The IBD process along four chromosomes

In this note, we present the continuous-time Markov rate matrix that models identity by descent (ibd) patterns among four chromosomes in a population. The equilibrium distribution of this Markov process along a chromosome is the set of 4-gene state probabilities given by the Ewens sampling formula. This model will facilitate inference of identity by descent among the four chromosomes of a pair of individuals, using data at dense SNP loci among which there may be linkage disequilibrium.     

The probability of electrophoretic idendity of proteins as a function of amino acid divergence

Summary Whenever proteins differ by two or more substitutions involving charged amino acids, there is a possibility of spurious electrophoreiic identity because one difference may cancel another. Probability of spurious identity can be calculated as a function of the total number of site differences between the two proteins. This in turn is a complex function of the number of evolutionary events in the divergence of the proteins from a common ancestor and of the number of sites able to accept evolutionary substitutions during the period of divergence. The probability of electrophoretic identity is a decidedly nonlinear, although monotonic, function of the genetic distance.     

The probability of fixation of a single mutant in an exchangeable selection model

The Cannings exchangeable model for a finite population in discrete time is extended to incorporate selection. The probability of fixation of a mutant type is studied under the assumption of weak selection. An exact formula for the derivative of this probability with respect to the intensity of selection is deduced, and developed in the case of a single mutant. This formula is expressed in terms of mean coalescence times under neutrality assuming that the coefficient of selection for the mutant type has a derivative with respect to the intensity of selection that takes a polynomial form with respect to the frequency of the mutant type. An approximation is obtained in the case where this derivative is a continuous function of the mutant frequency and the population size is large. This approximation is consistent with a diffusion approximation under moment conditions on the number of descendants of a single individual in one time step. Applications to evolutionary game theory in finite populations are presented.      

The survival probability of a mutant in a multidimensional population

We prove a general result about the asymptotic behaviour of the survival probability of a slightly supercritical multitype Bienaymé-Galton-Watson branching process. This is the complete analogue of a result which Ewens (1968) obtained for a Poisson branching process.Research supported by NSERC     

The relationships between the burden of adult parasites, host age and the microfilarial density in human onchocerciasis

We investigate the relationship between the microfilarial density in the skin and the burden of adult female Onchocerca volvulus by analysing pre-control nodulectomy data which allow for a direct approach, independent of exposure. The data of 169 patients in Burkina Faso and 182 patients in Liberia represent savannah and forest onchocerciasis in West Africa, respectively. Whereas in Burkina Faso, a saturating relationship between microfilarial density and worm burden suggests the operation of density-dependent processes within human hosts, the Liberian data show a linear relationship implying no density dependence. The differences may derive from differences between both parasite strains, i.e. the savannah or the forest strain of O. volvulus. Consistently for both parasite strains and independent of the worm burden, the microfilarial density increases with host age emphasising the concept of the acquisition of immunological tolerance. In male hosts in Liberia, the microfilarial density increases stronger with the worm burden than in female hosts, whereas such sex-specific differences cannot be found in Burkina Faso. In the methodological part of this investigation, we suggest the beta-distribution to be most appropriate for describing variability in microfilarial densities and we present an approach to consider the uncertainty in the adult parasite burden which cannot be determined precisely in helminth infections. Implications of density dependence are discussed with respect to immunological processes in the human host and with respect to the success of control programs. The relationships described show that regulatory processes between the parasite and the human host are multi-dimensional, operating within a high degree of biological variability.     

The inheritance of restriction fragment length polymorphisms in the flax rust Melampsora lini

Summary Random cDNA sequences synthesized from poly A⁺ RNA extracted from germinated urediospores of the flax rust fungus, Melampsora lini, were used as probes to detect restriction fragment length polymorphisms (RFLPs) in three races of M. lini originating from cultivated flax, Linum usitatissimum, and one race originating from Australian native flax, L. marginale. Fourteen out of 22 probes tested detected RFLPs in the three races from cultivated flax while 19 of the probes detected polymorphisms between these three races and the race from L. marginale. The segregation of seven RFLPs was determined in a family of 19 F₂ progeny derived from a cross between two of the rust races. With six of these the inheritance was consistent, in each case, with the segregation of alleles at a single locus. Inheritance of the seventh was unusual and an explanation involving two loci with null alleles at each was proposed. No linkage was detected between any of the RFLP loci and nine unlinked loci specifying avirulence.     

