Under-dominance constrains the evolution of negative autoregulation in diploids.

Regulatory networks have evolved to allow gene expression to rapidly track changes in the environment as well as to buffer perturbations and maintain cellular homeostasis in the absence of change. Theoretical work and empirical investigation in Escherichia coli have shown that negative autoregulation confers both rapid response times and reduced intrinsic noise, which is reflected in the fact that almost half of Escherichia coli transcription factors are negatively autoregulated. However, negative autoregulation is rare amongst the transcription factors of Saccharomyces cerevisiae. This difference is surprising because E. coli and S. cerevisiae otherwise have similar profiles of network motifs. In this study we investigate regulatory interactions amongst the transcription factors of Drosophila melanogaster and humans, and show that they have a similar dearth of negative autoregulation to that seen in S. cerevisiae. We then present a model demonstrating that this striking difference in the noise reduction strategies used amongst species can be explained by constraints on the evolution of negative autoregulation in diploids. We show that regulatory interactions between pairs of homologous genes within the same cell can lead to under-dominance--mutations which result in stronger autoregulation, and decrease noise in homozygotes, paradoxically can cause increased noise in heterozygotes. This severely limits a diploid's ability to evolve negative autoregulation as a noise reduction mechanism. Our work offers a simple and general explanation for a previously unexplained difference between the regulatory architectures of E. coli and yeast, Drosophila and humans. It also demonstrates that the effects of diploidy in gene networks can have counter-intuitive consequences that may profoundly influence the course of evolution.

Warning signals of regime shifts as intrinsic properties of endogenous dynamics.

Ecosystem dynamics can exhibit large, nonlinear changes after small changes in an environmental parameter that passes a critical threshold. These regime shifts are often associated with loss of biodiversity and ecosystem services. Because critical thresholds for regime shifts are hard to determine with precision, some recent studies have focused on deriving signals from dynamics leading up to the thresholds. Models in these studies depend on using noise terms independent of system parameters and variables to add stochasticity. However, demographic stochasticity, an important source of random variability, arises directly from system dynamics. In this study, a framework is developed for modeling demographic stochasticity in a mechanistic way, incorporating system variables and parameters. This framework is applied to a deterministic, dynamic model of a coral reef benthos. The resulting stochastic model indicates that increasing variance-but not skewness-is consistently found in system dynamics approaching a critical threshold of grazing pressure. Even if the threshold is breached, attraction of transient dynamics by a saddle point provides an opportunity for regime shift reversal by management intervention. These results suggest that early warning signals of regime shifts can arise intrinsically in endogenous dynamics and can be detected without reliance on random environmental forcings.

Dynamics of mitochondrial inheritance in the evolution of binary mating types and two sexes.

The uniparental inheritance (UPI) of mitochondria is thought to explain the evolution of two mating types or even true sexes with anisogametes. However, the exact role of UPI is not clearly understood. Here, we develop a new model, which considers the spread of UPI mutants within a biparental inheritance (BPI) population. Our model explicitly considers mitochondrial mutation and selection in parallel with the spread of UPI mutants and self-incompatible mating types. In line with earlier work, we find that UPI improves fitness under mitochondrial mutation accumulation, selfish conflict and mitonuclear coadaptation. However, we find that as UPI increases in the population its relative fitness advantage diminishes in a frequency-dependent manner. The fitness benefits of UPI 'leak' into the biparentally reproducing part of the population through successive matings, limiting the spread of UPI. Critically, while this process favours some degree of UPI, it neither leads to the establishment of linked mating types nor the collapse of multiple mating types to two. Only when two mating types exist beforehand can associated UPI mutants spread to fixation under the pressure of high mitochondrial mutation rate, large mitochondrial population size and selfish mutants. Variation in these parameters could account for the range of UPI actually observed in nature, from strict UPI in some Chlamydomonas species to BPI in yeast. We conclude that UPI of mitochondria alone is unlikely to have driven the evolution of two mating types in unicellular eukaryotes.

