Determinism, Noise, and Spurious Estimations in a Generalised Model of Population Growth

We study a generalised model of population growth in which the state variable is population growth rate instead of population size. Stochastic parametric perturbations, modelling phenotypic variability, lead to a Langevin system with two sources of multiplicative noise. The stationary probability distributions have two characteristic power-law scales. Numerical simulations show that noise suppresses the explosion of the growth rate which occurs in the deterministic counterpart. Instead, in different parameter regimes populations will grow with ``anomalous'' stochastic rates and (i) stabilise at ``random carrying capacities'', or (ii) go extinct in random times. Using logistic fits to reconstruct the simulated data, we find that even highly significant estimations do not recover or reflect information about the deterministic part of the process. Therefore, the logistic interpretation is not biologically meaningful. These results have implications for distinct model-aided calculations in biological situations because these kinds of estimations could lead to spurious conclusions.Comment: Accepted in Physica A. Updated with [minor] observations from the reffere

The role of endosymbionts in the evolution of haploid-male genetic systems in scale insects (Coccoidea)

There is an extraordinary diversity in genetic systems across species, but this variation remains poorly understood. In part, this is because the mechanisms responsible for transitions between systems are often unknown. A recent hypothesis has suggested that conflict between hosts and endosymbiotic microorganisms over transmission could drive the transition from diplodiploidy to systems with male haploidy (haplodiploidy, including arrhenotoky and paternal genome elimination [PGE]). Here, we present the first formal test of this idea with a comparative analysis across scale insects (Hemiptera: Coccoidea). Scale insects are renowned for their large variation in genetic systems, and multiple transitions between diplodiploidy and haplodiploidy have taken place within this group. Additionally, most species rely on endosymbiotic microorganisms to provide them with essential nutrients lacking in their diet. We show that species harboring endosymbionts are indeed more likely to have a genetic system with male haploidy, which supports the hypothesis that endosymbionts might have played a role in the transition to haplodiploidy. We also extend our analysis to consider the relationship between endosymbiont presence and transitions to parthenogenesis. Although in scale insects there is no such overall association, species harboring eukaryote endosymbionts were more likely to be parthenogenetic than those with bacterial symbionts. These results support the idea that intergenomic conflict can drive the evolution of novel genetic systems and affect host reproduction.Peer reviewe

Fledgling sex ratios in relation to brood size in size-dimorphic altricial birds

In six species of dimorphic raptors (females larger than males) and one passerine (males larger than females), the sex ratio at fledging varied systematically with brood size at fledging. In all species the strongest bias toward the smaller sex was established in the largest as well as the smallest broods; a more even distribution of males and females was observed in broods of intermediate size. We explored a specific differential mortality explanation for this sex ratio variation. Our hypothesis postulates that variation in mortality is caused by differences in food demand between broods of the same size, due to their sex composition. Data from the marsh harrier Circus aeruginosus on gender-related food demand and overall nestling mortality were used to predict the frequency of surviving males and females at fledging, assuming an even sex ratio at hatching and random mortality with respect to both sexes within broods. The model quantitatively fits the marsh harrier data well, especially in broods originating from large clutches. Although we anticipate that other mechanisms are also involved, the results support the hypothesis of sex-ratio-dependent mortality, differential between broods, as the process generating the observed broad-size dependence of fledgling sex ratios in sexually dimorphic birds

How fitness consequences of early-life conditions vary with age in a long-lived seabird:A Bayesian multivariate analysis of age-specific reproductive values

Evolutionary theory suggests that individuals can benefit from deferring the fitness cost of developing under poor conditions to later in life. Although empirical evidence for delayed fitness costs of poor developmental conditions is abundant, individuals that die prematurely have not often been incorporated when estimating fitness, such that age-specific fitness costs, and therefore the relative importance of delayed fitness costs are actually unknown. We developed a Bayesian statistical framework to estimate age-specific reproductive values in relation to developmental conditions. We applied it to data obtained from a long-term longitudinal study of common terns Sterna hirundo, using sibling rank to describe variation in developmental conditions. Common terns have a maximum of three chicks, and later hatching chicks acquire less food, grow more slowly and have a lower fledging probability than their earlier hatched siblings. We estimated fitness costs in adulthood to constitute c. 45% and 70% of the total fitness costs of hatching third and second, respectively, compared to hatching first. This was due to third-ranked hatchlings experiencing especially high pre-fledging mortality, while second-ranked hatchlings had lower reproductive success in adulthood. Both groups had slightly lower adult survival. There was, however, no evidence for sibling rank-specific rates of senescence. We additionally found years with low fledgling production to be associated with particularly strong pre-fledging selection on sibling rank, and with increased adult survival to the next breeding season. This suggests that adults reduce parental allocation to reproduction in poor years, which disproportionately impacts low-ranked offspring. Interpreting these results, we suggest that selection at the level of the individual offspring for delaying fitness costs is counteracted by selection for parental reduction in brood size when resources are limiting

Small herbivores and abiotic heterogeneity promote trait variation of a saltmarsh plant in local communities

