Bounds on the minimum number of recombination events in a sample history

Recombination is an important evolutionary factor in many organisms, including humans, and understanding its effects is an important task facing geneticists. Detecting past recombination events is thus important; this article introduces statistics that give a lower bound on the number of recombination events in the history of a sample, on the basis of the patterns of variation in the sample DNA. Such lower bounds are appropriate, since many recombination events in the history are typically undetectable, so the true number of historical recombinations is unobtainable. The statistics can be calculated quickly by computer and improve upon the earlier bound of Hudson and Kaplan 1985. A method is developed to combine bounds on local regions in the data to produce more powerful improved bounds. The method is flexible to different models of recombination occurrence. The approach gives recombination event bounds between all pairs of sites, to help identify regions with more detectable recombinations, and these bounds can be viewed graphically. Under coalescent simulations, there is a substantial improvement over the earlier method (of up to a factor of 2) in the expected number of recombination events detected by one of the new minima, across a wide range of parameter values. The method is applied to data from a region within the lipoprotein lipase gene and the amount of detected recombination is substantially increased. Further, there is strong clustering of detected recombination events in an area near the center of the region. A program implementing these statistics, which was used for this article, is available from http://www.stats.ox.ac.uk/mathgen/programs.html.     

Producing sons reduces lifetime reproductive success of subsequent offspring in pre-industrial Finns

Life-history theory states that reproductive events confer costs upon mothers. Many studies have shown that reproduction causes a decline in maternal condition, survival or success in subsequent reproductive events. However, little attention has been given to the prospect of reproductive costs being passed onto subsequent offspring, despite the fact that parental fitness is a function of the reproductive success of progeny. Here we use pedigree data from a pre-industrial human population to compare offspring life-history traits and lifetime reproductive success (LRS) according to the cost incurred by each individual's mother in the previous reproductive event. Because producing a son versus a daughter has been associated with greater maternal reproductive cost, we hypothesize that individuals born to mothers who previously produced sons will display compromised survival and/or LRS, when compared with those produced following daughters. Controlling for confounding factors such as socio-economic status and ecological conditions, we show that those offspring born after elder brothers have similar survival but lower LRS compared with those born after elder sisters. Our results demonstrate a maternal cost of reproduction manifested in reduced LRS of subsequent offspring. To our knowledge, this is the first time such a long-term intergenerational cost has been shown in a mammal species.     

Maternal developmental stress reduces reproductive success of female offspring in zebra finches

Environmental factors play a key role in the expression of phenotypic traits and life-history decisions, specifically when they act during early development. In birds, brood size is a main environmental factor affecting development. Experimental manipulation of brood sizes can result in reduced offspring condition, indicating that developmental deficits in enlarged broods have consequences within the affected generation. Yet, it is unclear whether stress during early development can have fitness consequences projecting into the next generation. To study such trans-generational fitness effects, we bred female zebra finches, Taeniopygia guttata, whose mothers had been raised in different experimental brood sizes. We found that adult females were increasingly smaller with increasing experimental brood size in which their mother had been raised. Furthermore, reproductive success at hatching and fledging covaried negatively with the experimental brood size in which their mothers were raised. These results illustrate that early developmental stress can have long-lasting effects affecting reproductive success of future generations. Such trans-generational effects can be life-history responses adapted to environmental conditions experienced early in life.     

On the minimum number of topologies explaining a sample of DNA sequences

In this article I derive an alternative algorithm to Hudson and Kaplan's (Genetics 111, 147-165) algorithm that gives a lower bound to the number of recombination events in a sample's history. It is shown that the number, T(M), found by the algorithm is the least number of topologies required to explain a set of DNA sequences sampled under the infinite-site assumption. Let Tao = (T(1),...,T(r)) be a list of topologies compatible with the sequences, i.e., T(k) is compatible with an interval, I(k), of sites in the alignment. A characterization of all lists having T(M) topologies is given and it is shown that T(M) relates to specific patterns in the alignment, here called chain series. Further, a number of theorems relating general lists of topologies to the number T(M) is presented. The results are discussed in relation to the true minimum number of recombination events required to explain an alignment.     

