Tipping points in fitness landscape of heterogeneous populations

Predicting fitness of biologically-active populations, communities or systems in fluctuating environments is a long-standing challenge. Phenotypic plasticity and bet-hedging strategy, two key evolutionary traits living systems harness to optimize fitness in dynamic environments, have been widely reported yet how interplays therein could mediate fitness landscapes of heterogeneous populations remain unknown. Leveraging the financial asset pricing model, here we provide a dynamical framework for fitness of heterogeneous populations, underpinned by the interrelations between sub-populations exhibiting phenotypic plasticity and bet-hedgeding. Our framework, independent of the definition of fitness, employs a nonlinear difference equation to present fitness dynamics, and capture the emergence of tipping points, marking the onset of critical state transitions which lead to catastrophic shifts. This study identifies limits on the selective advantage conferred by bet-hedging through reduction in the temporal variance of fitness, with far-reaching ramifications on our current understanding of hedging-mediated fitness enhancement of a population. The lower bound of the effective fitness variance is set by a maximum number of bet-hedgers, beyond which the fitness landscape approaches critical transition, as confirmed by critical slowing down in the vicinity of tipping points. We estimate the scaling law for the critical slowing down numerically and derive the characteristic recovery time for heterogeneous populations. Taken together, our work provides a generic theoretical framework to quantify fitness dynamics and predict critical transitions in heterogeneous populations. The results can be extended further to model fitness landscapes of natural and synthetic multi-species consortia exposed to environmental fluctuations mimicking climatic shifts and immunopathological settings.