The <i>d</i>₁-<i>d</i>₄ graphs of the theoretical and simulated solutions in a completely mixed population.

<p>The horizontal and vertical axes represent <i>d</i>₁ and <i>d</i>₄, respectively The lines in the graphs delineate the viability and competition conditions in the completely mixed population. Theoretical analysis predicts that the 2∶2 division strategy wins in the dark gray area, while the 1∶3 division strategy wins in the light gray area. Each pie chart shows the average densities of sites occupied by either of the two strategies, as well as the empty sites (open circles) after 10,000 iterations in 100 simulation runs. The black and gray portions of the filled circles indicate the average density of sites occupied by the 2∶2 and 1∶3 division strategies, respectively. In <i>d</i>₄ = 0.0, matured colonies adopting both strategies ultimately survive and neutrally coexist. Initial densities are <i>z</i>₀ = 0.2 and <i>x</i>₁ = <i>x</i>₂ = <i>x</i>₃ = <i>x</i>₄ = <i>y</i>₁ = <i>y</i>₂ = <i>y</i>₃ = <i>y</i>₄ = 0.1. Other parameters are: 2,500 sites in the population, <i>u</i> = 0 and <i>h</i> = 1. (A) Death probability function assumes that <i>d</i>₂ = <i>d</i>₃ = <i>d</i>₄. (B) Death probability function is linear. (C) Death probability function assumes that <i>d</i>₁ = <i>d</i>₂ = <i>d</i>₃.