian American databases in which samples from different geographic regions within the United States are pooled. We recommend that separate databases be constructed for different NA groups. Copyright © 2006 by American Academy of Forensic Sciences.
- Walsh, B. (2005). The struggle to exploit non-additive variation. Australian Journal of Agricultural Research, 56(9), 873-881.More infoAbstract: Whereas animal breeders largely focus on improvement using additive genetic variance, inbreeding and asexual reproduction allow plant breeders to at least partially exploit non-additive genetic variance as well. We briefly review various approaches used by breeders to exploit dominance and epistatic variance, discuss their constraints and limitations, and examine what (if anything) can be done to improve our ability to further use often untapped genetic variation. © CSIRO 2005.
- Walsh, B., & Henderson, D. (2004). Microarrays and beyond: what potential do current and future genomics tools have for breeders?. Journal of animal science., 82 E-Suppl, E292-299.More infoPMID: 15471810;Abstract: One of the most exciting tools from genomics is the ability to obtain a whole-genome snapshot of gene expression. This is typically called a microarray analysis, because probes for the genes of interest, which can run into the thousands, are spotted in a very small array on a glass slide or some other substrate. The resulting array is often called a gene chip, or simply a chip, in the case of short oligo arrays, or slides in the case of cDNA or long oligo arrays. Microarrays offer the awesome potential of simultaneously examining the level of expression, where expression is intended to measure the standing amount of mRNA, for all of the genes in a genome. Given this potential, it is not surprising that microarrays have attracted a great deal of attention from animal geneticists and breeders. The purpose of this review is to provide a brief, yet critical, overview of some of the potential uses of such whole-genome expression studies in applied animal breeding and to speculate about what additional forthcoming tools might be of use.
- Marnell, L. L., Garcia-Vargas, G. G., Chowdhury, U. K., Zakharyan, R. A., Walsh, B., Avram, M. D., Kopplin, M. J., Cebrián, M. E., Silbergeld, E. K., & Aposhian, H. V. (2003). Polymorphisms in the Human Monomethylarsonic Acid (MMAV) Reductase/hGSTO1 Gene and Changes in Urinary Arsenic Profiles. Chemical Research in Toxicology, 16(12), 1507-1513.More infoPMID: 14680363;Abstract: Large interindividual variability in urinary arsenic profiles, following chronic inorganic arsenic exposure, is well-known in humans. To understand this variability, we studied the relationship between polymorphisms in the gene for human monomethylarsonic acid (MMAv) reductase/hGSTO1 and the urinary arsenic profiles of individuals chronically exposed to arsenic in their drinking water. To ensure that we did not overlook rare polymorphisms, not included in the public databases, we amplified and sequenced all six exons of the gene and their flanking regions, using DNA isolated from peripheral blood samples of 75 subjects, living in the vicinity of Torreon, Mexico. Four groups, based on the levels of arsenic (9-100 μg/L) in their drinking water, were studied. We identified six novel polymorphisms and two reported previously. The novel polymorphisms were a three base pair deletion (delGGC) in the first intron; a G > C transversion, leading to a serine-to-cysteine substitution at amino acid 86; a G > T transversion and a A > T transversion in intron 5; a G > A transition resulting in glutamate-to-lysine substitution in amino acid 208; and a C > T transition producing an alanine-to-valine substitution in amino acid 236. Two subjects displayed significant differences in patterns of urinary arsenic; they had increased levels of urinary inorganic arsenic and reduced levels of methylated urinary arsenic species as compared to the rest of the study population. These two subjects had the same unique polymorphisms in hGSTO1 in that they were heterozygous for E155del and Glu208Lys. The identified SNPs may be one of the reasons for the large interindividual variability in the response of humans to chronic inorganic arsenic exposure. The findings suggest the need for further studies to identify unambiguously specific polymorphisms that may account for interindividual variability in the human response to chronic inorganic arsenic exposure.