The population genetics of cooperative gene regulation.

BACKGROUND: Changes in gene regulatory networks drive the evolution of phenotypic diversity both within and between species. Rewiring of transcriptional networks is achieved either by changes to transcription factor binding sites or by changes to the physical interactions among transcription factor proteins. It has been suggested that the evolution of cooperative binding among factors can facilitate the adaptive rewiring of a regulatory network. RESULTS: We use a population-genetic model to explore when cooperative binding of transcription factors is favored by evolution, and what effects cooperativity then has on the adaptive re-writing of regulatory networks. We consider a pair of transcription factors that regulate multiple targets and overlap in the sets of target genes they regulate. We show that, under stabilising selection, cooperative binding between the transcription factors is favoured provided the amount of overlap between their target genes exceeds a threshold. The value of this threshold depends on several population-genetic factors: strength of selection on binding sites, cost of pleiotropy associated with protein-protein interactions, rates of mutation and population size. Once it is established, we find that cooperative binding of transcription factors significantly accelerates the adaptive rewiring of transcriptional networks under positive selection. We compare our qualitative predictions to systematic data on Saccharomyces cerevisiae transcription factors, their binding sites, and their protein-protein interactions. CONCLUSIONS: Our study reveals a rich set of evolutionary dynamics driven by a tradeoff between the beneficial effects of cooperative binding at targets shared by a pair of factors, and the detrimental effects of cooperative binding for non-shared targets. We find that cooperative regulation will evolve when transcription factors share a sufficient proportion of their target genes. These findings help to explain empirical pattens in datasets of transcription factors in Saccharomyces cerevisiae and, they suggest that changes to physical interactions between transcription factors can play a critical role in the evolution of gene regulatory networks.

Fixed and dilutable benefits: female choice for good genes or fertility.

Benefits accruing to females who exercise mate choice have been defined to be either 'direct' or 'indirect'. We suggest an alternative distinction: benefits can be considered 'fixed', meaning they are on average equal to all females mating with the same male (e.g. good genes' benefits) or 'dilutable', meaning they are shared between females mating with the same male, so that the more mates a male has, the lower the average benefit to each (e.g. fertility benefits or many forms of direct benefit). Using a simple model, we show that this distinction has a major effect on the form of female preference. We predict that mating skew will be far greater in species where the benefits are fixed when compared with those where the benefits are dilutable.

Selection for mitonuclear co-adaptation could favour the evolution of two sexes.

Mitochondria are descended from free-living bacteria that were engulfed by another cell between one and a half to two billion years ago. A redistribution of DNA led to most genetic information being lost or transferred to a large central genome in the nucleus, leaving a residual genome in each mitochondrion. Oxidative phosphorylation, the most critical function of mitochondria, depends on the functional compatibility of proteins encoded by both the nucleus and mitochondria. We investigate whether selection for adaptation between the nuclear and mitochondrial genomes (mitonuclear co-adaptation) could, in principle, have promoted uniparental inheritance of mitochondria and thereby the evolution of two mating types or sexes. Using a mathematical model, we explore the importance of the radical differences in ploidy levels, sexual and asexual modes of inheritance, and mutation rates of the nucleus and mitochondria. We show that the major features of mitochondrial inheritance, notably uniparental inheritance and bottlenecking, enhance the co-adaptation of mitochondrial and nuclear genes and therefore improve fitness. We conclude that, under a wide range of conditions, selection for mitonuclear co-adaptation favours the evolution of two distinct mating types or sexes in sexual species.

Alternative stable states and phase shifts in coral reefs under anthropogenic stress.

