¹ Harris, W. V., ‘Towards a study of the Roman slave trade’, in D'Arms, J. H. and Kopff, E. C. (eds), The Seaborne Commerce of Ancient Rome (1980), 117Google Scholar. There would be little point in embarking on a comprehensive overview of previous research on this issue, which is why I will refer to only some of the most recent pertinent work.

² Harris, op. cit. (n. 1), 118, based on the assumption of a ‘social life expectancy’ of fewer than 20 years for 10 million slaves.

³ op. cit. (n. 1), 121. For a restatement of this view, see idem, ‘Child-exposure in the Roman Empire’, JRS 84 (1994), 18.

⁴ Harris, op. cit. (n. 1), 121–5, esp. 123–4. In his later article, op. cit. (n. 3), 10, Harris assumes that most exposed infants would die, while most of the survivors were enslaved. On the implications of this scenario see the text below at nn. 36–9.

⁵ Bradley, K. R., ‘On the Roman slave supply and slave breeding’, in Finley, M. I. (ed.), Classical Slavery (1987), 42Google Scholar.

⁶ ibid., 59.

⁷ ibid. In his (generally excellent) book Slavery and Society at Rome (1994), similar weight — in terms of space allotted — is given to different sources of vastly different potential, ranging from breeding to kidnapping of travellers (32–8).

⁸ Bradley, op. cit. (n. 7), 34.

⁹ op. cit. (n. 7), 43.

¹⁰ Herrmann-Otto, E., Ex ancilla natus: Untersuchungen zu den “hausgeborenen” Sklaven und Sklavinnen im Westen des römischen Kaiserreiches (1994)Google Scholar, e.g., 3, 3 n. 7, 6, and see below. Not having given enough thought to the matter, I adopted a comparably pessimistic stance in my ‘Columellas privates ius liberorum’, Latomus 53 (1994), 513–27Google Scholar. Cf. also Parkin, T. G., Demography and Roman Society (1992), 122Google Scholar: ‘a slave population is far from a natural one, and its demographic regime, which probably varied sharply over space and time, remains difficult to elucidate or even to make conjectures about’ (my italics), or Weaver, P. R. C., ‘Children of freedmen (and freedwomen)’, in Rawson, B. (ed.), Marriage, Divorce, and Children in Ancient Rome (1991), 176Google Scholar: ‘Slave origin comprises both those born as slaves (including vernae, born in the familia) and those who were born free but subsequently enslaved (from whatever cause or source). There are no means available of determining even approximately what proportion fell into each category’ (last italics mine).

¹¹ Herrmann-Otto, op. cit. (n. 10), 227. Cf. my review in Tyche 11 (1996), 274–8Google Scholar.

¹² Thus Herrmann-Otto, op. cit. (n. 10), 287, 411.

¹³ Patterson, O., Slavery and Social Death (1982), 132.Google Scholar

¹⁴ op. cit. (n. 13), 133. One might therefore wonder to what extent the slave populations of the Caribbean and Latin America which were shaped by continuous selective import and failed fully to reproduce themselves were intrinsically more ‘typical’ than the selfcontained and highly reproductive slave population of the United States. See below, in the appendix.

¹⁵ op. cit. (n. 13), 133.

¹⁶ For the total size of the population and a tentative breakdown according to provinces, see Frier, B. W., ‘The demography of the early Roman empire’, in CAH 11 (2nd edn, forthcoming)Google Scholar: between 45 million in A.D. 14 and 60 million before the Antonine plague. The much higher estimate implied by Lo Cascio, E., ‘The size of the Roman population: Beloch and the meaning of the Augustan census figures’, JRS 84 (1994), 23–40Google Scholar, is unconvincing; cf. briefly my Measuring Sex, Age and Death in the Roman Empire: Explorations in Ancient Demography (1996), 167–8Google Scholar (also in Arachnion (forthcoming)). About 11 per cent of the individuals in the census returns from Roman Egypt are slaves (118 of 1,084): Bagnall, R. S. and Frier, B. W., The Demography of Roman Egypt (1994), 48CrossRefGoogle Scholar (and cf. 48 n. 61 for similar estimates on the basis of other sources). This is the only yardstick for the extent of slave-ownership outside the central areas of Roman ‘slave society’. Hence, reckoning with a much higher proportion of slaves in Italy, my estimate of 10 per cent for the Empire as a whole seems rather a lower limit than a reasonable average. The larger the overall share of slaves was, the less likely extraneous sources would have been to meet the demand for replacement slaves: from a methodological point of view, my low estimate serves the useful purpose of making it more difficult for me to argue my case for a high incidence of natural reproduction (see below).

