section 4 : measurement and analysis of agroforestry experiments

The design and analysis of experiments to monitor agroforestry systems

S. Langton

Statistics Department
Rothamsted Experimental Station
Harpenden, Herts AL52JQ, England, UK

Abstract

The experimental designs available for monitoring agroforestry systems both on a large scale and for measurement of microclimate will be reviewed. These will include designs for investigating the tree/crop interface as well as conventional field plot trials. Analyses appropriate to the designs will be suggested.

Why design experiments?

A glance through the literature relating to the measurement of microclimate and other environmental variables will reveal large amounts of data which are the results of isolated observations rather than designed experiments. The usefulness of this work could be greatly improved by the use of properly designed experiments incorporating the principles of randomization and replication. Without replication it is impossible to judge whether an observation is an isolated freak result or is typical of the system being studied, and without randomization there is always a risk of bias.

Designs for agroforestry

It must be remembered that the same basic experimental designs are just as appropriate for agroforestry experiments as for other field experiments, and the same analyses are, in general, equally valid whether the variable being measured is yield or is an environmental variable. Thus the need for blocking and other devices to control the residual variation or 'error' still applies in agroforestry experiments, and the advantages of using a factorial design are just as great. Further details on these subjects may be found in any textbook on experimental design (e.g., Cox (1958), which is very readable). In addition the literature on the design of intercropping experiments is of considerable relevance to agroforestry and has been reviewed by Mead and Riley (1981).

It is not, of course, possible to list the best design for every conceivable experiment. Instead I will discuss those designs which seem to have the most potential for use in agroforestry, using the following headings:

• simple designs for investigating the tree/crop (or tree/tree) interface;

• systematic designs for spacing experiments; and

• general designs for agroforestry systems.

Simple designs for investigating the tree-crop interface

Figure 1 shows two designs given in Chetty (1986) which could be used to investigate the interface. The designs should be replicated unless they are purely observational and in the case of Figure la the orientation should be randomized (perhaps with just two possible orientations). In both cases the analysis will involve fitting response curves describing the change in the variable measured with increasing distance from the interface. In Figure la, the effect of orientation could be considered and in Figure Ib, aspect (north, south, east or west).

Figure 1 Two designs for investigating the tree-crop interface:
(a) parallel rows of trees and crops;
(b) concentric rows of crops around a single tree.
Thick lines represent hedges; thin lines, rows of crops.

Systematic designs

Many agroforestry experiments are designed to investigate the optimal plant spacing for a particular system and in this type of experiment traditional, fully-randomized designs have a number of shortcomings. Even where the spacing of only one component of the system is to be investigated, the number of 'treatments' (i.e., different spacings) is liable to be comparatively high and, combined with the need for adequate guard areas to separate the different spacings, this results in an unacceptably large block size for a randomized complete block design. Even when an incomplete block design is used a considerable proportion of the experimental area will be taken up with the guard areas. Secondly the size of the plots needed will depend on the spacing used: closely spaced plants requiring a smaller area. This may create problems in arranging the plots in the field, unless all plots are made the same size as the largest, which again results in a waste of the experimental area.

The solution to these problems is to use a systematic design in which spacing varies in a regular fashion, thus removing much of the need for growth areas. Figure 2 shows two very simple systematic designs for a hedge-crop intercropping situation. Suitably replicated, the effect of spacing could be investigated by examining the change in yield, or any other variable, along the length of the plot by fitting an appropriate response curve. One of the five systematic designs proposed by Nelder (1962) for use in mono-cropping situations is shown in Figure 3. The shape of the area available to each plant is constant, but its size increases radically; another of Nelder's designs varies the shape but keeps the area constant. These four designs suffer from the disadvantage that the crops are not rectangularly arranged, but lie on the arcs of circles. Bleasdale's (1967) parallel row design (Figure 4) avoids this, although at the cost of confounding the effects of area and shape.

Figure 2 Two simple designs in which spacing varies systematically. Thick lines represent hedges; thin lines, rows of crops.

These designs can be adapted to deal with a system involving more than one species in a number of ways. Where it is desired to keep the ratio of the two species constant but vary the overall density a certain proportion of the 'spokes' (radii) can be planted with each species. Planting alternate spokes in a fan design with different crops, for example, will produce the simple design of Figure 2b (although with the within spoke density varying as well as the distance between spokes). Where the density of only one of the species is to be varied it is planted in the positions indicated by the fan design while the other species is planted on the same land at its usual spacing.

