DESIGN AND ANALYSIS OF EXPERIMENTS FOR INVESTIGATING COMPETITION EFFECTS

Transcription

1 DESIG AD AALYSIS OF EXPERIMETS FOR IVESTIGATIG COMPETITIO EFFECTS Seema Jaggi I.A.S.R.I., Library Avenue, ew Delhi- 2. Introduction A plant s growth is affected greatly by the size and proximity of adjacent plants. Those surrounded by large and vigorous plants can be expected to produce less than those surrounded by less vigorous ones. Plants a greater distance from one another generally produce more than those nearer to each other. Interdependence of adjacent plants because of their common need for limited sunshine, soil nutrients, moisture, carbon dioxide, oxygen, and so on, is commonly referred to as competition effects. Interference between neighbouring units is a serious source of bias in many field and laboratory experiments. Interference, often interpreted as competition, can occur in different ways even in properly designed arrangements. Understanding the structure of these competition effects helps in minimizing such bias to a great extent. By properly organizing the experimental material, attempts can be made to estimate these competition effects. Field experiments are usually performed to assess the effect of several management factors or genetic factors, or both, on crop performance. The experimental plots planted to different varieties and subjected to different production techniques are commonly placed side by side in a field. As a consequence border plants have an environment different from those in the plot s center: plants in the same plot are exposed to differing competitive environments. The plants adjacent to nonplanted borders have relatively more space. They are, therefore, exposed to less competition than plants in the plot s center. For a given experiment, the significance of any competition effect depends primarily on the treatments being tested and the experimental layout. In trials involving different varieties of a given crop, adjacent plots are planted to different varieties. Because varieties generally differ in their ability to compete, plants in a plot will be subjected to different environments depending upon location relative to adjacent plots. This effect is called varietal competition. Fertilizer competition effect is similar to the varietal competition effect except that adjacent plots receive different levels of fertilizer instead of being planted to different varieties. Here the competition effect has two sources. First, plots with higher fertilizer application will be more vigorous and can probably compete better for sunshine and carbon dioxide. Second, the fertilizer could spread to the root zone of an adjacent plot, putting the plot with higher fertilizer at a disadvantage. Because these two effects are of different direction, their difference constitutes the net competition effect.

2 A missing plant in an experimental plot causes the plants surrounding its position to be exposed to less competition than the other plants. These plants, therefore, usually perform better than those surrounding a living plant. Competition between a crop species and weed species involves another level of complexity. Here the primary interest is in the crop yield as affected from the competition from weed species. Studies on interference between neighbouring units began with the work by Rees (967) on designing of plots to diffusion tests in virus research. These designs were developed considering the facts that an antigen and an antiserum will diffuse through a suitable media and if the antigen in question and the antigen in response to the antiserum have components in common then the first antigen and the antiserum will form a precipitate line at the meeting points of the diffusion areas. The test consists of arranging a set of antigens around an antiserum and observing such precipitates as occurred. The technique used is an arrangement in circles, samples from a number of virus preparations in such a way that the whole set of samples from each virus preparation appear next to a sample from every other virus preparation. Mead (979) has studied the effect of varying number of neighbouring plants on an individual plant as a natural development of physiological approach to understand plant competition. Here the competition is due to the presence of different numbers of neighbours and the differing distances of the neighbours. The competition effects of the neighbours on a given experimental unit (test plot) can be studied by raising the competitors in one or more left and right neighbouring units of the test plot. Introduction of more number of neighbours will increase the complexity by increasing the number of competition effects. In order to reduce this problem the assumption that only immediate neighbours will compete was introduced. The study of a competing situation needs construction of an environment in which it can happen; and the competing units have to appear in a predetermined pattern. As a result one of the important principles of design of experiments randomization cannot be met with full vigour. Initially non-randomized designs were used for such studies, but later, designs permitting restricted randomizations have been evolved. In an experiment involving the competition environment, treatments indicate a variety of a crop or genotype, different doses of nutrients, different fungicides etc. The treatments are applied to plots. The effect of a treatment applied to a given plot is also influenced by the treatments applied to its left and right neighbour positions. Hence in experiments on competition studies, the effect of a treatment applied to a plot can be written as the sum of (i) Direct effect due to the treatment applied to a given plot (ii) Left neighbour effect due to the competition with the treatment applied to the immediate left neighbour plot and (iii) Right neighbour effect due to the competition with the treatment applied to the immediate right neighbour plot. 66

