Wolbachia versus dengue: Evolutionary forecasts.

A novel form of biological control is being applied to the dengue virus. The agent is the maternally transmitted bacterium Wolbachia, naturally absent from the main dengue vector, the mosquito Aedes aegypti. Three Wolbachia-based control strategies have been proposed. One is suppression of mosquito populations by large-scale releases of males incompatible with native females; this intervention requires ongoing releases. The other interventions transform wild mosquito populations with Wolbachia that spread via the frequency-dependent fitness advantage of Wolbachia-infected females; those interventions potentially require just a single, local release for area-wide disease control. One of these latter strategies uses Wolbachia that shortens mosquito life, indirectly preventing viral maturation/transmission. The other strategy uses Wolbachia that block viral transmission. All interventions can be undermined by viral, bacterial or mosquito evolution; viral virulence in humans may also evolve. We examine existing theory, experiments and comparative evidence to motivate predictions about evolutionary outcomes. (i) The life-shortening strategy seems the most likely to be thwarted by evolution. (ii) Mosquito suppression has a reasonable chance of working locally, at least in the short term, but long-term success over large areas is challenging. (iii) Dengue blocking faces strong selection for viral resistance but may well persist indefinitely at some level. Virulence evolution is not mathematically predictable, but comparative data provide no precedent for Wolbachia increasing dengue virulence. On balance, our analysis suggests that the considerable possible benefits of these technologies outweigh the known negatives, but the actual risk is largely unknown

A one locus, biased mutation model and its equivalence to an unbiased model

Experimental data suggests that for some continuously varying characters under stabilising selection, mutation may cause a mean change in the value of the character. A one locus, mathematical model of a continuously varying biological character with this property of biased mutation is investigated. Via a mathematical transformation, the equilibrium equation describing a large population of individuals is reduced to the equilibrium equation describing a mutationally unbiased problem. Knowledge of an unbiased problem is thus su¢ cient to determine all equilibrium properties of the corresponding biased problem. In the biased mutation problem, the dependence of the mean equilibrium value of the character, as a function of the mutational bias, is non monotonic and remains small, for all levels of mutational bias. The analysis presented in this work sheds new light on Turelli's House of Cards approximation

Commentary: Fisher's infinitesimal model: A story for the ages.

Mendel (1866) suggested that if many heritable "factors" contribute to a trait, near-continuous variation could result. Fisher (1918) clarified the connection between Mendelian inheritance and continuous trait variation by assuming many loci, each with small effect, and by informally invoking the central limit theorem. Barton et al. (2017) rigorously analyze the approach to a multivariate Gaussian distribution of the genetic effects for descendants of parents who may be related. This commentary distinguishes three nested approximations, referred to as "infinitesimal genetics," "Gaussian descendants" and "Gaussian population," each plausibly called "the infinitesimal model." The first and most basic is Fisher's "infinitesimal" approximation of the underlying genetics - namely, many loci, each making a small contribution to the total variance. As Barton et al. (2017) show, in the limit as the number of loci increases (with enough additivity), the distribution of genotypic values for descendants approaches a multivariate Gaussian, whose variance-covariance structure depends only on the relatedness, not the phenotypes, of the parents (or whether their population experiences selection or other processes such as mutation and migration). Barton et al. (2017) call this rigorously defensible "Gaussian descendants" approximation "the infinitesimal model." However, it is widely assumed that Fisher's genetic assumptions yield another Gaussian approximation, in which the distribution of breeding values in a population follows a Gaussian - even if the population is subject to non-Gaussian selection. This third "Gaussian population" approximation, is also described as the "infinitesimal model." Unlike the "Gaussian descendants" approximation, this third approximation cannot be rigorously justified, except in a weak-selection limit, even for a purely additive model. Nevertheless, it underlies the two most widely used descriptions of selection-induced changes in trait means and genetic variances, the "breeder's equation" and the "Bulmer effect." Future generations may understand why the "infinitesimal model" provides such useful approximations in the face of epistasis, linkage, linkage disequilibrium and strong selection

