Genomic mutation rates that neutralize adaptive evolution and natural selection

When mutation rates are low, natural selection remains effective, and increasing the mutation rate can give rise to an increase in adaptation rate. When mutation rates are high to begin with, however, increasing the mutation rate may have a detrimental effect because of the overwhelming presence of deleterious mutations. Indeed, if mutation rates are high enough: (i) adaptive evolution may be neutralized, resulting in a zero (or negative) adaptation rate despite the continued availability of adaptive and/or compensatory mutations, or (ii) natural selection may be neutralized, because the fitness of lineages bearing adaptive and/or compensatory mutations—whether established or newly arising—is eroded by excessive mutation, causing such lineages to decline in frequency. We apply these two criteria to a standard model of asexual adaptive evolution and derive mathematical expressions—some new, some old in new guise—delineating the mutation rates under which either adaptive evolution or natural selection is neutralized. The expressions are simple and require no a priori knowledge of organism- and/or environment-specific parameters. Our discussion connects these results to each other and to previous theory, showing convergence or equivalence of the different results in most cases.     

Resistance and relatedness on an evolutionary graph

When investigating evolution in structured populations, it is often convenient to consider the population as an evolutionary graph—individuals as nodes, and whom they may act with as edges. There has, in recent years, been a surge of interest in evolutionary graphs, especially in the study of the evolution of social behaviours. An inclusive fitness framework is best suited for this type of study. A central requirement for an inclusive fitness analysis is an expression for the genetic similarity between individuals residing on the graph. This has been a major hindrance for work in this area as highly technical mathematics are often required. Here, I derive a result that links genetic relatedness between haploid individuals on an evolutionary graph to the resistance between vertices on a corresponding electrical network. An example that demonstrates the potential computational advantage of this result over contemporary approaches is provided. This result offers more, however, to the study of population genetics than strictly computationally efficient methods. By establishing a link between gene transfer and electric circuit theory, conceptualizations of the latter can enhance understanding of the former.     

Distribution of vaccine/antivirals and the ‘least spread line’ in a stratified population

We describe a prioritization scheme for an allocation of a sizeable quantity of vaccine or antivirals in a stratified population. The scheme builds on an optimal strategy for reducing the epidemic''s initial growth rate in a stratified mass-action model. The strategy is tested on the EpiSims network describing interactions and influenza dynamics in the population of Utah, where the stratification we have chosen is by age (0–6, 7–13, 14–18, adults). No prior immunity information is available, thus everyone is assumed to be susceptible—this may be relevant, possibly with the exception of persons over 50, to the 2009 H1N1 influenza outbreak. We have found that the top priority in an allocation of a sizeable quantity of seasonal influenza vaccinations goes to young children (0–6), followed by teens (14–18), then children (7–13), with the adult share being quite low. These results, which rely on the structure of the EpiSims network, are compared with the current influenza vaccination coverage levels in the US population.     

How sticky should a virus be? The impact of virus binding and release on transmission fitness using influenza as an example

Budding viruses face a trade-off: virions need to efficiently attach to and enter uninfected cells while newly generated virions need to efficiently detach from infected cells. The right balance between attachment and detachment—the right amount of stickiness—is needed for maximum fitness. Here, we design and analyse a mathematical model to study in detail the impact of attachment and detachment rates on virus fitness. We apply our model to influenza, where stickiness is determined by a balance of the haemagglutinin (HA) and neuraminidase (NA) proteins. We investigate how drugs, the adaptive immune response and vaccines impact influenza stickiness and fitness. Our model suggests that the location in the ‘stickiness landscape’ of the virus determines how well interventions such as drugs or vaccines are expected to work. We discuss why hypothetical NA enhancer drugs might occasionally perform better than the currently available NA inhibitors in reducing virus fitness. We show that an increased antibody or T-cell-mediated immune response leads to maximum fitness at higher stickiness. We further show that antibody-based vaccines targeting mainly HA or NA, which leads to a shift in stickiness, might reduce virus fitness above what can be achieved by the direct immunological action of the vaccine. Overall, our findings provide potentially useful conceptual insights for future vaccine and drug development and can be applied to other budding viruses beyond influenza.     

