Family Size Distribution Research Articles

The size distribution of protein families within different types of folds

It is well known that the structure is currently available only for a small fraction of known protein sequences. It is urgent to discover the important features of known protein sequences based on present protein structures. Here, we report a study on the size distribution of protein families within different types of folds. The fold of a protein means the global arrangement of its main secondary structures, both in terms of their relative orientations and their topological connections, which specify a certain biochemical and biophysical aspect. We first search protein families in the structural database SCOP against the sequence-based database Pfam, and acquire a pool of corresponding Pfam families whose structures can be deemed as known. This pool of Pfam families is called the sample space for short. Then the size distributions of protein families involving the sample space, the Pfam database and the SCOP database are obtained. The results indicate that the size distributions of protein families under different kinds of folds abide by similar power-law. Specially, the largest families scatter evenly in different kinds of folds. This may help better understand the relationship of protein sequence, structure and function. We also show that the total of proteins with known structures can be considered a random sample from the whole space of protein sequences, which is an essential but unsettled assumption for related predictions, such as, estimating the number of protein folds in nature. Finally we conclude that about 2957 folds are needed to cover the total Pfam families by a simple method.

Analysis of genetic diversity in a close population of Zandi sheep using genealogical information

In a Fisher–Wright idealized population (Fisher 1930; Wright 1931), characterized by Poisson distribution of family size, large number of breeders, random mating, equal sex ratio, absence of selection, mutation, or migration, and discrete generations, the rate of loss of heterozygosity is inversely proportional to population size. In real populations, however, genetic diversity is affected by several ongoing natural processes of mutation, migration, genetic drift and selection. For this reason, Wright (1931) proposed the concept of the effective population size (Ne) for extending population genetics theory developed for ideal populations to real populations. This parameter has been useful in designing strategies for conservation of endangered animal species because of its direct relationship with the level of inbreeding (Caballero and Toro 2000). However, when Ne is estimated from pedigree data, the parameter accuracy may be affected by several factors, as extensively reviewed by Boichard et al. (1997). Consequently, in recent decades, new complementary techniques have been developed for the analysis of genealogies. Lacy (1989) introduced the concept of effective number of founders ( fe) in order to measure the overall founder representation in a managed population accounting for the loss of genetic diversity from unequal founder contributions, and the concept of founder genome equivalents ( fg), also called effective number of founder genomes, to account the effects of bottlenecks, unequal founder contributions, and genetic drift. Boichard et al. (1997) developed the concept of effective number of ancestors ( fa) to supplement the effective number of founders. The numbers obtained from

Dispersal and Within‐Stream Spatial Population Structure of Brook Trout Revealed by Pedigree Reconstruction Analysis

AbstractSpatial patterns of spawning and early dispersal have important implications for the population dynamics of stream‐dwelling salmonids, but the limitations of marking technology have made it difficult to measure these processes in wild populations. We used microsatellite DNA markers and sibship and parentage analyses to follow the dispersal, spatial distribution, and distribution of reproductive success in a small, isolated western Virginia population of brook trout Salvelinus fontinalis at 4, 16, and 28 months after fry emergence. For the 2004 year‐class (high‐recruitment cohort), we identified 180 full‐sibling families representing individual spawning events. Offspring were unevenly distributed across families, with 16% of the families accounting for 50% of the offspring and 53% of the families being represented by fewer than three individuals. However, a large proportion of adults had some successful reproduction. Spatial and family size distributions at 4 months after emergence were similar between the 2004 and 2006 (low‐recruitment) year‐classes in spite of a threefold difference in abundance. The spatial locations of full sibs were closely associated, indicating limited dispersal in the first 4 months postemergence. The spatial locations of assigned parents were correlated with the locations of their offspring. For the 2004 cohort, sibling dispersal substantially increased after the 4‐month sample, but neither fish length, family size (number of individuals), nor fish density was related to dispersal distance at any postemergence time interval. In this study, we demonstrate the ability of sibship and parentage analyses to reveal important aspects of brook trout population structure and movement. Our results suggest that limited dispersal by age‐0 brook trout and their parents results in a high level of within‐stream spatial population structure even in the absence of barriers to movement, and this must be accounted for in genetic surveys and management studies.