Free mutual mate preferences in house mice affect reproductive success and offspring performance

When social constraints on the expression of mate preferences are absent, variation in offspring viability is predicted to favour females and males that display mate preferences. Earlier studies showed that female and male house mice, Mus domesticus, tested individually and mated with preferred (P) partners had higher reproductive success and better progeny performance than individuals mated with nonpreferred (NP) partners. Here we tested the effects of mutual mate preferences on reproductive success, offspring viability and performance. We conducted mate preference tests and created four types of reproductive pairings. One involved females and males that preferred each other (P-P); the second type had females that preferred the male but the male did not prefer the female (P-NP); the third had females that did not prefer the male but the male did prefer the female (NP-P). The last set consisted of females and males that did not prefer each other (NP-NP). We measured components of fitness for breeders (reproductive success) and offspring viability (birth-to-weaning viability and weight variation) as well as measures of offspring performance. There were no statistical differences in reproductive success of breeders or offspring viability and quality (weight variation) among the four types of pairings. There were, however, consistent differences between P-P versus NP-NP matings. The number of pups weaned, time to first litter, birth-to-weaning viability, pup body weight at birth and weaning, and the growth rates for pups of both sexes were consistently greater for progeny from P-P matings than NP-NP matings. Significant differences occurred among the four mating types in dominance of sons during aggression trials, nest construction and predator avoidance. Progeny from P-P matings displayed behaviour associated with higher fitness more often than progeny from NP-NP matings. These data show that breeders produce more highly competent progeny, most likely to survive, when social constraints on the expression of mate preferences in both sexes are relaxed.Copyright 2003 The Association for the Study of Animal Behaviour. Published by Elsevier Science Ltd. All rights reserved.      

Good genes and the maternal effects of polyandry on offspring reproductive success in the bulb mite

Genetic benefits are potentially the most robust explanation of the controversial issue of evolutionary maintenance of polyandry, but the unambiguous demonstration of such benefits has been hindered by the possibility of their confusion with maternal effects. Previous research has shown that polyandrous bulb mite females produce daughters with higher fecundity than monandrous females. Here, we investigate whether this effect arises because polyandrous females invest more in their offspring, or because their offspring inherit 'good genes' from their fathers. Females were mated with either one or four (different) males. However, by sterilizing three of the four males with ionizing radiation, we eliminated any chance of sexual selection (in the polyandrous treatment) so that any differences in the female mating regimes must have been owing to maternal effects. Polyandry had no significant effect on daughter fecundity, thus indicating that any previously documented effects must have been genetic. This was further supported by a significant association between fathers' offensive sperm-competitive ability and the fecundity of their daughters. The association with fathers' sperm defensive ability was not significant, and neither was the association between fathers' sperm competitiveness and sons' reproductive success. However, sons of polyandrous females had lower reproductive success than sons of monandrous females. This shows that the maternal effects of polyandry should be taken into account whenever its costs and benefits are being considered.     

A design-based method for estimating glomerular number in the developing kidney

Low glomerular (nephron) endowment has been associated with an increased risk of cardiovascular and renal disease in adulthood. Nephron endowment in humans is determined by 36 wk of gestation, while in rats and mice nephrogenesis ends several days after birth. Specific genes and environmental perturbations have been shown to regulate nephron endowment. Until now, design-based method for estimating nephron number in developing kidneys was unavailable. This was due in part to the difficulty associated with unambiguously identifying developing glomeruli in histological sections. Here, we describe a method that uses lectin histochemistry to identify developing glomeruli and the physical disector/fractionator principle to provide unbiased estimates of total glomerular number (N(glom)). We have characterized N(glom) throughout development in kidneys from 76 rats and model this development with a 5-parameter logistic equation to predict N(glom) from embryonic day 17.25 to adulthood (r(2) = 0.98). This approach represents the first design-based method with which to estimate N(glom) in the developing kidney.     