- Walsh, B. (2003). Population-genetic models of the fates of duplicate genes. Genetica, 118(2-3), 279-294.More infoPMID: 12868616;Abstract: The ultimate fate of a duplicated gene is that it either silenced through inactivating mutations or both copies are maintained by selection. This later fate can occur via neofunctionalization wherein one copy acquires a new function or by subfunctionalization wherein the original function of the gene is partitioned across both copies. The relative probabilities of these three different fates involve often very subtle iterations between of population size, mutation rate, and selection. All three of these fates are critical to the expansion and diversification of gene families.
- Redd, A. J., Roberts-Thomson, J., Karafet, T., Bamshad, M., Jorde, L. B., Naidu, J. M., Walsh, B., & Hammer, M. F. (2002). Gene flow from the Indian subcontinent to Australia: Evidence from the Y chromosome. Current Biology, 12(8), 673-677.More infoPMID: 11967156;Abstract: Phenotypic similarities between Australian Aboriginal People and some tribes of India were noted by T.H. Huxley during the voyage of the Rattlesnake (1846-1850) . Anthropometric studies by Birdsell  led to his suggestion that a migratory wave into Australia included populations with affinities to tribal Indians. Genetic evidence for an Indian contribution to the Australian gene pool is contradictory; most studies of autosomal markers have not supported this hypothesis ([3-5];  and references therein). On the other hand, affinities between Australian Aboriginal People and southern Indians were suggested based on maternally inherited mitochondrial DNA . Here, we show additional DNA evidence in support of Huxley's hypothesis of an Indian-Australian connection using single-nucleotide polymorphisms (SNPs) and short tandem repeats (STRs) on the nonrecombining portion of the Y chromosome (NRY). Phylogenetic analyses of STR variation associated with a major Australian SNP lineage indicated tight clustering with southern Indian/Sri Lankan Y chromosomes. Estimates of the divergence time for these Indian and Australian chromosomes overlap with important changes in the archaeological and linguistic records in Australia. These results provide strong evidence for an influx of Y chromosomes from the Indian subcontinent to Australia that may have occurred during the Holocene.
- Lynch, M., O'Hely, M., Walsh, B., & Force, A. (2001). The probability of preservation of a newly arisen gene duplicate. Genetics, 159(4), 1789-1804.More infoPMID: 11779815;PMCID: PMC1461922;Abstract: Newly emerging data from genome sequencing projects suggest that gene duplication, often accompanied by genetic map changes, is a common and ongoing feature of all genomes. This raises the possibility that differential expansion/contraction of various genomic sequences may be just as important a mechanism of phenotypic evolution as changes at the nucleotide level. However, the population-genetic mechanisms responsible for the success vs. failure of newly arisen gene duplicates are poorly understood. We examine the influence of various aspects of gene structure, mutation rates, degree of linkage, and population size (N) on the joint fate of a newly arisen duplicate gene and its ancestral locus. Unless there is active selection against duplicate genes, the probability of permanent establishment of such genes is usually no less than 1/(4N) (half of the neutral expectation), and it can be orders of magnitude greater if neofunctionalizing mutations are common. The probability of a map change (reassignment of a key function of an ancestral locus to a new chromosomal location) induced by a newly arisen duplicate is also generally >1/(4N) for unlinked duplicates, suggesting that recurrent gene duplication and alternative silencing may be a common mechanism for generating microchromosomal rearrangements responsible for postreproductive isolating barriers among species. Relative to subfunctionalization, neofunctionalization is expected to become a progressively more important mechanism of duplicate-gene preservation in populations with increasing size. However, even in large populations, the probability of neofunctionalization scales only with the square of the selective advantage. Tight linkage also influences the probability of duplicate-gene preservation, increasing the probability of subfunctionalization but decreasing the probability of neofunctionalization.
- Walsh, B. (2001). Estimating the time to the most recent common ancestor for the Y chromosome or mitochondrial DNA for a pair of individuals. Genetics, 158(2), 897-912.More infoPMID: 11404350;PMCID: PMC1461668;Abstract: Bayesian posterior distributions are obtained for the time to the most recent common ancestor (MRCA) for a nonrecombining segment of DNA (such as the nonpseudoautosomal arm of the Y chromosome or the mitochondrial genome) for two individuals given that they match at k out of n scored markers. We argue that the distribution of the time t to the MRCA is the most natural measure of relatedness for such nonrecombining regions. Both an infinite-alleles (no recurring mutants) and stepwise mutation model are examined, and these agree well when n is moderate to large and k/n is close to one. As expected, the infinite alleles model underestimates t relative to the stepwise model. Using a modest number (20) of microsatellite markers is sufficient to obtain reasonably precise estimates of t for individuals separated by 200 or less generations. Hence, the multilocus haplotypes of two individuals can be used not only to date very deep ancestry but also rather recent ancestry as well. Finally, our results have forensic implications in that a complete match at all markers between a suspect and a sample excludes only a modest subset of the population unless a very large number of markers (>500 microsatellites) are used.
