Detecting signals of chronic shedding to explain pathogen persistence: Leptospira interrogans in California sea lions.

Identifying mechanisms driving pathogen persistence is a vital component of wildlife disease ecology and control. Asymptomatic, chronically infected individuals are an oft-cited potential reservoir of infection, but demonstrations of the importance of chronic shedding to pathogen persistence at the population-level remain scarce. Studying chronic shedding using commonly collected disease data is hampered by numerous challenges, including short-term surveillance that focuses on single epidemics and acutely ill individuals, the subtle dynamical influence of chronic shedding relative to more obvious epidemic drivers, and poor ability to differentiate between the effects of population prevalence of chronic shedding vs. intensity and duration of chronic shedding in individuals. We use chronic shedding of Leptospira interrogans serovar Pomona in California sea lions (Zalophus californianus) as a case study to illustrate how these challenges can be addressed. Using leptospirosis-induced strands as a measure of disease incidence, we fit models with and without chronic shedding, and with different seasonal drivers, to determine the time-scale over which chronic shedding is detectable and the interactions between chronic shedding and seasonal drivers needed to explain persistence and outbreak patterns. Chronic shedding can enable persistence of L. interrogans within the sea lion population. However, the importance of chronic shedding was only apparent when surveillance data included at least two outbreaks and the intervening inter-epidemic trough during which fadeout of transmission was most likely. Seasonal transmission, as opposed to seasonal recruitment of susceptibles, was the dominant driver of seasonality in this system, and both seasonal factors had limited impact on long-term pathogen persistence. We show that the temporal extent of surveillance data can have a dramatic impact on inferences about population processes, where the failure to identify both short- and long-term ecological drivers can have cascading impacts on understanding higher order ecological phenomena, such as pathogen persistence.

Inferring patterns of influenza transmission in swine from multiple streams of surveillance data.

Swine populations are known to be an important source of new human strains of influenza A, including those responsible for global pandemics. Yet our knowledge of the epidemiology of influenza in swine is dismayingly poor, as highlighted by the emergence of the 2009 pandemic strain and the paucity of data describing its origins. Here, we analyse a unique dataset arising from surveillance of swine influenza at a Hong Kong abattoir from 1998 to 2010. We introduce a state-space model that estimates disease exposure histories by joint inference from multiple modes of surveillance, integrating both virological and serological data. We find that an observed decrease in virus isolation rates is not due to a reduction in the regional prevalence of influenza. Instead, a more likely explanation is increased infection of swine in production farms, creating greater immunity to disease early in life. Consistent with this, we find that the weekly risk of exposure on farms equals or exceeds the exposure risk during transport to slaughter. We discuss potential causes for these patterns, including competition between influenza strains and shifts in the Chinese pork industry, and suggest opportunities to improve knowledge and reduce prevalence of influenza in the region.

Society, demography and genetic structure in the spotted hyena.

Spotted hyenas (Crocuta crocuta) are large mammalian carnivores, but their societies, called 'clans', resemble those of such cercopithecine primates as baboons and macaques with respect to their size, hierarchical structure, and frequency of social interaction among both kin and unrelated group-mates. However, in contrast to cercopithecine primates, spotted hyenas regularly hunt antelope and compete with group-mates for access to kills, which are extremely rich food sources, but also rare and ephemeral. This unique occurrence of baboon-like sociality among top-level predators has favoured the evolution of many unusual traits in this species. We briefly review the relevant socio-ecology of spotted hyenas, document great demographic variation but little variation in social structure across the species' range, and describe the long-term fitness consequences of rank-related variation in resource access among clan-mates. We then summarize patterns of genetic relatedness within and between clans, including some from a population that had recently gone through a population bottleneck, and consider the roles of sexually dimorphic dispersal and female mate choice in the generation of these patterns. Finally, we apply social network theory under varying regimes of resource availability to analyse the effects of kinship on the stability of social relationships among members of one large hyena clan in Kenya. Although social bonds among both kin and non-kin are weakest when resource competition is most intense, hyenas sustain strong social relationships with kin year-round, despite constraints imposed by resource limitation. Our analyses suggest that selection might act on both individuals and matrilineal kin groups within clans containing multiple matrilines.

Escherichia coli rpoB mutants have increased evolvability in proportion to their fitness defects.