The Distribution of Family Sizes Under a Time-Homogeneous Birth and Death Process

The number of extant individuals within a lineage, as exemplified by counts of species numbers across genera in a higher taxonomic category, is known to be a highly skewed distribution. Because the sublineages (such as genera in a clade) themselves follow a random birth process, deriving the distribution of lineage sizes involves averaging the solutions to a birth and death process over the distribution of time intervals separating the origin of the lineages. In this article, we show that the resulting distributions can be represented by hypergeometric functions of the second kind. We also provide approximations of these distributions up to the second order, and compare these results to the asymptotic distributions and numerical approximations used in previous studies. For two limiting cases, one with a relatively high rate of lineage origin, one with a low rate, the cumulative probability densities and percentiles are compared to show that the approximations are robust over a wide range of parameters. It is proposed that the probability distributions of lineage size may have a number of relevant applications to biological problems such as the coalescence of genetic lineages and in predicting the number of species in living and extinct higher taxa, as these systems are special instances of the underlying process analyzed in this article.

Management to ensure effective population size in a breeding programme for the small Norwegian horse breeds – a simulation study

A simulation study relevant for the Norwegian horse populations (Døle, Fjord and Nordland/Lyngen), compared with how the effective population size per generation is affected by: the population size, the proportion of offspring from three-year-old sires, performing phenotypic selection of sires at three years of age and random selection amongst these at four years of age (mating for 4 years). The distribution of family size (number of mated mares per sire) was as observed in the Døle. The population size had the largest effect on the effective population size per generation, and therefore at least 200 foals should be born and registered per year. The second most limiting factor was the proportion of young sires, where higher effective population size could be obtained by having more offspring from three-year-old sires (allowing more sires selected). Omitting selection only had a minor effect on the effective size.

The formation of the Baptistina family by catastrophic disruption: Porous versus non‐porous parent body

Abstract— In this paper, we present numerical simulations aimed at reproducing the Baptistina family based on its properties estimated by observations. A previous study by Bottke et al. (2007) indicated that this family is probably at the origin of the K/T impactor, is linked to the CM meteorites and was produced by the disruption of a parent body 170 km in size due to the head‐on impact of a projectile 60 km in size at 3 km s−1. This estimate was based on simulations of fragmentation of non‐porous materials, while the family was assumed to be of C taxonomic type, which is generally interpreted as being formed from a porous body. Using both a model of fragmentation of non‐porous materials, and a model that we developed recently for porous ones, we performed numerical simulations of disruptions aimed at reproducing this family and at analyzing the differences in the outcome between those two models.Our results show that a reasonable match to the estimated size distribution of the real family is produced from the disruption of a porous parent body by the head‐on impact of a projectile 54 km in size at 3 km s−1. Thus, our simulations with a model consistent with the assumed dark type of the family requires a smaller projectile than previously estimated, but the difference remains small enough to not affect the proposed scenario of this family history.We then find that the break‐up of a porous body leads to different outcomes than the disruption of a non‐porous one. The real properties of the Baptistina family still contain large uncertainties, and it remains possible that its formation did not involve the proposed impact conditions. However, the simulations presented here already show some range of outcomes and once the real properties are better constrained, it will be easy to check whether one of them provides a good match.

