No. of meiotic divisions to produce specific no. of seeds

Question

If I want to produce 100 seeds. Then the no. of meiotic divisions is 125 which can be calculated by the formula x + x / 4.

x = no. of seeds produced.

How is this formula derived?

Answer 1

Assuming that you have studied megasporogenesis and microsporogenesis. To produce a seed, you require the production of pollen(n) and egg(n) and their fusion.

Let's start with pollen grain(n):

4 pollen grains are produced after 1 meiotic division in the pollen sacs.

$$4~\text{pollen grains} = 1~\text{meiotic division}$$

To produce 1 pollen grain.

$$ 1~\text{pollen grain} = 1/4~\text{meiotic division} $$

For production of $x$ pollen grains.

$$ x~\text{pollen grains}=x/4~ \text{meiotic divisions}\quad(1) $$

Now coming to egg(n):

Only 1 egg is produced after 1 meiotic division in the megasporangium.

$$ 1~\text{egg}= 1~\text{meiotic division}$$

For production of $x$ no. of eggs.

$$ x~\text{eggs}=x~\text{meiotic divisions}\quad(2) $$

For production of $x$ no of seeds(2n):

$x$ pollen grains and eggs are required. No. of meiotic divisions to produce $x$ pollen grains and eggs.

$$x~\text{seeds}=x + x/4~\text{meiotic divisions} \quad\text{From}~(1)~\text{and}~(2) $$

Answer 2

For producing $x$ number of seeds (or say zygote) $x$ number of egg cells must fuse with $x$ number of male gametes.

In angiosperms, 1 meiotic division of Megaspore mother cell leads to formation of one egg cell.

So $x$ egg cells are formed from $x$ number of meiotic division.

But 1 meiotic division of Sperm mother cell (2n) leads to formation off 4 haploid cells (male gametes).

So by Unitary method,

4 functional male gametes are formed from 1 Meiotic division

$x$ functional male gametes are formed from 1/4 x $x$ Meiotic divisions

So total number of meiosis needed to produce $x$ seeds = $x$ + $x$/4.

Prerequisite: Knowledge about Sexual reproduction in Angiosperms (ncert)