Two waves of adaptation: speciation induced by dormancy in a model with changing environment

TL;DR

This work models a population with a seed bank facing seasonal environmental cycles, integrating dormancy, mutation, and selection to reveal how two waves of adaptation can emerge—one favoring summer and the other winter. Through two parameter regimes, the authors prove that mutation times converge to Poisson event times aligned with seasonal phases, and that the active population typically tracks a dominant, environment-correlated type while the seed bank preserves opposing specialists. The dormant population converges to a mixed, slowly evolving distribution, and the combined dynamics drive increasing genetic and genealogical distances between seasonal cohorts, offering a mechanism for speciation in fluctuating environments. Simulations corroborate the analytic results, illustrating rapid adaptation and sustained divergence due to seed-bank dynamics, with potential implications for understanding speciation in microbes and other organisms with dormancy.

Abstract

We consider a population model in which the season alternates between winter and summer, and individuals can acquire mutations either that are advantageous in the summer and disadvantageous in the winter, or vice versa. Also, we assume that individuals in the population can either be active or dormant, and that individuals can move between these two states. Dormant individuals do not reproduce but do not experience selective pressures. We show that, under certain conditions, over time we see two waves of adaptation. Some individuals repeatedly acquire mutations that are beneficial in the summer, while others repeatedly acquire mutations that are beneficial in the winter. Individuals can survive the season during which they are less fit by entering a dormant state. This result demonstrates that, for populations in fluctuating environments, dormancy has the potential to induce speciation.

Figures (3)

• Figure 1: The adaptation of populations in changing environments is depicted in this figure. The crosses represent mutations that increase the type and the circles represent mutations that decrease the type. The black lines indicate the predominant type as a function of time. The panel on the left is for a population with a seed bank, and the panel on the right is for a population without a seed bank.
• Figure 2: The mean type of the active individuals is plotted as a function of the generation number. Positive mutations became established in the population early in each of the first two summers and late in the third summer. Two more positive mutations became established during the fourth summer, and a sixth positive mutation appeared during the fifth summer. Negative mutations became established in the population during the first, second, fourth, and fifth winters.
• Figure 3: The top row shows the type distribution in the active population at the end of the 10th summer, the 10th winter, the 40th summer, and the 40th winter. The bottom row shows the dormant population after 10 years, 20 years, 30 years, and 40 years. We see the emergence of two subpopulations, whose genetic distance gets further apart over time.

Theorems & Definitions (82)

• Theorem 1
• Theorem 2
• Theorem 3
• Theorem 4
• Theorem 5
• Proposition 6
• Proposition 7
• Definition 8
• Lemma 9
• Lemma 10