The unstable dynamics of multiple alternative reproductive tactics

Although negative frequency-dependent fitness is argued to allow the stable coexistence of two alternative reproductive types (such as resource defenders and reproductive parasites), no existing theory has considered a third strategy where resource defenders invest differentially in defence against reproductive parasites. Here, we present the results of a three-strategy game, where reproductive parasites interact with two resource defenders: 'Susceptibles' defend more resources but lose more reproductive success to parasites. 'Immunes' lose less to parasites, but immunity carries a reproductive cost. We show that the inclusion of a third strategy dramatically changes the evolutionary dynamics, such that for a wide range of parameter values, our model predicts the continuous sequential invasion of the three strategies instead of stable coexistence. Our results therefore limit the generality of the prediction that frequency-dependent fitness necessarily allows alternative reproductive tactics to coexist at equilibrium and may also explain the observed dynamics of some multiple-strategy systems.     

Reproductive competition promotes the evolution of female weaponry

Secondary sexual traits in females are a relatively rare phenomenon. Empirical studies have focused on the role of male mate choice in their evolution; however, recently it has been suggested that secondary sexual traits in females are more likely to be under selection via reproductive competition. We investigated female competition and the influence of female phenotype on fitness in Onthophagus sagittarius, a species of dung beetle that exhibits female-specific horns. We compared reproductive fitness when females were breeding in competition versus breeding alone and found that competition for breeding resources reduced fitness for all females, but that smaller individuals suffered a greater fitness reduction than larger individuals. When females were matched for body size, those with the longest horns gained higher reproductive fitness. The fitness function was positive and linear, favouring increased horn expression. Thus, we present evidence that female body size and horn size in O. sagittarius are under directional selection via competition for reproductive resources. Our study is a rare example of female contest competition selecting for female weaponry.     

Using potential reproductive rates to predict mating competition among individuals qualified to mate

The potential reproductive rate (PRR), which is the offspringproduction per unit time each sex would achieve if unconstrainedby mate availability, often differs between the sexes. An increasingsexual difference in PRR predicts an intensified mating competitionamong the sex with the higher PRR. The use of PRR can providedetailed predictions of when, where, and how the intensityin mating competition and hence sexual selection will vary.Previous models have focused on the "time out" from mate searchingas a major component of PRR. Here, we suggest some improvementsand clarifications: in a population where individuals haveto compete for specific resources that are prerequisites formating (e.g., nest sites), individuals unable to obtain sucha resource will not qualify to mate. We suggest how a conceptof the ratio of males and females qualified to mate, Q, canimprove previous models designed to use the sexual differencein PRR to estimate the operational sex ratio (OSR). Further,when estimating the sexual difference in PRR of a population,it is important that each sex is given free access to matingpartners. Jointly, this provides an empirical approach basedon estimates of Q and the sexual difference in PRR.     

Improving estimates of the basic reproductive ratio: using both the mean and the dispersal of transition times

In both within-host and epidemiological models of pathogen dynamics, the basic reproductive ratio, R(0), is a powerful tool for gauging the risk associated with an emerging pathogen, or for estimating the magnitude of required control measures. Techniques for estimating R(0), either from incidence data or in-host clinical measures, often rely on estimates of mean transition times, that is, the mean time before recovery, death or quarantine occurs. In many cases, however, either data or intuition may provide additional information about the dispersal of these transition times about the mean, even if the precise form of the underlying probability distribution remains unknown. For example, we may know that recovery typically occurs within a few days of the mean recovery time. In this paper we elucidate common situations in which R(0) is sensitive to the dispersal of transition times about their respective means. We then provide simple correction factors that may be applied to improve estimates of R(0) when not only the mean but also the standard deviation of transition times out of the infectious state can be estimated.     