Parameter estimation in a generalized discrete-time model of density dependence

Flexible discrete-time per-capita-growth-rate models accommodating a variety of density-dependent relationships offer parsimonious explanations for the variation of population abundance through time. However, the accuracy of standard approaches to parameter estimation and confidence interval construction for such models has not been explored in a generalized setting or with consideration of limited sample sizes typical for ecology. Here, we use simulated data to quantify the relative effects of sample size, population perturbations, and environmental stochasticity on statistical inference. We focus on the key parameters that inform population dynamic predictions in a generalized Beverton–Holt model. We find that reliable parameter estimation requires data spanning ranges where both low and high density dependence act. However, the asymptotic distribution of the likelihood ratio test statistic can be fairly accurate for constructing confidence regions even when point estimation is poor. Consideration of the joint profile likelihood surface is shown to be useful for assessing reliability of point estimates and dynamical population predictions. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Effects of density dependent sex allocation on the dynamics of a simultaneous hermaphroditic population: Modelling and analysis

In this work we present a mathematical model describing the dynamics of a population where sex allocation remains flexible throughout adult life and so can be adjusted to current environmental conditions. We consider that the fractions of immature individuals acquiring male and female sexual roles are density dependent through nonlinear functions of a weighted total population size. The main goal of this work is to understand the role of life-history parameters on the stabilization or destabilization of the population dynamics.The model turns out to be a nonlinear discrete model which is analysed by studying the existence of fixed points as well as their stability conditions in terms of model parameters. The existence of more complex asymptotic behaviours of system solutions is shown by means of numerical simulations.Females have larger fertility rate than males. On the other hand, increasing population density favours immature individuals adopting the male role. A positive equilibrium of the system exists whenever fertility and survival rates of one of the sexual roles, if shared by all adults, allow population growing while the opposite happens with the other sexual role. In terms of the female inherent net reproductive number, η_F, it is shown that the positive equilibria are stable when η_F is larger and closed to 1 while for larger values of η_F a certain asymptotic assumption on the investment rate in the female function implies that the population density is permanent. Depending on the other parameters values, the asymptotic behaviour of solutions becomes more complex, even chaotic. In this setting the stabilization/destabilization effects of the abruptness rate in density dependence, of the survival rates and of the competition coefficients are analysed.     

The probability of extinction in a bovine respiratory syncytial virus epidemic model

Backward bifurcation is a relatively recent yet well-studied phenomenon associated with deterministic epidemic models. It allows for the presence of multiple subcritical endemic equilibria, and is generally found only in models possessing a reasonable degree of complexity. One particular aspect of backward bifurcation that appears to have been virtually overlooked in the literature is the potential influence its presence might have on the behaviour of any analogous stochastic model. Indeed, the primary aim of this paper is to investigate this possibility. Our approach is to compare the theoretical probabilities of extinction, calculated via a particular stochastic formulation of a deterministic model exhibiting backward bifurcation, with those obtained from a series of stochastic simulations. We have found some interesting links in the behaviour between the deterministic and stochastic models, and are able to offer plausible explanations for our observations.     

The density distribution of gene loci over the genetic map ofEscherichia coli: Its structural,functional and evolutionary implications

Summary A quantitative analysis was carried out on the dispersion of gene loci over theE. coli genetic map. Therefore, the map was divided into regions characterized by an homogeneous gene density. This created a distribution pattern of gene loci that contained a symmetry axis located near to the origin of DNA replication. The pattern could be subdivided into a set of 22 functional domains containing gene loci whose products revealed a biochemical or functional relatedness. A correlation was found between the boundary positions of these domains and the distribution of F plasmid- and DNA insertion sites over theE. coli chromosome. The structural, functional and evolutionary implications of these findings are discussed.     

The relationships among physical,geometrical and mechanical properties of bone,with a note on the properties of nonhuman primate bone

Since bone reacts to imposed loads by formation and resorption of tissue, analysis of tissue distribution within a bone provides evidence of the adaptation of that bone to a given mechanical function. Definition of these structure-function relationships permits the physical anthropologist to clarify the wide variety of behavioral/morphological adaptations to specific ecological niches in extant primates. From this information, behavior and locomotor function can ultimately be inferred in fossil primates. This paper reviews research which shows the relationships between the physical, geometrical and mechanical properties of bone, so that researchers who are investigating the properties of bone are aware of the numerous interpretations which may be made about structure and function from basic data. In addition, this paper is an attempt to apprise investigators working with primates that comparative data on the properties of primate bone are available, though sparse.     