3 Therefore the competition treatment can be thought of as an ordered triplet. In order to save resources these triplets are joined together to get a sequence, such that a treatment applied to a plot can be used both for providing direct treatment effect and also neighbour effects. Such sequence of the chosen triplets will provide the design for competition experiment in the minimum number of plots. Blocks of these competition designs are the sets of these triplets arranged in sequence. Thus as in the case of block designs, the designs for competition effects consists of treatments, in the form of triplets. When the number of chosen triplets is large, the sequence will also become large and as such accomodating the complete sequence would result in increase in error variance. Incomplete sequences similar to incomplete blocks can be adopted. Martin (973) has developed Beehive designs in which plants of two species are arranged on a hexagonal grid such that for one species the number of neighbouring plants of the second species varies between zero and six. These designs allow the experimenter to carry out the investigations in a much smaller area and each plant is either a recorded plant or a competing plant. Dyke and Shelly (976) introduced the term Serial designs for designs that allow the independent estimation of the effects of treatments to neighbouring plots and have constructed serial designs based on computer programmes. The aim of the experiments was to study interference between plots with regard to spread of diseases. onrandomized designs were attempted in which treatments appear repeatedly in one or more chosen orders. For a particular case of four treatments the designs had the following properties. (i) Every possible ordered set of three treatments (excluding repeated treatments) occurs exactly once i.e. all sets such as ABA and ABC were included, but sets like AAB, BAA etc. were excluded. There were 36 distinct ordered triplets. (ii) The 36 ordered sets were arranged in a design of 38 units in a sequence. (iii) Omitting the first and the last plots the remaining plots were divided into nine sets of four consecutive plots each set containing A,B,C and D once. Jenkin et al. (979) have investigated interactions between plots of spring barley with four spray treatments using the serially balanced design described by Dyke and Shalley (976). The following layout shows the first nine plots of balanced designs with four spray treatments (O = unsprayed, E = early, L = late, R = repeatedly), D O L R O E O E L R D is a dummy plot to provide the left-hand neighbour to plot. 66

4 Following are the triplets occurring in the nine plots: O L R L R O R O E O E O E O E O E L E L R The experiment comprised of 38 plots arranged in a single line. The plots at each end of the line were dummies (to provide left-and right-hand neighbours to plots and 36 respectively); their yields were disregarded. The 36 plots included in the analysis were grouped in nine blocks of four. The experiment was, therefore, treated as block design. Each strip of 38 plots gives 36 relevant yields and each of these corresponds to one of 36 treatments in terms of triplets (denoted by ABC say). Lin et al (985) introduced a similar treatment sequence and computer aided non random designs. It was assumed that the neighbour effects were the same for the left and right hand side arrangements on the test plot i.e. sequences BAC and CAB produce equal neighbour effect on the treatment A. Thus the total number of competition treatments for four treatments is 4. Subramanyam (99) used 6 units in a sequence for four treatments. To reduce the number of triplets, triplets of the type AAA and ABA or BAB were used. Of the v 2 treatments, (v+) C 2 were chosen and arranged in v blocks, each comprising 3 v+ C 2 units. Azais (993) obtained a series of designs that are balanced in t - blocks of size t and t blocks of size t-, where t is the number of treatments. The block design for studying competition effects is balanced in the sense that every treatment has every other treatment appearing once as a right and once as a left neighbour. When the neighbour effect is present on one side only say from left-hand side, as caused by a prevailing wind, simply omit the right - hand border plot from every block. This situation includes change over experiments. Following is a complete block design for 5 treatments balanced for neighbouring competition effects Incomplete block design for 4 treatments in 4 blocks of size 3 each. 662