¹⁷ It is hard to tell whether Beloch, J., Die Bevölkerung der griechisch-römischen Welt (1886), 416, 418Google Scholar (2 million slaves in Italy) or Brunt, P. A., Italian Manpower 225 B.C.-A.D. 14 (1971), 121–30Google Scholar (3 million) is closer to the mark. In favour of Beloch's figure, see my ‘The demography of Roman slavery and manumission’, proceedings of Premier colloque international de démographie de l'antiquité (Arras, November 1996) (forthcoming). Despite its title, Menaut, G. Pereira, ‘El número de esclavos en las provincias romanas del Mediterráneo occidental, en el Imperio’, Klio 63 (1981), 373–99CrossRefGoogle Scholar, is rather unhelpful.

¹⁸ The significance of these different sources is (virtually) the same irrespective of whether the size of the slave population remained stable or decreased by one half over three centuries. At the same time, no demographic model can help to determine the existence, direction, and extent of any long-term changes.

¹⁹ cf. Coale, A. J. and Demeny, P., Regional Model Life Tables and Stable Populations (2nd edn, 1983), 56, 81Google Scholar.

²⁰ While this seems a reasonable premise in the case of enslaved foundlings, the import of grown-up slaves would have left its mark on the rates of birth and death. However, given the relatively small contribution of this group overall, any such effects are bound to be negligible within a rough model. Moreover, everyone is born at age o. Therefore, if the average age of the replacement slaves were put at, say, five years instead of zero, my figures would remain unchanged. If, say, half of all children died between birth and age five, n children enslaved at age five equal 2n children enslaved at birth, or, in other words, for every 1,000 children enslaved at age five, 2,000 would have been born five years previously. On the supply side, the actual average age at enslavement is immaterial.

²¹ Biraben, J.-N., ‘Essai sur l'évolution de nombre des hommes’, Population 34 (1979), 16CrossRefGoogle Scholar tab. 2, puts the total population of Europe (without Russia) and North Africa around A.D. 200 at forty-four and sixteen million, respectively. If both these and Frier's (op. cit. (n. 16)) guesstimates as to the size of the population of various provinces are anywhere near correct, about 80 per cent of all Europeans and North Africans may have lived within the Roman Empire. Again excluding most of the Middle East, this would make twenty million seem too high an estimate for the total number of ‘neighbours’.

²² Based on a life expectancy of 22.5 years at birth for females (Model West Females Mortality Level 2 in Coale and Demeny, op. cit. (n. 19), 56); for that mortality level, see Frier, B. W., ‘Roman life expectancy: Ulpian's evidence’, HSCPh 86 (1982), 213–51Google ScholarPubMed (on Ulp., , Dig. 35.2.68Google Scholarpr.); it might be particularly appropriate for slaves, cf. Duncan-Jones, R., Structure and Scale in the Roman Economy (1990), 100–1CrossRefGoogle Scholar. On Mortality Level 3 for Roman Egypt and the Empire in general, cf. Frier, op. cit. (n. 16), also Bagnall and Frier, op. cit. (n. 16), 84, 90, 100.

²³ On the last notion, see Bradley, op. cit. (n. 7), 164.

²⁴ See Wiedemann, T. E. J., ‘The regularity of manumission at Rome’, CQ 35 (1985), 162–75CrossRefGoogle Scholar, who rightly dismisses the view of Alföldy, G., ‘Die Freilassung von Sklaven und die Struktur der Sklaverei in der römischen Kaiserzeit’, RSA 2 (1972), 97–129Google Scholar (various reprints), who on the basis of epigraphical attestation that must have been limited to a small fraction of privileged slaves and freedmen argues for habitual manumission around age thirty: see below, n. 38. Weaver, op. cit. (n. 10), 181, also tends to put too much weight on the epigraphic evidence.

²⁵ Bagnall and Frier, op. cit. (n. 16), 158; cf. also tab. D 342–3.

