Steady states in a structured epidemic model with Wentzell boundary condition

We introduce a nonlinear structured population model with diffusion in the state space. Individuals are structured with respect to a continuous variable which represents a pathogen load. The class of uninfected individuals constitutes a special compartment that carries mass, hence the model is equipped with generalized Wentzell (or dynamic) boundary conditions. Our model is intended to describe the spread of infection of a vertically transmitted disease, for example Wolbachia in a mosquito population. Therefore the (infinite dimensional) nonlinearity arises in the recruitment term. First we establish global existence of solutions and the Principle of Linearised Stability for our model. Then, in our main result, we formulate simple conditions, which guarantee the existence of non-trivial steady states of the model. Our method utilizes an operator theoretic framework combined with a fixed point approach. Finally, in the last section we establish a sufficient condition for the local asymptotic stability of the positive steady state

Science policies: How should science funding be allocated? An evolutionary biologists’ perspective

In an ideal world, funding agencies could identify the best scientists and projects and provide them with the resources to undertake these projects. Most scientists would agree that in practice, how funding for scientific research is allocated is far from ideal and likely compromises research quality. We, nine evolutionary biologists from different countries and career stages, provide a comparative summary of our impressions on funding strategies for evolutionary biology across eleven different funding agencies. We also assess whether and how funding effectiveness might be improved. We focused this assessment on 14 elements within four broad categories: (a) topical shaping of science, (b) distribution of funds, (c) application and review procedures, and (d) incentives for mobility and diversity. These comparisons revealed striking among‐country variation in those elements, including wide variation in funding rates, the effort and burden required for grant applications, and the extent of emphasis on societal relevance and individual mobility. We use these observations to provide constructive suggestions for the future and urge the need to further gather informed considerations from scientists on the effects of funding policies on science across countries and research fields

Phenotypic and genotypic parallel evolution in parapatric ecotypes of Senecio.

The independent and repeated adaptation of populations to similar environments often results in the evolution of similar forms. This phenomenon creates a strong correlation between phenotype and environment and is referred to as parallel evolution. However, we are still largely unaware of the dynamics of parallel evolution, as well as the interplay between phenotype and genotype within natural systems. Here, we examined phenotypic and genotypic parallel evolution in multiple parapatric Dune-Headland coastal ecotypes of an Australian wildflower, Senecio lautus. We observed a clear trait-environment association in the system, with all replicate populations having evolved along the same phenotypic evolutionary trajectory. Similar phenotypes have arisen via mutational changes occurring in different genes, although many share the same biological functions. Our results shed light on how replicated adaptation manifests at the phenotypic and genotypic levels within populations, and highlight S. lautus as one of the most striking cases of phenotypic parallel evolution in nature

Structured and unstructured continuous models for Wolbachia infections

We introduce and investigate a series of models for an infection of a diplodiploid host species by the bacterial endosymbiont Wolbachia. The continuous models are characterized by partial vertical transmission, cytoplasmic incompatibility and fitness costs associated with the infection. A particular aspect of interest is competitions between mutually incompatible strains. We further introduce an age-structured model that takes into account different fertility and mortality rates at different stages of the life cycle of the individuals. With only a few parameters, the ordinary differential equation models exhibit already interesting dynamics and can be used to predict criteria under which a strain of bacteria is able to invade a population. Interestingly, but not surprisingly, the age-structured model shows significant differences concerning the existence and stability of equilibrium solutions compared to the unstructured model

Red Queen Dynamics with Non-Standard Fitness Interactions

Antagonistic coevolution between hosts and parasites can involve rapid fluctuations of genotype frequencies that are known as Red Queen dynamics. Under such dynamics, recombination in the hosts may be advantageous because genetic shuffling can quickly produce disproportionately fit offspring (the Red Queen hypothesis). Previous models investigating these dynamics have assumed rather simple models of genetic interactions between hosts and parasites. Here, we assess the robustness of earlier theoretical predictions about the Red Queen with respect to the underlying host-parasite interactions. To this end, we created large numbers of random interaction matrices, analysed the resulting dynamics through simulation, and ascertained whether recombination was favoured or disfavoured. We observed Red Queen dynamics in many of our simulations provided the interaction matrices exhibited sufficient ‘antagonicity’. In agreement with previous studies, strong selection on either hosts or parasites favours selection for increased recombination. However, fast changes in the sign of linkage disequilibrium or epistasis were only infrequently observed and do not appear to be a necessary condition for the Red Queen hypothesis to work. Indeed, recombination was often favoured even though the linkage disequilibrium remained of constant sign throughout the simulations. We conclude that Red Queen-type dynamics involving persistent fluctuations in host and parasite genotype frequencies appear to not be an artefact of specific assumptions about host-parasite fitness interactions, but emerge readily with the general interactions studied here. Our results also indicate that although recombination is often favoured, some of the factors previously thought to be important in this process such as linkage disequilibrium fluctuations need to be reassessed when fitness interactions between hosts and parasites are complex

