Evolving graphs: dynamical models, inverse problems and propagation

Applications such as neuroscience, telecommunication, online social networking, transport and retail trading give rise to connectivity patterns that change over time. In this work, we address the resulting need for network models and computational algorithms that deal with dynamic links. We introduce a new class of evolving range-dependent random graphs that gives a tractable framework for modelling and simulation. We develop a spectral algorithm for calibrating a set of edge ranges from a sequence of network snapshots and give a proof of principle illustration on some neuroscience data. We also show how the model can be used computationally and analytically to investigate the scenario where an evolutionary process, such as an epidemic, takes place on an evolving network. This allows us to study the cumulative effect of two distinct types of dynamics.

Evolutionary bi-stability in pathogen transmission mode

Many pathogens transmit to new hosts by both infection (horizontal transmission) and transfer to the infected host's offspring (vertical transmission). These two transmission modes require speci®c adap- tations of the pathogen that can be mutually exclusive, resulting in a trade-off between horizontal and vertical transmission. We show that in mathematical models such trade-offs can lead to the simultaneous existence of two evolutionary stable states (evolutionary bi-stability) of allocation of resources to the two modes of transmission. We also show that jumping between evolutionary stable states can be induced by gradual environmental changes. Using quantitative PCR-based estimates of abundance in seed and vege- tative parts, we show that the pathogen of wheat, Phaeosphaeria nodorum, has jumped between two distinct states of transmission mode twice in the past 160 years, which, based on published evidence, we interpret as adaptation to environmental change. The ®nding of evolutionary bi-stability has impli- cations for human, animal and other plant diseases. An ill-judged change in a disease control programme could cause the pathogen to evolve a new, and possibly more damaging, combination of transmission modes. Similarly, environmental changes can shift the balance between transmission modes, with adverse effects on human, animal and plant health.

Managing threatened species – the ecological toolbox, evolutionary theory and the declining-population paradigm

1. The management of threatened species is an important practical way in which conservationists can intervene in the extinction process and reduce the loss of biodiversity. Understanding the causes of population declines (past, present and future) is pivotal to designing effective practical management. This is the declining-population paradigm identified by Caughley. 2. There are three broad classes of ecological tool used by conservationists to guide management decisions for threatened species: statistical models of habitat use, demographic models and behaviour-based models. Each of these is described here, illustrated with a case study and evaluated critically in terms of its practical application. 3. These tools are fundamentally different. Statistical models of habitat use and demographic models both use descriptions of patterns in abundance and demography, in relation to a range of factors, to inform management decisions. In contrast, behaviourbased models describe the evolutionary processes underlying these patterns, and derive such patterns from the strategies employed by individuals when competing for resources under a specific set of environmental conditions. 4. Statistical models of habitat use and demographic models have been used successfully to make management recommendations for declining populations. To do this, assumptions are made about population growth or vital rates that will apply when environmental conditions are restored, based on either past data collected under favourable environmental conditions or estimates of these parameters when the agent of decline is removed. As a result, they can only be used to make reliable quantitative predictions about future environments when a comparable environment has been experienced by the population of interest in the past. 5. Many future changes in the environment driven by management will not have been experienced by a population in the past. Under these circumstances, vital rates and their relationship with population density will change in the future in a way that is not predictable from past patterns. Reliable quantitative predictions about population-level responses then need to be based on an explicit consideration of the evolutionary processes operating at the individual level. 6. Synthesis and applications. It is argued that evolutionary theory underpins Caughley’s declining-population paradigm, and that it needs to become much more widely used within mainstream conservation biology. This will help conservationists examine critically the reliability of the tools they have traditionally used to aid management decision-making. It will also give them access to alternative tools, particularly when predictions are required for changes in the environment that have not been experienced by a population in the past.

Phylogenetic mixture models can reduce node-density artifacts

We investigate the performance of phylogenetic mixture models in reducing a well-known and pervasive artifact of phylogenetic inference known as the node-density effect, comparing them to partitioned analyses of the same data. The node-density effect refers to the tendency for the amount of evolutionary change in longer branches of phylogenies to be underestimated compared to that in regions of the tree where there are more nodes and thus branches are typically shorter. Mixture models allow more than one model of sequence evolution to describe the sites in an alignment without prior knowledge of the evolutionary processes that characterize the data or how they correspond to different sites. If multiple evolutionary patterns are common in sequence evolution, mixture models may be capable of reducing node-density effects by characterizing the evolutionary processes more accurately. In gene-sequence alignments simulated to have heterogeneous patterns of evolution, we find that mixture models can reduce node-density effects to negligible levels or remove them altogether, performing as well as partitioned analyses based on the known simulated patterns. The mixture models achieve this without knowledge of the patterns that generated the data and even in some cases without specifying the full or true model of sequence evolution known to underlie the data. The latter result is especially important in real applications, as the true model of evolution is seldom known. We find the same patterns of results for two real data sets with evidence of complex patterns of sequence evolution: mixture models substantially reduced node-density effects and returned better likelihoods compared to partitioning models specifically fitted to these data. We suggest that the presence of more than one pattern of evolution in the data is a common source of error in phylogenetic inference and that mixture models can often detect these patterns even without prior knowledge of their presence in the data. Routine use of mixture models alongside other approaches to phylogenetic inference may often reveal hidden or unexpected patterns of sequence evolution and can improve phylogenetic inference.