²⁶ In Diocletian's Price Edict, elderly slaves were still envisioned as subject to sale, even though they appear vastly overpriced: see my ‘Reflections on the differential valuation of slaves in Diocletian's price edict and in the United States’, MBAH 15, 1 (1996), 67–79Google Scholar.

²⁷ If anything, these records may give us a rough idea of manumission patterns outside the city of Rome and other major urban centres; see below in the text following n. 39.

²⁸ Following Bagnall and Frier, op. cit. (n. 16), 143 tab. 7.1 (predicted female fertility rates at different ages). On the underlying assumptions, see above in text at nn. 19–20. Under conditions of natural fertility, which prevailed in ancient societies (Frier, B. W., ‘Natural fertility and family limitation in Roman marriage’, CPh 89 (1994), 318–33Google ScholarPubMed; on slave fertility, see in the appendix), there is no need to consider significantly different age-specific fertility rates.

²⁹ For a recent discussion of determinants of slave fertility, see Herrmann-Otto, op. cit. (n. 10), 235–68. It should be noted, however, that in the Old South, frequent separation of slave families through sale was perfectly compatible with sustained population growth: Tadman, M., Speculators and Slaves (1989)Google Scholar, passim; cf. Parish, P. J., Slavery (1989), 86Google Scholar (one-third to one-fourth of all slave marriages in the Upper South were broken).

³⁰ For this important point, see the appendix, and below, n. 31.

³¹ That this rate is considerably lower than the highest rates attested for the Americas (see appendix) seems justified by the fact that in general, the slave population of the Principate was not a ‘young’ population in the sense that it was in the process of being created or had only recently been built up. Thus, the age-structure would not have been as skewed as in the emerging slave societies of the Americas. In addition, some extreme hardships characteristic of the Caribbean such as those connected with the cultivation of sugar cane in hostile environments (see Higman, B. W., Slave Populations of the British Caribbean 1807–1834 (1984), 260–302Google Scholar) would have been largely unknown in the Roman Empire. John, A. M. , The Plantation Slaves of Trinidad, 1783–1816 (1988), 159Google Scholar, finds that in that environment, slaves failed to reproduce themselves owing to extreme levels of mortality, notwithstanding substantial fertility, a phenomenon that could be ascribed to a ‘brutal slave system’ or the ‘appalling conditions prevalent in rural tropical areas’ (p. 156).

³² On these two terms, see Newell, C., Methods and Models in Demography (1988), 122–3Google Scholar. For a rate of decrease of 15 per 1,000, cf. Coale and Demeny, op. cit. (n. 19), 81.

³³ cf. above, n. 4.

³⁴ For occasional mass enslavement under the Empire, see the references in Bradley, op. cit. (n. 7), 33, 40. Frier, op. cit. (n. 16), reckons with an influx of 20,000 slaves per annum (who contrary to his tacit assumption need not have contributed to population net growth; they are not assumed to do so in any of my models). The occidental slave trade to the Americas reached an annual average of 70,000 in the late eighteenth century, roughly at the rate of two males per one female, thereby creating sex ratios of between 50 and 80 males to 100 females in the most affected parts of Africa: Manning, P., ‘The slave trade: the formal demography of a global system’, in Inikori, J. E. and Engerman, S. L. (eds), The Atlantic Slave Trade (1992), 120Google Scholar. More than ten million Africans reached the New World as slaves from 1500 to 1900 (p. 119). The rate of intake for the Roman Empire assumed here would have been considerably larger in the long run (at four million per century) — once again, a rather unlikely supposition. (For the problems of estimating the effects of the modern slave trade on African populations, cf. Henige, D., ‘Measuring the immeasurable: the Atlantic slave trade, West African population and the Pyrrhonic critic’, Journal of African History 27 (1986), 295–313CrossRefGoogle Scholar.)

³⁵ See above in the text at nn. 2–4.

³⁶ See above, Harris, op. cit. (n. 3), 10. Boswell, J., The Kindness of Strangers (1988), 129–31Google Scholar, unpersuasively argues against this assumption: contra, Tilly, L. A.et al., ‘Child abandonment in European history: a symposium’, Journal of Family History 17 (1992), 12CrossRefGoogle Scholar, 18. At any rate, a considerable proportion of all exposed babies would have died. In the context of my rough model, it does not make a great difference whether 20, 40, or 60 per cent of them did not survive; even on the basis of the lower estimates, as many as one child out of four or five would have had to be exposed.

