Coexistence in two-species competition with delayed maturation.

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Interspecific and intraspecific competition significantly impact species, particularly during immature life stages.
• Mosquito species, crucial disease vectors, often coexist and face intense competition during maturation.

Purpose of the Study:

• To generalize Lotka-Volterra competition models by incorporating distributed delays for maturation time.
• To analyze the impact of maturation delays on species competition, coexistence, and survival.

Main Methods:

• Utilized a distributed delay kernel represented by a truncated Erlang distribution.
• Transformed delay differential equations into ordinary differential equations via linear chain approximation.
• Employed nullclines and local stability analysis to determine stability conditions.

Main Results:

• Equilibrium solutions are determined by the shape, rate, and truncation of the Erlang distribution.
• Numerical solutions demonstrated scenarios of competitive exclusion and coexistence.
• Distributed delays were found to promote species coexistence and survival compared to discrete delays.

Conclusions:

• The generalized Lotka-Volterra model with distributed maturation delays offers insights into population dynamics.
• Incorporating distributed delays can enhance species survival and coexistence, crucial for managing ecologically and economically important species.