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The authors have declared that no competing interests exist.

Conceived and designed the experiments: EO . Performed the experiments: KG. Analyzed the data: EO. Contributed reagents/materials/analysis tools: KG. Wrote the paper: EO.

Textbooks on evolutionary psychology and biology cite the case of the Sharifian Emperor of Morocco, Moulay Ismael the Bloodthirsty (1672–1727) who was supposed to have sired 888 children. This example for male reproduction has been challenged and led to a still unresolved discussion. The scientific debate is shaped by assumptions about reproductive constraints which cannot be tested directly—and the figures used are sometimes arbitrary. Therefore we developed a computer simulation which tests how many copulations per day were necessary to reach the reported reproductive outcome. We based our calculations on a report dating 1704, thus computing whether it was possible to have 600 sons in a reproductive timespan of 32 years. The algorithm is based on three different models of conception and different social and biological constraints. In the first model we used a random mating pool with unrestricted access to females. In the second model we used a restricted harem pool. The results indicate that Moulay Ismael could have achieved this high reproductive success. A comparison of the three conception models highlights the necessity to consider female sexual habits when assessing fertility across the cycle. We also show that the harem size needed is far smaller than the reported numbers.

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

One problem lies in the historical facts. Fortunately, there is a report by Dominique Busnot

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

We used Python for the development of the simulation. The source code is available as

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

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

In the first step we simulated random access to the harem pool and calculated the number of copulations per day which were necessary to reach the given number of children. In subsequent steps we added constraints to the model to investigate their effect on the reproductive effort needed.

The constraints we used were religious taboos (no copulations for five days each cycle during menstruation), the possibility of ovulation detection (with an accuracy of 0.6, and foetal and child mortality. If copulations happened completely random, 1.97 (Wilcox), 0.83 (Jöchle) or 2.30 (Barrett-Marshall) copulations per day would have lead to a reproductive success of 1171 offspring. Cultural norms and ovulation detection decrease the required number of copulations substantially, while foetal loss and child mortality increase it. Taking all constraints into account leads to an average of 1.43 (Wilcox), 0.83 (Jöchle) or 1.63 (Barrett-Marshall) copulations per day. (see

Wilcox | Jöchle | Barrett-Marshall | |

Constraints | Copulations per Day (min-max) | Copulations per Day (min-max) | Copulations per Day (min-max) |

Random | 1.97 (1.83–2.13) | 0.83 (0.78–0.88) | 2.30 (2.14–2.45) |

Cultural Norms | 1.59 (1.50–1.75) | 0.75 (0.70–0.80) | 1.87 (1.76–1.99) |

Ovulation Detection | 1.27 (1.19–1.37) | 0.68 (0.64–0.73) | 1.44 (1.35–1.55) |

Foetal Loss | 2.08 (1.94–2.22) | 0.87 (0.81–0.93) | 2.43 (2.27–2.62) |

Child Mortality | 2.46 (2.30–2.66) | 1.03 (0.96–1.10) | 2.87 (2.71–3.06) |

All Constraints | 1.43 (1.33–1.52) | 0.83 (0.78–0.88) | 1.63 (1.53–1.73) |

In the second model we calculated the number of children which could be sired given one copulation a day throughout the reproductive period of 32 years. First, we calculated the number of offspring when copulating on a random basis. Then we calculated the effect of intervening variables. Besides the constraints of model one we included the possibility of ovulation synchronisation and the emergence of love and favouritism. In this simulation calculations with all three models indicate that the number of offspring could have been reached. Results indicate that with only one copulation per day, Moulay could have succeeded in siring the fabled number of offspring only when calculations are made based on the Jöchle model. In the simulation based on the Wilcox-Weinberg model Moulay it depends very much on the constraints included in the simulation, whether 1171 offspring can be achieved or not. Especially when taking into account the decrease of sperm quality with age, ovulation detection becomes crucial for reproductive outcome. The results based on the Barett-Marshall model indicate that it was impossible to achieve the reported number of offspring without ovulation detection given only one copulation per day. (

Wilcox | Jöchle | Barrett-Marshall | |

Constraints | Number of children (min-max) | Number of children (min-max) | Number of children (min-max) |

No Constraints | 583 (520–629) | 1380 (1309–1460) | 502 (452–556) |

Basic Constraints: Cultural Norms, Ovulation Detection, Foetal Loss & Child Mortality | |||

Basic Constraints Only | 802 (748–858) | 1387 (1315–1460) | 713 (665–765) |

Ovulation Sync. | 735 (686–780) | 1323 (1249–1381) | 650 (608–691) |

Moulay Falls in Love | 556 (515–604) | 903 (851–955) | 491 (451–525) |

Favourites | 805 (753–854) | 1386 (1309–1460) | 704 (649–754) |

All Constraints | 535 (496–589) | 892 (830–946) | 467 (424–506) |

Basic Constraints: Cultural Norms, Fetal Loss & Child Mortality | |||

Basic Constraints Only | 556 (502–625) | 1164 (1088–1220) | 475 (445–514) |

Ovulation Sync. | 555 (504–609) | 1159 (1100–1226) | 477 (439–523) |

Love | 445 (408–487) | 815 (771–855) | 390 (343–422) |

Favourites | 552 (511–599) | 1164 (1097–1233) | 479 (438–523) |

All Constraints | 446 (405–499) | 826 (773–883) | 392 (350–440) |

Basic Constraints: Cultural Norms, Ovulation Detection, Sperm Aging, Fetal Loss & Child Mortality | |||

Sperm Aging Only | 450 (398–497) | 1060 (994–1119) | 385 (342–432) |

Basic Constraints Only | 617 (565–659) | 1066 (989–1134) | 547 (492–600) |

Ovulation Sync. | 569 (526–604) | 1014 (946–1087) | 499 (449–542) |

Love | 437 (396–478) | 717 (672–768) | 386 (339–422) |

Favourites | 620 (557–659) | 1060 (997–1127) | 540 (480–591) |

All Constraints | 424 (391–459) | 708 (657–759) | 367 (324–401) |

Basic Constraints: Cultural Norms, Sperm Aging, Fetal Loss & Child Mortality | |||

Basic Constraints Only | 415 (364–457) | 898 (824–955) | 367 (333–402) |

Ovulation Sync. | 427 (383–481) | 896 (826–947) | 364 (330–402) |

Love | 357 (323–397) | 654 (616–694) | 309 (278–346) |

Favourites | 421 (386–465) | 896 (843–958) | 366 (330–404) |

All Constraints | 356 (327–388) | 656 (619–691) | 311 (270–353) |

All constraints used in the model have a significant effect on the number of offspring (t-test, p<0.001).

Our calculations indicate that the harem size necessary to reach the reproductive outcome of 1171 children is far lower than the reported 504. The number of offspring reaches saturation at much smaller breeding pools. Calculations based on the conception model by Jöchle indicate that a harem size beyond 110 does not lead to an increased number of offspring (Quadratic regression: R^{2} = .978, df = 2274, p<0.001; Y = 86.262−0.057x^{2}+17.041x). For the Wilcox-Weinberg model the saturation is reached at a harem size of about 70 (Quadratic regression: R^{2} = .864, df = 2274, p<0.001; Y = 133.701−0.028x^{2}+7.436x), and for the Barrett-Marshall model reproductive outcome does not increase beyond a harem size of 65 (Quadratic regression: R^{2} = .835, df = 2274, p<0.001; Y = 131.665−0.024x^{2}+6.241x). (

Saturation is reached at smaller harem sizes for the Wilcox-Weinberg and Barrett-Marshall models than for the Jöchle model.

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.

(PY)