Ecosystems with alternative stable states (ASS) may shift discontinuously from one stable state to another as environmental parameters cross a threshold. Reversal can then be difficult due to hysteresis effects. This contrasts with continuous state changes in response to changing environmental parameters, which are less difficult to reverse. Worldwide degradation of coral reefs, involving "phase shifts" from coral to algal dominance, highlights the pressing need to determine the likelihood of discontinuous phase shifts in coral reefs, in contrast to continuous shifts with no ASS. However, there is little evidence either for or against the existence of ASS for coral reefs. We use dynamic models to investigate the likelihood of continuous and discontinuous phase shifts in coral reefs subject to sustained environmental perturbation by fishing, nutrification, and sedimentation. Our modeling results suggest that coral reefs with or without anthropogenic stress can exhibit ASS, such that discontinuous phase shifts can occur. We also find evidence to support the view that high macroalgal growth rates and low grazing rates on macroalgae favor ASS in coral reefs. Further, our results suggest that the three stressors studied, either alone or in combination, can increase the likelihood of both continuous and discontinuous phase shifts by altering the competitive balance between corals and algae. However, in contrast to continuous phase shifts, we find that discontinuous shifts occur only in model coral reefs with parameter values near the extremes of their empirically determined ranges. This suggests that continuous shifts are more likely than discontinuous shifts in coral reefs. Our results also suggest that, for ecosystems in general, tackling multiple human stressors simultaneously maximizes resilience to phase shifts, ASS, and hysteresis, leading to improvements in ecosystem health and functioning.

Regional-scale scenario modeling for coral reefs: a decision support tool to inform management of a complex system.

The worldwide decline of coral reefs threatens the livelihoods of coastal communities and puts at risk valuable ecosystem services provided by reefs. There is a pressing need for robust predictions of potential futures of coral reef and associated human systems under alternative management scenarios. Understanding and predicting the dynamics of coral reef systems at regional scales of tens to hundreds of kilometers is imperative, because reef systems are connected by physical and socioeconomic processes across regions and often across international boundaries. We present a spatially explicit regional-scale model of ecological dynamics for a general coral reef system. In designing our model as a tool for decision support, we gave precedence to portability and accessibility; the model can be parameterized for dissimilar coral reef systems in different parts of the world, and the model components and outputs are understandable for nonexperts. The model simulates local-scale dynamics, which are coupled across regions through larval connectivity between reefs. We validate our model using an instantiation for the Meso-American Reef system. The model realistically captures local and regional ecological dynamics and responds to external forcings in the form of harvesting, pollution, and physical damage (e.g., hurricanes, coral bleaching) to produce trajectories that largely fall within limits observed in the real system. Moreover, the model demonstrates behaviors that have relevance for management considerations. In particular, differences in larval supply between reef localities drive spatial variability in modeled reef community structure. Reef tracts for which recruitment is low are more vulnerable to natural disturbance and synergistic effects of anthropogenic stressors. Our approach provides a framework for projecting the likelihood of different reef futures at local to regional scales, with important applications for the management of complex coral reef systems.

Differential regulation drives plasticity in sex determination gene networks.

BACKGROUND: Sex determination networks evolve rapidly and have been studied intensely across many species, particularly in insects, thus presenting good models to study the evolutionary plasticity of gene networks. RESULTS: We study the evolution of an unlinked gene capable of regulating an existing diploid sex determination system. Differential gene expression determines phenotypic sex and fitness, dramatically reducing the number of assumptions of previous models. It allows us to make a quantitative evaluation of the full range of evolutionary outcomes of the system and an assessment of the likely contribution of sexual conflict to change in sex determination systems. Our results show under what conditions network mutations causing differential regulation can lead to the reshaping of sex determination networks. CONCLUSION: The analysis demonstrates the complex relationship between mutation and outcome: the same mutation can produce many different evolved populations, while the same evolved population can be produced by many different mutations. Existing network structure alters the constraints and frequency of evolutionary changes, which include the recruitment of new regulators, changes in heterogamety, protected polymorphisms, and transitions to a new locus that controls sex determination.

Conditions for global dynamic stability of a class of resource-bounded model ecosystems.