Optimal allocation of reproductive effort: manipulation of offspring number and size in the bank vole

The number of offspring attaining reproductive age is an important measure of an individual's fitness. However, reproductive success is generally constrained by a trade-off between offspring number and quality. We conducted a factorial experiment in order to study the effects of an artificial enlargement of offspring number and size on the reproductive success of female bank voles (Clethrionomys glareolus). We also studied the effects of the manipulations on growth, survival and reproductive success of the offspring. Potentially confounding effects of varying maternal quality were avoided by cross-fostering. Our results showed that the number of offspring alive in the next breeding season was higher in offspring number manipulation groups, despite their smaller body size at weaning. Offspring size manipulation had no effect on offspring growth or survival. Further, the first litter size of female offspring did not differ between treatments. In conclusion, females may be able to increase the number of offspring reaching reproductive age by producing larger litters, whereas increasing offspring size benefits neither the mother nor the offspring.     

Enrichment materials do not negatively affect reproductive success and offspring survival and weight in mice

Environmental enrichment is designed to improve the overall welfare of laboratory animals, including mice. Few studies have directly assessed the effects of different types of enrichment on mouse offspring survival and growth. The authors examined how survival and growth of C57BL/6 mouse pups are affected by three kinds of cage enrichment materials: compressed cotton squares, two-ply tissues and plastic igloos. During the last week of gestation and the first two weeks postpartum, the authors observed cages with litters and noted use of the enrichment materials, quality of nest construction, number of pups per litter and weight of pups. Both the first and second litters were evaluated for each dam. Dams and pups had continuous contact with the enrichment materials, especially cotton squares and tissues. Neither the presence nor the type of enrichment material influenced the survival and weight of offspring, suggesting that the use of such materials does not negatively impact reproductive success or offspring survival.     

Free female mate choice in house mice affects reproductive success and offspring viability and performance

We tested a critical assumption of sexual dialectics theory (Gowaty 1997, Feminism and Evolutionary Biology, Chapman & Hall) using house mice, Mus musculus. We asked if female house mice accrue viability benefits for their offspring when they mate with males they prefer versus with males they do not prefer. Our experiment was designed to eliminate or control other mechanisms of reproductive competition besides female mate choice. After allowing females to discriminate behaviourally between two males, which were at random with respect to phenotypic variation discriminating females were paired with preferred (P) or nonpreferred (NP) males. We then tested whether females mating with males they preferred had offspring of higher viability than females mating with nonpreferred males. In pairwise comparisons, we tested for differences in offspring performance in dominance contests and in nest-building skill. At weaning, we exposed half of the pups to cold stress. We tested progeny performance and viability in the laboratory or in outdoor field enclosures. In comparison to P females, NP females produced significantly fewer litters. Sons from P matings were socially dominant to sons from NP matings. Adult offspring from P matings built better nests than those from NP matings. In field enclosures significantly fewer NP than P offspring survived to 60 days after introduction. Male and female progeny from P matings established larger home ranges and constructed better nests than progeny from NP matings. This is the first demonstration of progeny viability differences for females allowed to express mate preferences between males presented to them at random. Copyright 2000 The Association for the Study of Animal Behaviour.     

A hierarchical clustering method for estimating copy number variation

Microarray technologies allow for simultaneous measurement of DNA copy number at thousands of positions in a genome. Gains and losses of DNA sequences reveal themselves through characteristic patterns of hybridization intensity. To identify change points along the chromosomes, we develop a marker clustering method which consists of 2 parts. First, a "circular clustering tree test statistic" attaches a statistic to each marker that measures the likelihood that it is a change point. Then construction of the marker statistics is followed by outlier detection approaches. The method provides a new way to build up a binary tree that can accurately capture change-point signals and is easy to perform. A simulation study shows good performance in change-point detection, and cancer cell line data are used to illustrate performance when regions of true copy number changes are known.     

A chromosome-based model for estimating the number of conserved segments between pairs of species from comparative genetic maps

Comparative genetic maps of two species allow insights into the rearrangements of their genomes since divergence from a common ancestor. When the map details the positions of genes (or any set of orthologous DNA sequences) on chromosomes, syntenic blocks of one or more genes may be identified and used, with appropriate models, to estimate the number of chromosomal segments with conserved content conserved between species. We propose a model for the distribution of the lengths of unobserved segments on each chromosome that allows for widely differing chromosome lengths. The model uses as data either the counts of genes in a syntenic block or the distance between extreme members of a block, or both. The parameters of the proposed segment length distribution, estimated by maximum likelihood, give predictions of the number of conserved segments per chromosome. The model is applied to data from two comparative maps for the chicken, one with human and one with mouse.     

