Recurrence of atrial fibrillation after pulmonary vein isolation in dependence of arterial stiffness.

BACKGROUND: Arterial stiffness (AS) has emerged as a strong predictor of cardiovascular (CV) diseases. Although increased AS has been described as a predictor of atrial fibrillation (AF), its role as a risk marker for AF recurrence has not yet been elucidated. METHODS: Patients with AF who underwent pulmonary vein isolation (PVI) were included in this study. Presence of AS was evaluated by measuring aortic distensibility (AD) of the descending aorta by transoesophageal echocardiography. RESULTS: In total, 151 patients (mean ± standard deviation (SD) age 71.9 ± 9.8 years) were enrolled and followed for a median duration of 21 months (interquartile range 15.0-31.0). During follow-up, AF recurred in 94 (62.3%) patients. AF recurrence was seen more frequently in patients with permanent AF (27% vs 46%, p = 0.03) and in those who had undergone prior PVI (9% vs 23%, p = 0.02). AD was significantly reduced in patients with AF recurrence (mean ± SD 2.6 ± 2.3 vs 1.5 ± 0.7â€¯× 10-3 mm Hg-1, p < 0.0001), as well as left atrial volume index (LAVI) (mean ± SD 29 ± 12 vs 44 ± 15 ml/m2, p < 0.0001). Multivariable analysis revealed LAVI (odds ratio (OR) 2.9, 95% confidence interval (CI) 1.2-3.4) and AS (OR 3.6, 95% CI 2.8-4.1) as independent risk factors of AF recurrence. CONCLUSION: Increased AS and left atrial size were independent predictors of AF recurrence after PVI. AD as surrogate marker of AS seemed to reflect the overall CV risk. In addition, AD was significantly correlated with left atrial size, which suggests that increased AS leads to atrial remodelling and thus to AF recurrence. TRIAL REGISTRATION: German registry for clinical studies (DRKS), DRKS00019007.

Relatedness with different interaction configurations.

In an inclusive fitness model of social behaviour, a key concept is that of the relatedness between two interactants. This is typically calculated with reference to a "focal" actor taken to be representative of all actors, but when there are different interaction configurations, relatedness must be constructed as an average over all such configurations. We provide an example of such a calculation in an island model with local reproduction but global mortality, leading to variable island size and hence variable numbers of individual interactions. We find that the analysis of this example significantly sharpens our understanding of relatedness. As an application, we obtain a version of Hamilton's rule for a tag-based model of altruism in a randomly mixed population. For large populations, the selective advantage of altruism is enhanced by low (but not too low) tag mutation rates and large numbers of tags. For moderate population sizes and moderate numbers of tags, we find a window of tag mutation rates with critical benefit/cost ratios of between 1 and 3.

Capturing the superorganism: a formal theory of group adaptation.

Adaptation is conventionally regarded as occurring at the level of the individual organism. However, in recent years there has been a revival of interest in the possibility for group adaptations and superorganisms. Here, we provide the first formal theory of group adaptation. In particular: (1) we clarify the distinction between group selection and group adaptation, framing the former in terms of gene frequency change and the latter in terms of optimization; (2) we capture the superorganism in the form of a 'group as maximizing agent' analogy that links an optimization program to a model of a group-structured population; (3) we demonstrate that between-group selection can lead to group adaptation, but only in rather special circumstances; (4) we provide formal support for the view that between-group selection is the best definition for 'group selection'; and (5) we reveal that mechanisms of conflict resolution such as policing cannot be regarded as group adaptations.

Developments of the Price equation and natural selection under uncertainty.

Many approaches to the study of adaptation, following Darwin, centre on the number of offspring of individuals. Population genetics theory makes clear that predicting gene frequency changes requires more detailed knowledge, for example of linkage and linkage disequilibrium and mating systems. Because gene frequency changes underlie adaptation, this can lead to a suspicion that approaches ignoring these sophistications are approximate or tentative or wrong. Stochastic environments and sexual selection are two topics in which there are widespread views that focusing on number of offspring of individuals is not enough, and that proper treatments require the introduction of further details, namely variability in offspring number and linkage disequilibrium, respectively. However, the bulk of empirical research on adaptation and a great deal of theoretical work continue to employ these approaches. Here, a new theoretical development arising from the Price equation provides a formal justification in very general circumstances for focusing on the arithmetic average of the relative number of offspring of individuals.

Error-prone signalling.

The handicap principle of Zahavi is potentially of great importance to the study of biological communication. Existing models of the handicap principle, however, make the unrealistic assumption that communication is error free. It seems possible, therefore, that Zahavi's arguments do not apply to real signalling systems, in which some degree of error is inevitable. Here, we present a general evolutionarily stable strategy (ESS) model of the handicap principle which incorporates perceptual error. We show that, for a wide range of error functions, error-prone signalling systems must be honest at equilibrium. Perceptual error is thus unlikely to threaten the validity of the handicap principle. Our model represents a step towards greater realism, and also opens up new possibilities for biological signalling theory. Concurrent displays, direct perception of quality, and the evolution of 'amplifiers' and 'attenuators' are all probable features of real signalling systems, yet handicap models based on the assumption of error-free communication cannot accommodate these possibilities.