Extinction risk and eco-evolutionary dynamics in a variable environment with increasing frequency of extreme events

One of the most dramatic consequences of climate change will be the intensification and increased frequency of extreme events. I used numerical simulations to understand and predict the consequences of directional trend (i.e. mean state) and increased variability of a climate variable (e.g. temperature), increased probability of occurrence of point extreme events (e.g. floods), selection pressure and effect size of mutations on a quantitative trait determining individual fitness, as well as the their effects on the population and genetic dynamics of a population of moderate size. The interaction among climate trend, variability and probability of point extremes had a minor effect on risk of extinction, time to extinction and distribution of the trait after accounting for their independent effects. The survival chances of a population strongly and linearly decreased with increasing strength of selection, as well as with increasing climate trend and variability. Mutation amplitude had no effects on extinction risk, time to extinction or genetic adaptation to the new climate. Climate trend and strength of selection largely determined the shift of the mean phenotype in the population. The extinction or persistence of the populations in an ‘extinction window’ of 10 years was well predicted by a simple model including mean population size and mean genetic variance over a 10-year time frame preceding the ‘extinction window’, although genetic variance had a smaller role than population size in predicting contemporary risk of extinction.     

Space–time correlations in urban sprawl

Understanding demographic and migrational patterns constitutes a great challenge. Millions of individual decisions, motivated by economic, political, demographic, rational and/or emotional reasons underlie the high complexity of demographic dynamics. Significant advances in quantitatively understanding such complexity have been registered in recent years, as those involving the growth of cities but many fundamental issues still defy comprehension. We present here compelling empirical evidence of a high level of regularity regarding time and spatial correlations in urban sprawl, unravelling patterns about the inertia in the growth of cities and their interaction with each other. By using one of the world''s most exhaustive extant demographic data basis—that of the Spanish Government''s Institute INE, with records covering 111 years and (in 2011) 45 million people, distributed among more than 8000 population nuclei—we show that the inertia of city growth has a characteristic time of 15 years, and its interaction with the growth of other cities has a characteristic distance of 80 km. Distance is shown to be the main factor that entangles two cities (60% of total correlations). The power of our current social theories is thereby enhanced.     

Critical transition between cohesive and population-dividing responses to change

Globalization and global climate change will probably be accompanied by rapid social and biophysical changes that may be caused by external forcing or internal nonlinear dynamics. These changes often subject residing populations (human or otherwise) to harsh environments and force them to respond. Research efforts have mostly focused on the underlying mechanisms that drive these changes and the characteristics of new equilibria towards which populations would adapt. However, the transient dynamics of how populations respond under these new regimes is equally, if not more, important, and systematic analysis of such dynamics has received less attention. Here, we investigate this problem under the framework of replicator dynamics with fixed reward kernels. We show that at least two types of population responses are possible—cohesive and population-dividing transitions—and demonstrate that the critical transition between the two, as well as other important properties, can be expressed in simple relationships between the shape of reward structure, shift magnitude and initial strategy diversity. Importantly, these relationships are derived from a simple, yet powerful and versatile, method. As many important phenomena, from political polarization to the evolution of distinct ecological traits, may be cast in terms of division of populations, we expect our findings and method to be useful and applicable for understanding population responses to change in a wide range of contexts.     

Asymmetric interaction and indeterminate fitness correlation between cooperative partners in the fig�Cfig wasp mutualism

Empirical observations have shown that cooperative partners can compete for common resources, but what factors determine whether partners cooperate or compete remain unclear. Using the reciprocal fig–fig wasp mutualism, we show that nonlinear amplification of interference competition between fig wasps—which limits the fig wasps'' ability to use a common resource (i.e. female flowers)—keeps the common resource unsaturated, making cooperation locally stable. When interference competition was manually prevented, the fitness correlation between figs and fig wasps went from positive to negative. This indicates that genetic relatedness or reciprocal exchange between cooperative players, which could create spatial heterogeneity or self-restraint, was not sufficient to maintain stable cooperation. Moreover, our analysis of field-collected data shows that the fitness correlation between cooperative partners varies stochastically, and that the mainly positive fitness correlation observed during the warm season shifts to a negative correlation during the cold season owing to an increase in the initial oviposition efficiency of each fig wasp. This implies that the discriminative sanction of less-cooperative wasps (i.e. by decreasing the egg deposition efficiency per fig wasp) but reward to cooperative wasps by fig, a control of the initial value, will facilitate a stable mutualism. Our finding that asymmetric interaction leading to an indeterminate fitness interaction between symbiont (i.e. cooperative actors) and host (i.e. recipient) has the potential to explain why conflict has been empirically observed in both well-documented intraspecific and interspecific cooperation systems.     

