Complex epistatic interactions between ELF3, PRR9, and PRR7 regulate the circadian clock and plant physiology.

Circadian clocks are endogenous timekeeping mechanisms that coordinate internal physiological responses with the external environment. EARLY FLOWERING3 (ELF3), PSEUDO RESPONSE REGULATOR (PRR9), and PRR7 are essential components of the plant circadian clock and facilitate entrainment of the clock to internal and external stimuli. Previous studies have highlighted a critical role for ELF3 in repressing the expression of PRR9 and PRR7. However, the functional significance of activity in regulating circadian clock dynamics and plant development is unknown. To explore this regulatory dynamic further, we first employed mathematical modeling to simulate the effect of the prr9/prr7 mutation on the elf3 circadian phenotype. These simulations suggested that simultaneous mutations in prr9/prr7 could rescue the elf3 circadian arrhythmia. Following these simulations, we generated all Arabidopsis elf3/prr9/prr7 mutant combinations and investigated their circadian and developmental phenotypes. Although these assays could not replicate the results from the mathematical modeling, our results have revealed a complex epistatic relationship between ELF3 and PRR9/7 in regulating different aspects of plant development. ELF3 was essential for hypocotyl development under ambient and warm temperatures, while PRR9 was critical for root thermomorphogenesis. Finally, mutations in prr9 and prr7 rescued the photoperiod-insensitive flowering phenotype of the elf3 mutant. Together, our results highlight the importance of investigating the genetic relationship among plant circadian genes.

Feasibility and stability in large Lotka Volterra systems with interaction structure.

Complex system stability can be studied via linear stability analysis using random matrix theory (RMT) or via feasibility (requiring positive equilibrium abundances). Both approaches highlight the importance of interaction structure. Here we show, analytically and numerically, how RMT and feasibility approaches can be complementary. In generalized Lotka-Volterra (GLV) models with random interaction matrices, feasibility increases when predator-prey interactions increase; increasing competition/mutualism has the opposite effect. These changes have crucial impact on the stability of the GLV model.

ODE (Ordinary Differential Equation) Models for Plant Circadian Networks: What the Models Are and How They Should Be Used.

ODE models have been used for decades to help circadian biologists understand the rhythmic phenomena they observe and to predict the behavior of plant circadian rhythms under changed conditions such as genetic mutations or novel environments. The models vary in complexity, and for good reasons, but they share the same mathematical ingredients in their construction and the same computational methods in their solution. Here we explain the fundamental concepts which define ODE models. We sketch how ODE models can be understood, how they can be solved mathematically and computationally, and the important distinction between autonomous and non-autonomous phenomena. The concepts are illustrated with examples which illustrate the basic concepts and which may help to describe the strengths and limitations of these models and the computational investigations of their properties.

Variable bites and dynamic populations; new insights in Leishmania transmission.

Leishmaniasis is a neglected tropical disease which kills an estimated 50,000 people each year, with its deadly impact confined mainly to lower to middle income countries. Leishmania parasites are transmitted to human hosts by sand fly vectors during blood feeding. Recent experimental work shows that transmission is modulated by the patchy landscape of infection in the host's skin, and the parasite population dynamics within the vector. Here we assimilate these new findings into a simple probabilistic model for disease transmission which replicates recent experimental results, and assesses their relative importance. The results of subsequent simulations, describing random parasite uptake and dynamics across multiple blood meals, show that skin heterogeneity is important for transmission by short-lived flies, but that for longer-lived flies with multiple bites the population dynamics within the vector dominate transmission probability. Our results indicate that efforts to reduce fly lifespan beneath a threshold of around two weeks may be especially helpful in reducing disease transmission.

Temperature robustness in Arabidopsis circadian clock models is facilitated by repressive interactions, autoregulation, and three-node feedbacks.

The biological interactions underpinning the Arabidopsis circadian clock have been systematically uncovered and explored by biological experiments and mathematical models. This is captured by a series of published ordinary differential equation (ODE) models, which describe plant clock dynamics in response to light/dark conditions. However, understanding the role of temperature in resetting the clock (entrainment) and the mechanisms by which circadian rhythms maintain a near-24 h period over a range of temperatures (temperature compensation) is still unclear. Understanding entrainment and temperature compensation may elucidate the principles governing the structure of the circadian clock network. Here we explore the design principles of the Arabidopsis clock and its responses to changes in temperature. We analyse published clock models of Arabidopsis, spanning a range of complexity, and incorporate temperature-dependent dynamics into the parameters of translation rates in these models, to discern which regulatory patterns may best explain clock function and temperature compensation. We additionally construct three minimal clock models and explore what key features govern their rhythmicity and temperature robustness via a series of random parameterisations. Results show that the highly repressive interactions between the components of the plant clock, together with autoregulation patterns and three-node feedback loops, are associated with circadian function of the clock in general, and enhance its robustness to temperature variation in particular. However, because the networks governing clock function vary with time due to light and temperature conditions, we emphasise the importance of studying plant clock functionality in its entirety rather than as a set of discrete regulation patterns.

