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Journals
Applied Mathematics and Nonlinear Sciences
Volume 8 (2023): Issue 1 (January 2023)
Open Access
Selection by differential mortality rates
M. S. Cecconello
M. S. Cecconello
,
R. A. de Assis
R. A. de Assis
,
L. M. E. de Assis
L. M. E. de Assis
and
E. Venturino
E. Venturino
| May 26, 2021
Applied Mathematics and Nonlinear Sciences
Volume 8 (2023): Issue 1 (January 2023)
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Published Online:
May 26, 2021
Page range:
2049 - 2062
Received:
Jun 24, 2020
Accepted:
Feb 26, 2021
DOI:
https://doi.org/10.2478/amns.2021.2.00018
Keywords
evolution equation
,
natural selection
,
dynamical systems
© 2021 M. S. Cecconello et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.
Fig. 1
Schematic representation of a mortality function for directional selection.
Fig. 2
Non-zero equilibrium solutions of Eq. (2) with Neumann (left) and Dirichlet (right) boundary conditions, respectively. For this simulation we consider μ(x) = 0.15(5 − x). These simulations show the typical behaviour of evolution by directional selection.
Fig. 3
Schematic representation of a mortality function for disruptive selection.
Fig. 4
Numerical simulations of nonzero equilibrium solutions for Eq. (2) with Neumann (left) and Dirichlet (right) boundary conditions, respectively. Here we consider μ(x) = max{0,0.192(6.25 − x2)}. These simulations show the typical behaviour of evolution by disruptive selection.
Fig. 5
Schematic representation of a mortality function for stabilising selection.
Fig. 6
Numerical simulations of nonzero equilibrium solutions for Eq. (2) with Neumann (left) and Dirichlet (right) boundary conditions, respectively. For these simulations we consider μ(x) = min{0.184x2,1.15}. These simulations show the typical evolution behaviour by stabilising selection.
Fig. 7
Numerical simulation showing the transition from the fittest to the flattest as the mutation rate increases. Left: the function μ(x); right: the soultion for small V. Here, the horizontal line is y = 1.
Fig. 8
Numerical simulation showing the transition from the fittest to the flattest as mutation rate increases. Left V = 0.4; right V = 0.52.
Fig. 9
Numerical simulation showing the transition from the fittest to the flattest as the mutation rate increases. Left V = 0.54; right V = 0.7.