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‘Why only two sexes?’

Sexual reproduction - the fusion of two different genetic sets to create a new individual - has resulted in two and only two sexes in all complex species.

It’s practically inevitable.
Sexual reproduction relies on collisions between two gametes. The more successful collisions there are, the more efficient the process is.

Imagine a sea of gametes, all just floating around. Occasionally, two will collide, fuse and generate offspring.
When clever maths/modelling people create a virtual sea of gametes, they can adjust various parameters to see how that pans out in terms of maximising collisions.
What if a gamete is slightly larger? We predict it’s going to be slower as it floats around. We predict it is likely more robust. We predict it gets hit more because it’s a bigger target.
So modellers program in some natural, perhaps fluctuating, size variation. What if there are unlimited different sizes? What if upper size is limited or not limited? What if we add in a feedback loop so that size reinforces itself?

And then they press ‘start simulation’.
What rapidly emerges as the most efficient system - one that maximises the number of successful collisions while maintaining robustness of offspring - comprises two types of gamete.
The two gamete types that permit maximal reproductive efficiency are:
1. One slow/stationary large target that confers all the robustness to the offspring.
2. Multiple small, fast missiles peppering the target.
The possibility of multiple gamete sizes and multiple ways of conferring robustness are quickly weeded out as the system collapses into two extremes that represent optimum function.
That there are two sexes is not a happy ‘accident of evolution’ that complex life has exploited as a viable reproductive strategy.

It is a mathematical inevitability.
A slight correction here: I’ve suggested that parameters of gamete size can be unlimited. This is not the case. There is an upper limit based on what a parent can produce and a lower limit based on the minimum content. I meant to suggest artificially imposing size thresholds.
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