This paper studies a class of dynamical systems that model multi-species ecosystems. These systems are 'resource bounded' in the sense that species compete to utilize an underlying limiting resource or substrate. This boundedness means that the relevant state space can be reduced to a simplex, with coordinates representing the proportions of substrate utilized by the various species. If the vector field is inward pointing on the boundary of the simplex, the state space is forward invariant under the system flow, a requirement that can be interpreted as the presence of non-zero exogenous recruitment. We consider conditions under which these model systems have a unique interior equilibrium that is globally asymptotically stable. The systems we consider generalize classical multi-species Lotka-Volterra systems, the behaviour of which is characterized by properties of the community (or interaction) matrix. However, the more general systems considered here are not characterized by a single matrix, but rather a family of matrices. We develop a set of 'explicit conditions' on the basis of a notion of 'uniform diagonal dominance' for such a family of matrices, that allows us to extract a set of sufficient conditions for global asymptotic stability based on properties of a single, derived matrix. Examples of these explicit conditions are discussed.

The evolution of continuous variation in ejaculate expenditure strategy.

Sperm competition theory has largely focused on the evolution of ejaculate expenditure strategies across different species or populations or across discrete mating roles on which sperm competition operates differentially. Few studies have considered the extent to which male ejaculate expenditure is influenced by continuous change in male phenotype within a population. Here we model how optimal ejaculate expenditure responds to two sources of continuous variation: (1) the quantity of resources allocated by a male to mating within a breeding season and (2) the resource cost of obtaining a mate. We find that variation in the amount of resources available for mating does not alone produce selection for differing ejaculate investment strategies. However, when there is variation in the cost of obtaining a mate, males with a lower cost will be selected to invest fewer sperm per mating than males whose cost is higher. Any parameter decreasing this cost will also select for decreased ejaculate investment per mating. These results provide a novel insight into the evolution of male ejaculate expenditure strategies, revealing that individual constraints on the ability to secure matings can lead to variation in ejaculate expenditure even when the risk of sperm competition is the same for all males.

Degree dependence in rates of transcription factor evolution explains the unusual structure of transcription networks.

Transcription networks have an unusual structure. In both prokaryotes and eukaryotes, the number of target genes regulated by each transcription factor, its out-degree, follows a broad tailed distribution. By contrast, the number of transcription factors regulating a target gene, its in-degree, follows a much narrower distribution, which has no broad tail. We constructed a model of transcription network evolution through trans- and cis-mutations, gene duplication and deletion. The effects of these different evolutionary processes on the network structure are enough to produce an asymmetrical in- and out-degree distribution. However, the parameter values required to replicate known in- and out-degree distributions are unrealistic. We then considered variation in the rate of evolution of a gene dependent upon its position in the network. When transcription factors with many regulatory interactions are constrained to evolve more slowly than those with few interactions, the details of the in- and out-degree distributions of transcription networks can be fully reproduced over a range of plausible parameter values. The networks produced by our model depend on the relative rates of the different evolutionary processes. By determining the circumstances under which the networks with the correct degree distributions are produced, we are able to assess the relative importance of the different evolutionary processes in our model during evolution.

Duration of courtship effort as a costly signal.

We consider a male and a female in a courtship encounter over continuous time. Both parties pay participation costs per unit time. The game ends when either one or other of the parties quits or the female accepts the male as a mate. We assume that there is a binary variable which determines whether the male is a "good" or "bad" type from the female's point of view, according to either his condition or his willingness to care for the young after mating. This variable is not directly observable by the female, but has fitness consequences for her: she gets a positive fitness payoff from mating with a "good" male but a negative fitness payoff from mating with a "bad" male. We assume also that a "good" male has a higher ratio of fitness benefit from mating to fitness cost per unit time of courtship than a "bad" male. We show that, under suitable assumptions, there are evolutionarily stable equilibrium behaviours in which time-extended courtship takes place. A "good" male is willing to court for longer than a "bad" male; in this way the duration of a male's courtship signals his type, and acts as a costly handicap. By not being willing to mate immediately the female achieves a degree of screening because the posterior probability that the male is "good", conditional on his not having quit the game, increases with the duration of courtship.