Intraspecific sperm competition genes enforce post-mating species barriers in Drosophila

Sexual selection and sexual conflict are considered important drivers of speciation, based on both theoretical models and empirical correlations between sexually selected traits and diversification. However, whether reproductive isolation between species evolves directly as a consequence of intrapopulation sexual dynamics remains empirically unresolved, in part because knowledge of the genetic mechanisms (if any) connecting these processes is limited. Here, we provide evidence of a direct mechanistic link between intraspecies sexual selection and reproductive isolation. We examined genes with known roles in intraspecific sperm competition (ISC) in D. melanogaster and assayed their impact on conspecific sperm precedence (CSP). We found that two such genes (Acp36DE and CG9997) contribute to both offensive sperm competition and CSP; null/knockdown lines both had lower competitive ability against D. melanogaster conspecifics and were no longer able to displace heterospecific D. simulans sperm in competitive matings. In comparison, Sex Peptide (Acp70A)—another locus essential for ISC—does not contribute to CSP. These data indicate that two loci important for sperm competitive interactions have an additional role in similar interactions that enforce post-mating reproductive isolation between species, and show that sexual selection and sexual isolation can act on the same molecular targets in a gene-specific manner.     

A model for the transmission dynamics of Orientia tsutsugamushi among its natural reservoirs

The bacteria Orientia tsutsugamushi is the causative agent of scrub typhus, a prevalent disease in Asian countries that can affect humans and which shows an alarming increase of cases during the last years, especially in rural areas. Unfortunately, there is no vaccine for scrub typhus, and antibiotic treatments successfully used in the past appear to be inefficient to treat some strains of O. tsutsugamushi. We introduce a mathematical model that approximates the dynamics of the bacteria among its natural reservoirs. After computing the basic reproductive number from the proposed model, we explore its sensitivity to the parameter values that may be affected by application of control measures. This theoretical model may be of interest to pest managers as well as health authorities interested in gaining insight into the public management of the disease, through a better understanding of its qualitative dynamics.     

Contact rate calculation for a basic epidemic model

Mass-action epidemic models are the foundation of the majority of studies of disease dynamics in human and animal populations. Here, a kinetic model of mobile susceptible and infective individuals in a two-dimensional domain is introduced, and an examination of the contact process results in a mass-action-like term for the generation of new infectives. The conditions under which density dependent and frequency dependent transmission terms emerge are clarified. Moreover, this model suggests that epidemics in large mobile spatially distributed populations can be well described by homogeneously mixing mass-action models. The analysis generates an analytic formula for the contact rate (β) and the basic reproductive ratio (R₀) of an infectious pathogen, which contains a mixture of demographic and epidemiological parameters. The analytic results are compared with a simulation and are shown to give good agreement. The simulation permits the exploration of more realistic movement strategies and their consequent effect on epidemic dynamics.     

Kolmogorov-type competition model with finitely supported allocation profiles and its applications to plant competition for sunlight

A Kolmogorov-type competition model featuring allocation profiles, gain functions, and cost parameters is examined. For plant species that compete for sunlight according to the canopy partitioning model [R.R. Vance and A.L. Nevai, Plant population growth and competition in a light gradient: a mathematical model of canopy partitioning, J. Theor. Biol. 245 (2007), pp. 210–219] the allocation profiles describe vertical leaf placement, the gain functions represent rates of leaf photosynthesis at different heights, and the cost parameters signify the energetic expense of maintaining tall stems necessary for gaining a competitive advantage in the light gradient. The allocation profiles studied here, being supported on three alternating intervals, determine “interior” and “exterior” species. When the allocation profile of the interior species is a delta function (a big leaf) then either competitive exclusion or coexistence at a single globally attracting equilibrium point occurs. However, if the allocation profile of the interior species is piecewise continuous or a weighted sum of delta functions (multiple big leaves) then multiple coexistence states may also occur.     

