The scientific discussion about the case of the Sharifian Emperor of Morocco, Moulay Ismael the Bloodthirsty (1672–1727), who is reported to have sired 888 children in the Guinness Book of Records, is still ongoing. Recent findings on the genetic legacy of Genghis Khan and his male relatives show impressively how vast the distribution of genes of powerful males can be: About 8% of todays' Asian male population dates back to this family [1]. Einon [2] claimed that it is unlikely that Moulay Ismael could have had that many offspring, based on several factors potentially affecting reproduction: Ovulation frequency combined with sperm survival (resulting in women being fertile only 12.5% of the time), female infertility (8%), conception likelihood (58%), and prenatal mortality (15–20%). Contrarily, Gould [3] states that Einon's assumptions are unrealistic insofar, as some assumptions were not correct: First, Einon inaccurately used Moulay's duration of reign as life span, but also the biological parameters were flawed: Sperm survival is about twice as long as Einon posed [4], and fertility of cycles in women between 25 and 39 is as high as 93–98% [5]. The likelihood of foetal loss is highest in the first 14 days of pregnancy [6], after the first 14 days of pregnancy (which corresponds to the data basis of Jöchle) is around 5% [7], child mortality until the age of two around 20% [8], [9], [10]. To complete the picture, sperm aging and decline of sperm vitality have to be taken into account [11], [12].

One problem lies in the historical facts. Fortunately, there is a report by Dominique Busnot [13], a French diplomat, who was in Morocco in 1704, 1708 and 1712. We decided to use his report in the year 1704 as the data source for our calculations, as it provides figures not only about the number of offspring, but also about reproductive timespan. Moulay became emperor in 1672 at age 25 and was thus 57 when Busnot first visited Morocco. In 1704 Busnot reports Moulay to have 600 sons from four wives and 500 concubines. Daughters by his four wives were allowed to live, whereas daughters born by his concubines were suffocated by the midwifes at birth. This results in approximately 1171 children from 500 women in a reproductive time span of 32 years (25–57). Note that we neglect the reproduction before his becoming emperor, as he most likely did not have a comparable harem then. Moulay Ismael took extreme measures to ensure paternity security, which is partially responsible for his sobriquet “the bloodthirsty”. Any suspicion of adultery was severely punished: The women were either strangled by himself, or their breasts were cut off, or their teeth were torn out. This applied even to former concubines who had already left the harem - which they had to when reaching the age of 30. Men who merely looked at one of his wives or concubines were punished by death penalty [13].

As this report of Busnot appears to be the only reliable source of information available, we focus on the reproductive data of the 1704 report, rather than estimating his life-time reproductive success. Since Moulay died in 1727 it is likely that those numbers could have been substantially larger.

Calculations of reproductive effort have to include a number of interacting variables, and thus cannot be done sequentially, but have to take the dynamic nature of a reproduction pool into account. Thus, we decided to model Moulay Ismael's reproductive efforts in a computer simulation.

There are two conception models that are widely used to assess the conception likelihood across the female cycle: The Wilcox-Weinberg model [14] and the Barrett-Marshall [15] model. Both models are based on data from couples participating in longitudinal studies. The former participated in a general medical study, whereas the latter used the temperature method for birth control. In both cases the women had born at least one child before participation. The conception model by Jöchle [16] differs greatly from those two, not only regarding the nature of the data, but in the distribution of conception likelihood over the cycle. Jöchle's model is based on data from German soldiers' wives during the two world wars, who had intercourse with their husbands only when they were transferred from one front to the other, and on conceptions resulting from rape. Jöchle concluded from this data that under specific conditions induced ovulation might happen in humans: Rare sexual intercourse and strong emotional arousal [16]. It is likely that these conditions would have held true for the concubines of Moulay Ismael. Sperm potency seems to be unaffected by frequent intercourse [17].

We used Python for the development of the simulation. The source code is available as Script S1. For both simulations we used the following three models as a basis: a) the Wilcox-Weinberg Model of Conception [14], which integrates observational data with the survival rate of sperm and the viability of the cycle, b) the conception likelihood of Jöchle [16], and the Barrett-Marshall model [15]. These basic models were integrated in our simulation, in which we incorporated potential constraints (Fig. 1).