Polisemia di un gesto: l'emittere hastam dei duces e dei feziali

L’articolo presenta una riflessione intorno a un testo del commentario di Servio all’Eneide (Serv. Aen. 9.52), nel quale si descrivono taluni aspetti della procedura feziale per la dichiarazione di guerra. Interessa, in particolare, il gesto della emissio hastae in territorio nemico, quale atto conclusivo della fase ‘dialettica’ e inizio della fase di scontro armato. Servio cita un passaggio di Varrone (Varr. Logistorici frg. 2 Semi), nel quale viene ricordato l’identico gesto compiuto dal comandante militare al momento di entrare con l’esercito in «agrum hostilem», allo scopo di fissare un luogo per l’accampamento. Nell’ambito della dottrina ipercritica, tale frammento è stato letto come indizio di una scarsa conoscenza e diffusione dello ius fetiale (e delle sue pratiche) al tempo di Varrone, e dunque a conferma della teoria dello ius fetiale quale prodotto di una ricostruzione arcaizzante. Il presente lavoro tende, invece, a porre in evidenza come nel testo serviano siano sovrapposti due atti distinti e autonomi, accomunati, tuttavia, dall’identità materiale del gesto posto in essere. Una attenta lettura del documento di Servio, infatti, consente di cogliere come, pur nell’identità comportamentale, altro sia l’atto del condottiero, altro quello del sacerdote feziale: gesti identici, ma con funzioni e significati diversi

'Res incorporales' e 'beni immateriali': categorie affini, ma non congruenti

Il presente lavoro si propone un confronto tra la categoria romana delle res incorporales e quella moderna dei beni immateriali. Le due categorie non sono congruenti: infatti, la categoria romana riguarda i diritti (elementi del patrimonio) e serve a sistemare tutto il diritto privato entro la tre classi personae, res, actiones; invece, la categoria moderna riguarda gli oggetti del diritto, in particolare i beni immateriali. Tuttavia, tra Ottocento e Novecento, la scienza giuridica ha ragionato sulla categoria romana, ipotizzando che essa potesse venire impiegata per collocare i beni immateriali – in particolare i prodotti dell’attività intellettuale – all’interno dei ‘sistemi’ codicistici che in quegli anni si venivano elaborando. Si sono profilati in dottrina due atteggiamenti in proposito. Da un lato coloro che hanno ‘esteso’ la categoria romana dai ‘diritti’ agli ‘oggetti di diritto’; dall’altra, coloro che hanno visto una soluzione di continuità tra antico e moderno: essi hanno mantenuto l’espressione ‘cose incorporali’, ma ne hanno rinnovato il contenuto. In questo graduale rinnovamento sembra avere giocato un ruolo significativo Windscheid. Tra le due categorie si profila così, sul piano della speculazione scientifica, un nesso che si può definire di affinità, nel senso etimologico del termine (< lat. ‘ad-finis’)

Deploying dengue-suppressing Wolbachia : Robust models predict slow but effective spatial spread in Aedes aegypti.

A novel strategy for controlling the spread of arboviral diseases such as dengue, Zika and chikungunya is to transform mosquito populations with virus-suppressing Wolbachia. In general, Wolbachia transinfected into mosquitoes induce fitness costs through lower viability or fecundity. These maternally inherited bacteria also produce a frequency-dependent advantage for infected females by inducing cytoplasmic incompatibility (CI), which kills the embryos produced by uninfected females mated to infected males. These competing effects, a frequency-dependent advantage and frequency-independent costs, produce bistable Wolbachia frequency dynamics. Above a threshold frequency, denoted pˆ, CI drives fitness-decreasing Wolbachia transinfections through local populations; but below pˆ, infection frequencies tend to decline to zero. If pˆ is not too high, CI also drives spatial spread once infections become established over sufficiently large areas. We illustrate how simple models provide testable predictions concerning the spatial and temporal dynamics of Wolbachia introductions, focusing on rate of spatial spread, the shape of spreading waves, and the conditions for initiating spread from local introductions. First, we consider the robustness of diffusion-based predictions to incorporating two important features of wMel-Aedes aegypti biology that may be inconsistent with the diffusion approximations, namely fast local dynamics induced by complete CI (i.e., all embryos produced from incompatible crosses die) and long-tailed, non-Gaussian dispersal. With complete CI, our numerical analyses show that long-tailed dispersal changes wave-width predictions only slightly; but it can significantly reduce wave speed relative to the diffusion prediction; it also allows smaller local introductions to initiate spatial spread. Second, we use approximations for pˆ and dispersal distances to predict the outcome of 2013 releases of wMel-infected Aedes aegypti in Cairns, Australia, Third, we describe new data from Ae. aegypti populations near Cairns, Australia that demonstrate long-distance dispersal and provide an approximate lower bound on pˆ for wMel in northeastern Australia. Finally, we apply our analyses to produce operational guidelines for efficient transformation of vector populations over large areas. We demonstrate that even very slow spatial spread, on the order of 10-20 m/month (as predicted), can produce area-wide population transformation within a few years following initial releases covering about 20-30% of the target area

