Modeling Competitive Mixtures With the Lotka-Volterra Framework for More Complex Fitness Assessment Between Strains

Abstract

With increasing resolution of microbial diversity at the genomic level, experimental and modeling frameworks that translate such diversity into phenotypes are highly needed. This is particularly important when comparing drug-resistant with drug-sensitive pathogen strains, when anticipating epidemiological implications of microbial diversity, and when designing control measures. Classical approaches quantify differences between microbial strains using the exponential growth model, and typically report a selection coefficient for the relative fitness differential between two strains. The apparent simplicity of such approaches comes with the costs of limiting the range of biological scenarios that can be captured, and biases strain fitness estimates to polarized extremes of competitive exclusion. Here, we propose a mathematical and statistical framework based on the Lotka-Volterra model, that can capture frequency-dependent competition between microbial strains within-host and upon transmission. As a proof-of-concept, the model is applied to a previously-published dataset from in-vivo competitive mixture experiments with influenza strains in ferrets (McCaw et al., 2011). We show that for the same data, our model predicts a scenario of coexistence between strains, and supports a higher bottleneck size in the range of 35-145 virions transmitted from donor to recipient host. Thanks to its simplicity and generality, such framework could be applied to other ecological scenarios of microbial competition, enabling a more complex and nuanced view of possible outcomes between two strains, beyond competitive exclusion.

Sensitivity Equation for Competitive Model: Derivation, Numerical Realization and Parameter Estimation

“…The special case of ( 10) is when N = 2 which is well-known as the Lotka-Volterrra equation [13,16,18].…”

“…• define matrix functions G(t, Z) as G(t, Z) = ∂F ∂X (t) Z + ∂F ∂r (t) • apply Algorithm 4.2 to solve (16).…”

Methods of quantifying interactions among populations using Lotka-Volterra models

“…In spite of these simplifying assumptions, the LV model has proven to be a very valuable tool for gaining insights into the dynamics of numerous diverse biological interaction systems, for instance, among different mammalian or fish species (Wangersky, 1978), bacterial lake communities (Dam et al, 2016), and freshwater ciliates (Muhlbauer et al, 2020), to name just a few. Furthermore, recognizing the critical importance of microbiomes in recent years, LV systems have become an effective tool of analysis and, indeed, the default for quantitatively assessing interactions within these large microbial communities (Mounier et al, 2007;Buffie et al, 2015;Dakos et al, 2020;Dimas Martins and Gjini, 2020). LV models have moreover been proposed in non-ecological contexts, such as physics (Nambu, 1986;Hacinliyan et al, 2010), economics (Chiang, 2012), and to address pollution issues (Haas, 1981;Zhou and Chen, 2006).…”

Novel predator-prey model admitting exact analytical solution

“…The above deterministic model was created in the third decade of the twentieth century in the field of ecology [1,2]. Almost a century after it was first proposed it still attracts the interest of the scientific community, and an intense research activity has been carried out on this model up to the present day [3][4][5][6][7][8][9][10][11][12].…”