The probability of treatment induced drug resistance

We propose a discrete time branching process to model the appearance of drug resistance under treatment. Under our assumptions at every discrete time a pathogen may die with probability 1−p or divide in two with probability p. Each newborn pathogen is drug resistant with probability μ. We start with N drug sensitive pathogens and with no drug resistant pathogens. We declare the treatment successful if all pathogens are eradicated before drug resistance appears. The model predicts that success is possible only if p<1/2. Even in this case the probability of success decreases exponentially with the parameter m=μN. In particular, even with a very potent drug (i.e. p very small) drug resistance is likely if m is large.     

The frequency spectrum of a mutation,and its age,in a general diffusion model

General formulae are derived for the probability density and expected age of a mutation of frequency x in a population, and similarly for a mutation with b copies in a sample of n genes. A general formula is derived for the frequency spectrum of a mutation in a sample. Variable population size models are included. Results are derived in two frameworks: diffusion process models for the frequency of the mutation; and birth and death process models. The coalescent structure within the mutant gene group and the non-mutant group is considered.     

The roles of a process development group in biopharmaceutical process startup

The transfer of processes for biotherapeutic products into finalmanufacturing facilities was frequently problematic during the 1980's and early 1990's, resulting in costly delays to licensure(Pisano 1997). While plant startups for this class of products can become chaotic affairs, this is not an inherent or intrinsic feature. Major classes of process startup problems have been identified andmechanisms have been developed to reduce their likelihood of occurrence. These classes of process startup problems and resolution mechanisms are the major topic of this article. With proper planning and sufficient staffing, the probably of a smooth process startup for a biopharmaceutical product can be very high – i.e., successful process performance will often beachieved within the first two full-scale process lots in the plant. The primary focus of this article is the role of the Process Development Group in helping to assure this high probability of success.     

Introgression of resistance genes between populations: a model study of insecticide resistance in Bemisia tabaci

Introgression is a key process in conservation biology, genetic modification of (crop) species and in the evolutionary ecology of many species. Here we consider the case of introgression of insecticide resistance in the whitefly, Bemisia tabaci. B. tabaci is a species complex consisting of a range of biotypes, known to have a high degree of inter-biotype reproductive isolation. In areas where insecticide resistant and susceptible biotypes of B. tabaci coexist, introgression of the resistance gene will have considerable consequences for whitefly control. Using a stochastic branching process model we calculate the relative importance of life-history traits in determining the probability of introgression given that a hybridization event has occurred. We show that a fitness cost expressed through the average number of eggs laid, has the largest effect on the introgression probability as compared to fitness costs expressed through other life-history parameters. These results change when we consider a reproductive isolation mechanism, for which we show that the fitness cost expressed through the male survival and mating probability have the largest effect on the probability of introgression.     

Estimating a Key Parameter of Mammalian Mating Systems: The Chance of Siring Success for a Mated Male

Studies of multiple paternity in mammals and other animal species generally report proportion of multiple paternity among litters, mean litter sizes, and mean number of sires per litter. It is shown how these variables can be used to produce an estimate of the probability of reproductive success for a male that has mated with a female. This estimate of male success is more informative about the mating system that alternative measures, like the proportion of litters with multiple paternity or the mean number of sires per litter. The probability of success for a mated male can be measured both theoretically and empirically, and gives an estimate of the intensity of sperm competition and of a male's “confidence of paternity” upon mating. The probability of success for mated males for ten “exemplar” species of mammals is estimated and they are compared for insights into the functioning of their mating systems.     

Paternal reproductive success drives sex allocation in a wild mammal

Parents should bias sex allocation toward offspring of the sex most likely to provide higher fitness returns. Trivers and Willard proposed that for polygynous mammals, females should adjust sex‐ratio at conception or bias allocation of resources toward the most profitable sex, according to their own body condition. However, the possibility that mammalian fathers may influence sex allocation has seldom been considered. Here, we show that the probability of having a son increased from 0.31 to 0.60 with sire reproductive success in wild bighorn sheep (Ovis canadensis). Furthermore, our results suggest that females fertilized by relatively unsuccessful sires allocated more energy during lactation to daughters than to sons, while the opposite occurred for females fertilized by successful sires. The pattern of sex‐biased offspring production appears adaptive because paternal reproductive success reduced the fitness of daughters and increased the average annual weaning success of sons, independently of maternal allocation to the offspring. Our results illustrate that sex allocation can be driven by paternal phenotype, with profound influences on the strength of sexual selection and on conflicts of interest between parents.     

