Multiple scales of selection influence the evolutionary emergence of novel pathogens

Abstract

When pathogens encounter a novel environment, such as a new host species or treatment with an antimicrobial drug, their fitness may be reduced so that adaptation is necessary to avoid extinction. Evolutionary emergence is the process by which new pathogen strains arise in response to such selective pressures. Theoretical studies over the last decade have clarified some determinants of emergence risk, but have neglected the influence of fitness on evolutionary rates and have not accounted for the multiple scales at which pathogens must compete successfully. We present a cross-scale theory for evolutionary emergence, which embeds a mechanistic model of within-host selection into a stochastic model for emergence at the population scale. We explore how fitness landscapes at within-host and between-host scales can interact to influence the probability that a pathogen lineage will emerge successfully. Results show that positive correlations between fitnesses across scales can greatly facilitate emergence, while cross-scale conflicts in selection can lead to evolutionary dead ends. The local genotype space of the initial strain of a pathogen can have disproportionate influence on emergence probability. Our cross-scale model represents a step towards integrating laboratory experiments with field surveillance data to create a rational framework to assess emergence risk.

Figure 1.

Fitness landscapes at between-host and within-host scales. Example landscapes are shown for a simple genotype space, with three genotypes connected sequentially. For this illustrative example, we consider landscapes where the fitnesses of initial (A₁) and emergence (A₃) genotypes are fixed, and only the fitness of the intermediate genotype (A₂) varies. (a) At the between-host scale, the intermediate genotype may be more fit (yielding an ‘uphill’ landscape (dashed line)), of equal fitness (‘jackpot’ (solid line)) or less fit (‘valley’ (dotted line)) than the initial genotype but only the emergence genotype A₃ has R₀ > 1. (b) At the within-host scale, under the SSWM model, the gain in relative fitness determines the rate of substitution between neighbouring genotypes. The ‘equal-rate’ landscape arises when relative fitness gains are equal for each step, the ‘fast–slow’ landscape when the first step yields greater fitness gain than the second, and the ‘slow–fast’ landscape in the reverse case. Note that we plot the logarithm of the absolute within-host fitnesses w_i, as noted in the text, because w_j = (1 + s_i,j)w_i. We have normalized the fitnesses such that w₁ = 1. (R₀⁽ⁱ⁾ (uphill) = [0.5,0.9,1.3], R₀⁽ⁱ⁾ (jackpot) = [0.5,0.5,1.3], R₀⁽ⁱ⁾ (valley) = [0.5,0.1,1.3], w_i (equal − rate, solid, line) = [1,1.2,1.44], w_i (fast − slow, dashed line) = [1,1.38,1.44], w_i (slow − fast, dotted line) = [1,1.04,1.44].

Figure 2.

Example of the interaction between selection at different scales. (a) We consider a set of jackpot landscapes at the between-host scale, with a range of fitness values for the initial (A₁) and intermediate (A₂) genotypes (indicated by the shaded region). (b) The probability of emergence as a function of the between-host fitness of the A₁ and A₂ genotypes, showing the interaction with the three within-host landscapes. The equal-rate (solid line) landscape gives the highest probability of emergence because it gives the fastest substitutions overall. Results for fast–slow (dashed line) and slow–fast (dotted line) landscapes overlap almost exactly. Black lines show exact solutions; grey lines show the approximation from equation (2.2), which fits well until R₀⁽¹⁾ and R₀⁽²⁾ approach 1 (d₁ = d₂ = d₃ = 1; b₃ = 1.3, b₁ and b₂ adjusted to yield desired R₀⁽ⁱ⁾ values; N = 10⁶, μ = 10⁻⁶, constant of proportionality = 0.4).

Figure 3.

Cross-scale interactions for all combinations of landscapes in a three-genotype chain. (a) Heat-map showing the probability of emergence as the intermediate genotype is varied in fitness at both the within-host and between-host scales. Fitnesses of the initial and emergence genotypes are fixed, as in figure 1. The vertical solid line marks the between-host jackpot scenario and the horizontal solid line marks the within-host equal-rate scenario. The dotted and dashed lines represent the slow–fast (bottom) and fast–slow (top) from figure 1b, respectively. (b) Probability of emergence as a function of the between-host fitness of the intermediate genotype, R₀⁽²⁾, for three within-host landscapes (solid line, equal-rate; dashed line, fast–slow; dotted line, slow–fast), corresponding to the horizontal lines in (a). The grey vertical shows where R₀⁽²⁾ = 0.5, i.e. the same value as R₀⁽¹⁾.

Figure 4.

Alternative pathways can lead to conflict between scales. We assume the initial case is infected with genotype B₀, and two evolutionary pathways are available to the pathogen population. (a) At the between-host scale, fitness increases along the B₁, B₂ pathway, leading to possible emergence; fitness decreases along the B′₁, B′₂ pathway, leading to certain extinction. (b) At the within-host scale, we assume equal-rate landscapes on both pathways, but vary the slope of the B₁, B₂ pathway (as indicated by the shaded area). Depending on the slope of the B₁, B₂ pathway at the within-host scale, substitution rates towards B₁ and B₂ can be higher or lower than towards B′₁ and B′₂. (c) The correlation between fitnesses at within-host and between-host scales is a strong determinant of the probability of emergence. Positive correlations favour emergence, while negative correlations (which corresponds to lower slopes of the within-host B₁, B₂ landscape) cause the pathogen lineage to be drawn towards lower between-host fitness and extinction. We use Pearson's correlation coefficient to measure the linear dependence between the fitnesses at the two scales. ( were drawn uniformly from the ranges [1.44,1.2,1,1.01–2.24,1.02–2.25], within-host parameters N and μ as in previous figures).

Figure 5.

Exploration of alternative pathways for general within-host landscapes. This figure generalizes figure 4, such that (a) the between-host landscape is identical, but (b) the within-host landscapes sample a much broader set of possibilities. Within-host fitness of genotypes B′₂, B′₁, B₀, B₁ and B₂ were selected randomly, such that were drawn uniformly from the ranges [1.02−2.25,1.01−2.24,1,1.01−2.24,1.02−2.25]. (c) The probability of emergence shows a positive association with the correlation between fitnesses across scales, though with considerable scatter. (d) The probability of emergence is more strongly associated with the probability that the first substitution event is towards genotype B₁ (i.e. towards possible emergence). Points for plots in (c) and (d) show the results of 5000 simulated within-host landscapes. (All parameters as in figure 4.)