Density dependence triggers runaway selection of reduced senescence.

In the presence of exogenous mortality risks, future reproduction by an individual is worth less than present reproduction to its fitness. Senescent aging thus results inevitably from transferring net fertility into younger ages. Some long-lived organisms appear to defy theory, however, presenting negligible senescence (e.g., hydra) and extended lifespans (e.g., Bristlecone Pine). Here, we investigate the possibility that the onset of vitality loss can be delayed indefinitely, even accepting the abundant evidence that reproduction is intrinsically costly to survival. For an environment with constant hazard, we establish that natural selection itself contributes to increasing density-dependent recruitment losses. We then develop a generalized model of accelerating vitality loss for analyzing fitness optima as a tradeoff between compression and spread in the age profile of net fertility. Across a realistic spectrum of senescent age profiles, density regulation of recruitment can trigger runaway selection for ever-reducing senescence. This novel prediction applies without requirement for special life-history characteristics such as indeterminate somatic growth or increasing fecundity with age. The evolution of nonsenescence from senescence is robust to the presence of exogenous adult mortality, which tends instead to increase the age-independent component of vitality loss. We simulate examples of runaway selection leading to negligible senescence and even intrinsic immortality.

A coral-algal phase shift in Mesoamerica not driven by changes in herbivorous fish abundance.

Coral-algal phase shifts in which coral cover declines to low levels and is replaced by algae have often been documented on coral reefs worldwide. This has motivated coral reef management responses that include restriction and regulation of fishing, e.g. herbivorous fish species. However, there is evidence that eutrophication and sedimentation can be at least as important as a reduction in herbivory in causing phase shifts. These threats arise from coastal development leading to increased nutrient and sediment loads, which stimulate algal growth and negatively impact corals respectively. Here, we first present results of a dynamic process-based model demonstrating that in addition to overharvesting of herbivorous fish, bottom-up processes have the potential to precipitate coral-algal phase shifts on Mesoamerican reefs. We then provide an empirical example that exemplifies this on coral reefs off Mahahual in Mexico, where a shift from coral to algal dominance occurred over 14 years, during which there was little change in herbivore biomass but considerable development of tourist infrastructure. Our results indicate that coastal development can compromise the resilience of coral reefs and that watershed and coastal zone management together with the maintenance of functional levels of fish herbivory are critical for the persistence of coral reefs in Mesoamerica.

Simplification and its consequences in biological modelling: conclusions from a study of calcium oscillations in hepatocytes.

Systems Biology requires that biological modelling is scaled up from small components to system level. This can produce exceedingly complex models, which obscure understanding rather than facilitate it. The successful use of highly simplified models would resolve many of the current problems faced in Systems Biology. This paper questions whether the conclusions of simple mathematical models of biological systems are trustworthy. The simplification of a specific model of calcium oscillations in hepatocytes is examined in detail, and the conclusions drawn from this scrutiny generalized. We formalize our choice of simplification approach through the use of functional 'building blocks'. A collection of models is constructed, each a progressively more simplified version of a well-understood model. The limiting model is a piecewise linear model that can be solved analytically. We find that, as expected, in many cases the simpler models produce incorrect results. However, when we make a sensitivity analysis, examining which aspects of the behaviour of the system are controlled by which parameters, the conclusions of the simple model often agree with those of the richer model. The hypothesis that the simplified model retains no information about the real sensitivities of the unsimplified model can be very strongly ruled out by treating the simplification process as a pseudo-random perturbation on the true sensitivity data. We conclude that sensitivity analysis is, therefore, of great importance to the analysis of simple mathematical models in biology. Our comparisons reveal which results of the sensitivity analysis regarding calcium oscillations in hepatocytes are robust to the simplifications necessarily involved in mathematical modelling. For example, we find that if a treatment is observed to strongly decrease the period of the oscillations while increasing the proportion of the cycle during which cellular calcium concentrations are rising, without affecting the inter-spike or maximum calcium concentrations, then it is likely that the treatment is acting on the plasma membrane calcium pump.