Many ways to stay in the game: individual variability maintains high biodiversity in planktonic microorganisms

In apparent contradiction to competition theory, the number of known, coexisting plankton species far exceeds their explicable biodiversity—a discrepancy termed the Paradox of the Plankton. We introduce a new game-theoretic model for competing microorganisms in which one player consists of all organisms of one species. The stable points for the population dynamics in our model, known as strategic behaviour distributions (SBDs), are probability distributions of behaviours across all organisms which imply a stable population of the species as a whole. We find that intra-specific variability is the key characteristic that ultimately allows coexistence because the outcomes of competitions between individuals with variable competitive abilities are unpredictable. Our simulations based on the theoretical model show that up to 100 species can coexist for at least 10 000 generations, and that even small population sizes or species with inferior competitive ability can survive when there is intra-specific variability. In nature, this variability can be observed as niche differentiation, variability in environmental and ecological factors, and variability of individual behaviours or physiology. Therefore, previous specific explanations of the paradox are consistent with and provide specific examples of our suggestion that individual variability is the mechanism which solves the paradox.     

Modelling co-translational dimerization for programmable nonlinearity in synthetic biology

Nonlinearity plays a fundamental role in the performance of both natural and synthetic biological networks. Key functional motifs in living microbial systems, such as the emergence of bistability or oscillations, rely on nonlinear molecular dynamics. Despite its core importance, the rational design of nonlinearity remains an unmet challenge. This is largely due to a lack of mathematical modelling that accounts for the mechanistic basis of nonlinearity. We introduce a model for gene regulatory circuits that explicitly simulates protein dimerization—a well-known source of nonlinear dynamics. Specifically, our approach focuses on modelling co-translational dimerization: the formation of protein dimers during—and not after—translation. This is in contrast to the prevailing assumption that dimer generation is only viable between freely diffusing monomers (i.e. post-translational dimerization). We provide a method for fine-tuning nonlinearity on demand by balancing the impact of co- versus post-translational dimerization. Furthermore, we suggest design rules, such as protein length or physical separation between genes, that may be used to adjust dimerization dynamics in vivo. The design, build and test of genetic circuits with on-demand nonlinear dynamics will greatly improve the programmability of synthetic biological systems.     

Single passage in mouse organs enhances the survival and spread of Salmonella enterica

Intravenous inoculation of Salmonella enterica serovar Typhimurium into mice is a prime experimental model of invasive salmonellosis. The use of wild-type isogenic tagged strains (WITS) in this system has revealed that bacteria undergo independent bottlenecks in the liver and spleen before establishing a systemic infection. We recently showed that those bacteria that survived the bottleneck exhibited enhanced growth when transferred to naive mice. In this study, we set out to disentangle the components of this in vivo adaptation by inoculating mice with WITS grown either in vitro or in vivo. We developed an original method to estimate the replication and killing rates of bacteria from experimental data, which involved solving the probability-generating function of a non-homogeneous birth–death–immigration process. This revealed a low initial mortality in bacteria obtained from a donor animal. Next, an analysis of WITS distributions in the livers and spleens of recipient animals indicated that in vivo-passaged bacteria started spreading between organs earlier than in vitro-grown bacteria. These results further our understanding of the influence of passage in a host on the fitness and virulence of Salmonella enterica and represent an advance in the power of investigation on the patterns and mechanisms of host–pathogen interactions.     