Universal features of surname distribution in a subsample of a growing population

We examine the problem of family size statistics (the number of individuals carrying the same surname, or the same DNA sequence) in a given size subsample of an exponentially growing population. We approach the problem from two directions. In the first, we construct the family size distribution for the subsample from the stable distribution for the full population. This latter distribution is calculated for an arbitrary growth process in the limit of slow growth, and is seen to depend only on the average and variance of the number of children per individual, as well as the mutation rate. The distribution for the subsample is shifted left with respect to the original distribution, tending to eliminate the part of the original distribution reflecting the small families, and thus increasing the mean family size. From the subsample distribution, various bulk quantities such as the average family size and the percentage of singleton families are calculated. In the second approach, we study the past time development of these bulk quantities, deriving the statistics of the genealogical tree of the subsample. This approach reproduces that of the first when the current statistics of the subsample is considered. Surname statistics for the US in 1790 and 2000 and for Norway in 2008 are analyzed in the light of the theory and show satisfactory agreement, when the time-dependence of the growth rate is taken into account for the two contemporary data sets.

Do Socioeconomic Differences in Family Size Reflect Cultural Differences in Confidence and Social Support for Parenting?

This article details family size differences by socio-economic area in metropolitan South Australia and suggests that these differences may be linked to cultural differences in parenting confidence and skills, and in social supports for parenting. The paper analyses Census data on average completed family size and family size distribution in six different areas. In all age groups this shows a negative correlation between family size and the socio-economic status of the area. Secondly, based on analysis of interview data with 38 mothers and 24 fathers and a small survey of 44 parents-to-be, the article suggests that the quantitative patterns may partly reflect differences in the proportions of people in each area who see being parents and having larger families as desirable and achievable undertakings for which they have the requisite personal skills and social supports to minimise adverse impacts on their own parental health and lifestyle. The article concludes by hypothesising that differential fertility levels between groups or areas partly reflect differences in levels of confidence, skills and social support for parenting, and that a cultural “crisis in parenthood” as well as a greater focus on intensive parenting may be more widespread in higher status groups which is reflected in their lower fertility.

Teaching & Learning Guide for: The Emerging Field of Language Dynamics

Teaching & Learning Guide for: The Emerging Field of Language Dynamics

Whole-Genome Duplications in the Ancestral Vertebrate Are Detectable in the Distribution of Gene Family Sizes of Tetrapod Species

A clustering of all protein coding genes from the complete genomes of five tetrapod species into gene families shows a clear deviation from the expected power-law distribution of gene family size. We hypothesize that at least part of the deviation is the result of the two whole-genome duplications (WGDs) that are now known, with reasonable certainty, to have occurred prior to the fish-tetrapod split. We build a model of homologous gene family evolution and perform simulations to show that speciations alone cannot produce a distribution that resembles the empirical data. In order to replicate the features of the empirical distribution, the simulation must incorporate two WGD events. These WGDs must be such that a significant number of the gene duplicates generated in the WGDs have a higher retention rate than they do following small-scale duplication (SSD). This requirement is consistent with what is known about duplicate retention following a WGD, namely, that genes belonging to specific functional classes, such as genes regulating transcription, are much more likely to be retained following WGD than SSD. We conclude that the deviation from the power-law that we observe in the empirical data is the result of the two WGDs that occurred in the ancestral chordate. This implies that the two ancient WGDs continue to have a structural effect on gene families approximately 500 million years after the initial events. On the one hand, this is a surprising result, given the limited retention of duplicates generated by a WGD and the continual SSD, which further weakens the signal created by the fraction of duplicate pairs that are retained. On the other hand, WGD's capacity to fundamentally change the architecture of gene families in a profound and lasting way is consistent with the observed correlation between WGDs and important evolutionary transitions.

