Evolution Arrests Invasions of Cooperative Populations

Featured in Physics
Editors' Suggestion

Evolution Arrests Invasions of Cooperative Populations

Kirill S. Korolev

Phys. Rev. Lett. 115, 208104 – Published 13 November 2015

See Focus story: Evolution Sometimes Slows Things Down

Abstract

Population expansions trigger many biomedical and ecological transitions, from tumor growth to invasions of non-native species. Although population spreading often selects for more invasive phenotypes, we show that this outcome is far from inevitable. In cooperative populations, mutations reducing dispersal have a competitive advantage. Such mutations then steadily accumulate at the expansion front, bringing invasion to a halt. Our findings are a rare example of evolution driving the population into an unfavorable state, and they could lead to new strategies to combat unwelcome invaders.

Received 20 August 2015

DOI:https://doi.org/10.1103/PhysRevLett.115.208104

Physics Subject Headings (PhySH)

Evolutionary & population dynamics Mutation

Physics of Living Systems

Focus

Evolution Sometimes Slows Things Down

Published 13 November 2015

When a strongly cooperative species invades new territory, its spread can slow down or stop, according to a mathematical model, suggesting potential strategies against cancer and insect pests.

See more in Physics

Authors & Affiliations

Kirill S. Korolev^*

Department of Physics and Graduate Program in Bioinformatics, Boston University, Boston, Massachusetts 02215, USA

^*korolev@bu.edu

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 115, Iss. 20 — 13 November 2015

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
The effects of cooperative growth on the evolution of dispersal during invasion. (a) Simulations of the competition between a slow ( $D_{1} = 0.5$ ) and a fast ( $D_{2} = 1$ ) disperser during a spatial expansion. The fraction of the slower disperser decreases in populations with a low Allee threshold ( $c^{*} = 0.2$ ), but increases in populations with a high Allee threshold ( $c^{*} = 0.35$ ). (b) The fitness advantage of the slower disperser ( $D_{1} / D_{2} = 0.95$ ) changes from negative (deleterious) to positive (beneficial) as the Allee threshold is increased. In simulations, we never observed the coexistence of the two types; instead, extinction is observed for the types that are deleterious when rare ( $λ < 0$ ), and complete fixation is observed for the types that are beneficial when rare ( $λ > 0$ ).
Reuse & Permissions
Figure 2
Allee effect determines how fitness depends on dispersal. (a) Faster dispersers are unconditionally favored when the Allee effect is weak. Note that the fitness advantage reaches a maximum at a finite $D_{1} / D_{2}$ . (b) When the Allee effect is strong, but the Allee threshold is low, selection still favors faster dispersal. Very fast mutants, however, are at a disadvantage. (c) For high Allee threshold, only slower-dispersing mutants can succeed, but mutants that disperse too slowly are selected against. In all panels, the exact solution is plotted, and colors highlight beneficial (red) and deleterious (blue) mutations. The dashed line marks $D_{1} = D_{2}$ , where both types have the same fitness. Near this point, the fitness advantage of type 1 in the background of type 2 equals the fitness disadvantage of type 2 in the background of type 1, but this symmetry breaks down when the dispersal rates of the types are very different; see Supplemental Material [21]. Nevertheless, the exchange of $D_{1}$ and $D_{2}$ always converts a beneficial mutant to a deleterious one. In consequence, a mutation that is beneficial when rare will remain beneficial when it approaches fixation, indicating that the direction of natural selection is the same for small and large $f$ .
Reuse & Permissions
Figure 3
When the rate of dispersal is allowed to evolve, simulations show that invasions can both accelerate and decelerate depending on the strength of an Allee effect. (a) The mean dispersal rate increases to its maximally allowed value when the Allee threshold is low (green), but the dispersal rate decreases to zero when the Allee threshold is high (blue). (b) For the same simulations as in (a), we plot the extent of spatial spread by the populations. Invasions with a low Allee threshold ( $c^{*} / K = 0.2$ ) accelerate, while invasions with a high Allee threshold ( $c^{*} / K = 0.35$ ) come to a standstill.
Reuse & Permissions

Physical Review Letters