³⁷ It is true that in some places in Europe in the nineteenth century, a considerable proportion of all newborn children were abandoned. In the city of Milan in 1842, perhaps the most extreme case, 30 per cent of all babies were abandoned; the corresponding rate for the whole province of Milan is 10 per cent: Hunecke, V., ‘Intensità e fluttuazioni degli abbandoni dal XV al XIX secolo’, in Enfance abandonnée et société en Europe XIVe-XXe siècle (1991), 53Google Scholar. The situation was similar in a few other metropoleis such as Paris, Vienna, Florence, Moscow, and St Petersburg (Tilly et al., op. cit. (n. 36), 15). In most cases, however, even urban rates did not normally exceed 10 per cent while average rates for entire regions were lower by far (Regno di Napoli, 1836: 4.34 per cent; Lombardy, 1842: 4.81 per cent; Veneto, 1817/27: 2.2 per cent; Dipartimento di Reno, 1811: 3.02 per cent; France, 1846: 2.68 per cent): see Hunecke, op. cit., 52–4 tab. 5. Numbers aside, the background of this practice in early modern Europe is strikingly different from that in antiquity: most babies were not simply exposed and thus put at the mercy of the elements, predators, and slavers, but anonymously deposited in foundling homes. The extent of abandonment was clearly linked to the availability of such institutions. Moreover, the populations in question experienced steady net growth during this period and could therefore easily accommodate a certain degree of child abandonment (and frequent subsequent death in the foundling homes). Hence there is nothing to suggest that the modern data could be of much relevance for antiquity (but cf. below, n. 42). Boswell, op. cit. (n. 36), 133 n. 158, 135 n. 167, suggesting an overall rate of abandonment of urban children of 20 to 40 per cent in the Roman Empire (p. 135), places too much confidence in dubious premises advanced by Russell, J. C., Late Ancient and Medieval Populations (1985), xii–xiiiGoogle Scholar.

³⁸ He concludes, op. cit. (n. 24), 117, 128–9, that most urban slaves during the Empire would be manumitted. The most crucial observation made in his paper, viz., ‘Das epigraphische Quellenmaterial ergibt ebenfalls keine genauen Zahlen, aus denen der Proporz der Freigelassenen im Verhältnis zu jenen Sklaven ersichtlich wäre, die die Freiheit nie erlangten’ (p. 107), is unduly euphemistic (instead of ‘genaue Zahlen’, ‘precise figures’, read ‘no figures whatsoever’), and its powerful implications are moreover completely disregarded.

³⁹ In the context of the ‘intermediate’ estimate, an attested rate of manumission before age thirty of 67 per cent would be almost seven times as high as the predicted rate of 10 per cent. This could be taken to indicate, no doubt overly schematically, that only one-seventh of all slaves could hope to be commemorated in inscriptions. A slave population thus ‘privileged’ of close to one million might still seem quite large. As usual, there is no way of arriving at a precise estimate. However, given the impact of slave fertility on the slave supply, manumission before age thirty is unlikely to have benefited more than 5 per cent of all female slaves. This does not preclude significant differences between regions or generally between city and countryside; see below. (For such differences in Brazil, cf., e.g., M. C. Karasch, Slave Life in Rio de Janeiro 1808–1850 (1987), 345.) Sex-specific differences may have been even more considerable (cf. above on Roman Egypt).

⁴⁰ Frank, T., Economic Survey of Ancient Rome I (1933), 384Google Scholar, estimates that from 81 to 49 B.C., c. 500,000 slaves were manumitted in Roman Italy. Although Brunt, op. cit. (n. 17), 549–50, rightly points out that the underlying argument is methodologically unsound, Frank's figure as such need not be wide of the mark. Reckoning with an average slave population of 1,700,000 in Italy during that period (based on the schematic assumption of a linear increase from 500,000 slaves in 225 B.C. to 2,000,000 in 25 B.C.; cf. Brunt, 67), the rates of manumission posited in my ‘low’ estimate translate to about 16,000 manumissions per year, while the ‘intermediate’ scenario would yield about 19,000.

