• TABLE OF CONTENTS
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 Abstract
 Introduction
 Materials and methods
 Results and discussion
 Conclusion
 Acknowledgement
 Reference
 Tables and figures














Title: Making the most of modified stability analysis
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Title: Making the most of modified stability analysis
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Creator: Russell, John T.
Publisher: Food and Resource Economics Dept., Institute of Food and Agricultural Sciences, University of Florida,
Publication Date: 1990
Copyright Date: 1990
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Table of Contents
    Abstract
        Page 1
    Introduction
        Page 2
        Page 3
        Page 4
    Materials and methods
        Page 5
        Page 6
    Results and discussion
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
    Conclusion
        Page 15
        Page 16
    Acknowledgement
        Page 17
    Reference
        Page 18
    Tables and figures
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
Full Text



1 Making the Most of Modified Stability Analysis:

2 Finding "Best Fit" Regressions and Determining Specific Adaptation

3 to Recommendation Domains 1

4 by

5 John T. Russellt, Peter E. Hildebrand*, and Clifton K. Hiebsch' 2

6

7 Abstract

8 Modified stability analysis is a simple, powerful and flexible tool in the analysis of on-farm trials. As currently

9 used, however, too much emphasis is often placed on the rote calculation and graphical representation of linear

10 regression on an environmental index, on the statistics (R2, etc.) associated with the regressions, and on finding the

11 "most stable" treatment, variety, practice, etc. In addition, final "recommendation domains" are sometimes simply

12 described as high- or low-yielding (or "good" or "poor") environments, with little attempt to relate these

13 characteristics to environmental characteristics that farmers and extension personnel can identify prior to planting.

14 These practices tend to limit the practical usefulness of modified stability analysis. An example of modified stability

15 analysis of four years' data from on-farm sorghum variety tests in North Cameroon is used to illustrate several steps

16 to ensure getting the most useful information from the method. These steps include the plotting of data points, by

17 treatment, the comparison of various regression models, and the association of environmental index with non-

18 experimental environmental variables. Emphasis is placed on identifying technologies specifically suited to

19 particular recommendation domains, and not broadly adapted to (or stable over) all environments.

20

21


22 Contribution from the Institute of Food and Agricultural Sciences, Univ. of Florida, Gainesville, FL, 32611,
23 Journal Series R-03513. Research supported by Institute of Agronomic Research, Republic of Cameroon, and
24 United States Agency for International Development (ACPO/SAFGRAD and NCRE/IITA).

25 2 t Zanzibar Smallholder Support Project, Ministry of Agriculture, Box 159, Zanzibar Town, Tanzania.
26 t Corresponding author; Department of Food and Resource Economics, P.O. Box 110240, University of
27 Florida, Gainesville, Florida, 32611-0240, USA.
28 Department of Agronomy, University of Florida, Gainesville, Florida, 32611, USA.









1 Introduction

2 Modified stability analysis (MSA) is increasingly used by farming systems research

3 practitioners for the analysis of on-farm trials (Hildebrand, 1984; Hildebrand and Poey, 1985).

4 Its strength is that it allows, through simple regression analysis, evaluation of treatment-by-

5 environment interactions of on-farm trial treatments and identification of specific adaptation of

6 treatments to particular groups of farmers and environments, i.e., to specific recommendation

7 domains (Hildebrand, 1990).

8 As currently employed, however, its usefulness is often limited. It is sometimes used

9 as if it were a simple stability analysis, to determine which variety, treatment, practice, etc., is

10 most "stable" across all on-farm trial sites. The implication is that the most broadly adapted,

11 or most stable variety or treatment is the superior one. In fact, the use of MSA to determine

12 specific adaptation to particular environments, rather than broad, general adaptability, is a major

13 reason the method is said to be "modified" stability analysis. Even when specific adaptation is

14 recognized as a goal of the analysis, frequently little more is drawn from the analysis than that

15 some treatments are better in "good" environments and others better in "poor" environments.

16 Further, too much emphasis is given to reporting, comparing, and discussing regression

17 statistics such as the slope (b) and coefficient of determination (R2) of the various regression

18 lines. These statistics are at best problematic, given the well-known logical difficulties with this

19 type of regression of "dependent" variables on an independent variable directly derived from and

20 correlated to them (Freeman, 1973). They are also largely irrelevant to the purpose of

21 determining specific adaptation, at least in determining whether and how to delineate separate

22 recommendation domains.