- Walsh, B. (2001). Quantitative genetics in the age of genomics. Theoretical Population Biology, 59(3), 175-184.More infoPMID: 11444958;Abstract: Quantitative genetics is indeed very healthy in this coming age of genomics, and will play an even greater role as genotypes of potential interest are investigated by human geneticists breeders, and evolutionary geneticists. While we have (or soon will have) the ability to do experiments that the founders of quantitative genetics could never envision in their wildest imagination, the basic machinery they developed is easily adaptable to the new analyses that will be required. Far from "freeing" molecular biologists from mathematics, the age of genomics has forced an appreciation of the importance of quantitative methods. As we start to mine this genomic information and attempt to map molecular variation into trait variation, quantitative genetics will move even more to the forefront. I'm afraid my molecular colleagues will have to develop a deeper appreciation of Fisher (1918).
- Walsh, J. B. (1995). How often do duplicated genes evolve new functions?. Genetics, 139(1), 421-428.More infoPMID: 7705642;PMCID: PMC1206338;Abstract: A recently duplicated gene can either fix a null allele (becoming a pseudogene) or fix an (advantageous) allele giving a slightly different function, starting it on the road to evolving a new function. Here we examine the relative probabilities of these two events under a simple model. Null alleles are assumed to be neutral; linkage effects are ignored, as are unequal crossing over and gene conversion. These assumptions likely make our results underestimates for the probability that an advantageous allele is fixed first. When new advantageous mutations are additive with selection coefficient s and the ratio of advantageous to null mutations is ρ, the probability an advantageous allele is fixed first is ([1 - e(-s)]/[ρS] + 1)-1, where S = 4N(e)s with N(e) the effective population size. The probability that a duplicate locus becomes a pseudogene, as opposed to evolving a new gene function, is high unless ρS >> 1. However, even if advantageous mutations are very rare relative to null mutations, for sufficiently large populations ρS >> 1 and new gene function, rather than pseudogene formation, is the expected fate of most duplicated genes.
- Walsh, J. B. (1993). The effects of different levels of genetic exchange on organelle evolution. Journal of Heredity, 84(5), 415-418.More infoPMID: 8409363;
- Birky Jr., C. W., & Walsh, J. B. (1992). Biased gene conversion, copy number, and apparent mutation rate differences within chloroplast and bacterial genomes. Genetics, 130(3), 677-683.More infoPMID: 1551584;PMCID: PMC1204883;Abstract: We investigate the possibility that differences between synonymous substitution rates of organelle and bacterial genes differing only in copy number may be due to conversion bias. We find that the rather large observed difference in the synonymous rates between genes in the single copy and inverted-repeat regions of chloroplasts can be accounted for by a very small bias against new mutants. More generally, differences in the within-organelle fixation probability result in different apparent mutation rates as measured by the expected rate of appearance of cells homoplasmic for new mutants. Thus, differences in intracellular population parameters rather than molecular mechanisms can account for some variation in the apparent mutation rates of organelle genes, and possibly in other systems with variable numbers of gene copies. On the other hand, our analysis suggests that conversion bias is not a likely explanation for relatively low mutation rates observed near the replication origin of bacterial chromosomes.
