An Application To Teak Improvement

Teak (tectona grandis) is native to Thailand, Burma (Myanmar), Laos, and India. Plantations were established in Indonesia as early as the 14th century, and more recently in Bangladesh, Sri Lanka, China, Vietnam, and New Guinea. In addition, the tree has been grown in Mexico, Puerto Rico, Cote d'lvoire, Ghana, Togo, Tanzania, and Nigeria (Keiding, Wellendorf, and Lauridsen, 1986). There are today some 2.2 million hectares under cultivation in teak (Ball, Pandey, and Hirai, 1999).

Teak is the subject of selective breeding experiments in Thailand (Kaosaard, Suangtho, and Kjser, 1998). It has been estimated that selective breeding and the establishment of plantations incorporating genetically superior trees could result in improvements in yield of 17% or more. Areas of natural teak forest are being felled when land is converted to agriculture or other purposes. There is concern expressed then that genetic reservoirs that could be used to improve subsequent generations of commercial teak are being eliminated.

Teak breeders have found it useful to establish "provenance trials" in which they grow trees under controlled circumstances in order better to distinguish between genetic (and consequently, heritable) and environmental factors in performance. A provenance trial is an experiment in which teak trees (or other types of organisms) from different regions ("provenances")

are grown under controlled circumstances in order to identify the genetic contribution to the appearance of attributes of commercial importance. A number of such trials have been conducted in Thailand and elsewhere. I will employ data from a long-running experiment on several international provenances conducted in Thailand (Keiding, Wellendorf, and Lauridsen, 1986; Kjaer, Lauridsen, and Wellendorf, 1995; Anderson, 1997).

Such trials collect data on a large number of quantitative and qualitative characteristics of the trees in the sample. As my purpose at present is merely illustrative, I will concentrate only on "commercial height." Commercial height is defined to be the maximum height at which diameter is at least 10 centimeters. More generally, of course, one would care not only about height, but also diameter and, more generally, wood volume, as well as quality of wood. In addition, owners of commercial plantations would want to plant trees that are known to be resistant to infestations and have other desirable survival and input cost minimization properties. Again, however, let us, for simplicity, simply concentrate on commercial height as a measure of yield-per-hectare.

The sample mean and standard deviation are sufficient statistics for normally distributed variables. The mean commercial height among 578 trees from the provenance trial we are considering was 11.6 meters. The standard deviation was 4.0 meters. From these sufficient statistics, we can derive the cumulative normal distribution, its inverse, and the corresponding hazard rate. These figures can then be employed in Eq. (15) above. The remaining variables are N, the number of potential parent organisms, and f], the elasticity of demand. The number, N, is varied in the left-most column of Table 4-1, and the elasticity, r], is varied in the top row of the table. Entries in each cell of the table show, for that number and elasticity, the elasticity of expected social welfare with respect to the size of the size of the genetic base from which selection can occur.

Table 4-1. Elasticity of expected welfare as a function of number of potential parents and elasticity of demand_

Number of potential parents

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