Estimating the prevalence of inbreeding from incomplete pedigrees

A previous review of inbreeding in natural populations suggested that close inbreeding (inbreeding coefficient f = 0.25) is generally rare in wild birds and mammals. However, the review did not assess rates of moderate inbreeding (f = 0.125), which may make a rather larger contribution to overall inbreeding in a population. Furthermore, previous studies may have underestimated the prevalence of inbreeding in wild populations with incomplete pedigrees. By categorizing inbreeding events by the relationship of the parental pair, we suggest a simple method for estimating rates of close and moderate inbreeding from incomplete pedigree data. We applied this method to three wild populations of ruminants: red deer on Rum, Scotland, Soay sheep on Hirta, Scotland and reintroduced Arabian oryx on the Jiddat-al-Harasis, Oman. Although paternal half-sib pairs were the most common category of inbreeding in all three populations, there was considerable variation among populations in the frequencies of the various categories of inbreeding. This variation may be largely explained by differences in population size and dynamics, in maternal and paternal sibship size and in the overlap of reproductive lifespan of consecutive generations. Close and moderate inbreeding appear to be a routine part of breeding behaviour in these ruminant populations.     

Simulation of pedigree genotypes by random walks.

A random walk method, based on the Metropolis algorithm, is developed for simulating the distribution of trait and linkage marker genotypes in pedigrees where trait phenotypes are already known. The method complements techniques suggested by Ploughman and Boehnke and by Ott that are based on sequential sampling of genotypes within a pedigree. These methods are useful for estimating the power of linkage analysis before complete study of a pedigree is undertaken. We apply the random walk technique to a partially penetrant disease, schizophrenia, and to a recessive disease, ataxia-telangiectasia. In the first case we show that accessory phenotypes with higher penetrance than that of schizophrenia itself may be crucial for effective linkage analysis, and in the second case we show that impressionistic selection of informative pedigrees may be misleading.     

A variance-covariance model for analysis of pedigrees with inbreeding

A variance-covariance model is suggested for plotting the distribution of a quantitative trait analyzed in animal pedigrees resulting from crosses of outbred lines. The model takes inbreeding into account. A special parameter characterizing the degree of inbreeding has been introduced, which makes the model versatile. Pedigrees with the same structure that contain or not contain inbred individuals have been compared to analyze the effect of inbreeding on the parameters of the trait distribution, such as the mean genotypic value and variance of the trait.     

Search along persistent random walks

Optimal search strategies and their implementations in biological systems are a subject of active research. Here we study a search problem which is motivated by the hunt of sperm cells for the egg. We ask for the probability for an active swimmer to find a target under the condition that the swimmer starts at a certain distance from the target. We find that success probability is maximal for a certain level of fluctuations characterized by the persistence length of the swimming path of the swimmer. We derive a scaling law for the optimal persistence length as a function of the initial target distance and search time by mapping the search on a polymer physics problem.     

A variance-covariance model for analysis of hybrid pedigrees with inbreeding

A variance-covariance model is suggested for plotting the distribution of a quantitative trait analyzed in animal pedigrees resulting from crosses of outbred lines. The model takes inbreeding into account. A special parameter characterizing the degree of inbreeding has been introduced, which makes the model versatile. Pedigrees with the same structure that contain or not contain inbred individuals have been compared to analyze the effect of inbreeding on the parameters of the trait distribution, such as the genotypic mean and variance of the trait.     

Surname distribution and random inbreeding in Kirov oblast

Data on surname distribution in 24 raions of Kirov oblast with a total adult population of more than 785000 people were used to calculate the random inbreeding values for populations of the district and rural municipality levels and analyze the geographic distributions of these values. The data have been compared with the results of studies carried out in the 1980s.     

Dwell time symmetry in random walks and molecular motors

The statistics of steps and dwell times in reversible molecular motors differ from those of cycle completion in enzyme kinetics. The reason is that a step is only one of several transitions in the mechanochemical cycle. As a result, theoretical results for cycle completion in enzyme kinetics do not apply to stepping data. To allow correct parameter estimation, and to guide data analysis and experiment design, a theoretical treatment is needed that takes this observation into account. In this article, we model the distribution of dwell times and number of forward and backward steps using first passage processes, based on the assumption that forward and backward steps correspond to different directions of the same transition. We extend recent results for systems with a single cycle and consider the full dwell time distributions as well as models with multiple pathways, detectable substeps, and detachments. Our main results are a symmetry relation for the dwell time distributions in reversible motors, and a relation between certain relative step frequencies and the free energy per cycle. We demonstrate our results by analyzing recent stepping data for a bacterial flagellar motor, and discuss the implications for the efficiency and reversibility of the force-generating subunits.     