Fixation probability of rare nonmutator and evolution of mutation rates

Although mutations drive the evolutionary process, the rates at which the mutations occur are themselves subject to evolutionary forces. Our purpose here is to understand the role of selection and random genetic drift in the evolution of mutation rates, and we address this question in asexual populations at mutation‐selection equilibrium neglecting selective sweeps. Using a multitype branching process, we calculate the fixation probability of a rare nonmutator in a large asexual population of mutators and find that a nonmutator is more likely to fix when the deleterious mutation rate of the mutator population is high. Compensatory mutations in the mutator population are found to decrease the fixation probability of a nonmutator when the selection coefficient is large. But, surprisingly, the fixation probability changes nonmonotonically with increasing compensatory mutation rate when the selection is mild. Using these results for the fixation probability and a drift‐barrier argument, we find a novel relationship between the mutation rates and the population size. We also discuss the time to fix the nonmutator in an adapted population of asexual mutators, and compare our results with experiments.     

Sex-Age Selectivity and Correlates of Capture for Winter-Trapped White-Tailed Deer

ANDREW J. TYRE⁷ ABSTRACT Despite the common use of Clover traps to capture white-tailed deer (Odocoileus virginianus), little published information exists quantifying trap success, trap selectivity (sex-age selection), or weather correlates of trap success. We quantified these relationships using white-tailed deer data from 3 study sites in the Lower Peninsula of Michigan, USA, during winters 2001–2007. We captured 610 deer in 8,569 trap-nights; pooled capture success was 0.07 deer/trap-night, although site-year success varied from 0.021 to 0.086. We compared sex-age classes (fawn [pooled by sex], ad M, ad F) captured with sex-age classes estimated to be available on each study site during each capture season. We used generalized linear mixed modeling to construct 19 a priori models to describe probability of capture success as a function of weather covariates (daily min. temp [° C], daily snowfall [cm], daily snow depth [cm]), Julian day, site, and year. General selection patterns included fawns captured more than expected and adult males captured less than expected; adult females were generally neutrally selected. The quasi-Akaike's Information Criterion best model within our set was described by the global model without Julian day and contained all 3 weather covariates and site-year effects. Our model provided some evidence that as daily snow depth increased, probability of capture increased; the positive effect of daily snowfall on capture probability was dependent on decreasing daily minimum temperature. Our results may be used to increase efficacy of deer capture programs by researchers and managers through informed decision-making about when to allocate effort (e.g., if extreme winter weather conditions are predicted) and when to consider alternative methods (e.g., if capture of ad M is an objective).     

Sex-biased survival and breeding dispersal probability in a patchy population of the Rock Sparrow Petronia petronia

Demographic parameters of the polygynous Rock Sparrow Petronia petronia were investigated in a small patchy population in the Italian Alps. The population included two distinct breeding patches that differed in altitude and breeding success. Survival parameters were estimated by capture–recapture analysis of 170 individually marked animals. At the whole population level (Cormack–Jolly Seber model), no sex difference in local survival probability was detected. We then used a multisite capture–recapture approach (Arnason–Schwarz model) to investigate patch-specific survival probability and between-patch dispersal rate conditional on survival. Female local survival in the higher-altitude patch (mean ± se: 0.54 ± 0.04) was significantly greater than in the other patch (0.37 ± 0.04), probably because permanent emigration from the study area was greater. In the higher-altitude patch, breeding dispersal was constrained by the altitude limit and breeding movements were directed toward the patch at lower altitude. The probability of changing patch in the next breeding season was significantly higher for females (range 0.16–0.21) than for males (0.01–0.03). Breeding success varied between years and patches, being lower in the patch where frequency of polygamy and female local mortality were higher.     