资源竞争理论及其研究进展

介绍了国外近20年来发展起来的一种新的竞争理论——资源竞争理论。该理论包含两个主要假说,即R^*-法则和资源比假说。资源竞争理论已在微生物、微藻、高等植物及浮游动物中得到广泛的实验验证。阐述了资源竞争理论形成的基础——Monod竞争模型和Droop竞争模型。对两种模型在稳态及非稳态条件下的预测性能作了比较：对于稳态下的竞争,两种模型皆能做出较好的预测,但使用Monod模型更为简便;对于非稳态下的竞争,使用Droop模型更为合理。对资源竞争理论的发展趋势作了展望。     

Parameterization of individual-based models: comparisons with deterministic mean-field models

The relating of deterministic, mean-field models into network models, where epidemic spread occurs between interconnected susceptible and infectious individuals or populations, requires careful consideration. Here, we discuss models that consider differently the manner in which contact rate and infectiousness change over time, with different algorithms suitable for different underlying processes. Though these models give coincidental results to the mean-field in the case of large, highly connected networks, the results when sparsely connected networks are considered may differ. Different subsets of the parameters from the mean-field epidemic (R(0), generation time, infectiousness, etc.) are preserved in each case. Despite these differences, simulated epidemics generated under some model architectures are insensitive to the average degree of contact amongst nodes, k. Model-based estimates of k may be model dependent, and must therefore be viewed with caution.     

Optimal control of drug therapy: melding pharmacokinetics with viral dynamics

Pharmacokinetics were melded with a viral dynamical model to design an optimal drug administration regimen such that the basic reproductive number for the virus was minimized. One-compartmental models with two kinds of drug delivery routes, intravenous and extravascular with multiple dosages, and two drug elimination rates, first order and Michaelis-Menten rates, were considered. We defined explicitly the basic reproductive number for the viral dynamical model melded with pharmacokinetics. When the average plasma drug concentration was constant, intravenous administration of the drug with small dosages applied frequently minimized the basic reproductive number. For extravascular administration, the basic reproductive number initially decreases to a trough point and then increases as the drug dosage increases. When a therapeutic window is considered, numerical studies indicate that the wider the window, the smaller the basic reproductive number. Once the width of the therapeutic window is fixed, the basic reproductive number monotonously declines as the minimum therapeutic level increases. The findings suggest that the existence of drug dosage and drug administration interval that minimize the basic reproductive number could help design the optimal drug administration regimen.     

Female reproductive competition within families in rural Gambia

Many studies show that the extended human family can be helpful in raising offspring, with maternal grandmothers, in particular, improving offspring survival. However, less attention has been given to competition between female kin and co-residents. It has been argued that reproductive conflict between generations explains the evolution of menopause in cooperatively breeding species where females disperse, and that older females are related to the offspring of younger females through their sons, whereas younger, incoming females are unrelated to older females. This means the pattern of help will be asymmetric, so older females lose in reproductive conflict and become 'sterile helpers'. Here, we seek evidence for female reproductive competition using longitudinal demographic data from a rural Gambian population, and examine when women are helping or harming each other's reproductive success. We find that older women benefit and younger women suffer costs of reproductive competition with women in their compound. But the opposite is found for mothers and daughters; if mother and daughter's reproductive spans overlap, the older woman reduces her reproduction if the younger woman (daughter) reproduces, whereas daughters' fertility is unaffected by their mothers' reproduction. Married daughters are not generally co-resident with their mothers, so we find not only competition effects with co-resident females, but also with daughters who have dispersed. Dispersal varies across human societies, but our results suggest reproductive conflict could be influencing reproductive scheduling whatever the dispersal pattern. A cultural norm of late male marriage reduces paternal grandmother/daughter-in-law reproductive overlap almost to zero in this population. We argue that cultural norms surrounding residence and marriage are themselves cultural adaptations to reduce reproductive conflict between generations in human families.     

Reproductive competition and the evolution of extreme birth synchrony in a cooperative mammal

Reproductive events in animal societies often show a high degree of temporal clustering, but the evolutionary causes of this synchronization are poorly understood. Here, we suggest that selection to avoid the negative effects of competition with other females has given rise to a remarkable degree of birth synchrony in the communal-breeding banded mongoose (Mungos mungo). Within banded mongoose groups, births are highly synchronous, with 64 per cent of females giving birth on exactly the same night. Our results indicate that this extreme synchrony arises because offspring suffer an increased risk of infanticide if their mother gives birth before other females, but suffer in competition with older littermates if their mother gives birth after them. These findings highlight the important influence that reproductive competition can have for the evolution of reproductive synchrony.     