5 Jaggi et. al. (22) obtained some complete block designs that are partially balanced for neighbouring competition effects 2. Measuring Competition Effects Because the type and size of the competition effects can be expected to vary considerably from crop to crop and from one type of experiment to another, competition effects should be evaluated separately for different crops grown in different environments. Measurements of competition effects can be obtained from experiments planned specifically for that purpose or from those set up for other objectives. 2. Experiments to Measure Competition Effects Experiments can be set up specifically to measure competition effects by using treatments that simulate different types of competition. At least two treatments, representing the extreme types of competitor, should be used. For example, to evaluate fertilizer competition effects, use a no-fertilizer application and a high-fertilizer rate to represent the two extremes. For varietal competition, use a short and a tall variety, a high-tillering and a low-tillering variety, or an early-maturing and a late-maturing variety. When resources are not limited, intermediate treatments can be included to assess the trend in the effects under investigation. For example, to find out whether border effects are affected by the width of an unplanted alley, test several sizes of unplanted alley. Experiments specifically set up to measure competition effects have two distinctive features:. Because the competition effects are usually small relative to the treatment effects in the regular experiments, the number of replications is usually large. 2. The plot size that is optimum for the regular experiments may not necessarily be optimum for experiments to measure competition effects. First, the unit of measurement is usually the individual rows, or individual plants, rather than the whole plot. Second the plot must be large enough to ensure sufficient number of rows (mostly in the center of the plot) that are completely free of competition effects. Fertilizer Competition A fertilizer competition is illustrated with a rice experiment to study the effects of applying two widely different nitrogen levels on adjacent plots separated by a 4-cm nonplanted alley. Fertilized ( kg /ha) and unfertilized 28-row plots are arranged systematically in an alternating series. There are a total of 6 plots. Each plot is bordered on one side by plot of the same nitrogen level (control) and on the other side by plot of a different level as shown in the figure. Grain yields are determined from the center 5 hills of each of the 28 rows per plot. The first and the last unfertilized plots are excluded 663

6 from the determination of grain yield. Out of the 4 plots harvested, six are unfertilized plots and eight are fertilized plots. Each 28 row plot is divided into two parts, each consisting of 4 row positions with row being immediately adjacent to the adjacent plot, and so on. Fig. : Field layout of a nitrogen competition experiment involving unfertilized and fertilized plots The analysis of variance is performed, separately for the fertilized plots and the unfertilized plots, following the standard procedure for a split-plot design with plots as replications, the two nitrogen levels of adjacent plot as main-plot treatments and the 4 row positions as subplot treatment. The results, with suitable partitioning of sums of squares, are shown in Table. Source of Variation Between plots Adjacent nitrogen rate () Error (a) Row position (R) R: Row vs. inside rows R2: Between inside rows X R X R X R2 Error(b) CV(a), % CV(b), % Total Table : Analysis of Variance Unfertilized plots Degree of Mean Freedom square α 5 8, , ,49** () 823,862** (2) 2, ,27** () 62,732** (2),32 ns 3 2, Fertilized Plots Degree of Mean Freedom square α 7 3, , ,832** () 694,894*** (2), ,695 () 2,2* (2) 3, , α ** α significant at % level, * = F test significant at 5% level, α F test not significant. Some differences between row positions are expected because of the 4-cm nonplanted alley used to separate adjacent plots. Thus, the presence of fertilizer competition effect is indicated only by the presence of the interaction between row position and adjacent nitrogen rate. Results show significant interaction between row position and adjacent nitrogen rate, indicating the presence of fertilizer competition effect. The competition effects, however, 664