Stochasticity, invasions, and branching random walks

We link deterministic integrodifference equations to stochastic, individual-based simulations by means of branching random walks. Using standard methods, we determine speeds of invasion for both average densities and furthest-forward individuals. For density-independent branching random walks, demographic stochasticity can produce extinction. Demographic stochasticity does not, however, reduce the overall asymptotic speed of invasion or preclude continually accelerating invasions.     

Note on estimates of the inbreeding coefficient through study of pedigrees and isonymous marriages

Crow and Mange (1965) developed a method to estimate the inbreeding coefficient (F) through an ingenious surname analysis. Such formulations assume a regularity of transmission of surnames, monophyletism, and random occurrence of consanguineous marriages. Accordingly, the ratio of isonymous partners to F of the offspring is equal to 4. Nevertheless, genealogy analyses show that the consanguineous marriages do not necessarily occur regularly. Therefore the isonymy analysis gives a misestimation of the inbreeding coefficient, depending on the prevailing form of nonrandomness. We suggest a small correction to the formulation in situations when pedigree information is available. The weighted mean of the ratio of isonymous partners to F of the known consanguineous marriages is suggested as a way to improve the formulas. The technique was applied to a northeastern Brazilian sample, and the results agree well with those of bioassays and therefore provide an apparently more realistic estimate of the inbreeding coefficient by isonymy.     

Linkage and inbreeding coefficients in a finite random mating population

The notion of inbreeding coefficient associated with one single locus introduced by G. Malecot can be extended to two loci. For a panmictic model with separate generation the recurrence equations are given therein allowing to calculate the coefficients in the event of migration and mutation, or loss of kinship.Hence it is derived particularly that the limit genetic distance of two groups associated with two loci is, under specific hypotheses, little different from the sum of marginal genetic distances.For an isolat this paper studies, in terms of crossing over, mutations, and population size, the evolution of the inbreading coefficients of order 2 and especially the difference of this evolution from the evolution to independence of the two loci.     

Predicting genetic interactions with random walks on biological networks

Background  

Several studies have demonstrated that synthetic lethal genetic interactions between gene mutations provide an indication of functional redundancy between molecular complexes and pathways. These observations help explain the finding that organisms are able to tolerate single gene deletions for a large majority of genes. For example, system-wide gene knockout/knockdown studies in S. cerevisiae and C. elegans revealed non-viable phenotypes for a mere 18% and 10% of the genome, respectively. It has been postulated that the low percentage of essential genes reflects the extensive amount of genetic buffering that occurs within genomes. Consistent with this hypothesis, systematic double-knockout screens in S. cerevisiae and C. elegans show that, on average, 0.5% of tested gene pairs are synthetic sick or synthetic lethal. While knowledge of synthetic lethal interactions provides valuable insight into molecular functionality, testing all combinations of gene pairs represents a daunting task for molecular biologists, as the combinatorial nature of these relationships imposes a large experimental burden. Still, the task of mapping pairwise interactions between genes is essential to discovering functional relationships between molecular complexes and pathways, as they form the basis of genetic robustness. Towards the goal of alleviating the experimental workload, computational techniques that accurately predict genetic interactions can potentially aid in targeting the most likely candidate interactions. Building on previous studies that analyzed properties of network topology to predict genetic interactions, we apply random walks on biological networks to accurately predict pairwise genetic interactions. Furthermore, we incorporate all published non-interactions into our algorithm for measuring the topological relatedness between two genes. We apply our method to S. cerevisiae and C. elegans datasets and, using a decision tree classifier, integrate diverse biological networks and show that our method outperforms established methods.     

Biological organization,Jarkievich measures and asymmetric random walks

In this paper we analyze the organization imposed by the energy input during the migration of enzymes on DNA. We attempt to measure that organization by means of a concept proposed by A.A. Jarkievich in 1961. We found relationships among a Jarkievich measure, the energy dissipation, and the fluctuations in the kinematic velocity of the enzyme on the DNA.     

Aneuploidy and inbreeding depression in random mating and self-fertilizing autotetraploid populations

Summary Almost all autotetraploids produce aneuploid progeny because of irregularities at meiosis. Aneuploid plants produce high frequencies of aneuploids. If it were not for selection against aneuploid gametes and sporophytes the amount of aneuploidy would increase every generation. Most experimental and theoretical studies on population genetics and heterosis in autotetraploids have neglected aneuploidy as a factor. To take aneuploidy into account experimentally requires the cytological identification of all chromosomes and to consider it theoretically requires a huge amount of computations. Consequently, microcomputer programs have been devised to show the effects of random mating and self-fertilization in autotetraploid populations. According to the model aneuploidy rapidly increases in randomly mated and self-fertilized autotetraploid populations until they achieve an equilibrium where the amount of aneuploidy introduced into the population is balanced by the amount of aneuploidy removed from the population by selection. The model suggests that self-fertilized populations have greater frequencies of aneuploid gametes and zygotes than do randomly mated populations and therefore aneuploidy may be a significant cause of the great inbreeding depressions found in autotetraploids.Contribution from the Missouri Agricultural Experiment Station. Journal Series No. 9998     

