As explained elsewhere the current worldwide population of Kelsall is estimated to be about 4,500 with about 3,100 in the UK. This page examines how this population has grown over time and whether the growth can be explained in terms of a single origin around 1300 or earlier.
The first graph shows census counts for Kelsall in England and Wales from 1841 to 1911. The red triangles show the actual population from the census, 1841 to 1911. The blue diamonds show the predicted population proportioned from the actual Kelsall population in 1841 and the increase in the total population of England and Wales. The Kelsall population increases more than predicted from the general population especially from 1861 to 1891. The rate of population increase from one census to the next was 5% from 1841 to 1851 and 7% from 1851 to 1861, but it then increased to an average of 21% over the next three periods before starting to fall off after 1891. The result is that in 1881 the Kelsall population is 23% higher than would be predicted from the general population increase. This shows that the Kelsall population was relatively successful compared to the average. Other surnames would have lost population after 1841 and some would have died out completely.
The next graph shows the numbers of births and deaths recorded at 10-year intervals from 1841 to 1971. Thee data are obtained from online GRO indexes for years available (births 1841 to 1911, deaths 1841 to 192) otherwise from FreeBMD. Annual births rose from 1841 to 1871 but after 1871 they have remained steady generally between 50 and 60 (with a notable exception in 1941 that was presumably war related). A similar pattern is observed for deaths. On average for the whole period births exceed deaths by a factor of 1.7 (50 vs. 29).
The next graph shows data from 1841 to 1911 normalized to 1841 values. In this case the birth rate and death rate are adjusted according to the change in the Kelsall population. Both the birth rate and the death rate fell across the whole period when adjusted for population growth. The Kelsall population increased as the result of the birth rate exceeding the mortality rate.
The next graph shows the same data extended out in time. Again, the red triangles show the actual population from the census, 1841 to 1911, and the blue diamonds show the predicted population proportioned from the actual Kelsall population in 1841 and the total population of England and Wales. The brown dashed line approximates the increase in the worldwide population to the current estimate of 4,500, with the assumption that most emigration of the name occurred after 1841.
The growth of the Kelsall population over a longer time span is shown in the next graph.The dashed blue curve is a projection for Kelsall both ways in time based on the actual 1851 census population proportioned to the total population of England and Wales. An exponential fit to the data fairly closely models the data from 1851 back to an origin in the 14th Century or earlier. The dashed curve “predicts” a population of about 150 in 1551, about 100 in 1451 and about 150 in 1351. The drop from 1351 to 1451 is related to the Black Death which killed off about ½ the population starting in 1348. Another prediction can be made using the factors presented by Alan Bardsley also used to estimate current population. These factors allow a separate estimate of the 1551 population based on each census population from 1841 to 1911. The estimates range from 156 to 192 with an average of 176. It is noted that these extrapolations are based on census populations for England and Wales, whereas it is known that the current population of Kelsall overseas is as much as 40% of that remaining in England and Wales. It may be reasonable to conclude that the mid-16th Century Kelsall population was in the range 150 to 200.
Based on genealogical and parish registers, the Kelsall name originated in Cheshire, and the great majority of Kelsall families in the 16th Century were still living in Cheshire. The extrapolations presented above suggest a Kelsall population of about 150 to 200 in the mid-16th Century. The actual population at that time cannot be known but parish records presented here show that the Kelsall name was well established in multiple Cheshire parishes before the end of the century. Looking again at the factors presented by Alan Bardsley, applying his factors to the known 1911 Kelsall births yields an estimated 5 Kelsall births per year in 1551. In the Cheshire parish data there are no births in 1551 but the average for the period 1538 to 1599 was approximately 2/year (61 total births). While there are uncertainties in the method and data, it is also likely that the parish registers on line are not complete.
The data presented above are considered to be consistent with the growth of the Kelsall name from a single family at the beginning of the 14th Century. Corroboration that this is feasible is obtained from the work of John and Richard Plant published in the Journal of One-Name Studies (Vol. 11, Issues 7, 9 and 12). One objective of their work was to determine whether a surname population observed in 1881 could grow from a single individual in 1311. They used large numbers of computer simulations to predict the population in 1881 based on chance. In their results, 1,000,000 simulations are computed for an English family starting in 1311 and, by 1881, the family dies out in 92.5% of cases whereas, in the largest outcome, it grows purely by chance to 730 active males. This result was for growth patterns that match the whole of England. They later looked at industrial counties that have had higher growth and found the maximum possible number of active males to be 1,246 for Staffordshire. These results refer to reproductively active males in the age range of about 17 to 50. In the 1881 census for Kelsall there were 360 males in this age range. This would suggest that the population of Kelsall observed today is well within the range that could be generated from a single source.
Population growth for a single surname has also been examined by G.M. Astley in the Journal of One-Name Studies, Vol. 12-9 (2017). Astley developed a computer model to simulate growth of a surname based on probabilities of males in each generation producing at least male child necessary to propagate the name. He found that approximately 85% of males living in 1600 have no descendants living today bearing their surname. In the 15% of cases where the surname has survived the journey from a male in 1600 to today, each of those males from 1600 has on average about eighty male descendants in the middle generation currently alive sharing his surname (which translates to just under five hundred people assuming three generations and including females). Applying this to the current worldwide Kelsall population of 4,500 indicates a Kelsall population of about 340 in 1600. This is higher than estimated by other methods but it may be skewed by faster overseas population growth.
These studies show that the size of the Kelsall population is consistent with development from a single source. This fits the observed population in the census with about half of all Kelsall households in the U.K. found in two counties, Staffordshire and Lancashire. About 705 are in four counties, Staffordshire, Lancashire, Cheshire and Yorkshire. This is consistent with the name originating in Kelsall and spreading to neighbouring industrial counties.