7 were confined only to the outermost row (row ): the outermost row of the unfertilized plot adjacent to a fertilized plot gave significantly higher grain yield than the outermost row adjacent to a similarly unfertilized plot as shown in table2. Likewise, the grain yield of the outermost row of a fertilized plot adjacent to a unfertilized plot was significantly lower than that adjacent to a similarly fertilized plot. Table 2: Fertilizer competition effects as affected by the rate of fertilizer applied in adjacent plots itrogen Rate of Adjacent Mean Yield, g/m 2 a Plot, kg/ha Row Inside Rows (control) Difference (control) Difference Unfertilized plots ** Fertilized plots * ns ns a Inside are average of thirteen row positions; ** = significant at % level, * = significant at 5% level, ns = not significant. 2.2 Experiments Set up for other Purposes Any experiment undertaken for other purposes, such as fertilizer trials or variety trials, can also be used to test or measure competition effects. Because division of plots into subsections is an integral part in measuring competition effects, the experiments suited for this purpose are those having relatively large plots. For example, in experiments where the plants are grown in rows, and both sides of a plot are subjected to the same type of competition effect, a plot can be subdivided into a pair of outermost rows, a pair of second outermost, and so on, up to the center rows. Figure2 shows a plot consisting of rows divided into five row positions: R refers to the outermost pair of rows, R 2 the second outermost pair, and so on. For crops not planted in rows, area delineation can be used. 665

8 Fig.2: Sub division of -row plot for measuring competition effects Measurements of plant response, such as grain yield, are then made separately for each subunit (i.e., row position or area delineation). Because subunits in each plot differ primarily in their exposure to competition, their differences measure the competition effect. Apart from quantifying competition effects, this procedure also measures the interaction between competition effects and treatments that are tested in the experiment (i.e., varieties, fertilizers, etc.). The measurement of competition effects indicates whether certain rows or subunits are favored or are at a disadvantage because of their plot position, and the interaction shows whether such effects are consistent from one treatment to another. Large production plots or uniformity trials are usually subdivided into blocks using nonplanted alleys as markers. In such plantings, the effect of nonplanted alleys can be evaluated by comparing the performance of the outermost rows with the center rows. However, nonplanted alleys for such plantings are usually wide and because the effects in certain crops such as rice become larger as the nonplanted alley becomes wider, such a study could result in a much larger effect than that actually existing in a standard field experiment. evertheless such a study can be used as a guide for planning a more detailed study. For illustration, grain yield data collected from the border rows of a rice uniformity trial is presented. The nonplanted alley surrounding the experimental area was about m wide. Hill spacing was 2 X 2 cm. From the perimeter of the trial, grain yield data was collected from a total of 22 sections each 3 hills long. In each section, five successive rows starting from the nonplanted side were harvested separately. The data are presented by row positions in Table3. 666

9 Table 3: Grain yields of rice (IR8) from five successive rows a adjacent to nonplanted alley Section Grain Yield, g/3 hills umber Row Row 2 Row 3 Row 4 Row 5 Average 2, ,89 2, , , , , , , , , , , , , , , , , , ,46 Average, a Row refers to the outermost row, row 2 the second outermost row, and so on. The analysis of variance to test differences between the row positions is shown in Table3. The computation of this analysis of variance followed the procedures for randomized complete block design with the section treated as replication and row position as treatment. The results indicate a highly significant difference between yield of the outermost row (row ) and that of the four inside rows, but there was no significant difference between the yields of the four inside rows. That is, the effect of the -m nonplanted alley was shown to reach only the outermost row. 667

