Biased sex-ratio and sex-biased heterozygote disadvantage affect the maintenance of a genetic polymorphism and the properties of hybrid zones.

The evolution of biodiversity is a major issue of modern biology, and it is becoming increasingly topical as the ongoing erosion of diversity puts serious threats on human well-being. An elementary mechanism that allows maintaining diversity is the interplay between dispersal and heterozygote selective disadvantage, which can lead to self-sustainable spatial genetic structures and is central to the stability of hybrid zones. Theoretical studies supporting the importance of this mechanism assume a balanced sex-ratio and a heterozygote disadvantage equally affecting both sexes, despite the multiplicity of empirical evidence that (i) adult sex-ratio is usually biased towards either male or female and that (ii) heterozygote disadvantage often affects a single sex. We expanded the existing theory by weighting the strength of selection against heterozygote according to the biased in sex-ratio and in heterozygote disadvantage. The range of conditions allowing for the maintenance of polymorphism can then either double or vanish. We discuss the implications of such finding for birds, mammals and insects diversity. Finally, we provide simple analytical predictions about the effect of those biased on the width and speed of hybrid zones and on the time for the spread of beneficial mutations through such zones.

Testing the level of ant activity associated with quorum sensing: an empirical approach leading to the establishment and test of a null-model (response to the comment of Richardson et al.).

In a paper in this journal (Nouvellet et al., 2010), we presented results from experiments on the behaviour of the Pharaoh's ant, Monomorium pharaonis, along with a substantial statistical and theoretical analysis of the results. In a minor part of our paper, we compared our results with the related work of Richardson et al. (2010a). These authors have subsequently commented on our interpretation of their work (Richardson et al., 2011). In this Letter we respond to the comments of Richardson et al. (2011), and give detailed arguments why we stand by our original conclusions.

Testing the level of ant activity associated with quorum sensing: An empirical approach leading to the establishment and test of a null-model.

On the basis of experimental observations, this paper develops two well-defined mathematical models for the level of activity of Pharaoh's ants within their nesting area, with the aim of providing a more general understanding of animal activity. Under specific conditions, we observe that the activity of ants within their nesting area appears to show no dependence on their density. Making the assumption that all ants move independently of one another, this behaviour can be mathematically modelled as a random process based on the binomial distribution. Developing the model on this basis allows an exponential distribution to be exposed that underlies the time-intervals between ants leaving the nesting area. Such a distribution is present, irrespective of whether the ant population in the nesting area remains constant or steadily depletes, and suggests that ant-ant interactions do not play any significant role in determining ant activity under the experimental conditions adopted. The mathematical framework presented plays the role of a null model that will have a wide range of applications for detecting other determinants of activity-level (not addressed in this study) including environmental and social factors such as food availability, temperature, humidity, presence of pheromone trails, along with intraspecific and interspecific interactions outside the nest and, indeed, more generally. The null model should have applications to a range of organisms. Lastly, we discuss our data in relation to a recent study of ants leaving their nest (Richardson et al., 2010) in which the null model was rejected in favour of record dynamics, where ant-ant interactions were conjectured to play a role.

Fitness measures in selection analyses: sensitivity to the overall number of offspring produced in a lifetime.

Age at first (alpha) and last (omega) breeding are important life-history traits; however, the direction and strength of selection detected on traits may vary depending on the fitness measure used. We provide the first estimates of lifetime breeding success (LBS) and lambda(ind) (the population growth rate of an individual) of European badgers Meles meles, by genotyping 915 individuals, sampled over 18 years, for 22 microsatellites. Males are slightly larger than females, and the opportunity for selection was slightly greater for males, as predicted. lambda(ind) and LBS both performed well in predicting the number of grand-offspring, and both detected selection for a late omega, until the age of eight. Differential selection (S'(alpha)) for an early alpha, however, was only detected using LBS, not with lambda(ind). In declining populations (lambda(ind) < 1) selection favours reproduction later in life, whereas early reproduction is selected in increasing populations (lambda(ind) > 1). As 41% of badgers were assigned only one offspring (lambda(ind) < 1), whereas 40% were assigned more than two (lambda(ind) > 1), this cancelled out S'(alpha) measured by lambda(ind).

Fundamental insights into the random movement of animals from a single distance-related statistic.

Statistical theories of animal movement have often been based on models of random walks, where movements take place in discrete steps and occur at discrete times. The multiplicity of distributions required in these approaches to describe animal movement (i.e., the distributions of angles, discrete steps, and times) have effects that cannot be simply disentangled, and hence they cannot be unambiguously determined. Here we present a mathematical formulation of continuous animal movements. In this new framework, it is shown that a single time-dependent distance statistic, the mean square displacement, which may be directly measured or mathematically modeled, is a central determinant of such random walks and encapsulates key information about the statistical properties of animal movements. The model and methodology presented here not only allow the determination of what were previously viewed as independent aspects of animal movements, such as the distribution of angular changes in direction, but also, because of the new emphasis on the mean square displacement, they may open up a new set of questions concerning animal movement and related phenomena. The results established in this work are directly applied to the foraging behavior of Pharaoh's ants, and very close agreement is found between observation and theory.

Parameter-free testing of the shape of a probability distribution.

The Kolmogorov-Smirnov test determines the consistency of empirical data with a particular probability distribution. Often, parameters in the distribution are unknown, and have to be estimated from the data. In this case, the Kolmogorov-Smirnov test depends on the form of the particular probability distribution under consideration, even when the estimated parameter-values are used within the distribution. In the present work, we address a less specific problem: to determine the consistency of data with a given functional form of a probability distribution (for example the normal distribution), without enquiring into values of unknown parameters in the distribution. For a wide class of distributions, we present a direct method for determining whether empirical data are consistent with a given functional form of the probability distribution. This utilizes a transformation of the data. If the data are from the class of distributions considered here, the transformation leads to an empirical distribution with no unknown parameters, and hence is susceptible to a standard Kolmogorov-Smirnov test. We give some general analytical results for some of the distributions from the class of distributions considered here. The significance level and power of the tests introduced in this work are estimated from simulations. Some biological applications of the method are given.