TY - JOUR

T1 - A scaling law of multilevel evolution

T2 - how the balance between within- and among-collective evolution is determined

AU - Takeuchi, Nobuto

AU - Mitarai, Namiko

AU - Kaneko, Kunihiko

PY - 2022/2/4

Y1 - 2022/2/4

N2 - Numerous living systems are hierarchically organized, whereby replicating components are grouped into reproducing collectives-e.g., organelles are grouped into cells, and cells are grouped into multicellular organisms. In such systems, evolution can operate at two levels: evolution among collectives, which tends to promote selfless cooperation among components within collectives (called altruism), and evolution within collectives, which tends to promote cheating among components within collectives. The balance between within- and among-collective evolution thus exerts profound impacts on the fitness of these systems. Here, we investigate how this balance depends on the size of a collective (denoted by N) and the mutation rate of components (m) through mathematical analyses and computer simulations of multiple population genetics models. We first confirm a previous result that increasing N or m accelerates within-collective evolution relative to among-collective evolution, thus promoting the evolution of cheating. Moreover, we show that when within- and among-collective evolution exactly balance each other out, the following scaling relation generally holds: Nm(alpha) is a constant, where scaling exponent alpha depends on multiple parameters, such as the strength of selection and whether altruism is a binary or quantitative trait. This relation indicates that although N and m have quantitatively distinct impacts on the balance between within- and among-collective evolution, their impacts become identical if m is scaled with a proper exponent. Our results thus provide a novel insight into conditions under which cheating or altruism evolves in hierarchically organized replicating systems.

AB - Numerous living systems are hierarchically organized, whereby replicating components are grouped into reproducing collectives-e.g., organelles are grouped into cells, and cells are grouped into multicellular organisms. In such systems, evolution can operate at two levels: evolution among collectives, which tends to promote selfless cooperation among components within collectives (called altruism), and evolution within collectives, which tends to promote cheating among components within collectives. The balance between within- and among-collective evolution thus exerts profound impacts on the fitness of these systems. Here, we investigate how this balance depends on the size of a collective (denoted by N) and the mutation rate of components (m) through mathematical analyses and computer simulations of multiple population genetics models. We first confirm a previous result that increasing N or m accelerates within-collective evolution relative to among-collective evolution, thus promoting the evolution of cheating. Moreover, we show that when within- and among-collective evolution exactly balance each other out, the following scaling relation generally holds: Nm(alpha) is a constant, where scaling exponent alpha depends on multiple parameters, such as the strength of selection and whether altruism is a binary or quantitative trait. This relation indicates that although N and m have quantitatively distinct impacts on the balance between within- and among-collective evolution, their impacts become identical if m is scaled with a proper exponent. Our results thus provide a novel insight into conditions under which cheating or altruism evolves in hierarchically organized replicating systems.

KW - major evolutionary transitions

KW - multilevel selection

KW - group selection

KW - power law

KW - Price equation

KW - quantitative genetics

KW - GROUP SELECTION

KW - INTERACTING PHENOTYPES

KW - KIN SELECTION

KW - COOPERATION

KW - GENETICS

KW - MODEL

KW - RECIPROCITY

KW - DYNAMICS

KW - FITNESS

KW - PARADOX

U2 - 10.1093/genetics/iyab182

DO - 10.1093/genetics/iyab182

M3 - Journal article

C2 - 34849893

VL - 220

JO - Genetics

JF - Genetics

SN - 1943-2631

IS - 2

M1 - 182

ER -