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The reconstruction of a stationary population from skeletal remains
U. Drenhaus Institut fiir Anatomic (H) Ruler- Universitiit Boehum Postfach 102 148 D 4630 Boehum 1, West Germany
The Reconstruction o f a Stationary Population f r o m Skeletal R e m a i n s On the basis of the stationary population model, a technique is described for the complete demographic reconstruction of a prehistoric population from skeletal remains.
Palaeodemographic studies provide a useful insight into primeval conditions and make it possible to conduct detailed analyses of macro- and micro-evolutive processes in various fields. Their contribution is very evident in the case of investigations into the geography of settlements and the history of populations or within the scope of demographic model studies and theory formation. Their relevance is also being recognized to an increasing extent in connection with biological, medical or (ethno-) sociological themes. For instance, the variability of characters in a population is determined by, among other things, the relationship of fertility to mortality, which also affects allele substitution. Moreover, there is a close connection between the course of the evolutionary process and the speed of the succession of generations, so that a study of character expression in connection with population structure and its development can furnish a contribution to clarify the causal structure of the evolutionary process and population differentiation. An increase in life expectancy can, furthermore, lead to new family structures and group relationships and widens the scope for the handing down of traditions. A socialization process running parallel to the growth of populations embraces, among other things, questions of social differentiation and of means of subsistence, and, in the medical context, a more profound insight is produced into the secular fall in mortality or, respectively, the growth in life expectancy, as a consequence of improved medical or hygienic conditions. Thoughts such as these, and others, which can hardly be expanded upon here, are to be found in Schwidetzky (1971), Weiss (1976) or Drenhaus (1977) and stress the relevance of palaeodemographlc findings. Opportunities for application, however, are of course only given if appropriate results on populations are available. Now the demographic analyses of prehistoric populations are restricted mainly to estimates of the average age at death, the mean life expectancy, the scope of populations and to the construction of mortality tables. More far-reaching investigations required analogy transmissions from other (recent) populations or were based on comparative observations of population structures and the vital rates for estimates and (computer) simulations of the population development and their underlying dynamic processes (summary, inter alia, in Weiss, 1976, or Drenhaus, 1977). This situation stems above all from the fact that the skeletal population - no matter how long the period of its genesis - was regarded as one single birth cohort and no chance was seen of a Journal of Human Evolution (1978) 7, 509-511 0047-2484]78]060509+03 $02.0010 9 1978 Academic Press Inc. (London) Limited
510
U. DRENHAUS
breakdown. In the present pap_er, we wish to show that a breakdown into cohorts comes about in a quite natural fashion. For this purpose, we should like to observe the build-up of and the losses to a population whose structure is not affected by migration a n d which reveals fixed mortality a n d fertility rates over the period in question. Let its deceased be passed down to us as a skeletal population which shall be known to us with respect to its sex- and (mortality-) age-composition and to the period of its making ( = period over which the buriat ground was used). A population such as this can be equated with the stationary population model with a zero growth rate and a structure remaining constant over time. T o reconstruct a population, the question in the foreground is, first, that of the age-structure which can be answered by laying a cross-section through the population at any point in time (t) and observing the n u m b e r of individuals separately in each age-group. The n u m b e r of age-groups depends solely on the age-span selected (I) and the m a x i m u m age at death (t~) in the population, so that it can be determined from ta/I. Since the m a x i m u m age at death, given constant mortality, does not change, the number of age-groups remains constant over time, too. T h e individuals of each age-group were born in the same respective period which, though always of equal length for the age-groups, lies in different population periods. Hence, the age-groups of the cross-section belong to various birth cohorts whose numbers must be identical with those of the age-groups. Following from this, we equate the cohort interval, i.e. the period in which the respectively-grouped individuals were born, with the age-span. In this, the choice of age-span is restricted by the accuracy with which the age at death can be determined on skeletal characters. In general, the closer the age-grid is, the higher the accuracy of the informative content with respect to the population. Passing through the various age-stages in life the number of individuals in each cohort declines until, upon reaching the m a x i m u m age, at death all have dropped out. Thus, the skeletons originate from those age-groups which the birth cohorts pass through. During a period which is equal in length to an age-group ( = cohort) interval the deceased must derive from the ta/I birth cohorts respectively from the various age-groups. Given a (usage) period of T years, altogether 7"/1+ ta/I-- I age-groups existed, so that T/Icohorts, from which the deceased originate, passed through each age-group. T h e total n u m b e r of birth cohorts established in the skeletal population is determined by the n u m b e r of the cohorts entering the population during the period of usage ( T / I ) a n d the n u m b e r of cohorts in existence (immediately) prior to the period of usage which were still p a r t of the population during the period in which the burial ground was in use (ta/I) : the result is T/I + t~/I -- 1, and it can be demonstrated very well on a model developed by Becker. We wish to illustrate the further reconstruction of the population in a scheme. First of all, using the matrix (Table 1), we can verify our thoughts on the number of birth-cohorts or age-groups from which the skeletons originate. In the skeletal population, we are given all the deceased ( = skeletons) of each of the age-groups that have been formed: S i = x i , o'J-xi, t 2 7 x i , 2 + . . . + x i , k. Given the n u m b e r of cohorts which passed through each age-group (GK,~=k= T/I) and by forming the arithmetic m e a n separately for each age-group, we can compute the n u m b e r of deceased in each cohort, as the population structure is constant over time: k X i ~-
X,,~ ~k=O
--~.