Managing threatened species: the ecological toolbox, evolutionary theory and declining-population paradigm

1. The management of threatened species is an important practical way in which conservationists can intervene in the extinction process and reduce the loss of biodiversity. Understanding the causes of population declines (past, present and future) is pivotal to designing effective practical management. This is the declining-population paradigm identified by Caughley. 2. There are three broad classes of ecological tool used by conservationists to guide management decisions for threatened species: statistical models of habitat use, demographic models and behaviour-based models. Each of these is described here, illustrated with a case study and evaluated critically in terms of its practical application. 3. These tools are fundamentally different. Statistical models of habitat use and demographic models both use descriptions of patterns in abundance and demography, in relation to a range of factors, to inform management decisions. In contrast, behaviour-based models describe the evolutionary processes underlying these patterns, and derive such patterns from the strategies employed by individuals when competing for resources under a specific set of environmental conditions. 4. Statistical models of habitat use and demographic models have been used successfully to make management recommendations for declining populations. To do this, assumptions are made about population growth or vital rates that will apply when environmental conditions are restored, based on either past data collected under favourable environmental conditions or estimates of these parameters when the agent of decline is removed. As a result, they can only be used to make reliable quantitative predictions about future environments when a comparable environment has been experienced by the population of interest in the past. 5. Many future changes in the environment driven by management will not have been experienced by a population in the past. Under these circumstances, vital rates and their relationship with population density will change in the future in a way that is not predictable from past patterns. Reliable quantitative predictions about population-level responses then need to be based on an explicit consideration of the evolutionary processes operating at the individual level. 6. Synthesis and applications. It is argued that evolutionary theory underpins Caughley's declining-population paradigm, and that it needs to become much more widely used within mainstream conservation biology. This will help conservationists examine critically the reliability of the tools they have traditionally used to aid management decision-making. It will also give them access to alternative tools, particularly when predictions are required for changes in the environment that have not been experienced by a population in the past.

Parameter estimation based on stacked regression and evolutionary algorithms

A new parameter-estimation algorithm, which minimises the cross-validated prediction error for linear-in-the-parameter models, is proposed, based on stacked regression and an evolutionary algorithm. It is initially shown that cross-validation is very important for prediction in linear-in-the-parameter models using a criterion called the mean dispersion error (MDE). Stacked regression, which can be regarded as a sophisticated type of cross-validation, is then introduced based on an evolutionary algorithm, to produce a new parameter-estimation algorithm, which preserves the parsimony of a concise model structure that is determined using the forward orthogonal least-squares (OLS) algorithm. The PRESS prediction errors are used for cross-validation, and the sunspot and Canadian lynx time series are used to demonstrate the new algorithms.

Forecasting extinction risk of ectotherms under climate warming: an evolutionary perspective

1. It has been postulated that climate warming may pose the greatest threat species in the tropics, where ectotherms have evolved more thermal specialist physiologies. Although species could rapidly respond to environmental change through adaptation, little is known about the potential for thermal adaptation, especially in tropical species. 2. In the light of the limited empirical evidence available and predictions from mutation-selection theory, we might expect tropical ectotherms to have limited genetic variance to enable adaptation. However, as a consequence of thermodynamic constraints, we might expect this disadvantage to be at least partially offset by a fitness advantage, that is, the ‘hotter-is-better’ hypothesis. 3. Using an established quantitative genetics model and metabolic scaling relationships, we integrate the consequences of the opposing forces of thermal specialization and thermodynamic constraints on adaptive potential by evaluating extinction risk under climate warming. We conclude that the potential advantage of a higher maximal development rate can in theory more than offset the potential disadvantage of lower genetic variance associated with a thermal specialist strategy. 4. Quantitative estimates of extinction risk are fundamentally very sensitive to estimates of generation time and genetic variance. However, our qualitative conclusion that the relative risk of extinction is likely to be lower for tropical species than for temperate species is robust to assumptions regarding the effects of effective population size, mutation rate and birth rate per capita. 5. With a view to improving ecological forecasts, we use this modelling framework to review the sensitivity of our predictions to the model’s underpinning theoretical assumptions and the empirical basis of macroecological patterns that suggest thermal specialization and fitness increase towards the tropics. We conclude by suggesting priority areas for further empirical research.

