Monday, September 16, 2013

A network of New Zealand's livestock regions

If I was to burrow down from Sweden through the centre of the Earth and keep going, I would come up off the east coast of New Zealand. In spite of being as far apart as you can get on this planet, these two countries have one thing in common — most people don't know quite where they are (Sweden is usually thought to be somewhere in the Alps, and New Zealand apparently exists only as a figment of Tolkien's imagination).

New Zealand is full of New Zealanders, of course (about 4.5 million of them), but according to government statistics it is also full of dairy cattle, beef cattle, sheep, deer, pigs, goats, horses, ostriches & emus, alpacas & llamas, and miscellaneous other farm animals. Indeed, there appear to be as many dairy cattle as people, as many beef cattle as people, and ten times as many sheep as people. This is ridiculous — even Australia has only five times as many sheep as people!

Where are they keeping all of these animals? To find out, I have used a network to explore the official statistics from the recently released New Zealand 2012 Agricultural Census tables, broken down by geographical region. I have restricted the data to dairy cattle, beef cattle, sheep, deer, pigs, goats and horses, as the data are a bit sporadic for the rarer animals; and they are also sporadic for the Chatham Islands, which I thus excluded. Note that the official bureaucratic terms for missing data are "Confidential" and "Suppressed" — the mind boggles at the idea that the number of pigs in or near Auckland, for example, is a government secret. Anyway, I have done my best to impute the missing data (based on the reported totals for each island and on the 2007 census).

The map shows you that the geographical regions vary dramatically in size (compare Nelson and Canterbury, for example), and so I standardized the animal counts for each region using the reported area (to get density, as animals per square kilometre). I then used a double square-root transformation, which is a traditional technique in zoology for standardizing extreme differences in animal abundance.

I then calculated the similarity of the regions using the Manhattan distance. A Neighbor-net analysis was then used to display the between-region similarities as a phylogenetic network. So, regions that are closely connected in the network are similar to each other based on their livestock abundances, and those that are further apart are progressively more different from each other.

The main outcome will surprise no New Zealander — both the North Island (shown in red) and the South Island (in blue) have distinct groups of regions. Indeed, the North Island has two-thirds of the dairy cattle, beef cattle, goats and horses, and the South Island has two-thirds of the deer and pigs, while they split the sheep equally. This means that the North Island has about 22.5 million livestock and the South Island about 20.5 million.

Nelson, West Coast, Marlborough and Tasman, all from the South Island, are the regions with the lowest density of livestock, and hence are strongly associated in the network. The West Coast has the lowest density of all of the livestock types except dairy cattle and deer, which is why it stands out in the network. (It also has the lowest density of people.)

Much of the network is highly correlated with sheep density, not unexpectedly, with increasing density from top to bottom in the graph. For example, Northland and Bay of Plenty, from the North Island, are relatively devoid of sheep, just like Marlborough and Tasman, although there are still 30-40 of them per square kilometre in all four regions. Gisborne, Hawke's Bay, Manawatu-Wanganui and Wellington are the areas with the greatest sheep density on the North Island, along with Canterbury, Southland and Otago from the South Island.

Other positions in the network are often based on single livestock species. For example, Waikato and Taranaki are far and away the most popular areas for dairy cattle; and Waikato and Auckland are the best places to go to see goats (although, at one per square kilometre, you won't see too many). Gisborne and Hawke's Bay are the places to go beef-cattle watching. Deer are particularly popular in the Canterbury, Otago and Southland regions. No-one will be surprised that horses are densest in the region with the biggest city, Auckland, which has one-third of New Zealand's population and 1 horse for every 225 people. (This doesn't even remotely challenge Sweden's national average of 1 horse for every 25 people.)

Apart form the quality of its lamb, New Zealand is world-famous for its vinous products (and its phylogeneticists, although these things are not necessarily causally related). It is probably the grape-growing in Marlborough that is excluding the livestock, since it has two-thirds of the 35,000 hectares of New Zealand's wine-grape area, according to the Agricultural Census. The West Coast is the only region listed as officially having 0 hectares of grapes, but Bay of Plenty, Taranaki, Nelson and Southland are all listed as Confidential (they have less than 55 hectares between them).

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