Hemlady said: So, I am not sure flower size has anything to do with it.
Unfortunately, one would have to examine a large number of crosses using plants of different flower sizes and then do a statistical analysis. There is always variability in any characteristic and that variability affects whether we can easily see a relationship from a few values.
In this case we would be looking for a relationship between flower size and the number of seeds. Ovary size would presumably be related to pistil size and pistil size would presumably be related to flower size and the number of ovules (which develop into seed). But the relationship would never be tight - that is highly correlated but it might nevertheless be significantly correlated.
Below is an example of the correlation between flower size and scape height. These are relatively tightly correlated (for some unknown reason).
The correlation between flower size and scape height is 0.74 (it can range from -1 to +1 - a correlation coefficient that is not significantly different from zero means that we conclude that the two measurements are not related). The correlation coefficient of 0.74 is highly statistically significant and we can conclude that there is a relationship between flower size and scape height.
It is important to note that even though there is a very strong relationship between flower size and scape height seen in these observations there is also lots of variability. Many cultivars have flower sizes and scape heights that do not fit the relationship at all closely. The correlation coefficient can be much smaller (closer to zero) and as long as it is significantly different from zero then we conclude that there is a relationship. The closer to zero the more variability there is in the measurements and the relationship (that is presumably because other factors will affect the two measurements).
So we need to choose cultivars at random and measure their flower sizes and the number of seeds in their pods. But to be objective and accurate we would have had to pollinate all the cultivars we choose with pollen from the same cultivar. That is because different cultivars have pollen with different characteristics. We should probably also have pollinated the pod parents on the same days (and if we did not pollinate them all on one day then we should record which cultivars were pollinated on which days). The pollen we use needs to be the same because one cultivar may have pollen that is 85% effective and produces say 10,000 pollen grains in one anther while another cultivar may have pollen that is only 50% effective and produces say 7,000 pollen grains in one anther. Even if we counted pollen grains and placed the same number of grains on the stigmas of the same pod parent the pods produced by the different pollen parents would probably contain different numbers of seeds. Pods produced by pollen parent 1 would have more seeds than pods produced by pollen parent 2.
Doing a valid test of ideas using any living organism, such as daylilies, is always complex and involved, with many possible steps that can lead to failure if not properly accounted for.