3

1 Conversely, it is unusual that concerted attempts are made to identify and analyze the

2 important environmental characteristics that determine the goodness or poorness of the trial

3 environments. More seriously, too little attention is paid to determining which environmental

4 variables can be identified by farmers and extension personnel to decide the recommendation

5 domain into which a given farm environment will fall. If farmers knew before planting, whether

6 their field would be "high-yielding" or "low-yielding," domains could reasonably be delineated

7 along these lines. But farmers can rarely predict, at least in the semi-arid tropics where widely

8 variable rainfall causes large fluctuations in yield, whether the yield from any given field will

9 be above or below a given threshold of average yields. Recommendations to farmers should be

10 made on the basis of some characteristics) of their environment that farmers can identify

11 beforehand. Finally, users of MSA need to assess better the degree to which the environments

12 chosen for a trial are representative of the range of environments in the research domain.

13 After recommendation domains are decided upon, recommendations within a domain are

14 often made on the basis of differences between the predicted regression lines within each

15 domain. Those predictions, however, are based in part on data in the other domain(s). It is

16 preferable (both more honest and more accurate), once domains are determined by comparison

17 of the regression lines over environments, to analyze the results by recommendation domain.

18 This allows determination not just of mean differences among treatments within a domain but

19 also of the variability, error, and risk associated with those estimates of mean differences. The

20 present paper addresses these concerns and presents a number of guidelines and ideas for getting

21 the most information out of modified stability analysis of on-farm agronomic trials. It attempts







4

1 to illustrate an effective series of steps in MSA, using data from a series of multi-year on-farm

2 sorghum variety trials in North Cameroon.

3 The case used in this paper involves the development, testing, and extension of an

4 improved, short-cycle, photoperiod-insensitive sorghum variety, S35. This variety was tested

5 during four years of on-farm "pre-extension" tests. These tests, conducted in a vast area called

6 the Center North Zone, were a collaborative effort between the parastatal cotton development

7 agency SODECOTON and Cameroon's Institute of Agronomic Research (IRA). Despite

8 promising results in the on-farm tests and extensive recommendation of S35 by SODECOTON

9 throughout the Center North Zone, widespread adoption never occurred. It was remarked that

10 in some areas .35 was much in demand and well adopted. In other, more numerous areas,

11 however, the variety was poorly accepted by farmers. In effect, there were at least two

12 recommendation domains for the variety S35.

13 Analyses presented here were initially undertaken to determine if use of MSA could have

14 predicted and avoided the loss of time, expense and effort of extending this variety throughout

15 an entire research domain when in fact it was adapted to only a part of the domain (Russell,

16 1991). The results illustrated clearly the importance of the concerns with MSA listed above,

17 including finding the best fit of the response across environments, conducting adequate

18 environmental characterization, and ensuring representativeness of the sample of trial

19 environments.









1 Materials and Methods

2 A data set was compiled containing yield, date of seeding, and rainfall data from 239 on-

3 farm varietal trials of an improved short-cycle sorghum variety compared to locally adapted

4 traditional varieties. These trials took place in North Cameroon from 1984 to 1987 (Testing and

5 Liaison Unit, 1986; Testing and Liaison Unit, 1987; Johnson, 1988). Each trial included other

6 varieties; the present analysis, however, concerns only the data on S35 and locals. Tests in 1984

7 were done in two geographical groups, while in 1985 there were in two groups with different

8 target ranges of seeding dates. In 1986 there was just one set of tests. All tests in 1984, 1985

9 and 1986 had one replicate per on-farm site. In 1987 one set of tests had a single replicate per

10 test site and another set had two replicates; for the analyses presented here, the yields of those

11 tests with two replicates were averaged over replicates.

12 The treatment called "locals" was not a single variety; each collaborating farmer selected

13 a locally adapted variety as a local check. Given the huge number of local sorghum types in

14 North Cameroon, and their diversity and local adaptation, this approach was preferable to

15 imposing one local type on all farmers, some of whom had never grown and would never grow

16 it.

17 Each on-farm test was conducted on a 0.25-hectare field (i.e., 50 m X 50 m), with a

18 collaborating farmer chosen by the local SODECOTON field extension agent, and monitored

19 throughout the season by that agent. Between-row spacing was 0.80 m; within-row spacing was

20 0.40 m between hills. Plants were thinned, beginning seven days after planting, to two per hill,

21 resulting in densities of 62,500 plants ha1'. In 1984, seeding dates were 20 June to 10 July,

22 choice of preceding crop was left to the farmer, and all sites were fertilized with 61-13-25 kg







6
1 N-P-K ha'1. In 1985, fertilizer was reduced to just 46 kg N ha-1, and all sites had cotton as the

2 preceding crop. Test conditions in 1986 and 1987 were as in 1985 except that recommended

3 date of seeding was 10 to 20 June, to avoid favoring the early maturing, improved varieties

4 (Johnson, 1988). Means and standard errors from analysis of variance of these trials, as well

5 as mean rainfall and mean date of seeding, are presented in Table 1. Standard errors for each

6 test group were calculated from the yields of all varieties tested in that group.