The influence of environmental variables on the density of larval lampreys in different seasons

Summary The objective of the study was to identify a subset of a set of twenty environmental variables which could explain variations in the density of larval lampreys (Geotria australis) in a south-western Australian stream. Generalised linear modelling, assuming Poisson distributions for the larval counts, led to a different model for each of the four seasons, with variations in larval density being explained in each season by a combination of between five and eight environmental variables. The influence of stream region also had to be taken into account in the model for winter.Four environmental variables (substrate organic material and chlorophyll a, macrophyte roots and low-angle shading) were present in three of the four seasonal models. A further six variables (water depth, substrate depth and profile, medium-sized sands, light intensity, and the presence of an eddy) were each found useful for two models. Two variables (current velocity and substrate profile) were each retained in one model. Eight of the twenty variables were not required for any of the seasonal models. The importance of organic material, shade, eddies, current velocity substrate particle size and a sufficient depth of substrate in our models agree with the largely subjective assessments of larval lamprey habitats made in the field by many previous workers for other lamprey species in diverse geographical localities.Our finding that larval density increased with increases in organic material and unicellular algae in the substrate and with shade, contrasts with the results of a different model based on data collected in a northern European stream. These differences can be related to our use of a more rigorous and comprehensive sampling regime and a more appropriate form of statistical analysis.     

Long-term effects of selection based on the animal model BLUP in a finite population

Monte Carlo simulation was used to assess the long-term effects of truncation selection within small populations using indices (I=f+m) combining mid-parent [f=(a _i+a _d)/2] and Mendelian-sampling (m=a-f) evaluations provided by an animal model BLUP (a=f+m). Phenotypic values of panmictic populations were generated for 30 discrete generations. Assuming a purely additive polygenic model, heritability (h ₂) values were 0.10, 0.25 or 0.50. Two population sizes were considered: five males and 25 females selected out of 50 candidates of each sex (small populations, S) and 50 males and 250 females selected out of 500 candidates in each sex (large populations, L). Selection was carried out on the index defined above with = 1 (animal model BLUP), =1/2, or =0 (selection on within-family deviations). Mass selection was also considered. Selection based on the animal model BLUP (=1) maximized the cumulative genetic gain in L populations. In S populations, selection using = 1/2 and mass selection were more efficient than selection under an animal model (+ 3 to + 7% and + 1 to + 4% respectively, depending on h ²). Selection on within-family deviations always led to the lowest gains. In most cases, the variance of response to selection between replicates did not depend on the selection method. The within-replicate genetic variance and the average coefficient of inbreeding (F) were highly affected by selection with =1 or 1/2, especially in populations of size S. As expected, selection based on within-family deviations was less detrimental in that respect. The number of copies of founder neutral genes at a separate locus, and the probability vector of origin of the genes in reference to the founder animals, were also observed in addition to F values. The conclusion was that selection procedures placing less emphasis on family information might be interesting alternatives to selection based on animal model BLUP, especially for small populations with long-term selection objectives.     

Prediction of the performance of inbred lines derived from a population cross in autumn-sown onions (Allium cepa L.)

Summary A design and model are presented to allow the prediction, in early generations, of the mean and distribution of recombinant inbred lines derived from a cross between two parental populations or partially inbred lines. The procedure has been tested in autumn-sown onions (in the UK) using a wide cross between the openpollinated Japanese cultivar, Senshyu, and a partially inbred line derived from the European cultivar, Rawska. The early generations used for prediction included the first self-pollinated generation of the two parental populations and the F₃ generation produced from the hybrid population. The predictions were tested by reference to the field performance of a random array of inbred lines, which were produced by single-seed descent (SSD) and had been selfed for three generations. The early generations, used for prediction, and a sample of SSD lines were raised alongside each other in each of two seasons. Within each season, good agreement was found between the predicted and observed performance of the recombinant inbred lines for three characters — yield, quality and maturity. This is used as evidence of the validity of the genetical model and the assumptions made. The effects of genotype x environment interactions prevented predictions made in one season being reliably applied to those made in the other and, therefore, reduce the attraction of this type of prediction study to the plant breeder.     

