On the connections between the spatial Lambda-Fleming-Viot model and other processes for analysing geo-referenced...

Area of Science:

• Population genetics
• Mathematical biology
• Stochastic processes

Background:

• The spatial Lambda-Fleming-Viot (ΛV) model offers a robust mathematical framework for population evolution across spatial continua.
• It addresses limitations of previous models like isolation by distance and is suitable for statistical inference.
• Connections between the ΛV model and other spatial stochastic processes remain underexplored.

Purpose of the Study:

• To investigate the relationship between the spatial ΛV model and birth-death processes.
• To evaluate the accuracy of Brownian motion approximations for lineage movement within the ΛV framework.
• To develop efficient simulation algorithms for the ΛV model.

Main Methods:

• Simulations of a rapidly moving lineage version of the ΛV model.
• Comparison of ΛV model outputs with birth-death models.
• Analysis of Brownian motion and reflected Brownian motion approximations for lineage spatial dynamics.
• Development and testing of novel simulation algorithms.

Main Results:

• The ΛV tree-generating process is well-approximated by birth-death models under rapid lineage movement.
• Standard Brownian motions inadequately model ΛV lineage movement due to habitat boundary effects.
• Reflected Brownian motions significantly improve the approximation of ΛV dynamics by incorporating boundary effects.
• Efficient algorithms for simulating forward and backward ΛV processes were developed.

Conclusions:

• Birth-death models offer a viable approximation for specific spatial ΛV scenarios.
• Habitat boundaries are crucial factors influencing lineage dynamics in spatial population models.
• The developed algorithms facilitate more accessible and efficient simulation of the ΛV model.