A model for estimating the medium properties of Avicel to ethanol conversion

Simultaneous saccharification and fermentation received an increasing level of attention over recent decades, with the primary focus on the development of improved enzyme and organism performance. Little literature is available on the effects of the various fermentation components on the apparent dynamic viscosity of the fermentation broth for use in reactor design and analysis. This work investigates density and settling properties of Avicel PH-101 particles and the effects of base medium composition, yeast concentration and cellulose particles on the apparent dynamic viscosity of the fermentation mixture. Dynamic viscosity measurements were obtained using a rotational viscometer equipped with a DG 26.7 double gap concentric cylinder measuring system. Results indicated that Avicel particles experience a greater drag force compared to similar sized spherical particles and have a measured density of 1,605.7 kg m^?3. The Ostwäld-de Waele formulation was used to describe the dynamic viscosity of the particles due to it shear-thinning nature. Correlation between the predicted particle effects and experimental results deviated with a root mean square error of 8.46 %.     

A prediction-based resampling method for estimating the number of clusters in a dataset

Background  

Microarray technology is increasingly being applied in biological and medical research to address a wide range of problems, such as the classification of tumors. An important statistical problem associated with tumor classification is the identification of new tumor classes using gene-expression profiles. Two essential aspects of this clustering problem are: to estimate the number of clusters, if any, in a dataset; and to allocate tumor samples to these clusters, and assess the confidence of cluster assignments for individual samples. Here we address the first of these problems.     

Quantifying the percent increase in minimum sample size for SNP genotyping errors in genetic model-based association studies

Kang et al. [Genet Epidemiol 2004;26:132-141] addressed the question of which genotype misclassification errors are most costly, in terms of minimum percentage increase in sample size necessary (%MSSN) to maintain constant asymptotic power and significance level, when performing case/control studies of genetic association in a genetic model-free setting. They answered the question for single nucleotide polymorphisms (SNPs) using the 2 x 3 chi2 test of independence. We address the same question here for a genetic model-based framework. The genetic model parameters considered are: disease model (dominant, recessive), genotypic relative risk, SNP (marker) and disease allele frequency, and linkage disequilibrium. %MSSN coefficients of each of the six possible error rates are determined by expanding the non-centrality parameter of the asymptotic distribution of the 2 x 3 chi2 test under a specified alternative hypothesis to approximate %MSSN using a linear Taylor series in the error rates. In this work we assume errors misclassifying one homozygote as another homozygote are 0, since these errors are thought to rarely occur in practice. Our findings are that there are settings of the genetic model parameters that lead to large total %MSSN for both dominant and recessive models. As SNP minor allele approaches 0, total %MSSN increases without bound, independent of other genetic model parameters. In general, %MSSN is a complex function of the genetic model parameters. Use of SNPs with small minor allele frequency requires careful attention to frequency of genotyping errors to insure that power specifications are met. Software to perform these calculations for study design is available, and an example of its use to study a disease is given.     

A net reproductive number for periodic matrix models

We give a definition of a net reproductive number R ₀ for periodic matrix models of the type used to describe the dynamics of a structured population with periodic parameters. The definition is based on the familiar method of studying a periodic map by means of its (period-length) composite. This composite has an additive decomposition that permits a generalization of the Cushing–Zhou definition of R ₀ in the autonomous case. The value of R ₀ determines whether the population goes extinct (R ₀<1) or persists (R ₀>1). We discuss the biological interpretation of this definition and derive formulas for R ₀ for two cases: scalar periodic maps of arbitrary period and periodic Leslie models of period 2. We illustrate the use of the definition by means of several examples and by applications to case studies found in the literature. We also make some comparisons of this definition of R ₀ with another definition given recently by Bacaër.