Apparent competition and recovery from infection

We use mathematical models to analyse how the recovery rate from infection influences the fitness of a host in a setting of interspecific competition. We show that sub-optimal immunity against pathogens can be advantageous for the host in the presence of cross-species infection. Weaker immunity allows the parasite to be used as a biological weapon, and this increases the fitness of the host relative to a competitor. A parameter region is observed in which the outcome of competition depends on the initial conditions. We extend this model and consider the dynamics in a spatial setting and find that the outcome depends on the migration rate of the host species. At low migration rates, coexistence of the host species is possible across space. For higher migration rates, the host species characterized by a lower recovery rate can invade the territory of its competitor. Finally, we study these dynamics in an evolutionary setting. Although a lower recovery rate from infection can increase the competitive ability of a species, we find that evolution maximizes the recovery rate and minimizes parasite burden. The models presented are related to the concept of apparent competition, and our results are discussed in relation to both theoretical and empirical studies.     

Reproductive competition triggers mass eviction in cooperative banded mongooses

In many vertebrate societies, forced eviction of group members is an important determinant of population structure, but little is known about what triggers eviction. Three main explanations are: (i) the reproductive competition hypothesis, (ii) the coercion of cooperation hypothesis, and (iii) the adaptive forced dispersal hypothesis. The last hypothesis proposes that dominant individuals use eviction as an adaptive strategy to propagate copies of their alleles through a highly structured population. We tested these hypotheses as explanations for eviction in cooperatively breeding banded mongooses (Mungos mungo), using a 16-year dataset on life history, behaviour and relatedness. In this species, groups of females, or mixed-sex groups, are periodically evicted en masse. Our evidence suggests that reproductive competition is the main ultimate trigger for eviction for both sexes. We find little evidence that mass eviction is used to coerce helping, or as a mechanism to force dispersal of relatives into the population. Eviction of females changes the landscape of reproductive competition for remaining males, which may explain why males are evicted alongside females. Our results show that the consequences of resolving within-group conflict resonate through groups and populations to affect population structure, with important implications for social evolution.     

A generic theoretical model for biological control of foliar plant diseases

We have developed a generic modelling framework to understand the dynamics of foliar pathogen and biocontrol agent (BCA) populations in order to predict the likelihood of successful biocontrol in relation to the mechanisms involved. The model considers biocontrol systems for foliar pathogens only and, although it is most applicable to fungal BCA systems, does not address a specific biocontrol system. Four biocontrol mechanisms (competition, antibiosis, mycoparasitism and induced resistance) were included within the model rubric. Because of the wide range of mechanisms involved we use Trichoderma/Botrytis as an exemplar system. Qualitative analysis of the model showed that the rates of a BCA colonising diseased and/or healthy plant tissues and the time that the BCA remains active are two of the more important factors in determining the final outcome of a biocontrol system. Further evaluation of the model indicated that the dynamic path to the steady-state population levels also depends critically on other parameters such as the host-pathogen infection rate. In principle, the model can be extended to include other potential mechanisms, including spatio-temporal heterogeneity, fungicide effects, non-fungal BCA and strategies for BCA application, although with a cost in model tractability and ease of interpretation.     

A new SEIR epidemic model with applications to the theory of eradication and control of diseases, and to the calculation of R0

We present a novel SEIR (susceptible-exposure-infective-recovered) model that is suitable for modeling the eradication of diseases by mass vaccination or control of diseases by case isolation combined with contact tracing, incorporating the vaccine efficacy or the control efficacy into the model. Moreover, relying on this novel SEIR model and some probabilistic arguments, we have found four formulas that are suitable for estimating the basic reproductive numbers R(0) in terms of the ratio of the mean infectious period to the mean latent period of a disease. The ranges of R(0) for most known diseases, that are calculated by our formulas, coincide very well with the values of R(0) estimated by the usual method of fitting the models to observed data.