Summary
In a previous paper (When Valor Isn’t Always Superior to Numbers: homoioi oliganthrôpia Caused by Attrition in Incessant Warfare, KLIO 100, 2018, 626–666) I argued that the population of Ancient Spartan citizens, homoioi, declined predominantly due to attrition in warfare. Here, I revisit the argument and present a more refined model that includes additional samples, directly incorporates information on losses, and improves assumptions. I argue that Sparta may have experienced an initial population plunge in the early 5th century and was unable to recover. The results of this study reaffirm that warfare may have been an integral cause of oliganthrôpia.
Appendix
Appendix A: Model Population Tables
Population up to age (X), (after Bagnall – Frier, 2006)
|
Age |
Percentage of Population |
|
1 |
3 % |
|
5 |
13 % |
|
10 |
24 % |
|
15 |
34 % |
|
20 |
44 % |
|
25 |
53 % |
|
30 |
62 % |
|
35 |
69 % |
|
40 |
76 % |
|
45 |
82 % |
|
50 |
87 % |
|
55 |
91 % |
|
60 |
94 % |
Population up to age (X), assuming stable population (after Coale – Demeny, 1986)
|
Age |
Percentage of Population |
|
1 |
3 % |
|
5 |
12 % |
|
10 |
22 % |
|
15 |
31 % |
|
20 |
40 % |
|
25 |
48 % |
|
30 |
56 % |
|
35 |
63 % |
|
40 |
70 % |
|
45 |
76 % |
|
50 |
82 % |
|
55 |
87 % |
|
60 |
92 % |
Population up to age (X), (after U.N. publication sales no. E.81.XIII.7, 1982)
|
Age |
Percentage of Population |
|
1 |
2 % |
|
5 |
11 % |
|
10 |
20 % |
|
15 |
30 % |
|
20 |
39 % |
|
25 |
47 % |
|
30 |
55 % |
|
35 |
63 % |
|
40 |
70 % |
|
45 |
76 % |
|
50 |
82 % |
|
55 |
87 % |
|
60 |
91 % |
Appendix B: Correlation and Regression Tables between Appendix A Tables
‘C&D’ stands for Claude and Demeny, ‘Egypt’ represents Bagnall and Frier, ‘UN’ represents the U.N. general patter developing country model life table.
Correlation
|
|
C&D |
|
|
|
C&D |
1 |
Egypt |
|
|
Egypt |
99.8960 % |
1 |
UN |
|
UN |
99.9958 % |
99.8759 % |
1 |
Regression
|
|
C&D |
|
|
|
C&D |
1 |
Egypt |
|
|
Egypt |
96.0576 % |
1 |
UN |
|
UN |
98.7996 % |
97.2010 % |
1 |
Descriptive Statistics for Differences between Model Life Tables
|
Δ C&D and Egypt |
Δ Egypt and UN |
Δ C&D and UN |
|||||
|
Difference |
Descriptive Stat. |
Difference |
Descriptive Stat. |
Difference |
Descriptive Stat. |
||
|
0 % |
Mean |
1 % |
Mean |
1 % |
Mean |
||
|
–1 % |
–4 % |
2 % |
5 % |
1 % |
1 % |
||
|
–2 % |
Median |
4 % |
Median |
1 % |
Median |
||
|
–4 % |
–4 % |
5 % |
5 % |
1 % |
1 % |
||
|
–4 % |
Standard Deviation |
6 % |
Standard Deviation |
1 % |
Standard Deviation |
||
|
–5 % |
2 % |
6 % |
2 % |
1 % |
0 % |
||
|
–6 % |
|
6 % |
|
1 % |
|
||
|
–6 % |
|
6 % |
|
0 % |
|
||
|
–6 % |
|
6 % |
|
0 % |
|
||
|
–5 % |
|
5 % |
|
0 % |
|
||
|
–5 % |
|
5 % |
|
0 % |
|
||
|
–4 % |
|
4 % |
|
0 % |
|
||
|
–3 % |
|
3 % |
|
0 % |
|
||
Note: The applicable differences for this paper was the difference between C&D and the other sources, not the difference between Egypt and UN tables.