- Walsh, J. B. (1992). Intracellular selection, conversion bias, and the expected substitution rate of organelle genes. Genetics, 130(4), 939-946.More infoPMID: 1582568;PMCID: PMC1204942;Abstract: A key step in the substitution of a new organelle mutant throughout a population is the generation of germ-line cells homoplasmic for that mutant. Given that each cell typically contains multiple copies of organelles, each of which in turn contains multiple copies of the organelle genome, processes akin to drift and selection in a population are responsible for producing homoplasmic cells. This paper examines the expected substitution rate of new mutants by obtaining the probability that a new mutant is fixed throughout a cell, allowing for arbitrary rates of genome turnover within an organelle and organelle turnover within the cell, as well as (possibly biased) gene conversion and genetic differences in genome and/or organelle replication rates. Analysis is based on a variation of Moran's model for drift in a haploid population. One interesting result is that if the rate of unbiased conversion is sufficiently strong, it creates enough intracellular drift to overcome even strong differences in the replication rates of wild-type and mutant genomes. Thus, organelles with very high conversion rates are more resistant to intracellular selection based on differences in genome replication and/or degradation rates. It is found that the amount of genetic exchange between organelles within the cell greatly influences the probability of fixation. In the absence of exchange, biased gene conversion and/or differences in genome replication rates do not influence the probability of fixation beyond the initial fixation within a single organelle. With exchange, both these processes influence the probability of fixation throughout the entire cell. Generally speaking, exchange between organelles accentuates the effects of directional intracellular forces. Provided there is exchange among organelles, biparental inheritance further strengthens the role of directional intracellular forces in fixing the mutant throughout a population.
- Walsh, J. B. (1990). Inconsistencies in standard approximations for selection coefficients at loci affecting a polygenic character.. Journal of mathematical biology, 28(1), 21-31.More infoPMID: 2307910;Abstract: Inconsistencies exist in the standard expansions used to approximate selection coefficients for alleles at a locus underlying a quantitative character. Allelic (marginal) fitnesses obtained from expansions based on average excesses differ from allelic fitnesses obtained from expansions based on genotypic values. Similarly, W, the mean population fitness based on summing over either allelic or genotypic fitnesses usually differs mean population fitness obtained by averaging over the unrestricted phenotypic distribution. A consistent value of W requires no variation in genotypic values. If, as suggested by Nagylaki (1984), expansions are corrected for the decrease in phenotypic variance resulting from conditioning on the presence of a particular allele or genotype, inconsistencies still exist. Unless integral of W(z)[Vzp"(z) + zp'(z) + p(z)] dz = 0, where p(z) is the phenotypic probability density function, Vz the phenotypic variance, W(z) the fitness of phenotypic value z, the primes denote differentiation with respect to z, allelic fitnesses based on average effects differ from allelic fitnesses based on genotypic values. This condition must also be satisfied in order for either expansion to give a consistent W, as first shown by Nagylaki. For arbitrary W(z), this is satisfied if and only if phenotypes are normally distributed.
- Birky Jr., C. W., & Walsh, J. B. (1988). Effects of linkage on rates of molecular evolution. Proceedings of the National Academy of Sciences of the United States of America, 85(17), 6414-6418.More infoPMID: 3413105;PMCID: PMC281982;Abstract: When an advantageous mutation is fixed in a population by selection, a closely linked selectively neutral or mildly detrimental mutation may 'hitchhike' to fixation along with it. It has been suggested that hitchhiking might increase the rate of molecular evolution. Computer simulations and a mathematical argument show that complete linkage to either advantageous or deleterious mutations does not affect the substitution of selectively neutral mutations. However, the simulations show that linkage to selected background mutations decreases the rate of fixation of advantageous mutations and increases the rate of fixation of detrimental mutations. This is true whether the linked background mutations are advantageous or detrimental, and it verifies and extends previous observations that linkage tends to reduce the effects of selection on evolution. These results can be interpreted in terms of the Hill-Robertson effect: a locus linked to another locus under selection experiences a reduction in effective population size. The interpretation of differences in evolutionary rates between different genomes or different regions of a genome may be confounded by the effects of strong linkage and selection. Recombination is expected to reduce the overall rate of molecular evolution while enhancing the rate of adaptive evolution.
