A false paternity event (fpe) is often called instead a non paternity event (npe) or a misattributed paternity. For the surname Plant for example, it can arise when a Plant `offspring' does not have a true Plant father. It can arise variously: from a concealed wifely infidelity with a non-Plant father; from an unmarried Plant mother passing her own surname to the child; or, from the adoption of a non-Plant child. Each of these will lead to a 'non-Plant', from the father's genetic point of view, despite having the Plant surname.
For a single-ancestor surname, the probability that a living descendant will carry the Y-DNA signature of the originator of the surname is (1-p)^n, where n is the number of generations in the line of descent, ^n means raised to the power of n, and p is the probability of a so-called `false paternity event' (fpe) at each generation. Hence, clearly, p is the probability of an fpe at each generation provided that we assume, since there is a lack of better evidence, that this probability has been constant historically throughout the generations. It then follows that (1-p) is the probability that there has been no fpe at a particular generation; and, since probabilities multiply, (1-p)^n is the probability that there has been no fpe throughout n generations.
For a typical surname (such as Sykes or Plant) a value of around 25 to 30 can be estimated for the number of generations, n, since when the surname originated; a likely value for p is more difficult to estimate.
Various values for the non-paternity rate, p, have been reported by Jobling, Hurles and Tyler-Smith (2004) in their book `Human Evolutionary Genetics', p 490. They quote extreme values of rates between 30% and 1% per generation; or, in other words, p between 0.3 and 0.01. They mention: anecdotal rates of p=0.3 in the casework of social workers though these are involved with the non-general population; an urban myth of p=0.1 among human geneticists; p=0.0135 in a systic fibrosis screening study; less than p=0.01 in a Swiss study; p=0.12 for the Mexican population; and a `customary adoption' practice for the peoples of Torres Strait islands. More recently, Kermyt G Anderson (2006) in Current Anthropology, 48(3), pp 511-518 has reported: p=0.017 amongst men with high paternity confidence; p=0.033 amongst men with unknown paternity confidence; and p=0.29 amongst men with low paternity confidence. This gives quite a wide range of values and there is the added uncertainty that we do not know how fpe rates may have varied historically with changing mores and adoption practices.
It is accordingly appropriate to calculate the probability that a Y-DNA signature had descended down an intact male-line, for various values of n and p, with the comment that the higher values of p (around p=0.3 and perhaps even p=0.1) are probably unrepresentative of the general population though they are included here for the sake of completeness:
The table makes it clear that the higher fpe rates correspond to an expectation that hardly any of the living descendants will carry the Y-DNA signature of the originator of the surname. On the other hand, a finding that 50% or more match is consistent with a single family with quite a low (p~0.02) fpe rate. In such a case, it cannot be entirely ruled out that the fpe rate is still lower (say p~0.01) and that some of the mismatches have arisen from entirely separate families at the outset. Even so, finding that around half or more match is a significant finding, indicating that those matching have a single male-line ancestor and that many (if not all) of the mismatches have arisen from so-called `false paternity events' down the centuries.
As a further comment as to what we may expect for the nature of the mismatches, in the case of a single-ancestor surname with reasonably low fpe, we can consider a surname whose population has become quite high. The population of a prolific surname may have increased in something like an exponential manner and so most of the non-paternty-events can be expected to have been in relatively recent times. This implies that we can expect that there will be a large modal group of matches (carrying the single-ancestor signature) but that most of the mismatches (from fpe) will be grouped only rarely into clusters of more than a few.
A study of the English surname Sykes [Sykes and Irven, 2000, Surnames and the Y-chromosome, Am. J. Hum. Genet., 66, 1417-1419] showed that a total 21/48 (44%) unreleated men of this name matched. The Sykes men were sampled from three counties of England. This quite large percentage of matches was attributed to the surname having had a single-ancestor origin with the mismatches being ascribed to an fpe rate of p=0.013. This low fpe rate was apparently derived from a comparison with a computer simulation of the evolution of 1000 single-ancestor surnames over 23 generations [C.M.Sturges and B.C.Haggett (1987) Inheritance of English surnames, (Hagwood Computing, London), p 7]; whereas, using the more usual statistical model outlined above, the Sykes fpe rate would have been p=0.035 for n=23.