⁴¹ The ratio of freedmen to slaves would thus be roughly one to seven. As Bradley, op. cit. (n. 7), 163–4, points out, in Rio de Janeiro in 1849 (a society that with respect to slavery may have been quite similar to ancient Rome), under a regime of frequent and well-attested manumission, current slaves were about seven times as numerous as ex-slaves (based on Karasch, op. cit. (n. 39), 66 tab. 3.6).

⁴² For what it is worth (which is probably rather little), a rate of child exposure in the order of 5 per cent does not differ widely from respective rates attested in nineteenth-century Europe: see above, n. 37. Cf. also Harris, op. cit. (n. 3), 3.

⁴³ Both the ‘intermediate’ and the ‘low scenario’ suggest something like 60,000 manumissions per year for the whole Empire, or about 1 per cent of a slave population of six million.

⁴⁴ For a discussion of the conditions during the late Republic and the late Empire, see my paper cited in n. 17.

⁴⁵ The gist of the following argument has been anticipated by Brunt, op. cit. (n. 17), 143–6, who, however, does not attempt a quantitative appraisal. See also J. Andreau, ‘The freedman’, in Giardina, A. (ed.), The Romans (1993), 182–3Google Scholar; de Quiroga, P. L. Barja, ‘Freedmen social mobility in Roman Italy’, Historia 44 (1995), 329Google Scholar.

⁴⁶ Manumission was, therefore, unlikely to make a massive contribution to net growth of the free population overall pace Lo Cascio, E., ‘La dinamica della popolazione in Italia da Augusto al III secolo’, in L'ltalie d'Auguste à Dioclétien (1994), 114, 116Google Scholar. For a recent study of the offspring of liberti based on epigraphic material that would have benefited from a demographic perspective, see Weaver, op. cit. (n. 10).

⁴⁷ Columella's recommendation (RR 1.8.19) to manumit slave women after they had given birth to and raised four children was bound seriously to limit fertility after manumission. (For a discussion of this passage, see my article referred to above, n. 10.) Compare also stipulations in wills such as Salv. Iul., , Dig. 40.7.3.16Google Scholar: ‘si Arethusae liberta ita sit data, si tres servos pepererit, et per heredem steterit, quo minus pepererit’; also Tryph., , Dig. 1.5.15Google Scholar. This is reminiscent of the acquisition of freedom through the production of slave children in the manumission inscriptions of Delphi and Calymnos (Hopkins, K., Conquerors and Slaves (1978), 155–8Google Scholar).

⁴⁸ Gaius, , Inst. 1.194Google Scholar; Paul., , Sent. 4.9.1Google Scholar. The inference drawn by A. Watson, Roman Slave Law (1987), 39, that ‘under Augustus the procreation of children by freedwomen was officially encouraged’ and that the Romans therefore did not find it ‘objectionable to have large numbers of freeborn children of freed persons’ needs to be qualified in the light of the demographic circumstances.

⁴⁹ See, e.g., Huttunen, P., The Social Strata in the Imperial City of Rome (1974), 147, 151Google Scholar; Weaver, op. cit. (n. 10), 179; Barja de Quiroga, op. cit. (n. 45), 345. Cf. also Bürge, A., ‘Cum in familia nubas’, ZRG 105 (1988), 312–33Google Scholar.

⁵⁰ Coale and Demeny, op. cit. (n. 19), 42.

⁵¹ Saller, R. P., Patriarchy, Property and Death in the Roman Family (1994), 48 (assuming slightly lower mortality than in my models).CrossRefGoogle Scholar

⁵² Under normal conditions, a man aged fifty-five would have 2.6 living children and only 12 per cent would have none (Saller, op. cit. (n. 51), 51–2). If slavery resulted in deferred paternity, the respective rates for freedmen of that age might have been higher still. Some overall reduction in fertility would, however, have made it rather difficult for many of them to profit from three living children (see below).

⁵³ Gaius, Inst. 3.41–4 (transl. Watson, op. cit. (n. 48), 36–7). Liberti were released from their duty to perform operae for their patron when they had two children of their own in their potestas (Waldstein, W., Operae Libertorum (1986), 170–1Google Scholar). Patronae who were themselves libertae were permitted to inherit from their own former slaves only if they had given birth to three children (Tit. Ulp. 29.6).