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Co-infecting parasites and pathogens remain a leading challenge for global public health due to their consequences for individual-level infection risk and disease progression. However, a clear understanding of the population-level consequences of co-infection is lacking. Here, we constructed a model that includes three individual-level effects of co-infection: mortality, fecundity, and transmission. We used the model to investigate how these individual-level consequences of co-infection scale up to produce population-level infection patterns. To parameterize this model, we conducted a four-year cohort study in African buffalo to estimate the individual-level effects of co-infection with two bacterial pathogens, bovine tuberculosis (BTB) and brucellosis, across a range of demographic and environmental contexts. At the individual-level, our empirical results identified BTB as a risk factor for acquiring brucellosis, but we found no association between brucellosis and the risk of acquiring BTB. Both infections were associated with reductions in survival and neither infection was associated with reductions in fecundity. Results of the model reproduce co-infection patterns in the data and predict opposite impacts of co-infection at individual and population scales: whereas BTB facilitated brucellosis infection at the individual-level, our model predicts the presence of brucellosis to have a strong negative impact on BTB at the population-level. In modeled populations where brucellosis is present, the endemic prevalence and basic reproduction number (Ro) of BTB were lower than in populations without brucellosis. Therefore, these results provide a data-driven example of competition between co-infecting pathogens that occurs when one pathogen facilitates secondary infections at the individual level., Comment: 13 pages, 4 figures, 3 documents in the supporting information

Ecological trade-offs between species are often invoked to explain species coexistence in ecological communities. However, few mathematical models have been proposed for which coexistence conditions can be characterized explicitly in terms of a trade-off. Here we present a model of a plant community which allows such a characterization. In the model plant species compete for sites where each site has a fixed stress condition. Species differ both in stress tolerance and competitive ability. Stress tolerance is quantified as the fraction of sites with stress conditions low enough to allow establishment. Competitive ability is quantified as the propensity to win the competition for empty sites. We derive the deterministic, discrete-time dynamical system for the species abundances. We prove the conditions under which plant species can coexist in a stable equilibrium. We show that the coexistence conditions can be characterized graphically, clearly illustrating the trade-off between stress tolerance and competitive ability. We compare our model with a recently proposed, continuous-time dynamical system for a tolerance-fecundity trade-off in plant communities, and we show that this model is a special case of the continuous-time version of our model., Comment: To be published in Journal of Mathematical Biology. 30 pages, 5 figures, 5 appendices

A popular line of research in evolutionary biology is the use of time-calibrated phylogenies for the inference of diversification processes. This requires computing the likelihood of a given ultrametric tree as the reconstructed tree produced by a given model of diversification. Etienne & Rosindell (2012) proposed a lineage-based model of diversification, called protracted speciation, where species remain incipient during a random duration before turning good species, and showed that this can explain the slowdown in lineage accumulation observed in real phylogenies. However, they were unable to provide a general likelihood formula. Here, we present a likelihood formula for protracted speciation models, where rates at which species turn good or become extinct can depend both on their age and on time. Our only restrictive assumption is that speciation rate does not depend on species status. Our likelihood formula utilizes a new technique, based on the contour of the phylogenetic tree and first developed in Lambert (2010). We consider the reconstructed trees spanned by all extant species, by all good extant species, or by all representative species, which are either good extant species or incipient species representative of some good extinct species. Specifically, we prove that each of these trees is a coalescent point process, that is, a planar, ultrametric tree where the coalescence times between two consecutive tips are independent, identically distributed random variables. We characterize the common distribution of these coalescence times in some, biologically meaningful, special cases for which the likelihood reduces to an elegant analytical formula or becomes numerically tractable., Comment: 27 pages, 5 figures