An analytical approach to bistable biological circuit discrimination using real algebraic geometry

Biomolecular circuits with two distinct and stable steady states have been identified as essential components in a wide range of biological networks, with a variety of mechanisms and topologies giving rise to their important bistable property. Understanding the differences between circuit implementations is an important question, particularly for the synthetic biologist faced with determining which bistable circuit design out of many is best for their specific application. In this work we explore the applicability of Sturm''s theorem—a tool from nineteenth-century real algebraic geometry—to comparing ‘functionally equivalent’ bistable circuits without the need for numerical simulation. We first consider two genetic toggle variants and two different positive feedback circuits, and show how specific topological properties present in each type of circuit can serve to increase the size of the regions of parameter space in which they function as switches. We then demonstrate that a single competitive monomeric activator added to a purely monomeric (and otherwise monostable) mutual repressor circuit is sufficient for bistability. Finally, we compare our approach with the Routh–Hurwitz method and derive consistent, yet more powerful, parametric conditions. The predictive power and ease of use of Sturm''s theorem demonstrated in this work suggest that algebraic geometric techniques may be underused in biomolecular circuit analysis.     

Effects of heterogeneity in infection-exposure history and immunity on the dynamics of a protozoan parasite

Infection systems where traits of the host, such as acquired immunity, interact with the infection process can show complex dynamic behaviour with counter-intuitive results. In this study, we consider the traits ‘immune status’ and ‘exposure history’, and our aim is to assess the influence of acquired individual heterogeneity in these traits. We have built an individual-based model of Eimeria acervulina infections, a protozoan parasite with an environmental stage that causes coccidiosis in chickens. With the model, we simulate outbreaks of the disease under varying initial contaminations. Heterogeneity in the traits arises stochastically through differences in the dose and frequency of parasites that individuals pick up from the environment. We find that the relationship between the initial contamination and the severity of an outbreak has a non-monotonous ‘wave-like’ pattern. This pattern can be explained by an increased heterogeneity in the host population caused by the infection process at the most severe outbreaks. We conclude that when dealing with these types of infection systems, models that are used to develop or evaluate control measures cannot neglect acquired heterogeneity in the host population traits that interact with the infection process.     

Future climates: Markov blankets and active inference in the biosphere

We formalize the Gaia hypothesis about the Earth climate system using advances in theoretical biology based on the minimization of variational free energy. This amounts to the claim that non-equilibrium steady-state dynamics—that underwrite our climate—depend on the Earth system possessing a Markov blanket. Our formalization rests on how the metabolic rates of the biosphere (understood as Markov blanket''s internal states) change with respect to solar radiation at the Earth''s surface (i.e. external states), through the changes in greenhouse and albedo effects (i.e. active states) and ocean-driven global temperature changes (i.e. sensory states). Describing the interaction between the metabolic rates and solar radiation as climatic states—in a Markov blanket—amounts to describing the dynamics of the internal states as actively inferring external states. This underwrites climatic non-equilibrium steady-state through free energy minimization and thus a form of planetary autopoiesis.     

Effects of worker size on the dynamics of fire ant tunnel construction

Social insects work together to complete tasks. However, different individuals within a colony may vary in task proficiency. We investigated if fire ant (Solenopsis invicta) worker body size influenced the ability to construct tunnels—a key component of subterranean nests. We monitored excavation by worker groups in a substrate of small wetted glass particles in quasi-two-dimensional arenas. Morphological and network features of the tunnel system were measured. Total tunnel area did not differ significantly between groups of large and small workers, although the tunnel area of control sized workers was significantly larger than that of large workers. Moreover, large workers created wider but shorter tunnels, with slower growth rate of tunnel number. However, edge–vertex scaling and degree distribution of the tunnel network were similar across all treatments. In all cases, the amount of excavated material was correlated with the number of active workers. Our study reveals that morphological features of excavated tunnels show modest variation when constructed by workers of varying sizes, but topological features associated with the tunnel network are conserved. These results suggest that important behavioural aspects of tunnel construction—and thus nest building—are similar among morphologically distinct members of fire ant societies.     

The global spread of drug-resistant influenza

Resistance to oseltamivir, the most widely used influenza antiviral drug, spread to fixation in seasonal influenza A(H1N1) between 2006 and 2009. This sudden rise in resistance seemed puzzling given the low overall level of the oseltamivir usage and the lack of a correlation between local rates of resistance and oseltamivir usage. We used a stochastic simulation model and deterministic approximations to examine how such events can occur, and in particular to determine how the rate of fixation of the resistant strain depends both on its fitness in untreated hosts as well as the frequency of antiviral treatment. We found that, for the levels of antiviral usage in the population, the resistant strain will eventually spread to fixation, if it is not attenuated in transmissibility relative to the drug-sensitive strain, but not at the speed observed in seasonal H1N1. The extreme speed with which the resistance spread in seasonal H1N1 suggests that the resistant strain had a transmission advantage in untreated hosts, and this could have arisen from genetic hitchhiking, or from the mutations responsible for resistance and compensation. Importantly, our model also shows that resistant virus will fail to spread if it is even slightly less transmissible than its sensitive counterpart—a finding of relevance given that resistant pandemic influenza (H1N1) 2009 may currently suffer from a small, but nonetheless experimentally perceptible reduction in transmissibility.     