Appendix C: Earthquake Losses
Hypothesized no. of homoioi assuming a population drop due to earthquake/conflicts of early 5th century
|
Date (BC) |
Army Size |
|
479 |
5,000 |
|
464 |
2,783 |
|
430 |
2,898 |
|
425 |
2,755 |
|
421 |
2,756 |
|
418 |
2,100 |
|
417 |
2,002 |
|
400 |
2,085 |
|
399 |
2,045 |
|
394 |
1,833 |
|
392 |
1,760 |
|
390 |
1,783 |
|
385 |
1,475 |
|
379 |
1,784 |
|
378 |
1,798 |
|
377 |
1,807 |
|
376 |
1,827 |
|
375 |
1,806 |
|
371 |
938 |
|
370 |
563 |
|
369 |
561 |
|
368 |
510 |
|
364 |
633 |
|
364 |
547 |
|
362 |
876 |
Appendix D: Estimated Percent Lost Per Event
|
Event |
Percent Lost |
|
Battle of Platea (Hdt. X.10–11) |
5.00 % |
|
Stenyklaros Plain (Hdt. IX.64.2) |
6.27 % |
|
Ithome Campaign (Thuc. I.101) |
5.00 % |
|
Battle of Tanagra (Thuc. I.107) |
1.50 % |
|
vs. Platea (Thuc. II.71) |
3.36 % |
|
Battle of Sphacteria and Pylos (Thuc. IV.11–15, 23, 26, 31–38) |
2.18 % |
|
vs. Parrhasia (Thuc. V.33) |
3.33 % |
|
Battle of Mantinea (Thuc. V.64) |
5.00 % |
|
vs. Sicyon (Thuc. V.81) |
0.79 % |
|
vs. Argos, Battle of Hysiae (Thuc. V.83, Diod. XII.81.1) |
5.00 % |
|
vs. Elis, Agis’ 2nd invasion (Xen. III.2.25) |
5.00 % |
|
vs. Elis, Pausanias’ invasion (Diod. XIV.17) |
5.00 % |
|
Battle of Nemea (Xen. IV.2.15) |
5.00 % |
|
Battle of Coronea (Xen. IV.3.17) |
0.80 % |
|
Support Corinthians (Xen. IV.4.8) |
0.55 % |
|
vs. Piraeum (Xen. IV.5.1–2) |
0.00 % |
|
Battle of Lechaeum (Xen. IV.5.13–14) |
14.02 % |
|
vs. Mantinea (Xen. V.2.3) |
5.00 % |
|
vs. Thebes, Cleombrutus’ 1st invasion (Xen. V.4.14) |
3.62 % |
|
vs. Thebes, Agesilaus’ 1st campaign (Xen. V.4.35–36) |
0.11 % |
|
vs. Thebes, Agesilaus’ 2nd campaign (Xen. V.4.47) |
0.55 % |
|
vs. Thebes, Cleombrutus’ 2nd campaign (Xen. V.4.59) |
0.00 % |
|
Battle of Tegyra (Plut. Pel. XVII, Diod. XV.81.2) |
2.24 % |
|
Battle of Leuctra (Xen. VI.4.3) |
42.64 % |
|
vs. Mantineia (Xen. VI.5.10) |
5.00 % |
|
vs. Thebes (Diod. XV.68.2) |
13.50 % |
|
Tearless Battle (Xen. VII.1.31–33) |
0.00 % |
|
vs. Arcadians, to support Eleans and Archidamus’ relief force of Cromnus (Xen. VII.4.20–24) |
13.50 % |
|
vs. Arcadians, attempt to capture Cromnus (Xen. VII.4.27) |
13.50 % |
|
vs. Theban Army, Battle of Mantinea (Xen. VII.5.10) |
5.00 % |
Bayes’ rule allows one to describe the probability of an event, based on prior knowledge of conditions that might be related to the event. It is adapted here for updating a ratio rather than a probability.