The probability of evolutionary rescue: towards a quantitative comparison between theory and evolution experiments

Evolutionary rescue occurs when a population genetically adapts to a new stressful environment that would otherwise cause its extinction. Forecasting the probability of persistence under stress, including emergence of drug resistance as a special case of interest, requires experimentally validated quantitative predictions. Here, we propose general analytical predictions, based on diffusion approximations, for the probability of evolutionary rescue. We assume a narrow genetic basis for adaptation to stress, as is often the case for drug resistance. First, we extend the rescue model of Orr & Unckless (Am. Nat. 2008 172, 160–169) to a broader demographic and genetic context, allowing the model to apply to empirical systems with variation among mutation effects on demography, overlapping generations and bottlenecks, all common features of microbial populations. Second, we confront our predictions of rescue probability with two datasets from experiments with Saccharomyces cerevisiae (yeast) and Pseudomonas fluorescens (bacterium). The tests show the qualitative agreement between the model and observed patterns, and illustrate how biologically relevant quantities, such as the per capita rate of rescue, can be estimated from fits of empirical data. Finally, we use the results of the model to suggest further, more quantitative, tests of evolutionary rescue theory.     

Sons are made from old stores: sperm storage effects on sex ratio in a lizard

Sperm storage is a widespread phenomenon across taxa and mating systems but its consequences for central fitness parameters, such as sex ratios, has rarely been investigated. In Australian painted dragon lizards (Ctenophorus pictus), we describe elsewhere that male reproductive success via sperm competition is largely an effect of sperm storage. That is, sperm being stored in the female reproductive tract out-compete more recently inseminated sperm in subsequent ovarian cycles. Here we look at the consequences of such sperm storage for sex allocation in the same species, which has genetic sex determination. We show that stored sperm have a 23% higher probability of producing sons than daughters. Thus, shifts in sex ratio, for example over the reproductive season, can partly be explained by different survival of son-producing sperm or some unidentified female mechanism taking effect during prolonged storage.     

FEMALE-BIASED SEX RATIOS: INDIVIDUAL OR GROUP SELECTION?

The evolution of biased sex ratios in a randomly structured population stems from individual selection acting through local parental control (LPC) of the sex ratio and hence of the mating success of the sons and/or daughters. As a general rule, the sex ratio is biased away from the sex whose fitness is most affected by changes in the local sex ratio. This is the sex whose fitness is subject to the most effective parental control. The bias acts to increase the fitness of the rarer, controlled sex and to increase parental productivity. In the specific case of the evolution of the female-biased Hamiltonian ratios, LPC can affect the mating success of sons but has no effect on the success of daughters. It is argued here and elsewhere (Nunney, unpubl.) that group selection can only promote the spread of a genotype through the maintenance of a positive association of individuals of that genotype. The importance of positive association is well established in the special case of kin selection. Given such a definition, group selection plays no part in the evolution of the Hamiltonian sex ratios, although it is possible to conceive of circumstances under which group selection could favor an even more extreme sex ratio bias. In general, such circumstances involve kin selection. It is argued that the examination of differences in group productivity is not a useful way of looking at the process of natural selection, since (i) by dividing up almost any evolving population into random groups, some groups (those with the highest frequency of the fittest individuals) will be more productive than others; and (ii) in the specific case of the evolution of the Hamiltonian ratios, it is possible to develop models either with or without a group structure and get the same result. Hamilton (1967) originally suggested that a female-biased sex ratio arose in his model because of the advantage of reducing local mate competition (specifically, reducing competition between brothers for mates). This possibility was eliminated by developing a model in which competition between the brothers was prevented regardless of the sex ratio. It was found that the optimum sex-ratio strategy was unaffected. On the other hand, the idea of local parental control has, in each case examined, been able to account for the predicted optimum strategy.     