The size distributions of asteroid families in the SDSS Moving Object Catalog 4

Asteroid families, traditionally defined as clusters of objects in orbital parameter space, often have distinctive optical colors. We show that the separation of family members from background interlopers can be improved with the aid of SDSS colors as a qualifier for family membership. Based on an ∼88,000 object subset of the Sloan Digital Sky Survey Moving Object Catalog 4 with available proper orbital elements, we define 37 statistically robust asteroid families with at least 100 members (12 families have over 1000 members) using a simple Gaussian distribution model in both orbital and color space. The interloper rejection rate based on colors is typically ∼10% for a given orbital family definition, with four families that can be reliably isolated only with the aid of colors. About 50% of all objects in this data set belong to families, and this fraction varies from about 35% for objects brighter than an H magnitude of 13 and rises to 60% for objects fainter than this. The fraction of C-type objects in families decreases with increasing H magnitude for H > 13 , while the fraction of S-type objects above this limit remains effectively constant. This suggests that S-type objects require a shorter timescale for equilibrating the background and family size distributions via collisional processing. The size distribution varies significantly among families, and is typically different from size distributions for background populations. The size distributions for 15 families display a well-defined change of slope and can be modeled as a “broken” double power-law. Such “broken” size distributions are twice as likely for S-type familes than for C-type families (73% vs. 36%), and are dominated by dynamically old families. The remaining families with size distributions that can be modeled as a single power law are dominated by young families (<1 Gyr). When size distribution requires a double power-law model, the two slopes are correlated and are steeper for S-type families. No such slope–color correlation is discernible for families whose size distribution follows a single power law. For several very populous families, we find that the size distribution varies with the distance from the core in orbital-color space, such that small objects are more prevalent in the family outskirts. This “size sorting” is consistent with predictions based on the Yarkovsky effect.

Altered patterns of gene duplication and differential gene gain and loss in fungal pathogens

BackgroundDuplication, followed by fixation or random loss of novel genes, contributes to genome evolution. Particular outcomes of duplication events are possibly associated with pathogenic life histories in fungi. To date, differential gene gain and loss have not been studied at genomic scales in fungal pathogens, despite this phenomenon's known importance in virulence in bacteria and viruses.ResultsTo determine if patterns of gene duplication differed between pathogens and non-pathogens, we identified gene families across nine euascomycete and two basidiomycete species. Gene family size distributions were fit to power laws to compare gene duplication trends in pathogens versus non-pathogens. Fungal phytopathogens showed globally altered patterns of gene duplication, as indicated by differences in gene family size distribution. We also identified sixteen examples of gene family expansion and five instances of gene family contraction in pathogenic lineages. Expanded gene families included those predicted to be important in melanin biosynthesis, host cell wall degradation and transport functions. Contracted families included those encoding genes involved in toxin production, genes with oxidoreductase activity, as well as subunits of the vacuolar ATPase complex. Surveys of the functional distribution of gene duplicates indicated that pathogens show enrichment for gene duplicates associated with receptor and hydrolase activities, while euascomycete pathogens appeared to have not only these differences, but also significantly more duplicates associated with regulatory and carbohydrate binding functions.ConclusionDifferences in the overall levels of gene duplication in phytopathogenic species versus non-pathogenic relatives implicate gene inventory flux as an important virulence-associated process in fungi. We hypothesize that the observed patterns of gene duplicate enrichment, gene family expansion and contraction reflect adaptation within pathogenic life histories. These adaptations were likely shaped by ancient, as well as contemporary, intimate associations with monocot hosts.

The power-law distribution of gene family size is driven by the pseudogenisation rate's heterogeneity between gene families

Genome sequencing has shown that the number of homologous gene families of a given size declines rapidly with family size. A power-law has been shown to provide the best mathematical description of this relationship. However, it remains unclear what evolutionary forces drive this observation. We use models of gene duplication, pseudogenisation and accumulation of replacement substitutions, which have been validated and parameterised using genomic data, to build a model of homologous gene evolution. We use this model to simulate the evolution of the distribution of gene family size and show that the power-law distribution is driven by the pseudogenisation rate's heterogeneity across gene families and its correlation within families. Moreover, we show that gene duplication and pseudogenisation are necessary and sufficient for the emergence of the power-law.