- Walsh, J. B. (1988). Unusual behaviour of linkage disequilibrium in two-locus gene conversion models.. Genetical Research, 51(1), 55-58.More infoPMID: 3366380;
- Walsh, J. B. (1987). Persistence of tandem arrays: implications for satellite and simple-sequence DNAs.. Genetics, 115(3), 553-567.More infoPMID: 3569882;PMCID: PMC1216357;Abstract: Recombination processes acting on tandem arrays are suggested here to have probable intrinsic biases, producing an expected net decrease in array size following each event, in contrast to previous models which assume no net change in array size. We examine the implications of this by modeling copy number dynamics in a tandem array under the joint interactions of sister-strand unequal crossing over (rate gamma per generation per copy) and intrastrand recombination resulting in deletion (rate epsilon per generation per copy). Assuming no gene amplification or selection, the expected mean persistence time of an array starting with z excess copies (i.e., array size z + 1) is z(1 + gamma/epsilon) recombinational events. Nontrivial equilibrium distributions of array sizes exist when gene amplification or certain forms of selection are considered. We characterize the equilibrium distribution for both a simple model of gene amplification and under the assumption that selection imposes a minimal array size, n. For the latter case, n + 1/alpha is an upper bound for mean array size under fairly general conditions, where alpha(= 2 epsilon/gamma) is the scaled deletion rate. Further, the distribution of excess copies over n is bounded above by a geometric distribution with parameter alpha/(1 + alpha). Tandem arrays are unlikely to be greatly expanded by unequal crossing over unless alpha much less than 1, implying that other mechanisms, such as gene amplification, are likely important in the evolution of large arrays. Thus unequal crossing over, by itself, is likely insufficient to account for satellite DNA.
- Walsh, J. B. (1987). Sequence-dependent gene conversion: can duplicated genes diverge fast enough to escape conversion?. Genetics, 117(3), 543-557.More infoPMID: 3692140;PMCID: PMC1203229;Abstract: Conversion between duplicated genes limits their independent evolution. Models in which conversion frequencies decrease as genes diverge are examined to determine conditions under which genes can "escape" further conversion and hence escape from a gene family. A review of results from various recombination systems suggests two classes of sequence-dependence models: (1) the "k-hit" model in which conversion is completely inactivated by a few (k) mutational events, such as the insertion of a mobile element, and (2) more general models where conversion frequency gradually declines as genes diverge through the accumulation of point mutants. Exact analysis of the k-hit model is given and an approximate analysis of a more general sequence-dependent model is developed and verified by computer simulation. If mu is the per nucleotide mutation rate, then neutral duplicated genes diverging through point mutants are likely to escape conversion provided 2 mu/lambda much greater than 0.1, where lambda is the conversion rate between identical genes. If 2 mu/lambda much less than 0.1, the expected number of conversions before escape increases exponentially so that, for biological purposes, the genes never escape conversion. For single mutational events sufficient to block further conversions, occurring at rate nu per copy per generation, many conversions are expected if 2 nu/lambda much less than 1, while the genes essentially evolve independently if 2 nu/lambda much greater than 1. Implications of these results for both models of concerted evolution and the evolution of new gene functions via gene duplication are discussed.
- Walsh, J. B. (1986). Selection and biased gene conversion in a multigene family: consequences of interallelic bias and threshold selection.. Genetics, 112(3), 699-716.More infoPMID: 3957008;PMCID: PMC1202771;Abstract: In a previous paper, I investigated the interactions in a gene family of additive selection and biased gene conversion in a finite population when conversion events are rare. Here I extend my "weak-conversion limit" model by allowing biased interallelic conversion (conversion between alleles at the same locus) of arbitrary frequency and various threshold selection schemes for rare interlocus conversion events. I suggest that it is not unreasonable for gene families to experience threshold fitness functions, and show that certain types of thresholds can greatly constrain the rate at which advantageous alleles are fixed as compared to other fitness schemes, such as additive selection. It is also shown that the double sampling process operating on a gene family in a finite population (sampling over the number of genes in the gene family and over the number of individuals in the population) can have interesting consequences. For selectively neutral alleles that experience interallelic bias, the probability of fixation at each single locus may be essentially neutral, but the cumulative effects on the entire gene family of small departures from neutrality can be significant, especially if the gene family is large. Thus, in some situations, gene families can respond to directional forces that are weak in comparison to drift at single loci.
