250
15 Dating the First Settlement of New Zealand
history, in particular estimating the date for the first colonization of New Zealand,
is our task in this chapter.
For this task we have chosen a new approach to New Zealand palaeodemography,
an approach that involves minimal assumptions. Not only is it therefore robust but,
as we shall show, it has unusual potential for illuminating the early demographic
history of New Zealand. It involves a power law analysis based on the rank size
distribution of New Zealand pa.
In 2006 Tony Walton published rank size distribution curves for pa of all sizes in
a sample of 931 pa [1]. Walton commented on the pa rank distribution he obtained:
The distribution has a long upper-end tail. There is a small blip in the curve around 9000 m 2
(which could be a sampling error). Above about 10,000 m 2 (1 ha) there are 60 sites
(representing 6–7% of the total) of various sizes up to 18 ha.
A rank size distribution is used to show the relationship between pa size and rank. What is
important is any significant change in slope. Fig. 8 shows a change of slope at both ends
of the distribution and this may indicate a specialised role for the very large and the very
small sizes. The change at the upper end of the distribution is at around 10,000 m 2 (1 ha).
This is also a feature of other data sets such as the Western Bay of Plenty (Fig. 9) showing
that it is not just a peculiarity of the combined sample. If just the sites above 1 ha in size
are displayed, a similar pattern is evident (Fig. 10) in the upper-range tail, with a change of
slope at above 3.2 ha. (These figures show lower-tail and upper-tail power-law behaviour –
but it is not clear what this means.)
Walton then posed a number of questions:
The usual explanation for very large pa is that they are part of a wider regional system of
defence. They provided a place for people from across a region to gather in numbers to
protect themselves when threatened by large-scale incursions. Is this an explanation for the
6–7% of pa on the slope at the upper end of the rank-size distribution? Does this suggest
that large extra-regional threats and incursions were a common occurrence in prehistoric
times? Were the large-scale raids across large parts of the country in the early 19th century
a continuation of an older pattern? Or were all these large sites constructed in late prehistoric
times or the early contact period?
In answer to Walton’s last question, we argued in Chapter 14 that in a context
of falling populations it is likely that most large and very large pa were constructed
in the first two generations of the Little Ice Age, that is, roughly between 1400 and
1445, when there were large populations to build and defend them.
The answer to Walton’s more basic question as to the meaning of “lower tail
and upper-tail power law behaviour” is more complex. A comprehensive discussion
of the relevant aspects of the rank power law is beyond the scope of the book. We
offer a general explanation here as background to our attempt in the first instance
to use power laws to estimate a population growth rate for New Zealand from first
settlement to 1445.
The potential of a power law approach for casting new light on the early
palaeodemography of New Zealand arises from the fact that power laws associated
with pa rank size distribution not only reflect the immediate history of pa built in the
Little Ice Age. Pa rank size distribution curves retain an imprint of the prior history
of settlement in New Zealand. They do so because the pattern of pa settlement
15 Dating the First Settlement of New Zealand
history, in particular estimating the date for the first colonization of New Zealand,
is our task in this chapter.
For this task we have chosen a new approach to New Zealand palaeodemography,
an approach that involves minimal assumptions. Not only is it therefore robust but,
as we shall show, it has unusual potential for illuminating the early demographic
history of New Zealand. It involves a power law analysis based on the rank size
distribution of New Zealand pa.
In 2006 Tony Walton published rank size distribution curves for pa of all sizes in
a sample of 931 pa [1]. Walton commented on the pa rank distribution he obtained:
The distribution has a long upper-end tail. There is a small blip in the curve around 9000 m 2
(which could be a sampling error). Above about 10,000 m 2 (1 ha) there are 60 sites
(representing 6–7% of the total) of various sizes up to 18 ha.
A rank size distribution is used to show the relationship between pa size and rank. What is
important is any significant change in slope. Fig. 8 shows a change of slope at both ends
of the distribution and this may indicate a specialised role for the very large and the very
small sizes. The change at the upper end of the distribution is at around 10,000 m 2 (1 ha).
This is also a feature of other data sets such as the Western Bay of Plenty (Fig. 9) showing
that it is not just a peculiarity of the combined sample. If just the sites above 1 ha in size
are displayed, a similar pattern is evident (Fig. 10) in the upper-range tail, with a change of
slope at above 3.2 ha. (These figures show lower-tail and upper-tail power-law behaviour –
but it is not clear what this means.)
Walton then posed a number of questions:
The usual explanation for very large pa is that they are part of a wider regional system of
defence. They provided a place for people from across a region to gather in numbers to
protect themselves when threatened by large-scale incursions. Is this an explanation for the
6–7% of pa on the slope at the upper end of the rank-size distribution? Does this suggest
that large extra-regional threats and incursions were a common occurrence in prehistoric
times? Were the large-scale raids across large parts of the country in the early 19th century
a continuation of an older pattern? Or were all these large sites constructed in late prehistoric
times or the early contact period?
In answer to Walton’s last question, we argued in Chapter 14 that in a context
of falling populations it is likely that most large and very large pa were constructed
in the first two generations of the Little Ice Age, that is, roughly between 1400 and
1445, when there were large populations to build and defend them.
The answer to Walton’s more basic question as to the meaning of “lower tail
and upper-tail power law behaviour” is more complex. A comprehensive discussion
of the relevant aspects of the rank power law is beyond the scope of the book. We
offer a general explanation here as background to our attempt in the first instance
to use power laws to estimate a population growth rate for New Zealand from first
settlement to 1445.
The potential of a power law approach for casting new light on the early
palaeodemography of New Zealand arises from the fact that power laws associated
with pa rank size distribution not only reflect the immediate history of pa built in the
Little Ice Age. Pa rank size distribution curves retain an imprint of the prior history
of settlement in New Zealand. They do so because the pattern of pa settlement