Ecology and evolution of antimicrobial resistance in bacterial communities.

Accumulating evidence suggests that the response of bacteria to antibiotics is significantly affected by the presence of other interacting microbes. These interactions are not typically accounted for when determining pathogen sensitivity to antibiotics. In this perspective, we argue that resistance and evolutionary responses to antibiotic treatments should not be considered only a trait of an individual bacteria species but also an emergent property of the microbial community in which pathogens are embedded. We outline how interspecies interactions can affect the responses of individual species and communities to antibiotic treatment, and how these responses could affect the strength of selection, potentially changing the trajectory of resistance evolution. Finally, we identify key areas of future research which will allow for a more complete understanding of antibiotic resistance in bacterial communities. We emphasise that acknowledging the ecological context, i.e. the interactions that occur between pathogens and within communities, could help the development of more efficient and effective antibiotic treatments.

Heat the Clock: Entrainment and Compensation in Arabidopsis Circadian Rhythms.

The circadian clock is a biological mechanism that permits some organisms to anticipate daily environmental variations. This clock generates biological rhythms, which can be reset by environmental cues such as cycles of light or temperature, a process known as entrainment. After entrainment, circadian rhythms typically persist with approximately 24 hours periodicity in free-running conditions, i.e. in the absence of environmental cues. Experimental evidence also shows that a free-running period close to 24 hours is maintained across a range of temperatures, a process known as temperature compensation. In the plant Arabidopsis, the effect of light on the circadian system has been widely studied and successfully modelled mathematically. However, the role of temperature in periodicity, and the relationship between entrainment and compensation, are not fully understood. Here we adapt recent models to incorporate temperature dependence by applying Arrhenius equations to the parameters of the models that characterize transcription, translation, and degradation rates. We show that the resulting models can exhibit thermal entrainment and temperature compensation, but that these phenomena emerge from physiologically different sets of processes. Further simulations combining thermal and photic forcing in more realistic scenarios clearly distinguish between the processes of entrainment and compensation, and reveal temperature compensation as an emergent property which can arise as a result of multiple temperature-dependent interactions. Our results consistently point to the thermal sensitivity of degradation rates as driving compensation and entrainment across a range of conditions.

Evolutionarily Stable Strategies for Fecundity and Swimming Speed of Fish.

Many pelagic fish species have a life history that involves producing a large number of small eggs. This is the result of a trade-off between fecundity and larval survival probability. There are also trade-offs involving other traits, such as larval swimming speed. Swimming faster increases the average food encounter rate but also increases the metabolic cost. Here we introduce an evolutionary model comprising fecundity and swimming speed as heritable traits. We show that there can be two evolutionary stable strategies. In environments where there is little noise in the food encounter rate, the stable strategy is a low-fecundity strategy with a swimming speed that minimises the mean time taken to reach reproductive maturity. However, in noisy environments, for example where the prey distribution is patchy or the water is turbulent, strategies that optimise mean outcomes are often outperformed by strategies that increase inter-individual variance. We show that, when larval growth rates are unpredictable, a high-fecundity strategy is evolutionarily stable. In a population following this strategy, the swimming speed is higher than would be anticipated by maximising the mean growth rate.

Fishing for nutrients in heterogeneous landscapes: modelling plant growth trade-offs in monocultures and mixed communities.

The problem of how best to find and exploit essential resources, the quality and locations of which are unknown, is common throughout biology. For plants, the need to grow an efficient root system so as to acquire patchily distributed soil nutrients is typically complicated by competition between plants, and by the costs of maintaining the root system. Simple mechanistic models for root growth can help elucidate these complications, and here we argue that these models can be usefully informed by models initially developed for foraging fish larvae. Both plant and fish need to efficiently search a spatio-temporally variable environment using simple algorithms involving only local information, and both must perform this task against a backdrop of intra- and inter-specific competition and background mortality. Here we develop these parallels by using simple stochastic models describing the growth and efficiency of four contrasting idealized root growth strategies. We show that plants which grow identically in isolation in homogeneous substrates will typically perform very differently when grown in monocultures, in heterogeneous nutrient landscapes and in mixed-species competition. In particular, our simulations show a consistent result that plants which trade-off rapid growth in favour of a more efficient and durable root system perform better, both on average and in terms of the best performing individuals, than more rapidly growing ephemeral root systems. Moreover, when such slower growing but more efficient plants are grown in competition, the overall community productivity can exceed that of the constituent monocultures. These findings help to disentangle many of the context-dependent behaviours seen in the experimental literature, and may form a basis for future studies at the level of complex population dynamics and life history evolution.