The diversity of reproductive parasites among arthropods: Wolbachia do not walk alone

<p>Abstract</p> <p>Background</p> <p>Inherited bacteria have come to be recognised as important components of arthropod biology. In addition to mutualistic symbioses, a range of other inherited bacteria are known to act either as reproductive parasites or as secondary symbionts. Whilst the incidence of the α-proteobacterium <it>Wolbachia </it>is relatively well established, the current knowledge of other inherited bacteria is much weaker. Here, we tested 136 arthropod species for a range of inherited bacteria known to demonstrate reproductive parasitism, sampling each species more intensively than in past surveys.</p> <p>Results</p> <p>The inclusion of inherited bacteria other than <it>Wolbachia </it>increased the number of infections recorded in our sample from 33 to 57, and the proportion of species infected from 22.8% to 32.4%. Thus, whilst <it>Wolbachia </it>remained the dominant inherited bacterium, it alone was responsible for around half of all inherited infections of the bacteria sampled, with members of the <it>Cardinium</it>, <it>Arsenophonus </it>and <it>Spiroplasma ixodetis </it>clades each occurring in 4% to 7% of all species. The observation that infection was sometimes rare within host populations, and that there was variation in presence of symbionts between populations indicates that our survey will itself underscore incidence.</p> <p>Conclusion</p> <p>This extensive survey demonstrates that at least a third of arthropod species are infected by a diverse assemblage of maternally inherited bacteria that are likely to strongly influence their hosts' biology, and indicates an urgent need to establish the nature of the interaction between non-<it>Wolbachia </it>bacteria and their hosts.</p

Spiders do not escape reproductive manipulations by Wolbachia

<p>Abstract</p> <p>Background</p> <p>Maternally inherited bacteria that reside obligatorily or facultatively in arthropods can increase their prevalence in the population by altering their hosts' reproduction. Such reproductive manipulations have been reported from the major arthropod groups such as insects (in particular hymenopterans, butterflies, dipterans and beetles), crustaceans (isopods) and mites. Despite the observation that endosymbiont bacteria are frequently encountered in spiders and that the sex ratio of particular spider species is strongly female biased, a direct relationship between bacterial infection and sex ratio variation has not yet been demonstrated for this arthropod order.</p> <p>Results</p> <p>Females of the dwarf spider <it>Oedothorax gibbosus </it>exhibit considerable variation in the sex ratio of their clutches and were infected with at least three different endosymbiont bacteria capable of altering host reproduction i.e. <it>Wolbachia</it>, <it>Rickettsia </it>and <it>Cardinium</it>. Breeding experiments show that sex ratio variation in this species is primarily maternally inherited and that removal of the bacteria by antibiotics restores an unbiased sex ratio. Moreover, clutches of females infected with <it>Wolbachia </it>were significantly female biased while uninfected females showed an even sex ratio. As female biased clutches were of significantly smaller size compared to non-distorted clutches, killing of male embryos appears to be the most likely manipulative effect.</p> <p>Conclusions</p> <p>This represents to our knowledge the first direct evidence that endosymbiont bacteria, and in particular <it>Wolbachia</it>, might induce sex ratio variation in spiders. These findings are pivotal to further understand the diversity of reproductive phenotypes observed in this arthropod order.</p

Rapid De Novo Evolution of X Chromosome Dosage Compensation in Silene latifolia, a Plant with Young Sex Chromosomes

Evidence for dosage compensation in Silene latifolia, a plant with 10-million-year-old sex chromosomes, reveals that dosage compensation can evolve rapidly in young XY systems and is not an animal-specific phenomenon

Does Sex Speed Up Evolutionary Rate and Increase Biodiversity?

Most empirical and theoretical studies have shown that sex increases the rate of evolution, although evidence of sex constraining genomic and epigenetic variation and slowing down evolution also exists. Faster rates with sex have been attributed to new gene combinations, removal of deleterious mutations, and adaptation to heterogeneous environments. Slower rates with sex have been attributed to removal of major genetic rearrangements, the cost of finding a mate, vulnerability to predation, and exposure to sexually transmitted diseases. Whether sex speeds or slows evolution, the connection between reproductive mode, the evolutionary rate, and species diversity remains largely unexplored. Here we present a spatially explicit model of ecological and evolutionary dynamics based on DNA sequence change to study the connection between mutation, speciation, and the resulting biodiversity in sexual and asexual populations. We show that faster speciation can decrease the abundance of newly formed species and thus decrease long-term biodiversity. In this way, sex can reduce diversity relative to asexual populations, because it leads to a higher rate of production of new species, but with lower abundances. Our results show that reproductive mode and the mechanisms underlying it can alter the link between mutation, evolutionary rate, speciation and biodiversity and we suggest that a high rate of evolution may not be required to yield high biodiversity