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Mathmatical
model of six
generations		 Using a methematical model, similar numbers can be produced when certain values are assumed for average number of offspring and age of childbearing. The model appears to predict only for the second and fourth generation, but the mathematical model is an interesting exercise, and guessing at the sources of its imperfections give hints to why Morton births appear in such a pattern.

Below is calculated a series based on the 1740's generation, assuming each male survived long enough to have, on average, 1.39 male children and 2.4 children in total from age 26 to 28 years old:

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Assumptions:
min age of father
26
max age of father
28
# sons per father
1.4
# children per father 2.4


Results of mathmatical model:
generation
# males
 # all births
beginning
ending
(given) 1
3.0
 4.0
1743
1749
2
4.2
 7.2
1769
1777
3
5.9
 10.1
1795
1805
4
8.2
 14.1
1821
1833
5
11.5
 19.8
1847
1861
6
16.1
 27.7
1873
1889

Observed data:
generation
# males
 # all births
beginning
ending
1
3.0
 **
1743
1749
2
3.0
 **
1770
1782
*3
0.0
 **
----
----
4
8.0
 14.0
1820
1833
5
4.0
 6.0
1847
1861
6
2.0
 5.0
1873
1889

* the data shows no obvious generation during the 1790's

** # of all births calculated from burial records (before 1814) cannot reflect the true number born to Mortons, as some may represent Morton spouses instead of children.

n.b. female births were not used to calculate births because women did not carry the surname to successive generations, and the data for Morton-born women's children were not available in the registers

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