REGONSTRUGTION
OF A POPULATION
FROM SKELETAL
REMAINS
51 1
T h e n u m b e r of i n d i v i d u a l s b o r n into the cohort is d e t e r m i n e d b y Xo,1~+ xl,k+l + xe,k+2 + 9 9 9 + xi,k+~ (with k = 0,1,2 . . . , k). Since, b y definition, xi,k ~ xi, k + ~ = xi. k + 2 = x , e + ~, the s u m over the deceased of the age-groups thus d e t e r m i n e d m u s t p r o d u c e the initial stock of a cohort. By successively s u b t r a c t i n g the deceased of the s u b s e q u e n t age-groups from the i n d i v i d u a l s e n t e r i n g the respective age-groups (e.g. ao-x o -= al, ax-x 1 --= a2, etc.), we arrive at the l o n g i t u d i n a l structure of a cohort (a0,k, a~, ~+1, a2, k+2, 9 9 ai, ~+e; with k = 0, 1, 2 , . 9 k) which at a n y p o i n t i n time (t) is always identical to the cross-section of the p o p u l a t i o n (a0,k, al,k, a~,~, . . . , ai,~), since ai,~ = ~,~+1 ---- ai,~+e = ai,~+e (with k = 0, I, 2 . . .k). T h u s the structure of the p o p u l a t i o n a n d that of the b i r t h cohorts covered is reconstructed. T h e process of establishing the sex structure, etc., c a n be c o n d u c t e d accordingly a n d needs n o f u r t h e r e x p l a n a t i o n . O n this basis, one could follow u p with further d e m o g r a p h i c analyses a n d there is the o p p o r t u n i t y to use the d e t e r m i n e d p o p u l a t i o n structures a n d vital rates to o b t a i n indications of the completeness of the available material.
Added References
Adapted from: Drenhaus, U. (1976). Eine Methode zur Rekonstruktion und Beschreibung yon nichtrezenten Populatlonen in demographischer Sicht. Zeitsehriftfgr Morphologie undAnthropologie 67, 215230 (where the bibliography is to be found). Drenhaus, U. (1978a) Zur demographischen Rekonstruktion nicht-stationfirer vor- und frtihgeschichtlicher Populationen (in press). Drenhaus, U. (1977). Paliidemographie, ihre Aufgaben, Grundlagen und Methoden Zeitsehrift fiir Bey. wiss. 3, 3-40. Schwidetzky, I. (1971). Hauptprobleme der Anthropologie. Freiburg. Weiss, K. M. (1976). Demographic theory and anthropological inference. Annual Review of Anthropology 5, 351-381.
Table 1
Structure and development
of a stationary population
Age-groups with Population structure at various subsequent the age-group points in time, spaced at intervals equal Division of the corresponding interval (1) to the cohort interval (I) deceased respective skeletal population to
t1
t2
t8
0 1 2 3 4
U00 alo aeo aso a4o
n0I all a21 asl atl
ao2 a12 a22
Uoa alB a2a
aaz
aaa
a~2
aia
1
ato
all
at2
a~a
9 9
tk
to--t1 tx--t2
t2--t a .
t ~--t k+x
ao k al k ~2 ~ aag aak
Xoo Xlo X2o X30 Xao
XOl Xll X~l Xal xr
Xog x12 xag xBa xtg
X0 k Xl/r
a t 1:
Xio
xf. 1
xi2
Xfk
As per definition: tt-to
=
tk--tk--1 = no2 ~
I
aoo ~
not ~
X00 ~ XiO ~
a00--all ~ Xl0 ~ ~10--a21; X0k ~ UtO; X t k ~ a i k
a o ~ ~ aio ~
af2 ~
at~
a0~ ~
a0/~--gllk+t
X2 X8/r Xi k
The Reconstruction o f a Stationary Population f r o m Skeletal R e m a i n s On the basis of the stationary population model, a technique is described for the complete demographic reconstruction of a prehistoric population from skeletal remains.
