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Coexistence in two-species competition with delayed maturation.

Maud El-Hachem1, Nicholas J Beeton2

  • 1Data61, CSIRO, Battery Point, Tasmania, Australia. maud.el-hachem@data61.csiro.au.

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|December 19, 2023
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Summary

Competition during maturation is key for species survival. A new model using distributed delays promotes species coexistence and survival, impacting pest and threatened species management.

Keywords:
Distributed delayLinear chain approximationLotka–Volterra competitionMaturationTruncated Erlang distribution

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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.