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Abstract The article discusses the Crow-Kimura model in the context of random transitions between different fitness landscapes. The duration of epochs, during which the fitness landscape is constant over time, is modeled by an exponential distribution. To obtain an exact solution, a system of functional equations is required. However, to approximate the model, we consider the cases of slow or fast transitions and calculate the first-order corrections using either the transition rate or its inverse. Specifically, we focus on the case of slow transitions and find that the average fitness is equal to the average fitness for evolution on static fitness landscapes, but with the addition of a load term. We also investigate the model for a small number of genes and identify the exact transition points to the transient phase.
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Migration feedback induces emergent ecotypes and abrupt transitions in evolving populations
We explore the connection between migration patterns and emergent behaviors of evolving populations in spatially heterogeneous environments. Despite extensive studies in ecologically and medically important systems, a unifying framework that clarifies this connection and makes concrete predictions remains much needed. Using a simple evolutionary model on a network of interconnected habitats with distinct fitness landscapes, we demonstrate a fundamental connection between migration feedback, emergent ecotypes, and an unusual form of discontinuous critical transition. We show how migration feedback generates spatially non-local niches in which emergent ecotypes can specialize. Rugged fitness landscapes lead to a complex, yet understandable, phase diagram in which different ecotypes coexist under different migration patterns. The discontinuous transitions are distinct from the standard first-order phase transitions in statistical physics. They arise due to simultaneous transcritical bifurcations and exhibit a “fine structure” due to symmetry breaking between intra- and inter-ecotype interactions. We suggest feasible experiments to test our predictions.
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- Award ID(s):
- 2146581
- PAR ID:
- 10519769
- Publisher / Repository:
- arXiv
- Date Published:
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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