Competition at the front of expanding populations
TLDR
This paper introduces a model combining Fisher and KPZ equations to show how spatial expansion can overcome reproductive advantage in species competition.
Key contributions
- Introduces a model coupling Fisher and KPZ equations for competition at expansion fronts.
- Demonstrates that spatial expansion ability can overcome reproductive advantage in colonization.
- Identifies distinct growth morphologies influenced by expansion rates and competitive abilities.
- Shows fitness variations in range expansion can be described by the Tracy-Widom distribution.
Why it matters
This paper offers a novel theoretical framework for understanding how competing species colonize new territories. It highlights the critical role of spatial expansion ability, sometimes outweighing traditional reproductive fitness, and provides new insights into ecological dynamics and evolution.
Original Abstract
When competing species grow into new territory, the population is dominated by descendants of successful ancestors at the expansion front. Successful ancestry depends on both the reproductive advantage (fitness), as well as ability and opportunity to colonize new domains. We present a model that integrates both elements by coupling the classic description of one-dimensional competition (Fisher equation) to the minimal model of front shape (KPZ equation). Macroscopic manifestations of these equations are distinct growth morphologies controlled by expansion rates, competitive abilities, or spatial anisotropy. In some cases the ability to expand in space may overcome reproductive advantage in colonizing new territory. When new traits appear with accumulating mutations, we find that variations in fitness in range expansion may be described by the Tracy--Widom distribution.
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