This difference of calculated fpe rate of 1.3% or 3.5%, depending on the method of calculation, represents uncertainties about how exactly the single-ancestor surname model should be applied to real life. However, the difference is not sufficient to invalidate our general comments, made above, for the expectations for a single-ancetor surname: the Y-DNA results for Sykes (and Plant) are consistent with the expectations for a single-ancestor surname.
However, a note of caution should be added. It has been noted by Jobling et al. [Jobling et al., 2004, Human Evolutionary Genetics, p 492] that there are a number of other explanations that seem compatible with the observed results for Sykes, including the possibilty that there were a large number of initial founders of the name (i.e. men who originally took up the Sykes name) and that this was followed by so-called genetic drift such that only one founding Y-DNA signature reached a high frequency while the others became rare or even extinct. This would produce the semblance of a single-ancestor surname, in the results obtained from the modern population, even though there was more than one originator of the surname. For example, in a Sturges and Haggett computer simulation, only 350 families out of 1000 were found to have survived after 23 generations and 150 of those were under threat of extinction. In other words, if the Sykes (or Plant) name had orginated with six different progenitors, there is a fair chance that the families from only two of them would have survived with only one family having reached significant numbers.
Some simple calculations about genetic drift can be made using the so-called Wright-Fisher model [Jobling et al., 2004, p 131]. In this model, the mathematical probability that one particular signature will reach fixation (i.e. become the sole survivor) is 1/2N and the average time to fixation (in number of generations, t) is t=4N. Here, N is the number of people in the population. It is immediately clear that the fixation of a single Y-DNA signature (e.g. that of just one of several progenitors of a surname) will happen more likely and more quickly if N is small (note that N is small in the first few generations of a single-ancestor surname, even if it later becomes prolific). In principle, N is the size of the population; but, to correct for assumptions in the model, it needs to be replaced by an effective population size, Ne, which is generally much smaller than N. Such a correction is needed for such reasons as: the generations overlap; the population size is not constant; there is variance in reproductive success; and, there is transmission of reproductive success down each line of descent. At times of small Ne (e.g. in the first few generations of a single-ancestor surname) the genetic drift can be substantial.
Thus, the extinction of some lines of descent, including perhaps those from other founding fathers of the surname, can occur especially when the effective population size, Ne, is small. Clearly, the descendants of a particular founding father are few in number in the first few generations and this is a notable time when male-line descendants of a particular founding father can become extinct. Other particular times of low Ne are: population bottlenecks, such as the mid-fourteenth-century Black Death, when some of the genetic diversity for each particular surname could have been lost; and, founder events, such as the colonization of America, for which the genetic diversity in the new colony may not have been as great as that in its originating homeland.
It can also be noted that, if Sykes (or Plant) are truly single-ancestor surnames, then their number of family members must have increased at a much higher rate than the general expansion in the "English" population, even after allowing that there were many emigrants to the British colonies. As already explained, this is not unduly surprising given the phenomenon of "genetic drift". It can be estimated that there are around 25,000 Plants worldwide; and, judging by the Y-DNA evidence, about half of these have descended from the same Plant ancestor, with the remainder explicable by false paternity events within the same Plant family.
Besides random genetic drift, there is another factor: the fecundity of the rich and powerful as against the poor. Going back earlier into medieval times, there has been much debate of recent Y-DNA evidence on the basis of a contention that "Niall of the Nine Hostages" c450 AD, for example, had very many progeny, with Ui Neill (meaning descendants of Niall) leading to the O'Neil surname, and his progeny proliferating even more widely to the point where his Y-DNA signature is now common in various regions.
Even in more usual "surname times", it has often been argued [e.g. R.A.McKinley, A History of British Surnames, (London and new York, 1990)] that many of the most prolific surnames descend from rich individuals - the poor had relatively few surviving, healthy offspring. According to McKinley, it is particularly relevant for a surname to have become well established in the late medieval and early modern period; once well established, a rather more average behaviour can perhaps be expected for further growth of the family's numbers. The relevant rich, who established such single-ancestor surnames, are said by McKinley to be the late-medieval successful, or the junior or illegitimate offspring of the nobility on a downwards path to obscurity. The more senior nobilty themselves were more inclined, it seems, to keep changing their titles and names.
When considering a `single ancestor' model for a surname, it is relevant to consider the fraction that match amongst those who have been Y-DNA tested. When considering this fraction, it is important that the sample tested should be randomly selected and not biassed towards just one particular family branch. There is then a `rule of thumb' in Y-DNA surname studies that, when around half or more match, the surname can be termed `modal' or `single-ancestor' [Chris Pomery, DNA and Family History, (Richmond, Surrey, 2004)].
