18.6 Historical Evidence that the Canoes of the Heke Were Contemporaneous
311
error of 0.342 generations. This small standard error is a consequence of our having
the relatively large number of 48 genealogies.
At 25 years a generation, a figure commonly proposed by prehistorians, this
would date the Heke to AD 1412 ± 8.6. At the end of this chapter we shall derive
from rather different considerations 1403 as the most likely date for the Heke. The
choice 1403 corresponds to an average generation length of 25.5 years, based on
statistical analysis of 48 Heke lines. We note that the average generation length for
the major Rarotongan line considered in the next chapter is 25.2 years, a figure
computed from this single line over a period of more than 1,700 years. It may be
relevant that some of the Heke migrants had genealogical (and so genetic) links to
the main Rarotongan line. The difference in the generation lengths derived from 48
Heke lines and that of the main Rarotongan line is statistically insignificant – strong
affirmation not only of the reliability of the main Rarotongan line but also and more
generally of the reliability of carefully preserved Polynesian genealogies.
The data from the canoe genealogies also provides information about the relative
values of the mean μ and standard deviation σ of the distribution of the length of a
single whakapapa generation. Renewal theory (see Cox, pp. 46, 58) gives
var(N(t))
E(N(t))
≈
σ 2
μ 2 ,
so that the coefficient of variation c 2 = σ 2 /μ 2 of the distribution of length of a
generation may be derived as c 2 ≈ 0.31. For μ = 25.5 years, this provides σ =
14.2 years.
18.6 Historical Evidence that the Canoes of the Heke
Were Contemporaneous
Simmons may have had a valid point in claiming that European historians have overstressed the importance of the Heke. Certainly the Heke does need to be seen in the
wider context of Eastern Polynesian migrations to New Zealand during the Medieval
Climatic Optimum. Other fleets preceded it. At least ten canoes, for example, are
recorded as carrying the ancestors of the Ngati Ruanui and Nga Rauru tribes to New
Zealand in this period, though one, the Panga-atoru, was prevented from landing
and returned to Hawaiki [15]. The early European historians’ focus on the Heke is,
however, far from surprising. The Heke is unusual in that such rich traditions relating to its inception have been preserved in both Rarotonga and New Zealand and
because detailed traditions have also been preserved in New Zealand relating to its
passage to New Zealand and to the destination and later histories of its migrants.
Having used statistical methods to challenge Simmons’ claims that the canoes of
the Heke were not even contemporaneous, we now turn to traditional histories from
Rarotonga, Tahiti and New Zealand to challenge Simmons’ claim that the Heke was
not a migration from Eastern Polynesia to New Zealand but a series of migrations
311
error of 0.342 generations. This small standard error is a consequence of our having
the relatively large number of 48 genealogies.
At 25 years a generation, a figure commonly proposed by prehistorians, this
would date the Heke to AD 1412 ± 8.6. At the end of this chapter we shall derive
from rather different considerations 1403 as the most likely date for the Heke. The
choice 1403 corresponds to an average generation length of 25.5 years, based on
statistical analysis of 48 Heke lines. We note that the average generation length for
the major Rarotongan line considered in the next chapter is 25.2 years, a figure
computed from this single line over a period of more than 1,700 years. It may be
relevant that some of the Heke migrants had genealogical (and so genetic) links to
the main Rarotongan line. The difference in the generation lengths derived from 48
Heke lines and that of the main Rarotongan line is statistically insignificant – strong
affirmation not only of the reliability of the main Rarotongan line but also and more
generally of the reliability of carefully preserved Polynesian genealogies.
The data from the canoe genealogies also provides information about the relative
values of the mean μ and standard deviation σ of the distribution of the length of a
single whakapapa generation. Renewal theory (see Cox, pp. 46, 58) gives
var(N(t))
E(N(t))
≈
σ 2
μ 2 ,
so that the coefficient of variation c 2 = σ 2 /μ 2 of the distribution of length of a
generation may be derived as c 2 ≈ 0.31. For μ = 25.5 years, this provides σ =
14.2 years.
18.6 Historical Evidence that the Canoes of the Heke
Were Contemporaneous
Simmons may have had a valid point in claiming that European historians have overstressed the importance of the Heke. Certainly the Heke does need to be seen in the
wider context of Eastern Polynesian migrations to New Zealand during the Medieval
Climatic Optimum. Other fleets preceded it. At least ten canoes, for example, are
recorded as carrying the ancestors of the Ngati Ruanui and Nga Rauru tribes to New
Zealand in this period, though one, the Panga-atoru, was prevented from landing
and returned to Hawaiki [15]. The early European historians’ focus on the Heke is,
however, far from surprising. The Heke is unusual in that such rich traditions relating to its inception have been preserved in both Rarotonga and New Zealand and
because detailed traditions have also been preserved in New Zealand relating to its
passage to New Zealand and to the destination and later histories of its migrants.
Having used statistical methods to challenge Simmons’ claims that the canoes of
the Heke were not even contemporaneous, we now turn to traditional histories from
Rarotonga, Tahiti and New Zealand to challenge Simmons’ claim that the Heke was
not a migration from Eastern Polynesia to New Zealand but a series of migrations