A Short-Term Advantage for Syngamy in the Origin of Eukaryotic Sex: Effects of Cell Fusion on Cell Cycle Duration and Other Effects Related to the Duration of the Cell Cycle—Relationship between Cell Growth Curve and the Optimal Size of the Species, and Circadian Cell Cycle in Photosynthetic Unicellular Organisms

Table 2

Analysis of the probability of occurrence of cell fusions according to cell sizes. (a) Double-entry math table for the calculation of the probability of fusion between two age classes (i, j) according to the number of individuals (𝑁) surviving and not yet fused, in each class, if we divide the suitable period for fusions into ten equal periods. The instantaneous death rate is 2% and the fusion rate is 10%. (b) Ditto expressed as a percentage (number of fusions in the two classes i, j, divided by the total number of fusions). (c) Table of results. The probability of no fusion is 0.910 = 35%; the probability of fusion is the additional 65%. Of the fusions occurring, only 20% occur between individuals of the same age-size class (lengthening their cell cycle compared to asexual) and 80% occur between individuals of different age-size class (matching or shortening their cell cycle with regard to asexual). This group is unevenly distributed according to the degree of difference between the two cell sizes, with more “barely anisogamous” than “highly anisogamous” fusions.

(a)

i, j		1	2	3	4	5	6	7	8	9	10
	𝑁	10.00	8.82	7.78	6.86	6.05	5.34	4.71	4.15	3.66	3.23
1	10.00	100.00	88.20	77.79	68.61	60.52	53.38	47.08	41.52	36.62	32.30
2	8.82		77.79	68.61	60.52	53.38	47.08	41.52	36.62	32.30	28.49
3	7.78			60.52	53.38	47.08	41.52	36.62	32.30	28.49	25.13
4	6.86				47.08	41.52	36.62	32.30	28.49	25.13	22.16
5	6.05					36.62	32.30	28.49	25.13	22.16	19.55
6	5.34						28.49	25.13	22.16	19.55	17.24
7	4.71							22.16	19.55	17.24	15.21
8	4.15								17.24	15.21	13.41
9	3.66									13.41	11.83
10	3.23										10.43

(b)

i, j		1	2	3	4	5	6	7	8	9	10
	𝑁	10.00	8.82	7.78	6.86	6.05	5.34	4.71	4.15	3.66	3.23
1	10.00	4.89%	4.32%	3.81%	3.36%	2.96%	2.61%	2.30%	2.03%	1.79%	1.58%
2	8.82		3.81%	3.36%	2.96%	2.61%	2.30%	2.03%	1.79%	1.58%	1.39%
3	7.78			2.96%	2.61%	2.30%	2.03%	1.79%	1.58%	1.39%	1.23%
4	6.86				2.30%	2.03%	1.79%	1.58%	1.39%	1.23%	1.08%
5	6.05					1.79%	1.58%	1.39%	1.23%	1.08%	0.96%
6	5.34						1.39%	1.23%	1.08%	0.96%	0.84%
7	4.71							1.08%	0.96%	0.84%	0.74%
8	4.15								0.84%	0.74%	0.66%
9	3.66									0.66%	0.58%
10	3.23										0.51%

(c)

35%	No fusion probability
65%	Fusion probability
20%	Fusions between cells of the same size
80%	Fusions between cells of different size
		%
Difference between age classes	1	17%
	2	15%
	3	13%
	4	10%
	5	8%
	6	7%
	7	5%
	8	3%
	9	2%