Of the first batch of Plants that were tested, 6 out of 7 matched (86%). These Plants were largely random volunteers from the Plant Family History Group. Since then, random volunteers have come forward after finding out about this project from the web. By mid-2005, 9 out of 14 matched (64%); and, at August 2007, 12 out of 21 (57%). Though there is no reason to suppose that those tested are unrepresentative of the Plant/Plantt family as a whole (except perhaps that they may tend to be slightly more affluent than the average), further changes in the percentage matching can be expected as the sample size increases, in other words as more volunteers with the Plant/Plantt surname come forward to be tested. In the meantime, it may be noted, at least so far, that around a half or more of the Plants tested have matched and so, by Pomery's rule of thumb, the Plant/Plantt family may be considered as `single ancestor'. In keeping with the single-ancestor model outlined above, the mismatches for Plant, as for Sykes, lagely occur singly as is in keeping with expections for relatively recent false paternity events.
There is, however, often room for uncertainty. Complete rigour in an argument is rarely attained. In such a circumstance, it is often appropriate to pick out a particular possibility for consideration. The scientific rule of parsimony (rather similar to Occam's razor) states that: when there are several, possible explantions, the simplest one is the best. To that extent, to speak of a single-ancestor surname is the simplest, though there is no proof that there was not more than one founder of the English Sykes surname or of the Plant/Plantt surname at their outsets.
Turning to the modern population of the English Plant/Plantt surname, only a few so far have been Y-DNA tested. Clearly, those matching can be considered to have a single ancestor (leaving aside a very small chance that they match by random chance) though, more strictly, it is not of course necessary that this single ancestor dates back to as early as an original sole-founder of the surname. Those currently matching (at August 2007) are the volunteers: P1a, P1b, P2a, P2b, P3a, P5a, P7a, P12a, P14a, P19a, PT1a, and PT2a. Their earliest known male-line ancestors include ones in: Cheshire England c1565; VA USA c1655; and Ct USA 1646-91. This implies that their most recent common ancestor (MRCA) was at least as early as the first half of the seventeenth century. Whether the Y-DNA signature of this MRCA was inherited down an intact male-line of descent from a single founder of the entire Plant/Plantt surname is less certain however. A dominant signature has been found for Plant to date back to at least the early seventeenth century but it remains merely comjecture whether this originated from a single founder in the main Plant/Plantt homeland of east Cheshire/north Staffordshire after the mid-fourteenth century Black Death; and, before this, there is further uncertainty, because of genetic dift, whether this dominant signature may have been inherited, in turn, from a still earlier Plant/Plantt, such as from the thirteenth century for when there is scattered evidence around more than one region of England for the Plant name.
The following comments, at least, can be made. Though it had previously been published that Plant was a multi-origin surname [Hey, 1998, Staffordshire Studies, 10, pps 1-28], there is now sufficient name-distribution and Y-DNA evidence [Plant, 2005, Nomina, 28, pps 115-133] to make it reasonable to consider that there is an unusually large manin-family English Plant/Plantt surname from a single-ancestor at its outset. Certainly, the Y-DNA evidence so far indicates that many of the living Plants descend down intact male-lines from a single ancestor. It is a simple conjecture to consider that the most-common Y-DNA signature for the Plants is that of the founding father of the surname; though, as indicated, it has not been proved that there was not more than one such founder since it is possible that other early Plant families may have died out and indeed it seems that a fraction of the Plants likely survived as more normal sized, relatively-small Plant families . The name distribution and other evidence indicates that there was a main Plant homeland in east Cheshire with possible migration to there from far away Norfolk and there are some early Plants of moderate note who may have been mobile: this is at first sight consistent with contending that Plant is a so-called `single-ancestor' surname. This is sometimes termed a `mono-genetic' surname, though this is somewhat misleading in that this term seems to imply that there is no 'fpe'.. More certainly, Plant/Plantt can be described as a `modal' surname with, so far, more than half matching implying that those are male-line related whilst the remainder evidently arise from false paternity events.
More recently, a further geographical breakdown of the Plant Y-DNA results suggests that it could well have been a multi-origin surname around its main homeland of NE Staffordshire but with only one male-line Plant family growing unusually large and migrating far and wide.
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