Female‐biased size dimorphism in a diapausing caddisfly,Mesophylax aspersus: effect of fecundity and natural and sexual selection

1. The effect of mating success, female fecundity and survival probability associated with intra‐sex variation in body size was studied in Mesophylax aspersus, a caddisfly species with female‐biased sexual size dimorphism, which inhabits temporary streams and aestivates in caves. Adults of this species do not feed and females have to mature eggs during aestivation. 2. Thus, females of larger size should have a fitness advantage because they can harbour more energy reserves that could influence fecundity and probability of survival until reproduction. In contrast, males of smaller size might have competitive advantages over others in mating success. 3. These hypotheses were tested by comparing the sex ratio and body size of individuals captured before and after the aestivation period. The associations between body size and female fecundity, and between mating success and body size of males, were explored under laboratory conditions. 4. During the aestivation period, the sex ratio changed from 1 : 1 to male biased (4 : 1), and a directional selection on body size was detected for females but not for males. Moreover, larger clutches were laid by females of larger size. Finally, differences in mating success between small and large males were not detected. These results suggest that natural selection (i.e. the differential mortality of females associated with body size) together with possible fecundity advantages, are important factors responsible of the sexual size dimorphism of M. aspersus. 5. These results highlight the importance of taking into account mechanisms other than those traditionally used to explain sexual dimorphism. Natural selection acting on sources of variation, such as survival, may be as important as fecundity and sexual selection in driving the evolution of sexual size dimorphism.     

Reproductive success in reindeer males in a herd with varying sex ratio

In polygynous species, male reproductive success is often correlated with dominance status of individual males and sex ratio in the population. Reindeer, Rangifer tarandus, is a polygynous species, and here we compared the variation in male reproductive success and dominance status during two successive years in a herd with a male:female sex ratio of 1:7 and 1:3. Copulations were recorded, together with data on male dominance hierarchy and size of mating groups. Male reproductive success was estimated by paternity analysis of calves using microsatellite DNA markers. The distribution of reproductive success among the males was highly skewed for both years with the most dominant male also being the most successful. The largest mating group was established in the herd with the least skew in sex ratio. In this herd some of the adult males present were less reproductively successful than some of the more subordinate younger males. Estimates of the mating group size of males, correcting for dominance status when more than one male is present in the groups, gave good prediction of individual males' reproductive success.     

Female mating success and risk of pre-reproductive death in a protandrous grasshopper

Numerous studies have assessed the adaptive value of protandry for males in several insect species, considering that male emergence is determined by female availability. However, the possible advantage of the time of emergence for females on their mating success in protandrous insect species has only been explored theoretically. By studying the grasshopper Sphenarium purpurascens we evaluated the hypothesis that late emergence could be adaptive for females. If female maturation occurs when the population density is higher and the sex ratio (males/females) is biased to males, their probability of mating increases. Thus, in this study we estimated (1) the opportunity for mating in females as a function of their sexual maturation time, population density, and sex ratio at the moment they reached sexual maturity. In addition, (2) an analysis incorporating female body size and the total number of female matings was performed. Both analyses support the occurrence of protandry in the studied population. Under the first approach, females with intermediate maturation time had a higher probability of being mated than earlier and late matured females. Thus, it suggests that stabilising selection is acting on female maturation time and this may affect selection on male maturation time. Furthermore, the proportion of mated females increased when the sex ratio was biased to males, and stabilising selection on maturation time was detected also. However, the number of matings of a female depended on her body size. Females with larger body size had more matings than smaller ones at the beginning of the reproductive season. Because selection acts differently on maturation time in males and females of S. purpurascens this result is consistent with a condition for the maintenance of protandry in the population. The present results are discussed in the light of the models for the evolution of protandry.     

Selection and reproductive success in males of the dragonfly,Orthetrum japonicum (Odonata: Libellulidae)

Reproductive success, copulation success, and mating success were measured for a population of male dragonflies,Orthetrum japonicum. Copulation success explained the greatest variation in reproductive success. The proportion of copulations followed by oviposition was positively correlated with the number of oviposited eggs per mating. Directional selection on four morphological characters was estimated. The effect of selection on correlated traits was comparable to that of direct selection. Directional selection varied between traits and between episodes in a single trait. The probability that the observed directional selection on the four morphological traits was expected under the condition of the selective neutrality of traits was not smaller than 5%.     