The breeding pool consists of 504 women (500 concubines plus 4 wives), the cycle day was assigned randomly in the first simulation, in the second we allowed for 50% synchronisation, i.e. 50% of the women would cycle simultaneously. This value was chosen completely arbitrarily for the purpose of investigating whether this would have an effect at all. Cycle synchronization is still much disputed [18], [19], [20]. Cultural norms stand for the copulation taboo during menstruation, i.e. five days of the period of the female cycle with lowest fertility [21]. The mucus test allows to detect ovulation ±4 days with an accuracy of 97% [22], but as it is unknown whether it was practiced in Morocco at that time, we chose to base our simulation on behavioural data: Ovulatory faces are perceived as most attractive in a forced choice task at 60% [23], which aligns well with other studies on attractiveness over the female cycle [24], [25]. Another advantage is that we do not need to assume detailed knowledge about fertility and menstrual cycle, but base our calculations on mere increased sexual attraction in the most fertile period. Copulation leads to conception depending on the viability of sperm, with a decrease of 1.52% per year [11], [12], fertility of the female's cycle [5], and on the cycle day [14], [15], [16]. Taking all these constraints into account, we calculate the conception probability leading to fertilisation as detected through observation, i.e. absence of monthly bleeding. Once fertilisation has been detected (after day 14 of pregnancy), foetal loss [7] and offspring survival rate [8], [9], [10] again reduce the number of offspring.

In the first model we calculated how many copulations per day would be necessary to reach 1171 offspring in 32 years, and how the constraints delineated above modulate this number. In the second model we calculated the number of offspring reached in the reproductive period of 32 years and how the variables affect this number. For these models we calculated 200 iterations.

We reran the simulations four times, once with ovulation detection and without sperm ageing, once without ovulation detection and sperm ageing, once with both, ovulation detection and sperm ageing, and once with sperm ageing and without ovulation detection.

Lastly, we calculated how the harem size affects the calculations. Based on the restrictions used in model number one, we calculated the number of offspring for harem sizes between 1 and 200. Pregnant women were removed from the reproductive pool for a period of 18 months, allowing for pregnancy and lactation [26].

In general, results indicate that the Emperor could have reached his notorious reproductive success with fewer copulations than assumed so far - thus the historic reports could be facts and not fancy. With our simulation we could also provide evidence that the harem size is of lesser importance for the achievement of the reported reproductive success than thought so far. A breeding pool of 65 to 110 women leads to the maximum reproductive outcome. This highlights the importance of incorporating cost-benefit calculations – increasing the size of the breeding pool beyond that point increases the costs without additional benefits to outweigh them. Having a harem of 500 concubines might have been due to other considerations than maximization of individual reproductive outcome. For example, it could have been a means to remove the additional women from the reach of other men, thus depriving them of reproductive potential.

We also show that the choice of conception model has to be carefully considered. Sexual habits have a strong impact on the distribution of conception likelihood over the female cycle. Therefore it is essential to take frequency of intercourse into account when trying to estimate the likelihood of pregnancy resulting from intercourse. In our case, the sexual habits of the concubines were most likely similar to the sexual habits of women in the Jöchle databases, i.e. rare intercourse due to the large number of women in the harem.

In our models, we intentionally chose to incorporate more conservative assumptions about the effect sizes of the involved variables (i.e. foetal loss, child mortality, …). This means, that we always chose the figure most adverse to number of offspring. As the goal was to investigate whether the historic reports about the reproductive success of Moulay Ismael can be correct, rather than estimating the maximum number of offspring possible for a man, this was the method of choice. When addressing different scientific questions, one might choose to change these figures.

Besides contributing to the dispute about the limits of male potential reproductive success by shedding light on the most popular example in this debate, this study also provides a rationale for the choice of conception models. While female sexual habits have not been considered so far, this study emphasizes the importance to take them into account.