Predicting connectivity of green turtles at Palmyra Atoll,central Pacific: a focus on mtDNA and dispersal modelling

Population connectivity and spatial distribution are fundamentally related to ecology, evolution and behaviour. Here, we combined powerful genetic analysis with simulations of particle dispersal in a high-resolution ocean circulation model to investigate the distribution of green turtles foraging at the remote Palmyra Atoll National Wildlife Refuge, central Pacific. We analysed mitochondrial sequences from turtles (n = 349) collected there over 5 years (2008–2012). Genetic analysis assigned natal origins almost exclusively (approx. 97%) to the West Central and South Central Pacific combined Regional Management Units. Further, our modelling results indicated that turtles could potentially drift from rookeries to Palmyra Atoll via surface currents along a near-Equatorial swathe traversing the Pacific. Comparing findings from genetics and modelling highlighted the complex impacts of ocean currents and behaviour on natal origins. Although the Palmyra feeding ground was highly differentiated genetically from others in the Indo-Pacific, there was no significant differentiation among years, sexes or stage-classes at the Refuge. Understanding the distribution of this foraging population advances knowledge of green turtles and contributes to effective conservation planning for this threatened species.     

The Measurement of Little g: A Fertile Ground for Precision Measurement Science

The occasion of the 100th anniversary of Einstein’s “golden year” provides a wonderful opportunity to discuss some aspects of gravity—gravitation being an interest of Einstein’s that occurred a few years after 1905. I’ll do this by talking about the measurement of little g, the free-fall acceleration on the Earth’s surface that is mainly due to the Earth’s gravity but whose value is also affected by centrifugal forces that are a result of the Earth’s rotation. I will also describe two equivalence experiments and a test of the inverse-square law of gravitation. Finally, I will make some observations on the science of precision measurement—a subject that underpins much of scientific progress.     

Knowing one's place: a free-energy approach to pattern regulation

Understanding how organisms establish their form during embryogenesis and regeneration represents a major knowledge gap in biological pattern formation. It has been recently suggested that morphogenesis could be understood in terms of cellular information processing and the ability of cell groups to model shape. Here, we offer a proof of principle that self-assembly is an emergent property of cells that share a common (genetic and epigenetic) model of organismal form. This behaviour is formulated in terms of variational free-energy minimization—of the sort that has been used to explain action and perception in neuroscience. In brief, casting the minimization of thermodynamic free energy in terms of variational free energy allows one to interpret (the dynamics of) a system as inferring the causes of its inputs—and acting to resolve uncertainty about those causes. This novel perspective on the coordination of migration and differentiation of cells suggests an interpretation of genetic codes as parametrizing a generative model—predicting the signals sensed by cells in the target morphology—and epigenetic processes as the subsequent inversion of that model. This theoretical formulation may complement bottom-up strategies—that currently focus on molecular pathways—with (constructivist) top-down approaches that have proved themselves in neuroscience and cybernetics.     

Analysis of a complete DNA–protein affinity landscape

Properties of biological fitness landscapes are of interest to a wide sector of the life sciences, from ecology to genetics to synthetic biology. For biomolecular fitness landscapes, the information we currently possess comes primarily from two sources: sparse samples obtained from directed evolution experiments; and more fine-grained but less authentic information from ‘in silico’ models (such as NK-landscapes). Here we present the entire protein-binding profile of all variants of a nucleic acid oligomer 10 bases in length, which we have obtained experimentally by a series of highly parallel on-chip assays. The resulting complete landscape of sequence-binding pairs, comprising more than one million binding measurements in duplicate, has been analysed statistically using a number of metrics commonly applied to synthetic landscapes. These metrics show that the landscape is rugged, with many local optima, and that this arises from a combination of experimental variation and the natural structural properties of the oligonucleotides.