An inclusive fitness analysis of altruism on a cyclical network.

A recent model studies the evolution of cooperation on a network, and concludes with a result connecting the benefits and costs of interactions and the number of neighbours. Here, an inclusive fitness analysis is conducted of the only case solved analytically, of a cycle, and the identical result is obtained. This brings the result within a biologically familiar framework. It is notable that the benefits and costs in the inclusive fitness framework need to be derived, and are not the benefits and costs that are the parameters in the original model. The relatedness is a quadratic function of position in a cycle of size N: an individual is related by 1 to itself, by (N - 5)/(N + 1) to an immediate neighbour, and by very close to -1/2 to the most distant individuals. The inclusive fitness analysis explains hitherto puzzling features of the results.

The formal Darwinism project: a mid-term report.

For 8 years I have been pursuing in print an ambitious and at times highly technical programme of work, the 'Formal Darwinism Project', whose essence is to underpin and formalize the fitness optimization ideas used by behavioural ecologists, using a new kind of argument linking the mathematics of motion and the mathematics of optimization. The value of the project is to give stronger support to current practices, and at the same time sharpening theoretical ideas and suggesting principled resolutions of some untidy areas, for example, how to define fitness. The aim is also to unify existing free-standing theoretical structures, such as inclusive fitness theory, Evolutionary Stable Strategy (ESS) theory and bet-hedging theory. The 40-year-old misunderstanding over the meaning of fitness optimization between mathematicians and biologists is explained. Most of the elements required for a general theory have now been implemented, but not together in the same framework, and 'general time' remains to be developed and integrated with the other elements to produce a final unified theory of neo-Darwinian natural selection.

A centrosomal theory of the short term evolutionary maintenance of sexual reproduction.

A new mode of inheritance is postulated in which a sexual offspring receives a contribution from each parent and selects the better to pass on to its own offspring. This could provide a simple advantage to sex over a sex whose magnitude is shown to be of the order of a doubling of fitness in each generation, large enough to cancel the twofold cost of sex. This possible advantage to sex can be realized only if a cell component is in fact inherited in this selectively ambiguous way. No such component is known of, but the eukaryotic centrosome is a possible candidate. The possibility is discussed that the centrosome contains an obligatorily non-digital replicator which has an essential function in the initiation of microtubules. If this theory is true, it has the capacity to apply as widely as sex is found, and it would rescue theories of the long-term maintenance of sex from the necessity to provide a twofold advantage in each generation. If false, the theory will soon be disproved.

Sexual selection unhandicapped by the Fisher process.

A population genetic model of sexual selection is constructed in which, at equilibrium, males signal their quality by developing costly ornaments, and females pay costs to use the ornaments in mate choice. It is shown that the form of the equilibrium is uninfluenced by the Fisher process, that is, by self-reinforcement of female preferences. This is a working model of the handicap principle applied to sexual selection, and places Zahavi's handicap principle on the same logical footing as the Fisher process, in that each can support sexual selection without the presence of the other. A way of measuring the relative importance of the two processes is suggested that can be applied to both theories and facts. A style of modelling that allows simple genetics and complicated biology to be combined is recommended.

Biological signals as handicaps.

An ESS model of Zahavi's handicap principle is constructed. This allows a formal exposition of how the handicap principle works, and shows that its essential elements are strategic. The handicap model is about signalling, and it is proved under fairly general conditions that if the handicap principle's conditions are met, then an evolutionarily stable signalling equilibrium exists in a biological signalling system, and that any signalling equilibrium satisfies the conditions of the handicap principle. Zahavi's major claims for the handicap principle are thus vindicated. The place of cheating is discussed in view of the honesty that follows from the handicap principle. Parallel signalling models in economics are discussed. Interpretations of the handicap principle are compared. The models are not fully explicit about how females use information about male quality, and, less seriously, have no genetics. A companion paper remedies both defects in a model of the handicap principle at work in sexual selection.

Fertility and labour supply in Femina economica.

This paper sets out a formal framework for the biological-evolutionary study of human economic behaviour. Femina economica is a hypothetical parthenogenetic species with a simple economy. Individuals make decisions about labour supply and fertility subject to time and resource constraints. Labour is of differing types and a parent determines the type of her offspring's labour. Wages are determined as marginal productivities from an economy-wide production function. Three propositions are proved, of which the first shows that under very general conditions there exists a population genetic equilibrium, in which individuals' decisions are assumed to be under genetic control. The second shows that at a population genetic equilibrium, individuals have the same behaviour as they would at an economic equilibrium, in which individuals are assumed to maximise a common utility function. The third proposition shows that if the common utility function fulfils certain conditions, the attainment of an economic equilibrium brings about the same behaviour as a population genetic equilibrium. This suggests a way in which evolutionarily stable behaviour can be brought about without the necessity for changes in gene frequencies. Demographic implications include the possibility of interpreting in Darwinian terms the reductions in offspring number that occur in fertility transitions, and the weak or even negative correlation in economically developed societies between control of resources and offspring number. There are implications for economics of deriving utility maximisation from population genetics.