Palaeodemographic studies provide a useful insight into primeval conditions and make it possible to conduct detailed analyses of macro- and micro-evolutive processes in various fields. Their contribution is very evident in the case of investigations into the geography of settlements and the history of populations or within the scope of demographic model studies and theory formation. Their relevance is also being recognized to an increasing extent in connection with biological, medical or (ethno-) sociological themes. For instance, the variability of characters in a population is determined by, among other things, the relationship of fertility to mortality, which also affects allele substitution. Moreover, there is a close connection between the course of the evolutionary process and the speed of the succession of generations, so that a study of character expression in connection with population structure and its development can furnish a contribution to clarify the causal structure of the evolutionary process and population differentiation. An increase in life expectancy can, furthermore, lead to new family structures and group relationships and widens the scope for the handing down of traditions. A socialization process running parallel to the growth of populations embraces, among other things, questions of social differentiation and of means of subsistence, and, in the medical context, a more profound insight is produced into the secular fall in mortality or, respectively, the growth in life expectancy, as a consequence of improved medical or hygienic conditions. Thoughts such as these, and others, which can hardly be expanded upon here, are to be found in Schwidetzky (1971), Weiss (1976) or Drenhaus (1977) and stress the relevance of palaeodemographlc findings. Opportunities for application, however, are of course only given if appropriate results on populations are available. Now the demographic analyses of prehistoric populations are restricted mainly to estimates of the average age at death, the mean life expectancy, the scope of populations and to the construction of mortality tables. More far-reaching investigations required analogy transmissions from other (recent) populations or were based on comparative observations of population structures and the vital rates for estimates and (computer) simulations of the population development and their underlying dynamic processes (summary, inter alia, in Weiss, 1976, or Drenhaus, 1977). This situation stems above all from the fact that the skeletal population - no matter how long the period of its genesis - was regarded as one single birth cohort and no chance was seen of a Journal of Human Evolution (1978) 7, 509-511 0047-2484]78]060509+03 $02.0010 9 1978 Academic Press Inc. (London) Limited
510
U. DRENHAUS
breakdown. In the present pap_er, we wish to show that a breakdown into cohorts comes about in a quite natural fashion. For this purpose, we should like to observe the build-up of and the losses to a population whose structure is not affected by migration a n d which reveals fixed mortality a n d fertility rates over the period in question. Let its deceased be passed down to us as a skeletal population which shall be known to us with respect to its sex- and (mortality-) age-composition and to the period of its making ( = period over which the buriat ground was used). A population such as this can be equated with the stationary population model with a zero growth rate and a structure remaining constant over time. T o reconstruct a population, the question in the foreground is, first, that of the age-structure which can be answered by laying a cross-section through the population at any point in time (t) and observing the n u m b e r of individuals separately in each age-group. The n u m b e r of age-groups depends solely on the age-span selected (I) and the m a x i m u m age at death (t~) in the population, so that it can be determined from ta/I. Since the m a x i m u m age at death, given constant mortality, does not change, the number of age-groups remains constant over time, too. T h e individuals of each age-group were born in the same respective period which, though always of equal length for the age-groups, lies in different population periods. Hence, the age-groups of the cross-section belong to various birth cohorts whose numbers must be identical with those of the age-groups. Following from this, we equate the cohort interval, i.e. the period in which the respectively-grouped individuals were born, with the age-span. In this, the choice of age-span is restricted by the accuracy with which the age at death can be determined on skeletal characters. In general, the closer the age-grid is, the higher the accuracy of the informative content with respect to the population. Passing through the various age-stages in life the number of individuals in each cohort declines until, upon reaching the m a x i m u m age, at death all have dropped out. Thus, the skeletons originate from those age-groups which the birth cohorts pass through. During a period which is equal in length to an age-group ( = cohort) interval the deceased must derive from the ta/I birth cohorts respectively from the various age-groups. Given a (usage) period of T years, altogether 7"/1+ ta/I-- I age-groups existed, so that T/Icohorts, from which the deceased originate, passed through each age-group. T h e total n u m b e r of birth cohorts established in the skeletal population is determined by the n u m b e r of the cohorts entering the population during the period of usage ( T / I ) a n d the n u m b e r of cohorts in existence (immediately) prior to the period of usage which were still p a r t of the population during the period in which the burial ground was in use (ta/I) : the result is T/I + t~/I -- 1, and it can be demonstrated very well on a model developed by Becker. We wish to illustrate the further reconstruction of the population in a scheme. First of all, using the matrix (Table 1), we can verify our thoughts on the number of birth-cohorts or age-groups from which the skeletons originate. In the skeletal population, we are given all the deceased ( = skeletons) of each of the age-groups that have been formed: S i = x i , o'J-xi, t 2 7 x i , 2 + . . . + x i , k. Given the n u m b e r of cohorts which passed through each age-group (GK,~=k= T/I) and by forming the arithmetic m e a n separately for each age-group, we can compute the n u m b e r of deceased in each cohort, as the population structure is constant over time: k X i ~-
X,,~ ~k=O
--~.