Spatial scale and the detection of density dependence in spruce budworm outbreaks in eastern North America

Using two tests for direct density dependence and standard techniques of time series analysis, we identified density dependence in defoliation time series of the spruce budworm across its outbreak range in eastern North America over the years 1945–1988. We carried out analyses for the entire region and for grid cells of defoliation maps at five spatial scales created by aggregating the smallest grid cells. The rate of detection of direct density dependence, as assessed by two previously published methods, decreased with increasing spatial scale. Using both methods, density dependence was detected more frequently at the periphery of the outbreak range, where defoliation rate was lower. This result suggested that density-dependent regulation may be stronger in those areas. The first order autoregressive process was the basic model for defoliation dynamics overall and the most common model across spatial scales. Second-order processes were encountered much less frequently, and those commonly identified as resulting from delayed density dependence generally occurred across spatial scales at a rate expected by chance alone. Our results were similar to those of other published studies, which have found the detection of density dependence to decrease at larger spatial scales. The results also reinforced the importance of considering spatial scale when diagnosing population processes using time series of abundance for single species. Received: 26 December 1999 / Accepted: 17 March 2000     

The metal bonding domain of the antitumor drug Fe(II)-bleomycin: a DFT investigation

The geometric and electronic structure of ferrous complexes of bleomycin (Fe(II)BLM) has been investigated by means of density functional theory (DFT) calculations. The active site of this antitumor drug is a highly distorted octahedral complex, with the coordination sphere completed by the five known endogenous ligands, including pyrimidine, imidazole, deprotonated amide, and secondary and primary amines. We have addressed the controversial issue of the nature of the sixth axial ligand, which we have identified as the oxygen of the carbamoyl group. Our conclusions are further validated by a comparison with structural data derived from NMR experiments. Moreover, because of the high sensitivity of structural data on the pH of the environment, we have investigated the effect of a different protonation state of the histidine amide on the geometric structure of the Fe(II)BLM complex. The extensive model of the active site of bleomycin considered in this work allows us to check the limitations of previous investigations based on simplified models.Electronic Supplementary Material Supplementary material is available for this article if you access the article at . A link in the frame on the left on that page takes you directly to the supplementary material.An erratum to this article can be found at     

Density-dependent growth and reproduction of the apple snail, Pomacea canaliculata: a density manipulation experiment in a paddy field

To examine density dependence in the survival, growth, and reproduction of Pomacea canaliculata, we conducted an experiment in which snail densities were manipulated in a paddy field. We released paint-marked snails of 15–20 mm shell height into 12 enclosures (pens) of 16 m² at one of five densities – 8, 16, 32, 64, or 128 snails per pen. The survival rate of released snails was 95% and was independent of snail density. The snail density had a significant effect on the growth and egg production of individual snails. This density dependence may have been caused by reduced food availability. The females at high density deposited fewer and smaller egg masses than those at low density, and consequently produced fewer eggs. The females at densities 8 and 16 deposited more than 3000 eggs per female, while the females at density 128 oviposited only 414 eggs. The total egg production per pen was, however, higher at higher snail density. The survival rates of juvenile snails were 21%–37% and were independent of adult density. The juvenile density was positively correlated with the total egg production per pen and hence was higher at higher adult density. However, the density of juveniles larger than 5 mm in shell height, i.e., juveniles that can survive an overwintering period, was not significantly different among density treatments. These results suggest that snail density after the overwintering period is independent of the density in the previous year. Thus, density dependence in growth and reproduction might regulate the population of P. canaliculata in paddies. Received: October 23, 1998 / Accepted: July 16, 1999     

The effects of density,rainfall and environmental temperature on body condition and fecundity in the common toad,Bufo bufo

The body length and body weight of all adult common toads (Bufo bufo) breeding at a pond in south Dorset were measured between 1983 and 1993. Each toad was placed into one of four categories depending on its sex and whether it was either a first time breeder or an animal that had previously bred. The body condition of each male and female toad for each year was compared with the average body condition of all the male and female toads captured over the 11 years of the study so that between-year differences in condition could be detected. Changes in body condition were compared with changes in body condition were compared with changes in toad density, rainfall and climatic temperature during the previous summer (March–September), during hibernation (October–February) and during the month preceding the start of spawning. During the study there was a decline in the body condition of all toad categories and these changes were significantly correlated with changes in toad density and climatic temperature. Toads were also more likely to enter hibernation in poor condition following a hot dry summer than after either cool wet or hot wet summers. Body condition explained 41% of the size-specific variation in fecundity.