Inbreeding of selfing and outcrossing plant

Question

I am reading John H. Gillespie's Population Genetics A Concise Guide Section 4.3 Inbreeding. I do not understand these two paragraphs quoted below concerning selfing and outcrossing.

1. The first paragraph states that an outcrosser individual leaves behind on average two gametes one in an ovule and the other in a pollen.

2. The second paragraph states that a mutant selfer will leave behind three gametes for every two of the outcrossing plants, with two in its selfed offspring and one in its outcrossed offspring.

What are the effect of the ovules and pollen here? How are these two statistical conclusions drawn? I would like to have a very detailed explanation.

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Some interesting evolutionary questions arise with species that are capable of both selfing and outcrossing. For example, in many plant species there is an intrinsic advantage to selfing, which leads to the evolutionary conundrum: Why don't all plant species self? The situation is illustrated in Figure 4.4. The outcrossing pedigree on the right represents a typical individual in an outcrossing population of constant size. This individual leaves behind, on average, two gametes, one carried in an ovule and the other in a pollen grain. These gametes appear as filled circles in the figure.

Figure 4.4: The gametes produced by a selfer and an outcrosser. The p to the right of an arrow indicates that the parent’s contribution came from pollen; an o indicates it came from an ovule. The filled circles represent gametes from the illustrated parents; the open circles represent gametes chosen at random from the gamete pool.

Suppose a mutant appears that self-fertilizes all of its ovules, M illustrated on the left side of the figure. Suppose also that there is enough pollen in each individual of this species that the few grains needed for self-pollination by the mutant represent a small fraction of the total pollen. As a consequence, the selfing mutant has essentially the same quantity of pollen available for outcrossing as does a nonselfing individual. All else being equal, the selfing mutant will leave behind three gametes for every two of the outcrossing plants, as indicated by the three filled circles in the figure. Two of the gametes are in its selfed offspring; one is in its outcrossed offspring. Thus, the mutant should increase in frequency, perhaps leading to the establishment of selfing as the usual mode of reproduction.

Answer 1

I don't think it's a terribly rigorous statistical argument, so much as a toy model arguing that there can be a reproductive advantage to selfing in an outcrossing population. Here is the logic as I see it:

1. Ovule and pollen represent the female and the male reproductive gametes in a monoecious plant (monoecious means that it has both male and female reproductive organs in the same individual).
2. In sexual organisms that do standard sex (i.e. not a complicated variety of sex), both ovule and pollen (gametes) are necessary to generate a fertilized offspring (zygote).
3. In outcrossing individuals, pollen is broadcast to fertilize other individuals (1 pollen gamete) and ovules receive pollen from other individuals (1 ovule gamete). Total: 2 gametes
4. In selfing individuals in an outcrossing population, selfing individuals guarantee that they fertilize their own ovules. Thus, they replace the pollen of other individuals (1 pollen gamete + 1 ovule gamete).
5. Selfing individuals still broadcast pollen to fertilize other outcrossing individuals (+1 pollen gamete). Total: 3 gametes

The key is in looking at the figure and understanding what it's arguing.

Again, these are not really rigorous ratios, details will be determined by exact biology of any case in real life. As far as I can tell from the text, the argument is not "these are the exact ratios in all organisms", but rather that "selfing gives the advantage that a selfer contributes all of the same gametes as the outcrosser, plus the male gametes to fertilize its own male gametes".

Secondary note: this model is only true when the proportion of selfers in the outcrossing population is very small. Note that as the proportion of selfers increases, everyone is just fertilizing their own ovules, and the net contribution goes back down to 2 gametes per generation. So this does not describe an equilibrium case for population composition. [As noted in comments, it is likely the case that it is equilibrium for population size, e.g. number of individuals.]

For more theory about this, you can read about the evolution of self-(in)compatibility. Here is a somewhat recent review. Evolution of self-compatibility in plants is extremely dynamic, as you might expect from the arms-race aspect.

Update:

Pulling up some notes from the comments on the assumptions of the model:

• I think that this example works when population number is at equilibrium, but population composition (e.g. selfers vs. outcrossers) might not be at equilibrium.
• I think that for the amount of pollen, we have to assume that all organisms contribute an equal, infinite amount of pollen. So selfers fertilize their own, and then also dump pollen into a pool into which outcrossers also dump infinite pollen.
• However, there are only a few ovules; every individual contributes one. That is, outcrossers and selfers contribute one ovule per individual.
• On average, everyone's pollen will be sampled roughly once (actually a little less) if every non-selfed ovule takes one pollen from an infinite pollen pool of uniform composition.
• As number of selfers in the population increases, less and less of the common pool of pollen will be sampled.
• If everyone in the population is a selfer, there will obviously be no outcrossing, because everyone just fertilizes their own ovule. This is the equilibrium state, if selfing is heritable and this stated advantage to selfing holds.