MATHEMATICAL CONTRIBUTIONS TO THE THEORY OF EVOLUTION. 293 
In considering the inheritance of fertility I had two different problems in my 
mind: (i.) Is fertility pare and simple inherited ? i.e., Does a very fertile mare have 
offspring more fertile than the average? And (ii.) What effect does reproductive 
selection actually have on the population ? i.e., To what extent is it screened by 
other factors of evolution ; does the very fertile mare actually have more offspring 
than the less fertile ? Is, for example, her stock weed}^ and likely to die early ? In 
the case of mankind, the fertility of a woman is, as a rule, effectively brought to 
its limit with the end of her marriage, and accordingly I started with completed 
marriages. In the case of a brood-mare her effective fertility depends not on the 
offspring she has but on the number of these which survive foaldom. It would doubt¬ 
less have been better to have treated these two problems of fertility separately, but 
being fairly confident from Proposition L, p. 260, that fertility must be inherited, I was 
more interested to test the actual effect of reproductive selection. Accordingly I 
selected as the numerator of my fecundity ratio, not the number of foals born, but 
those who survived to the yearling sales. The difference is not very great, but quite 
sensible. For example, the mean fecundity of 3909 brood-mares, measured in my 
way, = ’6343, i.e., 63 surviving offspring on the average of 100 coverings. 
The following table gives the result of reckoning merely barren mares and those 
slipping foals or giving birth to dead foals in a twenty-year period ;— 
Average Fecundity of Brood-mares. 
Year. 
Average fecundity. 
Year. 
Average fecundity. 
1873 
•712 
1883 
•693 
1874 
•70:3 
1884 
•678 
1875 
•707 
1885 
•702 
1876 
697 
1886 
•700 
1877 
•692 
1887 
•682 
1878 
•680 
1888 
■695 
1879 
•683 
1889 
•685 
' 1880 
•666 
1890 
•686 
1881 
•680 
1891 
•679 
1882 
•667 
1892 
•675 
The averages of five-year periods are : 
•702, -675, -691, ‘684, 
and of the whole period, '688. 
There does not appear to be sufficient evidence for any secular change here, and 
we may take '688 to represent the average fecundity of the brood-mare, reckoning 
viable offspring to the number of coverings. The difference of '688 and ‘634 gives 
a death-rate of 5'4 foals in 68 8, or a death-rate of 7'85 per cent, of foals before 
maturity. If a considerable part of this death-rate be differential, we have room 
for natural selection inffuencing the drift of reproductive selection. The standard 