REGONSTRUGTION
OF A POPULATION
FROM SKELETAL
REMAINS
51 1
T h e n u m b e r of i n d i v i d u a l s b o r n into the cohort is d e t e r m i n e d b y Xo,1~+ xl,k+l + xe,k+2 + 9 9 9 + xi,k+~ (with k = 0,1,2 . . . , k). Since, b y definition, xi,k ~ xi, k + ~ = xi. k + 2 = x , e + ~, the s u m over the deceased of the age-groups thus d e t e r m i n e d m u s t p r o d u c e the initial stock of a cohort. By successively s u b t r a c t i n g the deceased of the s u b s e q u e n t age-groups from the i n d i v i d u a l s e n t e r i n g the respective age-groups (e.g. ao-x o -= al, ax-x 1 --= a2, etc.), we arrive at the l o n g i t u d i n a l structure of a cohort (a0,k, a~, ~+1, a2, k+2, 9 9 ai, ~+e; with k = 0, 1, 2 , . 9 k) which at a n y p o i n t i n time (t) is always identical to the cross-section of the p o p u l a t i o n (a0,k, al,k, a~,~, . . . , ai,~), since ai,~ = ~,~+1 ---- ai,~+e = ai,~+e (with k = 0, I, 2 . . .k). T h u s the structure of the p o p u l a t i o n a n d that of the b i r t h cohorts covered is reconstructed. T h e process of establishing the sex structure, etc., c a n be c o n d u c t e d accordingly a n d needs n o f u r t h e r e x p l a n a t i o n . O n this basis, one could follow u p with further d e m o g r a p h i c analyses a n d there is the o p p o r t u n i t y to use the d e t e r m i n e d p o p u l a t i o n structures a n d vital rates to o b t a i n indications of the completeness of the available material.
Added References
Adapted from: Drenhaus, U. (1976). Eine Methode zur Rekonstruktion und Beschreibung yon nichtrezenten Populatlonen in demographischer Sicht. Zeitsehriftfgr Morphologie undAnthropologie 67, 215230 (where the bibliography is to be found). Drenhaus, U. (1978a) Zur demographischen Rekonstruktion nicht-stationfirer vor- und frtihgeschichtlicher Populationen (in press). Drenhaus, U. (1977). Paliidemographie, ihre Aufgaben, Grundlagen und Methoden Zeitsehrift fiir Bey. wiss. 3, 3-40. Schwidetzky, I. (1971). Hauptprobleme der Anthropologie. Freiburg. Weiss, K. M. (1976). Demographic theory and anthropological inference. Annual Review of Anthropology 5, 351-381.
Table 1
Structure and development
of a stationary population
Age-groups with Population structure at various subsequent the age-group points in time, spaced at intervals equal Division of the corresponding interval (1) to the cohort interval (I) deceased respective skeletal population to
t1
t2
t8
0 1 2 3 4
U00 alo aeo aso a4o
n0I all a21 asl atl
ao2 a12 a22
Uoa alB a2a
aaz
aaa
a~2
aia
1
ato
all
at2
a~a
9 9
tk
to--t1 tx--t2
t2--t a .
t ~--t k+x
ao k al k ~2 ~ aag aak
Xoo Xlo X2o X30 Xao
XOl Xll X~l Xal xr
Xog x12 xag xBa xtg
X0 k Xl/r
a t 1:
Xio
xf. 1
xi2
Xfk
As per definition: tt-to
=
tk--tk--1 = no2 ~
I
aoo ~
not ~
X00 ~ XiO ~
a00--all ~ Xl0 ~ ~10--a21; X0k ~ UtO; X t k ~ a i k
a o ~ ~ aio ~
af2 ~
at~
a0~ ~
a0/~--gllk+t
X2 X8/r Xi k