The evolutionary basis for differences between the immune systems of man, mouse, pig and ruminants

Studying the pathogenesis of an infectious disease like colibacillosis requires an understanding of the responses of target hosts to the organism both as a pathogen and as a commensal. The mucosal immune system constitutes the primary line of defence against luminal micro-organisms. The immunoglobulin-superfamily-based adaptive immune system evolved in the earliest jawed vertebrates, and the adaptive and innate immune system of humans, mice, pigs and ruminants co-evolved in common ancestors for approximately 300 million years. The divergence occurred only 100 mya and, as a consequence, most of the fundamental immunological mechanisms are very similar. However, since pressure on the immune system comes from rapidly evolving pathogens, immune systems must also evolve rapidly to maintain the ability of the host to survive and reproduce. As a consequence, there are a number of areas of detail where mammalian immune systems have diverged markedly from each other, such that results obtained in one species are not always immediately transferable to another. Thus, animal models of specific diseases need to be selected carefully, and the results interpreted with caution. Selection is made simpler where specific host species like cattle and pigs can be both target species and reservoirs for human disease, as in infections with Escherichia coli.

Sex differences in the programming effects of prenatal stress on psychopathology and stress responses: an evolutionary perspective

There is strong evidence from animal studies that prenatal stress has different effects on male and female offspring. In general, although not always, prenatal stress increases anxiety, depression and stress responses, both hypothalamic–pituitary–adrenal and cardiovascular, in female offspring rather than in male. Males are more likely to show learning and memory deficits. There have been few studies so far in humans which differentiate effects of prenatal stress on male and female psychopathology. Some studies support the animal models, but the evidence is inconsistent. The mediating mechanisms for any sex specific effects are little understood, but there is evidence that placental function can differ depending on the sex of the fetus. We suggest that there may be an evolutionary reason for any sex differences in the long term effects of prenatal stress. In a stressful environment it may be adaptive for females, who are more likely to stay in one place and look after children, to be more vigilant, alert to danger and thus show more stress responsiveness. This can give rise to a more anxious or depressed phenotype. With males it may be more adaptive to go out and explore new environments, compete with other males, and be more aggressive. For this it may help to be less responsive to external stressors. More research is needed into sex differences in the effects of prenatal stress in humans, to test these ideas.

Predicting how many animals will be where: how to build, calibrate and evaluate individual-based models

Individual-based models (IBMs) can simulate the actions of individual animals as they interact with one another and the landscape in which they live. When used in spatially-explicit landscapes IBMs can show how populations change over time in response to management actions. For instance, IBMs are being used to design strategies of conservation and of the exploitation of fisheries, and for assessing the effects on populations of major construction projects and of novel agricultural chemicals. In such real world contexts, it becomes especially important to build IBMs in a principled fashion, and to approach calibration and evaluation systematically. We argue that insights from physiological and behavioural ecology offer a recipe for building realistic models, and that Approximate Bayesian Computation (ABC) is a promising technique for the calibration and evaluation of IBMs. IBMs are constructed primarily from knowledge about individuals. In ecological applications the relevant knowledge is found in physiological and behavioural ecology, and we approach these from an evolutionary perspective by taking into account how physiological and behavioural processes contribute to life histories, and how those life histories evolve. Evolutionary life history theory shows that, other things being equal, organisms should grow to sexual maturity as fast as possible, and then reproduce as fast as possible, while minimising per capita death rate. Physiological and behavioural ecology are largely built on these principles together with the laws of conservation of matter and energy. To complete construction of an IBM information is also needed on the effects of competitors, conspecifics and food scarcity; the maximum rates of ingestion, growth and reproduction, and life-history parameters. Using this knowledge about physiological and behavioural processes provides a principled way to build IBMs, but model parameters vary between species and are often difficult to measure. A common solution is to manually compare model outputs with observations from real landscapes and so to obtain parameters which produce acceptable fits of model to data. However, this procedure can be convoluted and lead to over-calibrated and thus inflexible models. Many formal statistical techniques are unsuitable for use with IBMs, but we argue that ABC offers a potential way forward. It can be used to calibrate and compare complex stochastic models and to assess the uncertainty in their predictions. We describe methods used to implement ABC in an accessible way and illustrate them with examples and discussion of recent studies. Although much progress has been made, theoretical issues remain, and some of these are outlined and discussed.

A cautionary note on the use of Ornstein Uhlenbeck models in macroevolutionary studies

Phylogenetic comparative methods are increasingly used to give new insights into the dynamics of trait evolution in deep time. For continuous traits the core of these methods is a suite of models that attempt to capture evolutionary patterns by extending the Brownian constant variance model. However, the properties of these models are often poorly understood, which can lead to the misinterpretation of results. Here we focus on one of these models – the Ornstein Uhlenbeck (OU) model. We show that the OU model is frequently incorrectly favoured over simpler models when using Likelihood ratio tests, and that many studies fitting this model use datasets that are small and prone to this problem. We also show that very small amounts of error in datasets can have profound effects on the inferences derived from OU models. Our results suggest that simulating fitted models and comparing with empirical results is critical when fitting OU and other extensions of the Brownian model. We conclude by making recommendations for best practice in fitting OU models in phylogenetic comparative analyses, and for interpreting the parameters of the OU model.