Estimation of individual level of inbreeding using relatedness measures in haplodiploids

Although male haploidy in haplodiploid species aids purging of deleterious alleles, haplodiploid animals may nevertheless suffer significant negative effects of inbreeding. The effects may even be stronger in social Hymenoptera because the negative fitness consequences may be expressed at two levels: the individual level (inbred queens) and colony level (inbred workers). Surprisingly, in natural populations the impact of inbreeding on fitness has been studied in very few insects, and even fewer haplodiploid ones. Hence there is currently little understanding of the potential effects of inbreeding. One reason may be the difficulties in estimating inbreeding especially at the individual level, apart from the additional problems posed by haplodiploidy. In order to study the impact of inbreeding, its individual level must be estimated as precisely as possible. When the population pedigree is unknown, relatedness-based estimates of the individual inbreeding coefficient can be used to estimate inbreeding. Here we examine the relationship between inbreeding coefficients and relatedness in diploid and haplodiploid organisms, and provide guidelines for estimating inbreeding both at the individual and the colony level. Received 7 March 2005; revised 18 April 2005, accepted 20 April 2005. An erratum to this article is available at .     

Lowering the barriers to random walks on the cell surface

We used fluorescence recovery after photobleaching (FRAP) and single particle tracking (SPT) techniques to compare diffusion of class I major histocompatibility complex molecules (MHC) on normal and alpha-spectrin-deficient murine erythroleukemia (MEL) cells. Because the cytoskeleton mesh acts as a barrier to lateral mobility of membrane proteins, we expected that diffusion of membrane proteins in alpha-spectrin-deficient MEL cells would differ greatly from that in normal MEL cells. In the event, diffusion coefficients derived from either FRAP or SPT analysis were similar for alpha-spectrin-deficient and normal MEL cells, differing by a factor of approximately 2, on three different timescales: tens of seconds, 1-10 s, and 100 ms. SPT analysis showed that the diffusion of most class I MHC molecules was confined on both cell types. On the normal MEL cells, the mean diagonal length of the confined area was 330 nm with a mean residency time of 40s. On the alpha-spectrin-deficient MEL cells, the mean diagonal length was 650 nm with a mean residency time of 45s. Thus there are fewer barriers to lateral diffusion on cytoskeleton mutant MEL cells than on normal MEL cells, but this difference does not strongly affect lateral diffusion on the scales measured here.     

Estimation of random regression parameters

The problem of the best linear unbiased estimation (BLUE) of random regression parameters is considered. It is proved that increasing informations about the mean value of the parameters both extend the class of estimable linear functionals and improve on the estimation. In all investigated cases the uniqueness of BLUE is proved. In the case of known mean values the BLUE is shown to be numerically equivalent with the MMSEE almost everywhere. A numerical example shows the improvements of BLUE due to increasing informations about the mean values of the parameters.     

Estimation of the inbreeding coefficient through use of genomic data

Many linkage studies are performed in inbred populations, either small isolated populations or large populations with a long tradition of marriages between relatives. In such populations, there exist very complex genealogies with unknown loops. Therefore, the true inbreeding coefficient of an individual is often unknown. Good estimators of the inbreeding coefficient (f) are important, since it has been shown that underestimation of f may lead to false linkage conclusions. When an individual is genotyped for markers spanning the whole genome, it should be possible to use this genomic information to estimate that individual's f. To do so, we propose a maximum-likelihood method that takes marker dependencies into account through a hidden Markov model. This methodology also allows us to infer the full probability distribution of the identity-by-descent (IBD) status of the two alleles of an individual at each marker along the genome (posterior IBD probabilities) and provides a variance for the estimates. We simulate a full genome scan mimicking the true autosomal genome for (1) a first-cousin pedigree and (2) a quadruple-second-cousin pedigree. In both cases, we find that our method accurately estimates f for different marker maps. We also find that the proportion of genome IBD in an individual with a given genealogy is very variable. The approach is illustrated with data from a study of demyelinating autosomal recessive Charcot-Marie-Tooth disease.     

Sampling rate effects on measurements of correlated and biased random walks

When observing the two-dimensional movement of animals or microorganisms, it is usually necessary to impose a fixed sampling rate, so that observations are made at certain fixed intervals of time and the trajectory is split into a set of discrete steps. A sampling rate that is too small will result in information about the original path and correlation being lost. If random walk models are to be used to predict movement patterns or to estimate parameters to be used in continuum models, then it is essential to be able to quantify and understand the effect of the sampling rate imposed by the observer on real trajectories. We use a velocity jump process with a realistic reorientation model to simulate correlated and biased random walks and investigate the effect of sampling rate on the observed angular deviation, apparent speed and mean turning angle. We discuss a method of estimating the values of the reorientation parameters used in the original random walk from the rediscretized data that assumes a linear relation between sampling time step and the parameter values.