Rate of deleterious mutation and the distribution of its effects on fitness in vesicular stomatitis virus

Despite their importance, the parameters describing the spontaneous deleterious mutation process have not been well described in many organisms. If mutations are important for the evolution of every living organism, their importance becomes critical in the case of RNA-based viruses, in which the frequency of mutation is orders of magnitude larger than in DNA-based organisms. The present work reports minimum estimates of the deleterious mutation rate, as well as the characterization of the distribution of deleterious mutational effects on the total fitness of the vesicular stomatitis virus (VSV). The estimates are based on mutation-accumulation experiments in which selection against deleterious mutations was minimized by recurrently imposing genetic bottlenecks of size one. The estimated deleterious mutation rate was 1.2 mutations per genome and generation, with a mean fitness effect of –0.39% per generation. At the end of the mutation-accumulation experiment, the average reduction in fitness was 38% and the distribution of accumulated deleterious effects was, on average, left-skewed. The magnitude of the skewness depends on the initial fitness of the clone analysed. The implications of our findings for the evolutionary biology of RNA viruses are discussed.     

Restriction-modification systems and bacteriophage invasion: Who wins?

The success of a phage that infects a bacterial cell possessing a restriction-modification (R-M) system depends on the activities of the host methyltransferase and restriction endonuclease, and the number of susceptible sites in the phage genome. However, there is no model describing this dependency and linking it to observable parameters such as the fraction of surviving cells under excess phage, or probability of plating at low amount of phages. We model the phage infection of a cell with a R-M system as a pure birth process with a killing state. We calculate the transitional probabilities and the stationary distribution for this process. We generalize the model developed for a single cell to the case of multiple identical cells invaded by a Poisson-distributed number of phages. The R-M enzyme activities are assumed to be constant, time-dependent, or random. The obtained results are used to estimate the ratio of the methyltransferase and endonuclease activities from the observed fraction of surviving cells.     

Modeling parasitism rate and parasitism risk: an illustration using a colonially nesting songbird, the red-winged blackbird Agelaius phoeniceus

Ornithologists interested in the drivers of nest success and brood parasitism benefit from the development of new analytical approaches. One example is the development of so-called "log exposure" models for analyzing nest success. However, analyses of brood parasitism data have not kept pace with developments in nest success analyses. The standard approach uses logistic regression which does not account for multiple parasitism events, nor does it prevent bias from using observed proportions of parasitized nests. Likewise, logistic regression analyses do not capture fine scale temporal variation in parasitism. At first glance, it might be tempting to apply log exposure models to parasitism data, but the process of parasitism is inherently different from the process of nest predation. We modeled daily parasitism rate as a Poisson process, which allowed us to correct potential biases in parasitism rate. We were also able to use our estimated parasitism rate to model parasitism risk as the probability of one or more parasitism events. We applied this model to red-winged blackbird Agelaius phoeniceus nesting colonies subject to parasitism by brown-headed cowbirds Molothrus ater . Our approach allowed us to model parasitism using a wider rage of covariates, especially functions of time. We found strong support for models combining temporal fluctuations in parasitism rate and nest-site characteristics. Similarly, we found that our annual predicted parasitism risk was lower on average than the risk estimated from observed parasitism levels. Our approach improves upon traditional logistic regression analyses and opens the door for more mechanistic modeling of the process of parasitism.     

Artificial selection on ant female caste ratio uncovers a link between female‐biased sex ratios and infection by Wolbachia endosymbionts

Social insect sex and caste ratios are well‐studied targets of evolutionary conflicts, but the heritable factors affecting these traits remain unknown. To elucidate these factors, we carried out a short‐term artificial selection study on female caste ratio in the ant Monomorium pharaonis. Across three generations of bidirectional selection, we observed no response for caste ratio, but sex ratios rapidly became more female‐biased in the two replicate high selection lines and less female‐biased in the two replicate low selection lines. We hypothesized that this rapid divergence for sex ratio was caused by changes in the frequency of infection by the heritable bacterial endosymbiont Wolbachia, because the initial breeding stock varied for Wolbachia infection, and Wolbachia is known to cause female‐biased sex ratios in other insects. Consistent with this hypothesis, the proportions of Wolbachia‐infected colonies in the selection lines changed rapidly, mirroring the sex ratio changes. Moreover, the estimated effect of Wolbachia on sex ratio (~13% female bias) was similar in colonies before and during artificial selection, indicating that this Wolbachia effect is likely independent of the effects of artificial selection on other heritable factors. Our study provides evidence for the first case of endosymbiont sex ratio manipulation in a social insect.