Evolvability is the capacity of an organism or population for generating descendants with increased fitness. Simulations and comparative studies have shown that evolvability can vary among individuals and identified characteristics of genetic architectures that can promote evolvability. However, little is known about how the evolvability of biological organisms typically varies along a lineage at each mutational step in its history. Evolvability might increase upon sustaining a deleterious mutation because there are many compensatory paths in the fitness landscape to reascend the same fitness peak or because shifts to new peaks become possible. We use genetic marker divergence trajectories to parameterize and compare the evolvability--defined as the fitness increase realized by an evolving population initiated from a test genotype--of a series of Escherichia coli mutants on multiple timescales. Each mutant differs from a common progenitor strain by a mutation in the rpoB gene, which encodes the beta subunit of RNA polymerase. Strains with larger fitness defects are proportionally more evolvable in terms of both the beneficial mutations accessible in their immediate mutational neighborhoods and integrated over evolutionary paths that traverse multiple beneficial mutations. Our results establish quantitative expectations for how a mutation with a given deleterious fitness effect should influence evolvability, and they will thus inform future studies of how deleterious, neutral, and beneficial mutations targeting other cellular processes impact the evolutionary potential of microorganisms.

Evolutionary dynamics, epistatic interactions, and biological information.

We investigate a definition of biological information that connects population genetics with the tools of information theory by focusing on the distribution of genotypes found in a population. Previous research has treated loci as non-interacting by making specific approximations in the calculation of information-theoretic quantities. We expand earlier mathematical forms to include epistasis, or interactions between mutations at all pairs of loci. Application of our improved measure of biological information to evolution on two-locus, two-allele fitness landscapes demonstrates that mutual information between loci reflects epistatic interaction of mutations. Finally, we consider four-locus, two-allele fitness landscapes with modular structure. As modular interactions are inherently epistatic, we demonstrate that our refined approximation provides insight into the underlying structure of these non-trivial fitness landscapes.

Inferring Markov chains: Bayesian estimation, model comparison, entropy rate, and out-of-class modeling.

Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer kth order Markov chains, for arbitrary k , from finite data by applying Bayesian methods to both parameter estimation and model-order selection. Extending existing results for multinomial models of discrete data, we connect inference to statistical mechanics through information-theoretic (type theory) techniques. We establish a direct relationship between Bayesian evidence and the partition function which allows for straightforward calculation of the expectation and variance of the conditional relative entropy and the source entropy rate. Finally, we introduce a method that uses finite data-size scaling with model-order comparison to infer the structure of out-of-class processes.

Bayesian structural inference for hidden processes.

We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian structural inference (BSI) relies on a set of candidate unifilar hidden Markov model (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of topological ε-machines. (A sequel then removes the topological restriction.) This subset of the uHMM topologies has the added benefit that inferred models are guaranteed to be ε-machines, irrespective of estimated transition probabilities. Properties of ε-machines and uHMMs allow for the derivation of analytic expressions for estimating transition probabilities, inferring start states, and comparing the posterior probability of candidate model topologies, despite process internal structure being only indirectly present in data. We demonstrate BSI's effectiveness in estimating a process's randomness, as reflected by the Shannon entropy rate, and its structure, as quantified by the statistical complexity. We also compare using the posterior distribution over candidate models and the single, maximum a posteriori model for point estimation and show that the former more accurately reflects uncertainty in estimated values. We apply BSI to in-class examples of finite- and infinite-order Markov processes, as well to an out-of-class, infinite-state hidden process.

Optimal instruments and models for noisy chaos.

Analysis of finite, noisy time series data leads to modern statistical inference methods. Here we adapt Bayesian inference for applied symbolic dynamics. We show that reconciling Kolmogorov's maximum-entropy partition with the methods of Bayesian model selection requires the use of two separate optimizations. First, instrument design produces a maximum-entropy symbolic representation of time series data. Second, Bayesian model comparison with a uniform prior selects a minimum-entropy model, with respect to the considered Markov chain orders, of the symbolic data. We illustrate these steps using a binary partition of time series data from the logistic and Henon maps as well as the Rössler and Lorenz attractors with dynamical noise. In each case we demonstrate the inference of effectively generating partitions and kth-order Markov chain models.

Medium-term prediction of chaos.

We study prediction of chaotic time series when a perfect model is available but the initial condition is measured with uncertainty. A common approach for predicting future data given these circumstances is to apply the model despite the uncertainty. In systems with fold dynamics, we find prediction is improved over this strategy by recognizing this behavior. A systematic study of the Logistic map demonstrates prediction of the most likely trajectory can be extended three time steps. Finally, we discuss application of these ideas to the Rössler attractor.