Intraspecific trait variation (ITV) enables plants to respond to global changes. However, causes for ITV, especially from biotic components such as herbivory, are not well understood. We explored whether small vertebrate herbivores (hares and geese) impact ITV of a dominant clonal plant (Elytrigia atherica) in local communities. Moreover, we looked at the relative importance of their direct (e.g., selective grazing) and indirect effects (altering genotypic richness/diversity and abiotic environment) on ITV. We used exclosures at two successional stages in a Dutch saltmarsh, where grazing pressure at the early successional stage was ca. 1.5 times higher than that of the intermediate successional stage. We measured key functional traits of E. atherica including height, aboveground biomass, flowering (flower or not), specific leaf area, and leaf dry matter content in local communities (1 m × 1 m plots) inside and outside the exclosures. We determined genotypic richness and diversity of each plant using molecular markers. We further measured abiotic variations in topography and clay thickness (a proxy for soil total nitrogen). Structural equation models revealed that small herbivores significantly promoted ITV in height and flowering at the early successional stage, while they marginally promoted ITV in height at the intermediate successional stage. Moreover, the direct effects of herbivores played a major role in promoting ITV. Small herbivores decreased genotypic diversity at the intermediate successional stage, but genotypic richness and diversity did not impact ITV. Small herbivores did not alter topographic variation and variation in clay thickness, but these variations increased ITV in all traits at the early successional stage. Small herbivores may not only impact trait means in plants as studies have shown but also their ITV

Antagonistic pleiotropy and the evolution of extraordinary lifespans in eusocial organisms

Queens of eusocial species live extraordinarily long compared to their workers. So far, it has been argued that these lifespan divergences are readily explained by the classical evolutionary theory of ageing. As workers predominantly perform risky tasks, such as foraging and nest defense, and queens stay in the well-protected nests, selection against harmful genetic mutations expressed in old age should be weaker in workers than in queens due to caste differences in extrinsic mortality risk, and thus, lead to the evolution of longer queen and shorter worker lifespans. However, these arguments have not been supported by formal models. Here, we present a model for the evolution of caste-specific ageing in social insects, based on Williams’ antagonistic pleiotropy theory of ageing. In individual-based simulations, we assume that mutations with antagonistic fitness effects can act within castes, that is, mutations in early life are accompanied by an antagonistic effect acting in later life, or between castes, where antagonistic effects emerge due to caste antagonism or indirect genetic effects between castes. In monogynous social insect species with sterile workers, large lifespan divergences between castes evolved under all different scenarios of antagonistic effects, but regardless of the degree of caste-specific extrinsic mortality. Mutations with antagonistic fitness effects within castes reduced lifespans of both castes, while mutations with between-caste antagonistic effects decreased worker lifespans more than queen lifespans, and consequently increased lifespan divergences. Our results challenge the central explanatory role of extrinsic mortality for caste-specific ageing in eusocial organisms and suggest that antagonistic pleiotropy affects castes differently due to reproductive monopolization by queens, hence, reproductive division of labor. Finally, these findings provide new insights into the evolution of tissue-specific ageing in multicellular organisms in general

Epistatic interactions between sex chromosomes and autosomes can affect the stability of sex determination systems

Sex determination (SD) is an essential and ancient developmental process, but the genetic systems that regulate this process are surprisingly variable. Why SD mechanisms vary so much is a longstanding question in evolutionary biology. SD genes are generally located on sex chromosomes which also carry genes that interact epistatically with autosomes to affect fitness. How this affects the evolutionary stability of SD mechanisms is still unknown. Here, we explore how epistatic interactions between a sexually antagonistic (SA) non‐SD gene, located on either an ancestral or novel sex chromosome, and an autosomal gene affect the conditions under which an evolutionary transition to a new SD system occurs. We find that when the SD gene is linked to an ancestral sex‐chromosomal gene which engages in epistatic interactions, epistasis enhances the stability of the sex chromosomes so that they are retained under conditions where transitions would otherwise occur. This occurs both when weaker fitness effects are associated with the ancestral sex chromosome pair or stronger fitness effects associated with a newly evolved SD gene. However, the probability that novel SD genes spread is unaffected if they arise near genes involved in epistasis. This discrepancy occurs because, on autosomes, SA allele frequencies are typically lower than on sex chromosomes. In our model, increased frequencies of these alleles contribute to a higher frequency of epistasis which may therefore more readily occur on sex chromosomes. Because sex chromosome–autosome interactions are abundant and can take several forms, they may play a large role in maintaining sex chromosomes

A unified model of Hymenopteran preadaptations that trigger the evolutionary transition to eusociality

Explaining the origin of eusociality, with strict division of labour between workers and reproductives, remains one of evolutionary biology's greatest challenges. Specific combinations of genetic, behavioural and demographic traits in Hymenoptera are thought to explain their relatively high frequency of eusociality, but quantitative models integrating such preadaptations are lacking. Here we use mathematical models to show that the joint evolution of helping behaviour and maternal sex ratio adjustment can synergistically trigger both a behavioural change from solitary to eusocial breeding, and a demographic change from a life cycle with two reproductive broods to a life cycle in which an unmated cohort of female workers precedes a final generation of dispersing reproductives. Specific suits of preadaptations are particularly favourable to the evolution of eusociality: lifetime monogamy, bivoltinism with male generation overlap, hibernation of mated females and haplodiploidy with maternal sex ratio adjustment. The joint effects of these preadaptations may explain the abundance of eusociality in the Hymenoptera and its virtual absence in other haplodiploid lineages