Costly but worthless gifts facilitate courtship.

What are the characteristics of a good courtship gift? We address this question by modelling courtship as a sequential game. This is structured as follows: the male offers a gift to a female; after observing the gift, the female decides whether or not to accept it; she then chooses whether or not to mate with the male. In one version of the game, based on human courtship, the female is uncertain about whether the male intends to stay or desert after mating. In a second version, there is no paternal care but the female is uncertain about the male's quality. The two versions of the game are shown to be mathematically equivalent. We find robust equilibrium solutions in which mating is predominantly facilitated by an "extravagant" gift which is costly to the male but intrinsically worthless to the female. By being costly to the male, the gift acts as a credible signal of his intentions or quality. At the same time, its lack of intrinsic value to the female serves to deter a "gold-digger", who has no intention of mating with the male, from accepting the gift. In this way, an economically inefficient gift enables mutually suitable partners to be matched.

To age or not to age.

According to the antagonistic pleiotropy theory of ageing, natural selection has favoured genes conferring short-term benefits to the organism at the cost of deterioration in later life. The 'disposable soma' theory expresses this as a life-history strategy in which somatic maintenance is below the level required to prevent ageing, thus enabling higher immediate fertility. It has been argued that a non-ageing strategy will always be bettered by a low but non-zero rate of ageing, because the costs of such ageing will be felt only in the distant future when they are of negligible importance. Here, we examine this argument critically. We find that a non-ageing strategy will be locally optimal if, in the presence of ageing, the onset of deterioration is sufficiently rapid or early. Conversely, ageing will be optimal if deterioration is sufficiently slow or late. As the temporal profile of ageing changes from one of steady deterioration to one involving a sudden loss of vitality after a period of little or no decline, the conditions for a non-ageing strategy to be locally optimal become progressively more stringent. But for all forms of profile considered, conditions can be found for which a strategy involving no ageing is locally optimal.

Augmented discounting: interaction between ageing and time-preference behaviour.

Discounting occurs when an immediate benefit is systematically valued more highly than a delayed benefit of the same magnitude. It is manifested in physiological and behavioural strategies of organisms. This study brings together life-history theory and time-preference theory within a single modelling framework. We consider an animal encountering reproductive opportunities as a random process. Under an external hazard, optimal life-history strategy typically prioritizes immediate reproduction at the cost of declining fertility and increasing mortality with age. Given such ageing, an immediate reproductive reward should be preferred to a delayed reward because of both the risk of death and declining fertility. By this analysis, ageing is both a consequence of discounting by the body and a cause of behavioural discounting. A series of models is developed, making different assumptions about external hazards and biological ageing. With realistic ageing assumptions (increasing mortality and an accelerating rate of fertility decline) the time-preference rate increases in old age. Under an uncertain external hazard rate, young adults should also have relatively high time-preference rates because their (Bayesian) estimate of the external hazard is high. Middle-aged animals may therefore be the most long term in their outlook.

Evolution of the human ABO polymorphism by two complementary selective pressures.

The best-known example of terminal-glycan variation is the ABO histo-blood group polymorphism in humans. We model two selective forces acting on histo-blood group antigens that may account for this polymorphism. The first is generated by the invasion of opportunistic bacterial or other pathogens that interact with the epithelial-mucosal surfaces. The bacteria adapt to the microenvironments of common host phenotypes and so create frequency-dependent selection for rarer host alleles. The second is generated by intracellular viruses, and accounts for the observed differentials between the ABO-phenotype frequencies. It is thought that viruses acquire histo-blood group structures as part of their envelope from their previous host. The presence of host antigens on the viral envelope causes differential transmission of the virus between host types owing to the asymmetric action of ABO natural antibodies. Our model simulations show that these two forces acting together can account for the major features of the ABO polymorphism in humans.