Multiple Periods with Recharge

Plant breeding programmes have developed several types of recharge mechanisms.9 These include:

1. Genetic resource collection and evaluation programmes. These programmes are designed to discover uncollected materials and make them available to breeders.

2. Pre-breeding programmes where landrace materials are systematically combined into potential breeding lines by specialized research programmes. These programmes do not seek to develop 'final products' (i.e. new cultivars). Instead they seek to evaluate and produce 'advanced lines' that are then used by final product inventors.

3. Wide-crossing programmes where techniques for inter-specific combinations of genetic resources (between related species) are made possible. This expands the size and scope of the original materials that can be utilized in breeding programmes.

4. Transgenic breeding programmes where DNA insertion techniques allow traits associated with alien genes (i.e. from unrelated species) to be incorporated into cultivated plants.

These programmes are 'pre-invention' science or recharge science programmes. They provide recharge to the invention distributions by shifting both the mean and the right-hand tail of the search distribution.

Figure 1.4 depicts the nature of these shifts for search distributions and IPFs with recharge. Note that the TD point moves with recharge. The reader can readily see that one could have cases of 'super-recharge' for a number of periods where inventions per inventor might increase over time (e.g. in sugarcane breeding; Evenson and Kislev, 1975). But recharge science itself is likely to be subject to diminishing returns, unless it is also recharged by the more basic sciences. (See below for a discussion of this issue.)

These ideas can be clarified with a little algebra. Describe the breeding (invention) process as:

Fig. 1.4. Multi-period search with recharge.

This system of equations describes the incorporation of traits as a function of germplasm Gi and breeding activity B. The functional form is based on the search model.10

It is relatively straightforward to show that the first-order condition for allocating breeding research between any two traits is:

Bj~ XJGJVJ

where Vt and V. are measures of the marginal contribution to crop value of traits i and j. (Note that each trait may appear in several varieties and that each variety may be planted to different areas.)

Now consider the production of germplasm (Gi). This is characterized as being produced in a pre-breeding process:

In this pre-breeding process, pre-breeding activity converts evaluated genetic resources Gc into germplasmic breeding materials. This process is also a search process. Again, the first-order conditions for pre-breeding activities are straightforward:

Evaluated germplasm is produced by the natural stock of genetic resources (Gn) and collection (C) and evaluation (E) activities

The following features of this simple model can be noted:

In plant breeding, if the marginal search coefficients are equal (X1 = X.), the breeding activity obeys 'the congruence rule' where inventive activity is proportional to the value of the units affected (see equations (14) and (16)).

Departures from congruence (a strong form of induced innovation) are justified when search parameters differ.

It can be further noted that the optimal conditions for pre-breeding (or germplasmic recharge science) (equation 15) also imply that if the germplas-mic search coefficients are equal, then congruence occurs for both pre-breed-ing and breeding. This is a strong form of multi-period-induced innovation. The multi-period invention path is a ray from the origin (if prices do not change) that is parallel to the TD expansion path. A change in prices (values) will result in a change in the invention path and in the TD path (Fig. 1.4). Both will have the same slope.

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