Estimation of effective population size using bivariate discrete distributions for modeling family size in beef cattle

Pedigree records of 72,808 animals (45,668 females and 27,140 males) from the genetic evaluation program of the Argentine Brangus Association were used to estimate effective number of founders ( N f ), effective number of ancestors ( N a ), and effective population size under random mating ( N e ) or selection ( N eS ), in order to assess genetic variability. The average level of completeness of the pedigree was low (0.17) and the average level of inbreeding ( F) calculated from the pedigree was equal to 0.24%. Animals in the reference population were 21,662 calves born from 2001 to 2005. The estimated measures of variability were N f = 765.7 and N a = 387.5. The numbers of ancestors responsible for 100%, 50%, or 20% of the genes in the reference group, were equal to 12,471, 273, and 22, respectively. Direct estimates of N e and N eS were calculated using the variances and covariances of family sizes, i.e. male and female progeny numbers for bulls and cows. Estimates of the dispersion parameters were from the Bivariate Poisson model for the cows, and from the Generalized Bivariate Negative Binomial (GBIVARNB) distribution for the bulls. The latter probability mass function accounted for overdispersion, a characteristic present in the sampling distribution of family size of bulls. The estimated variances of male and female progeny and the covariance between them for the bulls were 5.70, 271.28, and 30.15, respectively, and 1.15, 2.10, and 1.06 for the cows. Generation intervals (in years) were: sires of bulls = 5.0, sires of cows = 5.7, dams of bulls = 4.4, and dams of cows = 5.2. The estimated N e was 274, which corresponds to a rate of inbreeding ( F) of 0.18%, whereas N eS = 125 and F = 0.40%. As a check of the proposed methodology, all analyses were also performed using the pedigree records of 10,483 Angus animals from a herd with an average level of completeness of 0.68. Using the GBIVARNB model for both bulls and cows the estimated N e = 95.4, thus F = 0.5% in perfect agreement with the calculated average inbreeding from pedigree records. Under selection, N eS = 79.3 and F = 0.6%. The larger difference between estimated N e and N eS in the Brangus was related to the smaller bull to cow ratio in the breed. Therefore, it seems desirable to continue monitoring the effective size of the Argentine Brangus to prevent problems of inbreeding and lack of variability in the future.

Colorectal Cancer Risks in Relatives of Young-Onset Cases: Is Risk the Same Across All First-Degree Relatives?

During the last 15 years, several single-gene mendelian disorders have been discovered that might account for some of the familial aggregation detected in large population studies of colorectal cancer (CRC). Mutations in DNA mismatch repair (MMR) genes cause hereditary nonpolyposis colorectal cancer-Lynch syndrome, the most common of the recognized CRC-predisposition syndromes, in which one major feature is a young age for cancer onset. However, for young-onset microsatellite stable (MSS) CRC, the familial risk for CRC is unknown. Patients with CRC who were <50 years old were identified through Minnesota Cancer Surveillance System (MCSS) and Mayo Clinic, Rochester, MN. CRCs in which the DNA MMR function was deficient as evidenced by high level microsatellite instability and/or loss of expression of MMR gene product by immunostaining were excluded. A total of 278 probands (131 from MCSS; 147 from Mayo Clinic) were included. Data on 1862 relatives were collected, of whom 68 were found to have had CRC, and an additional 165 had primary cancers of other types. Compared with Surveillance Epidemiology and End Results program data, relatives of young-onset CRC probands had increased risks for CRC. This relative risk (RR) was increased among first-degree relatives (RR, 1.65; 95% confidence interval [CI], 1.29-2.07) and was greater for siblings (RR, 2.67; 95% CI, 1.50-4.41) than parents (RR, 1.5; 95% CI, 1.14-1.94). We studied 278 probands with young-onset MSS CRC. We determined that the RR for CRC was greatest in siblings, which is consistent with an autosomal recessive inheritance pattern.

Evolution of protein families: Is it possible to distinguish between domains of life?