10 Table 4: Analysis of Variance Source of Variation Replication Row position Row vs. inside rows Between inside rows Error Total Degree of Freedom 2 4 () (3) 84 9 Mean Square 24,65 3,59,49 4,64,766 4,289 8,58 F 9.5** ** < Analysis of Designs for Competition Experiments The fixed effects model of response assumed for the designs for competition effects in a block design setting is as follows. y uivj = µ + t + β + l + r + e, u=i=v=,2,,s; j=,2,,b; i j ui iv uivj where y uivj is the response of the i th treatment with left treatment u and right treatment v appearing in the j th block of a design. µ is the general mean, t i is the effect of the i th test treatment, is the effect of the j th block. l ui is the effect of the u th treatment on the left of β j the i th treatment, r iv is the effect of the v th treatment on the right of i th treatment. E uivj are 2 error terms independently and normally distributed with mean zero and variance σ. The analysis of variance table for the block design for competition experiments is as follows. AOVA Source of variation Degrees of Sum of Squares freedom Blocks b- R(β/µ) R(µ) Treatments s(2s-)- R(t, l, r/ µ, β) Test treatments (Adjusted s- R(t / µ, β) for blocks) Left neighbours (Adjusted for s(s-) R(l / µ, β, t) blocks and test treatments) Right neighbours (Adjusted s(s-) R(r / µ, β, t, l) for blocks, test treatments and left effects) Left neighbours (Adjusted for s(s-) R(l / µ, β, t, r) blocks, test treatments and right effects) Right neighbours (Adjusted s(s-) R(r / µ, β, t) for blocks and test treatments) Error n-b-s(2s-)+ Total n- Y Y R(µ) 3. Control of Competition Effects 668

11 Competition effects can be a major source of experimental error in field experiments. At times, competition effects may even alter the treatment comparisons for example, in variety tests where the competition effect favors certain varieties more than others. The need to minimize, if not entirely eliminate competition effects in field experiments is clear. 3. Removal of Border Plants Because the effects of varietal competition, fertilizer competition, and nonplanted borders are usually shown only on plants in the outer rows, an obvious solution is to exclude those form plot measurements. The width of borders or the number of rows (or plants) to be discarded on each side of the plot depends primarily upon the size of competition effects expected. In general, competition between plots is greater in grain crops where plant spacing is narrow. 3.2 Grouping of Homogeneous Treatments Because competition between adjacent plots in a variety trial is magnified by large morphological differences of test varieties, and in a fertilizer trial by large differences in the fertilizer rates applied, an obvious remedy is to ensure that adjacent plots are planted to varieties of fairly similar morphology or are subjected to similar fertilizer rates. In the case of variety trials, this could be done by grouping together varieties that are fairly homogeneous in competition ability, and use a Group balanced block design. In the case of fertilizer trials, fertilizer is generally tested together with several varieties or several management practices, in a factorial experiment. The use of a split-plot type of designs with fertilizer as main-plot factor would allow the grouping together of plots having the same fertilizer rate and thus minimize fertilizer competition. References Azais, J. M., Bailey, R. A. and Monod, H. (993). A catalogue of efficient neighbour designs with border plots. Biometrics, 49: Jenkin, J. F., Bainbridge, A., Dyke, G. V. and Todd, A. D. (979). An investigation into inter-plot interaction in experiments with mildew on barley, using balanced designs. Ann. Appl. Biol., 92: -28. Dyke, G.V. and Shelly, C.F.(976). Serial designs balanced for the effect of neighbours on both sides. J. Agric. Sci., 87, Jaggi,S. Gupta,V.K. and Ashraf,J. (22). Block designs partially balanced for neighbouring competition effects. Aust. & ew Zealand Jour. of Statistics. Communicated Lin,C.S., Poushinsky,G. and Voldeng, H.G.(985). Design and model for investigating competition effects for neighbouring test plots. Can. J. Plant Sci., 65, Martin, P.B.(973). Beehive designs for observing variety competition. Biometrics, 25, Mead, R.(979). Competition experiments. Biometrics, 35,

12 Rees, D.H.(967). Some designs of use in serology. Biometrics, 23, Subramanyan, G.S.V.(99). Modified serial designs for the effect of intergenotypic competition in cultivated species. Proceed. ational Symp. Statist. Method for Dryland Agric., CRIDA, Hyderabad,