Bacteriophages limit the existence conditions for conjugative plasmids.

UNLABELLED: Bacteriophages are a major cause of bacterial mortality and impose strong selection on natural bacterial populations, yet their effects on the dynamics of conjugative plasmids have rarely been tested. We combined experimental evolution, mathematical modeling, and individual-based simulations to explain how the ecological and population genetics effects of bacteriophages upon bacteria interact to determine the dynamics of conjugative plasmids and their persistence. The ecological effects of bacteriophages on bacteria are predicted to limit the existence conditions for conjugative plasmids, preventing persistence under weak selection for plasmid accessory traits. Experiments showed that phages drove faster extinction of plasmids in environments where the plasmid conferred no benefit, but they also revealed more complex effects of phages on plasmid dynamics under these conditions, specifically, the temporary maintenance of plasmids at fixation followed by rapid loss. We hypothesized that the population genetic effects of bacteriophages, specifically, selection for phage resistance mutations, may have caused this. Further mathematical modeling and individual-based simulations supported our hypothesis, showing that conjugative plasmids may hitchhike with phage resistance mutations in the bacterial chromosome. IMPORTANCE: Conjugative plasmids are infectious loops of DNA capable of transmitting DNA between bacterial cells and between species. Because plasmids often carry extra genes that allow bacteria to live in otherwise-inhospitable environments, their dynamics are central to understanding bacterial adaptive evolution. The plasmid-bacterium interaction has typically been studied in isolation, but in natural bacterial communities, bacteriophages, viruses that infect bacteria, are ubiquitous. Using experiments, mathematical models, and computer simulations we show that bacteriophages drive plasmid dynamics through their ecological and evolutionary effects on bacteria and ultimately limit the conditions allowing plasmid existence. These results advance our understanding of bacterial adaptation and show that bacteriophages could be used to select against plasmids carrying undesirable traits, such as antibiotic resistance.

Obstacle avoidance in social groups: new insights from asynchronous models.

For moving animals, the successful avoidance of hazardous obstacles is an important capability. Despite this, few models of collective motion have addressed the relationship between behavioural and social features and obstacle avoidance. We develop an asynchronous individual-based model for social movement which allows social structure within groups to be included. We assess the dynamics of group navigation and resulting collision risk in the context of information transfer through the system. In agreement with previous work, we find that group size has a nonlinear effect on collision risk. We implement examples of possible network structures to explore the impact social preferences have on collision risk. We show that any social heterogeneity induces greater obstacle avoidance with further improvements corresponding to groups containing fewer influential individuals. The model provides a platform for both further theoretical investigation and practical application. In particular, we argue that the role of social structures within bird flocks may have an important role to play in assessing the risk of collisions with wind turbines, but that new methods of data analysis are needed to identify these social structures.

Constructing random matrices to represent real ecosystems.

Models of complex systems with n components typically have order n(2) parameters because each component can potentially interact with every other. When it is impractical to measure these parameters, one may choose random parameter values and study the emergent statistical properties at the system level. Many influential results in theoretical ecology have been derived from two key assumptions: that species interact with random partners at random intensities and that intraspecific competition is comparable between species. Under these assumptions, community dynamics can be described by a community matrix that is often amenable to mathematical analysis. We combine empirical data with mathematical theory to show that both of these assumptions lead to results that must be interpreted with caution. We examine 21 empirically derived community matrices constructed using three established, independent methods. The empirically derived systems are more stable by orders of magnitude than results from random matrices. This consistent disparity is not explained by existing results on predator-prey interactions. We investigate the key properties of empirical community matrices that distinguish them from random matrices. We show that network topology is less important than the relationship between a species' trophic position within the food web and its interaction strengths. We identify key features of empirical networks that must be preserved if random matrix models are to capture the features of real ecosystems.

Integrated Testing Strategies (ITS) for safety assessment.

