We have a sex ratio at birth which slightly favors men 107/100, and a total sex ratio which also slightly favors men 101/100.
This needs to be clarified. Yes, the sex ratio equalizes as time goes on due to men dying sooner and at a higher rate than women. But this starts mostly later in life. Censuses will show that going into puberty (when the sexual/reproductive marketplace begins) and for most of a women's reproductively viable lifetime there will be more men than women.
I repeat- censuses of all countries show there are more men than women in the sexual/reproductive marketplace.
From Table 1 in this article the average American man has a reproductive value of 2. The average American woman also has a reproductive value of 2.
By your definition that you gave above, they are equal.
This is mathematically impossible. This study is clearly not comprehensive enough.
A biological child requires EXACTLY 1 male and 1 female. This is the reason for the mathematical impossibility. We've established there are more males than females in the market. Therefore the average cannot be the same. Please take the time to understand this.
Lets say we have a group of 100 females and 101 males. They have 500 children. (you can use any number of children)
The average number of children per female is - 500/100 = 5
The average number of children per male is 500/101 = 4.95
A male cannot increase the number of children he has without increasing a female's number of children at the same time. The contribution to the creation of a child is equal - 1 male + 1 female, so if we start out with an imbalance that imbalance will be reflected when taking the average.
Does this make sense? If so, we arrive at the conclusion that reproductively speaking, women are more valuable than men from the perspective of BOTH median value and average value. (I think you already agreed to the median value part)
Only that a bias in sex ratios at birth can indicate a greater reproductive advantage of the favored gender,
Fischer's principle predicts a reproductive advantage for the gender with a higher sex ratio. But, Fischer's principle is only ONE factor. Other factors can end up mattering more. 'Sperm is cheap' ends up mattering much more and negates the prediction from Fischer's principle.
Here is an analogy. The rules of elementary probability ( Fischer' principle in this analogy) would predict a 50% chance of heads in a coin flip. This would be valid given no other information. But if I told you half the coin weighed less than the other half (sperm is cheap, eggs are expensive), this new information will change the chances.
I'm not sure if that was a good analogy, but my point is you can't just use Fischer's principle in a vacuum and ignore everything else. You cannot ignore that sperm is cheap. The implications are so MASSIVE that they override the simplistic predictions from Fischer's principle.
Say an evolutionary biologist found a new species on an island. He studied the species over the course of a few years and found that more males were consistently being born than females. He would conclude that producing male offspring must have some reproductive advantage. Here men have more reproductive value.
I'm guessing this biologist is an alien and he's studying humans. But yes, he might initially assume that males must have some advantage due to Fischer's principle, but if he's a smart alien, he'll realize that sperm is cheap in this species and factor that into his assessment of reproductive advantage/value.