A new model for discrete character evolution.

The paper provides an explicit justification for the principle that a uniform taxon should contribute only one datapoint in comparative analyses with discrete variables. The justification is that phylogenetic patterns in variables unincluded in the proposed test vitiate the assumption of independence, both at the level of species and at the level of branch segments. The consequence is that a uniform taxon cannot safely be counted as more than one datapoint. The arguments use a branching discrete Markov process in continuous time, with the new feature that the tested variables are only a subset of the evolving characters. This model is proposed as a useful criterion for measuring the merit of proposed tests, and illustrates the necessity for models in evaluating comparative methods.

Genetic scrambling as a defence against meiotic drive.

Genetic recombination has important consequences, including the familiar rules of Mendelian genetics. Here we present a new argument for the evolutionary function of recombination based on the hypothesis that meiotic drive systems continually arise to threaten the fairness of meiosis. These drive systems act at the expense of the fitness of the organism as a whole for the benefit of the genes involved. We show that genes increasing crossing over are favoured, in the process of breaking up drive systems and reducing the fitness loss to organisms.

Sex and flagellation.

The centriole is one of the cell's more enigmatic structures. It lives a Jekyll and Hyde existence, changing from the basal body, which seeds the production of cilia and flagellae, into the centriole, in which guise it is of uncertain function. Recent work has indicated the possibility of DNA tightly packed into the structure's core. This finding sheds light on theories of the evolutionary origins of the centriole and of its possible involvement in the evolution of sex. Recent experimental work has been testing this latter possibility.

The continuous Sir Philip Sidney game: a simple model of biological signalling.

An analysis of Maynard Smith's two-player, ESS model of biological signalling, the "Sir Philip Sidney game", is presented. The stable strategies of the players in this game are shown to satisfy the conditions of Zahavi's handicap principle. At equilibrium, signals are honest, costly, and costly in a way that is related to the true quality revealed. Further analysis reveals that the level of cost required to maintain stability is inversely related to the degree of relatedness between the players. It therefore seems likely that stable biological signalling systems will feature lower signalling costs when communication occurs between relatives. A three-player, extended version of the model is investigated, in which signals are passed via an intermediate, or "messenger". It is shown that this destabilizes the signalling system, and leads to increased signalling costs. This result suggests that "kin conflict" theories of the evolution of the endosperm in flowering plants require further refinement. The introduction of a novel resource acquisition tissue, which mediates parent-offspring interaction during development, cannot be assumed to limit parent-offspring conflict simply because it carries an extra copy of the maternally inherited genes. The ability to add such complications to the Sir Philip Sidney game and still obtain solutions makes it a very useful modelling tool.

INTRASPECIFIC VARIATION IN ANT SEX RATIOS AND THE TRIVERS-HARE HYPOTHESIS.

We consider worker-controlled sex investments in eusocial Hymenoptera (ants in particular) and assume that relatedness asymmetry is variable among colonies and that workers are able to assess the relatedness asymmetry in their own colony. We predict that such "assessing" workers should maximize their inclusive fitness by specializing in the production of the sex to which they are relatively most related, i.e., colonies whose workers have a relatedness asymmetry below the population average should specialize in males, whereas colonies whose workers have a higher than average relatedness asymmetry should specialize in making females. Our argument yields the expectation that colony sex ratios will be bimodally distributed in ant populations where relatedness asymmetry is variable owing to multiple mating, worker reproduction, and/or polygyny. No such bimodality is expected, however, in ant species where relatedness asymmetry is known to be constant, or in cases where relatedness asymmetry is supposed to be irrelevant due to allospecific brood rearing under queen control, as in the slave-making ants. Comparative data on colony sex ratios in ants are reviewed to test the predictions. The data partly support our contentions, but are as yet insufficient to be considered as decisive evidence.

Why we need ESS signalling theory.

Evolutionarily stable strategy (ESS) models of biological signalling are important because the intimate coevolution of signalling and receiving strategies is complicated. Tentative results from a numerical study of error-prone signalling show the value of formal modelling. Error in perception can create discreteness in the distribution of signals produced, and so observed discreteness in nature may call for no more complicated explanation. Further developments in the theory of signalling may include a link with theories of aggression such as the sequential assessment game. The technical device of a 'scratch space' may allow a natural development of 'two-way' information games in which each contestant plays the roles of signaller and receiver simultaneously. This device may also incidentally derive mental states from purely strategic considerations.

Does the negative binomial distribution add up?

The negative binomial distribution (NBD) is widely used to describe the distribution of parasitic helminths in a number of host individuals and has proved a useful, though possibly overused, empirical and theoretical device. It is therefore important that the limits to the applicability of the NBD be clearly defined. In this paper, Alan Grafen and Mark Woolhouse consider applications of the NBD in situations where either the host or parasite population can be divided into subpopulations of different types (eg. by age, sex or genotype), and they describe the relationships between the frequency distributions relevant to the different subpopulations and those relevant to the total population.