Near-periodic substitution and the genetic variance induced by environmental change

We investigate a model that describes the evolution of a diploid sexual population in a changing environment. Individuals have discrete generations and are subject to selection on the phenotypic value of a quantitative trait, which is controlled by a finite number of bialleic loci. Environmental change is taken to lead to a uniformly changing optimal phenotypic value. The population continually adapts to the changing environment, by allelic substitution, at the loci controlling the trait. We investigate the detailed interrelation between the process of allelic substitution and the adaptation and variation of the population, via infinite population calculations and finite population simulations. We find a simple relation between the substitution rate and the rate of change of the optimal phenotypic value

The statistical mechanics of a polygenic characterunder stabilizing selection, mutation and drift

By exploiting an analogy between population genetics and statistical mechanics, we study the evolution of a polygenic trait under stabilizing selection, mutation, and genetic drift. This requires us to track only four macroscopic variables, instead of the distribution of all the allele frequencies that influence the trait. These macroscopic variables are the expectations of: the trait mean and its square, the genetic variance, and of a measure of heterozygosity, and are derived from a generating function that is in turn derived by maximizing an entropy measure. These four macroscopics are enough to accurately describe the dynamics of the trait mean and of its genetic variance (and in principle of any other quantity). Unlike previous approaches that were based on an infinite series of moments or cumulants, which had to be truncated arbitrarily, our calculations provide a well-defined approximation procedure. We apply the framework to abrupt and gradual changes in the optimum, as well as to changes in the strength of stabilizing selection. Our approximations are surprisingly accurate, even for systems with as few as 5 loci. We find that when the effects of drift are included, the expected genetic variance is hardly altered by directional selection, even though it fluctuates in any particular instance. We also find hysteresis, showing that even after averaging over the microscopic variables, the macroscopic trajectories retain a memory of the underlying genetic states.Comment: 35 pages, 8 figure

Implications of long tails in the distribution of mutant effects

Long-tailed distributions possess an in nite variance, yet a nite sample that is drawn from such a distribution has a nite variance. In this work we consider a model of a population subject to mutation, selection and drift. We investigate the implications of a long-tailed distribution of mutant allelic e¤ects on the distribution of genotypic e¤ects in a model with a continuum of allelic e¤ects. While the analysis is confined to asexual populations, it does also have implications for sexual populations. We obtain analytical results for a selectively neutral population as well as one subject to selection. We supplement these analytical results with numerical simulations, to take into account genetic drift. We nd that a long-tailed distribution of mutant e¤ects may a¤ect both the equilibrium and the evolutionary adaptive behaviour of a population

Species assembly in model ecosystems, II: Results of the assembly process

In the companion paper of this set (Capitan and Cuesta, 2010) we have developed a full analytical treatment of the model of species assembly introduced in Capitan et al. (2009). This model is based on the construction of an assembly graph containing all viable configurations of the community, and the definition of a Markov chain whose transitions are the transformations of communities by new species invasions. In the present paper we provide an exhaustive numerical analysis of the model, describing the average time to the recurrent state, the statistics of avalanches, and the dependence of the results on the amount of available resource. Our results are based on the fact that the Markov chain provides an asymptotic probability distribution for the recurrent states, which can be used to obtain averages of observables as well as the time variation of these magnitudes during succession, in an exact manner. Since the absorption times into the recurrent set are found to be comparable to the size of the system, the end state is quickly reached (in units of the invasion time). Thus, the final ecosystem can be regarded as a fluctuating complex system where species are continually replaced by newcomers without ever leaving the set of recurrent patterns. The assembly graph is dominated by pathways in which most invasions are accepted, triggering small extinction avalanches. Through the assembly process, communities become less resilient (e.g., have a higher return time to equilibrium) but become more robust in terms of resistance against new invasions.Comment: 14 pages, 13 figures. Revised versio