Moran model as a dynamical process on networks and its implications for neutral speciation.

Area of Science:

• Population Genetics
• Evolutionary Biology
• Network Theory

Background:

• The Moran model is a fundamental tool for studying neutral evolution in haploid populations.
• It traditionally assumes panmixia (random mating) within the population.
• Understanding evolution in structured populations is crucial for biodiversity and speciation theories.

Purpose of the Study:

• To map the Moran model onto an influence dynamical process on networks.
• To analyze the impact of population structure on neutral evolution and speciation.
• To investigate the conditions and speed of speciation in structured populations.

Main Methods:

• Mapping the Moran model to influence dynamics on networks.
• Analyzing fully connected networks (panmictic case) using hypergeometric functions.
• Developing approximate solutions for structured populations (e.g., spatial grids).
• Connecting network structures to the isolation-by-distance mechanism.

Main Results:

• The panmictic Moran model is solvable using hypergeometric functions on fully connected networks.
• Structured populations, particularly those with local mating, significantly enhance mutation effects.
• Speciation can occur via pattern formation when diversity-promoting and diversity-reducing forces balance.
• An explicit condition for speciation is derived, showing reduced speciation times.

Conclusions:

• The network-based approach provides new insights into the Moran model and population structure.
• Enhanced mutation effects in structured populations can drive topopatric and neutral speciation.
• Pattern formation offers a mechanism for speciation, particularly in populations with mating constraints.
• Speciation is accelerated in structured populations compared to panmictic ones.