Figure 5 provides a design which allows the effect of independent variation of the densities of two crops to be examined. It consists of two parallel row designs arranged at right angles; the scale of the two designs can, of course, be different to allow for differences in size and desired density between the two crops. Analysis is again by examining response curves, but since both densities are varied, the response surface in two dimensions is now of interest. A nearest-neighbour type of analysis, which will be discussed later in this paper, may also be of use in this experiment.

Before leaving the subject of systematic designs a word of caution should be added. These designs were developed by Nelder, Bleasdale and others for use at experimental stations in Britain where the land was known to be fairly homogeneous. They should not be used on land with a trend across it, or on land that has not been studied previously, since any such trend could seriously distort the results. Even where no trends are believed to exist, the experiments should be replicated, with the replications at different orientations; this will in any case help to eliminate factors such as wind funnelling, the effect of which depends on orientation. As long as the design is properly replicated small scale heterogeneity is less important, but will result in differences in the response curves between the replications.

Figure 3 A fan design (Nelder 1962).

Another disadvantage of the designs is that the death of one tree has an effect on the effective spacing of the neighbouring trees. It is therefore important to grow some non-experimental plants of a similar species and age nearby to act as replacements in the event of this occurring. For similar reasons systematic designs are not generally useful when thinning must be carried out during the course of an experiment. Finally it should be noted that while guard rows are not necessary within each replication, they are still needed at the edges and between the treatments where the experiment involves factors other than spacing.

Figure 4 A parallel-row design (Bleasdale 1967). Individual plants are shown only in the central section.

Figure 5 Two superimposed parallel-row designs. Vertical lines indicate rows of trees; horizontal lines indicate rows of crops.

General designs

As was stated above, agroforestry experiments can use the same designs that are used in single-species agronomic or forestry experiments. However, I want in this section to look at one or two more unusual designs which are particularly useful for agroforestry.

Figure 6 shows an example of a nearest-neighbour design; it can be seen that each treatment occurs next to each other treatment (i.e. to the right, left, above or below) on four occasions. Thus any deleterious or beneficial effects of one treatment on its neighbours should balance out. This may permit some reduction in the area needed for guard rows, although it is still preferable to have an adequate guard row in order to minimize such interactions. More complex designs taking account of the relative positions of the treatments are to be found in Freeman (1979). Analysis of these designs can be by the usual methods for Latin squares or special nearest-neighbour methods can be used. The latter form of analysis is still the subject of statistical research, but involves adjusting each treatment by the yield (or whichever variable is being measured) of the neighbouring plots in order to remove the effect of local heterogeneity. Nearest-neighbour analyses are of particular relevance to agroforestry since it may be possible to adjust the yields of one species in a two-species system by the yields of neighbouring plants of the other species.

Designs balanced for neighbours have also been worked out for the situation where plots are arranged in a long strip, so that only two neighbours need to be considered. These designs and their analysis are considered by Dyke and Shelley (1976).

Figure 6 A nearest-neighbour design based on a 5x5 Latin square. The numbers represent five different treatments.

Figure 7 A beehive design. The symbols o and x represent two different species. The full design consists of two hexagons, with the positions of the two species interchanged in the second one.

In most experiments plants are arranged in rows but, if the interactions between individual plants are of interest, a hexagonal grid can be useful and such arrangements have been used in competition experiments. These designs are termed beehive designs and further information about them may be found in Veevers and Boffey (1975) and Martin (1973). An example is shown in Figure 7 in which o and x represent two different species. It can be seen that different plants have different numbers of neighbours of the other species, thus allowing the measurement of competitive effects. Hexagonal designs can be easily adapted to the situation where more than two species are involved and provide a greater number of inter-specific interfaces than in a row layout.

References

Bleasdale, J.K.A. 1967. Systematic designs for spacing experiments. Exp. Agric. 3: 73-85.

Cox, D.R. 1958. Planning of Experiments. New York: Wiley.

Dyke, G.V. and C.F. Shelley. 1976. Serial designs balanced for effects of neighbours on both sides.J. Agric. Sci. 87: 303-305.

Freeman, G.H. 1979. Some two-dimensional designs balanced for nearest-neighbours J. R. Statist. Soc. B. 41: 88-95.

Martin, F.B. 1973. Beehive designs for observing variety competition. Biometrics 29:397-402.

Mead, R. and J. Riley. 1981. A review of statistical ideas relevant to intercropping research (with discussion). J. R. Statist. Soc. A. 144: 462-509.

Nelder, J.A. 1962. New kinds of systematic designs for spacing experiments. Biometrics 18: 283-307.

Veevers, A. and T.B. Bofley. 1975. On the existence of levelled beehive designs. Biometrics 31: 963-967.