Why do we say "per egg" instead of "per clutch"

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Originally Posted by Simple Man

Probability is what people should be saying. Not statistically... The probability of this happening is ____. That might clear things up a bit?

Regards,

B

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then i guess my question is, how do you use the word statistically correctly?

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Originally Posted by wolfy-hound

Well, if you are counting which egg will be which in a clutch(instead of just 11 possibilities) aren't you counting 'per egg' rather than 'per clutch'? Since it doesn't matter which egg was lesser and which was normal, if you are just counting numbers?

Just wondering on that.

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Its all the possible outcomes of the clutch over all. it does matter which egg was lesser, because each egg is different and has the 50/50 shot. there are more ways to get the 50/50 spilt than anything else. To say you have the same chance of getting 0 Lessers (1/1024) as 5 Lesser (252/1024) isn't correct, but the chance of getting 0 lessers as 10 Lessers is. With a big enough sample size according to the law of averages, the real world data will reflect that. If You have 11x 10 egg clutches, your most likely not going to see one with 0 lesser, one with 1, one with 2 lessers,...., one with 10 lessers.

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Originally Posted by purplemuffin

Because you can still get all lessers or no lessers. Each egg has a 50/50 percent chance. So while in a mathematical sense that means the clutch should be 50/50 in the real world it just doesn't always work out that way. If each egg ends up being normal you do not have a clutch that matches the odds, but it still makes sense per egg

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This makes perfect sense to me BTW. I don't see why there is so much confusion, or a debate..

Cheers.

The probabilities that people so often use in snake genetics are based off of the probability of a certain gene being passed to an individual based off the population of potential genes. Each time the gametes are formed in a lesser, there is a 50% chance that it will contain the lesser gene and a 50% chance it will contain the normal gene. So lets say the lesser is a male. If every meiotic division is successful and leads to 4 sperm cells, then we'd expect 2 sperm to carry the lesser gene and 2 sperm to carry the normal gene. Now do this thousands of times and you have a large number of both. This is your population of gametes that can be passed to the next generation. 50% are normal and 50% are lesser. Now this male is paired with a female. She is a normal so every egg she develops carries that normal gene. Now if every sperm went to a single egg, there were no other factors (though there can be!), and every egg went full term, then you'd could expect a 50/50 ration in the clutch as you're stating. Instead, out of those thousands or millions of sperm, only 4-12 make it to eggs so instead of 4 eggs being fertilized by four sperm, 2 carrying the lesser gene and 2 carrying the normal gene, the eggs are fertilized by a "random" sampling of all the possible sperm.


Here is another way to recreate what I was saying above:
Get two colors of M&M's and take 100 of each color and mix them in a container. Pour out 10 and see how often you get 5 of each color. Try this and I doubt you'll get 5 of each color each trial even though there is a 50/50 chance of pulling either one.

Each egg has a 50% chance of getting the lesser gene. If you hatch 10000, or more eggs, then you may expect to see ratios similar to 50/50. Until that time, your numbers are based on the probability of a gene being inherited by a particular individual from the total possible combination of genes.

The "per clutch" statements don't take into account the random sampling (think M&Ms). Just because there are equal amounts of both colors in the vat, it doesn't mean that equal proportions will be drawn when a very small sample is pulled from the population.

If the M&Ms don't do it, you can take a coin toss too. Each flip of a fair coin has a 50/50 shot of being either side. Flip it once and the next flip is not guaranteed to be the other side. Even "statistically speaking". If each flip is independent, then each flip has a 50/50 shot of being either heads or tails. Just like if you have four eggs from a lesser and normal pairing, just because you have 2 normals, you're not guaranteed 2 lessers (the statistics are based on a much larger population of gametes, and not the finite number of eggs in the clutch). The inheritance of the lesser gene is still a 50/50 shot regardless of what the siblings inherited.


As a final thought using the coin example:
If you were to flip the coin for the rest of your life. As you near infinity (much more than the number of eggs in a BP clutch), the totals will look more like the 50/50 ratio you expect from each flip. Likewise take every lesser X normal cross that ever has been and ever will be done. Plus a few more for good measure and you may notice a 50/50 ratio of normals and lessers in the offspring even though the numbers don't hold per clutch. A single clutch is very finite sample drawn from an independent "random" population of possible outcomes. Because of this the ratios are per egg and not per clutch or sample.

I've really simplified some genetic concepts as well as some aspects of probability so hopefully this makes some sense.

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Originally Posted by OhhWatALoser

then i guess my question is, how do you use the word statistically correctly?

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Here is the fourth definition of "probability" from http://dictionary.com:

4.
Statistics .
a. the relative possibility that an event will occur, as expressed by the ratio of the number of actual occurrences to the total number of possible occurrences.
b. the relative frequency with which an event occurs or is likely to occur.

And here is the definition of "statistically":

of, pertaining to, consisting of, or based on statistics.

And the definition of statistics is

the science that deals with the collection, classification, analysis, and interpretation of numerical facts or data, and that, by use of mathematical theories of probability, imposes order and regularity on aggregates of more or less disparate elements.

To me, statistics includes but is not limited to probability. IMO, "statistically" is acceptable useage in this thread but "probability" is more accurate. YMMV.