|
|
|
|
Prior ratio of losses |
|
|
|
|
|
Losses assuming the model is correct |
|
|
x |
21 % |
|||
|
|
|
|
Additional considerations |
|
|
||
|
Ratio of losses if deaths in war caused the drop in homoioi numbers |
y |
40 % |
|||||
|
Ratio of losses of homoioi in case deaths in war did not cause drop in population |
z |
19 % |
|||||
|
|
|
|
Posterior ratio of losses |
|
|
||
|
Revised ratio of losses, given the possibility that so many homoioi died in war |
xy/(xy–z(1–x)) |
36 % |
|||||
Appendix F: Robustness Test and Discussion
How good is our model at explaining population decline? While we have already discussed its merits and limitations, one possible way to test the robustness is to align the expected output deaths of the model with the implied deaths extracted from other historians’ approximations. As was shown in Decety (2018), several historians have approximated the decrease in the population of homoioi over time. In the table below, I extrapolated the implied population decrease between points in time (“Time Span”).
|
Time Span |
Cartledge |
Hansen |
Cawkwell |
Grundy |
Figueira |
Median |
|
479–460 BC |
1,500 |
1,600 |
1,600 |
2,344 |
1,945 |
1,600 |
|
459–440 BC |
2,000 |
1,600 |
2,000 |
3,125 |
300 |
2,000 |
|
439–420 BC |
1,000 |
200 |
300 |
1,750 |
655 |
655 |
|
419–400 BC |
1,000 |
800 |
100 |
1,500 |
267 |
800 |
|
399–380 BC |
500 |
550 |
740 |
800 |
905 |
740 |
|
379–360 BC |
500 |
650 |
400 |
1,000 |
52 |
500 |
|
Sum |
6,500 |
5,400 |
5,140 |
10,519 |
4,124 |
6,295 |
The columns below each name are the implied losses of each historian per time segment. On the far right side is the median loss of all authors. Below these columns are the sum losses (“sum”).
In the following table, I sum the losses predicted by the model. Both models are shown, the one on the left is the simple sum of deaths including only attrition in combat (“Model: No Disaster”), and the one on the right is the sum of deaths including both attrition and a presumed additional loss of 2,000 homoioi in the early 5th century (“Model: Disaster”). Each model is summarized based upon the sum average losses per time span. At the bottom I show the percent losses, dividing the sum loss above by the median sum of 6,295 (“% of median sum”) and by Figueira’s sum losses (“% of Figueira sum”). The closer percentages sums are to 100 %, the more explanatory the model can be of losses.
|
|
Model: No Disaster |
Model: Disaster |
|
Time Span |
Average |
Average |
|
479–460 BC |
684 |
2,200 |
|
459–440 BC |
59 |
0 |
|
439–420 BC |
266 |
700 |
|
419–400 BC |
257 |
15 |
|
399–380 BC |
485 |
506 |
|
379–360 BC |
345 |
755 |
|
|
|
|
|
Sum |
1,396 |
4,175 |
|
% of Median sum |
22 % |
66 % |
|
% of Figueira sum |
34 % |
101 % |
Recall that we used confidence intervals, and that the resulting average total deaths for the model without the presumed deaths in the 5th century should be about ±700, yielding a % of median sum of between 22 % and 44 % and a % of Figueira sum of between 34 % and 68 %.
As was discussed in the introduction section of this paper, we utilized the population sizes provided by Figueira. His implied approximate decrease is 4,124, by far the lowest one (about 35 % smaller than the average of other historians showcased in this test). It is therefore not surprising that the comparison of the model be more aligned when taken as a percentage of Figueira’s losses than the median sum. Had we used a different set of numbers as the basis of our model, the losses would indubitably be higher (based on a contrast of Figueira’s total with the median, approximately a ratio of 2:3, the percentages lost would more or less increase by about 50 % – thereby aligning them far better to the median sum). Note however that even with lower losses, the model with the presumed earthquake and additional conflict deaths do align fairly well with not only Figueira’s losses but the median as well – so perhaps 2,000 deaths was in fact unnecessarily high, a range of between 1,000 and 2,000 would be sufficient, a range that has been suggested as highly plausible in this essay.
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