Understanding evolutionary relationships between species can shed new light into the rooting of the tree of life and the origin of eukaryotes, thus, resulting in a long standing interest in accurately assessing evolutionary parameters at time scales on the order of a billion of years. Prior work suggests large variability in molecular substitution rates, however, we still do not know whether such variability is due to species-specific trends at a genomic scale, or whether it can be attributed to the fluctuations inherent in any stochastic process. Here, we study the statistical properties of gene and protein-family sizes in order to quantify the long time scale evolutionary differences and similarities across species. We first determine the protein families of 209 species of bacteria and 20 species of archaea. We find that we are unable to reject the null hypothesis that the protein-family sizes of these species are drawn from the same distribution. In addition, we find that for species classified in the same phylogenetic branch or in the same lifestyle group, family size distributions are not significantly more similar than for species in different branches. These two findings can be accounted for in terms of a dynamical birth, death, and innovation model that assumes identical protein-family evolutionary rates for all species. Our theoretical and empirical results thus strongly suggest that the variability empirically observed in protein-family size distributions is compatible with the expected stochastic fluctuations for an evolutionary process with identical genomic evolutionary rates. Our findings hold special importance for the plausibility of some theories of the origin of eukaryotes which require drastic changes in evolutionary rates for some period during the last 2 billion years.

Modelling linguistic taxonomic dynamics

AbstractThis paper presents the results of the application of a bit‐string model of languages (Schulze &amp; Stauffer 2005) to problems of taxonomic patterns. The questions addressed include the following: (1) Which parameters are minimally needed for the development of a taxonomic dynamics leading to the type of distribution of language family sizes currently attested (as measured in the number of languages per family), which appears to be a power‐law? (2) How may such a model be coupled with one of the dynamics of speaker populations leading to the type of language size seen today, which appears to follow a log‐normal distribution?

A DISCRETE MODEL OF EVOLUTION OF SMALL PARALOG FAMILIES

We introduce and analyze a simple probabilistic model of genome evolution. It is based on three fundamental evolutionary events: gene loss, duplication and accumulated change. We are mainly interested in asymptotic size distribution of small paralogous gene families in a genome. This is motivated by previous works which consisted in fitting the available genomic data into, what is called, paralog distributions. This formalism is described as a discrete-time Markov chain. The formulas for equilibrium paralog family sizes are derived. Moreover, we show that when probabilities of gene removal and duplication are small and close to each other, then the resulting distribution is close to logarithmic distribution. Some empirical results for microbial genomes are presented.

Cooperation is less likely to evolve in a finite population with a highly skewed distribution of family size

In the context of the finitely repeated Prisoner's Dilemma with the possibility of cooperating or defecting each time, the strategy tit-for-tat (TFT) consists in cooperating the first time and copying the strategy previously used by the opponent the next times. Assuming random pairwise interactions in a finite population of always defecting individuals, TFT can be favoured by selection to go to fixation following its introduction as a mutant strategy. We deduce the condition for this to be the case under weak selection in the framework of a general reproduction scheme in discrete time. In fact, we show when and why the one-third rule for the evolution of cooperation holds, and how it extends to a more general rule. The condition turns out to be more stringent when the numbers of descendants left by the individuals from one time-step to the next may substantially differ. This suggests that the evolution of cooperation is made more difficult in populations with a highly skewed distribution of family size. This is illustrated by two examples.

Evolution of Gene Families Based on Gene Duplication, Loss, Accumulated Change, and Innovation

We introduce and analyze a simple discrete probabilistic model of genome evolution. It is based on four fundamental evolutionary events: gene duplication, loss, accumulated change and innovation. We call it the DLCI model. It is the first such model rigorously analyzed. The focus of the paper is on the size distribution of gene families. We derive formulae for the equilibrium of gene family sizes, and show that they follow a logarithmic distribution. We also consider a disjoint union of DLCI models and present empirical results for bacterial genomes.