Integrated testing strategies (ITS), as opposed to single definitive tests or fixed batteries of tests, are expected to efficiently combine different information sources in a quantifiable fashion to satisfy an information need, in this case for regulatory safety assessments. With increasing awareness of the limitations of each individual tool and the development of highly targeted tests and predictions, the need for combining pieces of evidence increases. The discussions that took place during this workshop, which brought together a group of experts coming from different related areas, illustrate the current state of the art of ITS, as well as promising developments and identifiable challenges. The case of skin sensitization was taken as an example to understand how possible ITS can be constructed, optimized and validated. This will require embracing and developing new concepts such as adverse outcome pathways (AOP), advanced statistical learning algorithms and machine learning, mechanistic validation and "Good ITS Practices".

Disentangling nestedness from models of ecological complexity.

Complex networks of interactions are ubiquitous and are particularly important in ecological communities, in which large numbers of species exhibit negative (for example, competition or predation) and positive (for example, mutualism) interactions with one another. Nestedness in mutualistic ecological networks is the tendency for ecological specialists to interact with a subset of species that also interact with more generalist species. Recent mathematical and computational analysis has suggested that such nestedness increases species richness. By examining previous results and applying computational approaches to 59 empirical data sets representing mutualistic plant­pollinator networks, we show that this statement is incorrect. A simpler metric­the number of mutualistic partners a species has­is a much better predictor of individual species survival and hence, community persistence. Nestedness is, at best, a secondary covariate rather than a causative factor for biodiversity in mutualistic communities. Analysis of complex networks should be accompanied by analysis of simpler, underpinning mechanisms that drive multiple higher-order network properties.

Evolutionary optimality in stochastic search problems.

'Optimal' behaviour in a biological system is not simply that which maximizes a mean, or temporally and spatially averaged, fitness function. Rather, population dynamics and demographic and environmental stochasticity are fundamental evolutionary ingredients. Here, we revisit the problem of optimal foraging, where some recent studies claim that organisms should forage according to Lévy walks. We show that, in an ecological scenario dominated by uncertainty and high mortality, Lévy walks can indeed be evolutionarily favourable. However, this conclusion is dependent on the definition of efficiency and the details of the simulations. We analyse measures of efficiency that incorporate population-level characteristics, such as variance, superdiffusivity and heavy tails, and compare the results with those generated by simple maximizing of the average encounter rate. These results have implications on stochastic search problems in general, and also on computational models of evolutionary optima.

Exact results for the evolution of stochastic switching in variable asymmetric environments.

The ability of bacteria to spontaneously switch their expressed phenotype from an identical underlying genotype is now widely acknowledged. Mechanisms behind these switches have been shown to be evolvable. Important questions thus arise: In a fluctuating environment, under what conditions can stochastic switching evolve and how is the evolutionarily optimal switching rate related to the environmental changes? Here we derive exact analytical results for the long-term exponential population growth rate in a two-state periodically changing environment, where the environmental states vary in both their duration and in their impact on the fitness of each phenotype. Using methods from statistical physics we derive conditions under which nonswitching is evolutionarily optimal, and we furthermore demonstrate that the transition between the nonswitching and switching regimes is discontinuous (a first-order phase transition). Our general analytical method allows the evolutionary effects of asymmetries in selection pressures and environmental growth rates to be quantified. The evolutionary implications of our findings are discussed in relation to their to real-world applications in the light of recent experimental evidence.

Efficient or inaccurate? Analytical and numerical modelling of random search strategies.

A large number of observational and theoretical studies have investigated animal movement strategies for finding randomly located food items. Many of these studies have claimed that a particular strategy is advantageous over other strategies or that the spatial distribution of the food items affects the search efficiency. Here, we study a deliberately idealised problem, in which a blind forager searches for re-visitable food items. We show analytically that the forager's efficiency is completely independent of both its movement strategy and the spatial pattern of the food items and depends only on the density of food in the environment. However, in some cases, apparent optima in search strategies can arise as artefacts of inappropriate and inaccurate numerical simulations. We discuss modifications to the idealised foraging problem that can confer an advantage on certain strategies, including when the forager has some memory or knowledge of the environment; when the food items are non-revisitable; and when the problem is viewed in an evolutionary context.

Significance and importance: some common misapprehensions about statistics.

There are many common misapprehensions about statistics that occur in the literature. We are sure that the three misapprehensions we deal with in this short review are widespread. They concern: 1)what P values mean;2)what an insignificant result means, and what it does not mean; the question of the 'power' of a statistical test;3)the difference between importance and statistical significance.We produce no formulae or recipes for dealing with particular situations, instead we concentrate on the commonsense use of simple statistics. We emphasise that if the use of any but the simplest statistics is intended, it is much better to get proper statistical help before starting experiments, rather than afterwards.