- Walsh, J. B., & Marks, J. (1986). Sequencing the human genome. Nature, 322(6080), 590-.More infoPMID: 3748137;
- Walsh, J. B. (1985). How many processed pseudogenes are accumulated in a gene family?. Genetics, 110(2), 345-364.More infoPMID: 2408963;PMCID: PMC1202568;Abstract: A simple kinetic model is developed that describes accumulation of processed pseudogenes in a functional gene family. Insertion of new pseudogenes occurs at rate v per gene and is countered by spontaneous deletion (at rate δ per DNA segment) of segments containing processed pseudogenes. If there are k functional genes in a gene family, the equilibrium number of processed pseudogenes is k(v/δ), and the percentage of functional genes in the gene family at equilibrium is 1/[1 + (v/δ)]. v/δ values estimated for five gene gene family at equilibrium is 1/[1 + (v/δ)]. v/δ values estimated for five gene families ranged from 1.7 to 15. This fairly narrow range suggests that the rates of formation and deletion of processed pseudogenes may be positively correlated for these families. If δ is sufficiently large relative to the per nucleotide mutation rate μ (δ > 20μ), processed pseudogenes will show high homology with each other, even in the absence of gene conversion between pseudogenes. We argue that formation of processed pseudogenes may share common pathways with transposable elements and retroviruses, creating the potential for correlated responses in the evolution of processed pseudogenes due to direct selection for control of transposable elements and/or retroviruses. Finally, we discuss the nature of the selective forces that may act directly or indirectly to influence the evolution of processed pseudogenes.
- Walsh, J. B. (1985). Interaction of selection and biased gene conversion in a multigene family. Proceedings of the National Academy of Sciences of the United States of America, 82(1), 153-157.More infoPMID: 3855539;PMCID: PMC396990;Abstract: A model of the evolutionary dynamics of a multigene family in a finite population under the joint effects of selection and (possibly biased) gene conversion is analyzed. It is assumed that the loss or fixation of a polymorphism at any particular locus in the gene family occurs on a much faster time scale than the introduction of new alleles to a monomorphic locus by gene conversion. A general formula for the fixation of a new allele throughout a multigene family for a wide class of selection functions with biased gene conversion is given for this assumption. Analysis for the case of additive selection shows that (i) unless selection is extremely weak or bias is exceptionally strong, selection usually dominates the fixation dynamics, (ii) if selection is very weak, then even a slight conversion bias can greatly alter the fixation probabilities, and (iii) if both selection and conversion bias are sufficiently small, the substitution rate of new alleles throughout a multigene family is approximately the single locus mutation rate, the same result as for neutral alleles at a single-copy gene. Finally, I analyze a fairly general class of underdominant speciation models involving multigene families, concluding for these models under weak conversion that although the probability of fixation may be relatively high, the expected time of fixation is extremely long, so that speciation by 'molecular drive' is unlikely. Furthermore, speciation occurs faster by fixing underdominant alleles of the same effect at single-copy genes than by fixing the same number of loci in a single multigene family under the joint effects of selection, conversion, and drift.
- Walsh, J. B. (1984). Hard lessons for soft selection.. American Naturalist, 124(4), 518-526.More infoAbstract: The relative stringencies of hard and soft selection in protecting an allele in a geographically structured population is an important question in the maintenance of genetic variability. It is shown for the generalized two-deme case that hard selection is expected to be less stringent than soft selection roughly half of the time, in sharp contrast to the widely held view that hard selection is almost always more stringent than soft selection. Hard selection is usually expected to be less stringent than soft selection in the n-deme case when those demes in which the allele is favored are more fit than in those demes where the allele is at a disadvantage. This results from reduced migration into the favored demes under hard selection compared with soft selection, enhancing the protection of the allele. -Author
- Walsh, J. B. (1983). Conditions for protection of an allele in linear homogeneous stepping stone models. Theoretical Population Biology, 24(1), 78-106.More infoAbstract: The one-dimensional linear homogeneous stepping stone migration structure is an important model in that it represents a short-range migration extreme for geographically structured populations and also serves as the underlying discretespace model for much of the work on continuous-space clines. We examine conditions for the protection of an allele under a stepping stone migration structure by using a recursive method based on Sturm sequences. Necessary and sufficient conditions for protection of an allele are found for a generalized step-cline selection gradient, which is the selection scheme used in much of the early cline work. Sufficient conditions for the protection of an allele are also found for (i) an advantageous patch at the stepping stone boundary which is followed by an arbitrary selection gradient, and for (ii) an advantageous patch embedded within an otherwise arbitrary selection gradient. We let m be the migration rate between neighboring demes. If within the advantageous patch WAa Waa = 1 + s, then for (i) s ≥ m (1 - m) is sufficient to protect allele A, even if the patch consists of only a single deme, while for (ii) s ≥ 2m (1 - 2m) guarantees that a single deme will protect A. If the advantageous patch consists of k demes, each with WAa Waa = 1 + s, then s ≥ ( π2 4) m k2 is sufficient for protection of A in (i), while s ≥ π2m k2 is sufficient for protection of A in (ii). Sufficient conditions for a protected polymorphism are found, and a bound on the level of migration is determined, below which a protected polymorphism exists, as predicted from Karlin and McGregor's (1972. Theor. Pop. Biol. 3, 186-209, 210-238) small parameter results. Finally, our patch swamping conditions (protection of an allele given a single advantageous patch) are compared to Nagylaki's (1975. Genetics 80, 595-615) conditions for the existence of continuous-space clines under analogous selection schemes and are shown to be identical for the two specific cases examined. We also discuss extensions of some of the above results to circular stepping stone migration structures. © 1983.
- Walsh, J. B. (1983). Role of biased gene conversion in one-locus neutral theory and genome evolution. Genetics, 105(2), 461-468.More infoPMID: 17246166;PMCID: PMC1202168;Abstract: The implications of biased gene conversion acting on selectively neutral alleles are investigated for a single diallelic locus in a finite population. Even a very slight conversion bias can significantly alter fixation probabilities. We argue that most newly arising mutants will be at a conversion disadvantage, resulting in a potentially greatly decreased substitution rate of new alleles compared with predictions from strict neutral theory. Thus, conversion bias potential allows for conservation of particular alleles without having to invoke selection. Conversely, we also show that bias can be important in the maintenance of repeated gene families without altering the substitution rate at other loci that experience the same amount of conversion bias, provided that the number of genes in the family is sufficiently large. Bias can, therefore, be important at the genomic level and yet be unimportant at the populational level. Finally, we discuss the role of biased gene conversion in speciation events, concluding that this type of molecular turnover acting independently at many individual loci is very unlikely to decrease the time required for two allopatric populations to speciate.
- Walsh, J. B. (1982). Rate of accumulation of reproductive isolation by chromosome rearrangements.. American Naturalist, 120(4), 510-532.More infoAbstract: In populations with small or moderate effective population size, in the absence of strong homozygote advantage or drive, chromosomally induced isolation can occur only by the fixation of many weakly underdominant rearrangements. For these populations the minimal speciation time is an increasing function of Ne/u, the ratio of the effective population size and the spontaneous rearrangement rate. With moderate Ne and either strong rearrangement homozygote selective advantage or drive, isolation can occur by fixation of a few strongly underdominant rearrangements. Under these circumstances, speciation occurs at a more rapid rate, provided that such rearrangements occur with sufficient frequency. For large Ne, only rearrangements which are meiotically driven can become fixed, so that isolation times reflect the average strength of drive. A somewhat counterintuitive result for meiotic drive is that in certain cases the minimal speciation times decrease as the effective population size increases. The implications of these results for stasipatric speciation are that mildly to strongly underdominant rearrangements (those with h > .01) can contribute to hybrid sterility only in very small populations (Ne < 50) which are likely to have a high extinction probability and suffer inbreeding depression, or in moderate to large populations which have a high spontaneous occurrence rate of driven rearrangements. Even in populations with a high occurrence of driven rearrangements, only those rearrangements with D > h (the drive coefficient) can contribute to increasing hybrid sterility. Thus, the conditions under which the stasipatric model of speciation will operate in a reasonable time are fairly strict and speciation by fixation of a large number of weakly underdominant (cryptic) rearrangements is often more likely. -Author