7 Modified stability analysis was performed both on the combined data set and also by

8 year. The goals of the analysis were 1) to examine the structure of the variety-by-environment

9 interaction across farm environments; 2) to determine if more than one recommendation domain

10 existed for these varieties; 3) to determine those variables identifiable before planting which

11 could serve to predict in which recommendation domain a given farm environment would

12 belong; and 4) to determine whether MSA--had it been done in any one or two of the four years

13 of trials--might have predicted the patterns of S35 adoption actually seen.

14 The yield data for S35 and locals were plotted against environmental index (EI), i.e., site

15 mean, over years and by year. Linear regressions of yield of each variety on EI were done, as

16 were quadratic regressions and quadratic regressions constrained to pass through the origin. The

17 resulting response lines were compared, both visually and statistically.

18 Based on the regressions of the two varieties, tentative recommendation domains based

19 on low or high average site yields were identified. Linear regression of EI on rainfall and date

20 of seeding--the only two non-experimental variables common to the data sets of all four years

21 of trials--was done to see if recommendation domains could be established on the basis of date

22 of seeding or of average annual rainfall. Analysis of variance was performed, by







7
1 recommendation domain, with domains based on mean date of seeding. Assessment of risk

2 associated with the two varieties was done by calculating and graphing the distribution of lower

3 confidence limits for the mean of each variety in each domain. Finally, mean dates of seeding

4 were calculated, by SODECOTON sector (the smallest SODECOTON administrative division),

5 to determine if average date of seeding corresponded to known patterns of adoption.

6

7 Results and Discussion

8 Linear regression over four years

9 The difficulty with analyzing the results of these varietal trials derives from there being

10 an important variety-by-year interaction. In 1984, S35 yields were far higher than yields of

11 locals, and in late-seeded tests in 1985, S35 yielded over 20% more, although this difference

12 was not statistically significant at a = 0.05. In all other tests, yields of S35 and locals were

13 essentially the same (Table 1). The reason for these differences is that 1984 was a very low-

14 rainfall year. On the basis of this fact, S35 had been extended as a "drought tolerant" variety.

15 The 1984 tests, however, were also characterized by generally late seeding dates (Table 1), in

16 part because of late onset of rains in many areas, but also because of logistical difficulties in this

17 first year of tests. The rainfall and date-of-seeding factors are confounded in the general "year

18 effect" in combined analysis of variance of these trials.

19 A scatter plot of the data from the 1984-1987 tests is presented in Figure la; linear

20 regressions from modified stability analysis of S35 and locals yields in the 239 on-farm

21 environments are presented in Figure lb. The predicted responses of the two varieties converges

22 in the range of high Eis; they diverge as EI approaches zero. In the range 0 < EI < 250, the







8
1 predicted yield of locals is less than zero. We know this cannot be the case. First, yields

2 obviously cannot be negative; second, and more to the point for study of MSA, any "true"

3 picture of a response on El must have regression lines that converge at the origin. This axiom

4 derives simply from the nature of the calculation of El as the average of the yields of individual

5 treatments; that is, when El = 0, yield of each variety must also equal zero. The data points

6 themselves obviously converge at the origin (Figure la). Comparing Figures la and lb, another

7 shortcoming of the linear regressions is evident; they do not accurately reflect the divergence

8 and greatest difference between S35 and locals yields in the range 500 < EI < 1500.

9 Before investigating how better to estimate the response of these two varieties across EI,

10 a comment about statistics is appropriate. Note that the mean square deviations from regression

11 are identical for the two varieties. This again is an inescapable statistical artifact of the nature

12 of this analysis; when only two treatments are involved in MSA the calculated regression lines

13 will be "mirror images" of each other, on either side of an "average" response line with a slope

14 of one. This relationship is not so clear with three or more treatments, although the mean of

15 the slopes of all the regression lines will still equal one, but it must never be forgotten that all

16 statistics in this type of regression are highly dependent one on the others and of little intrinsic,

17 absolute value. Similarly, when there are only two treatments in MSA, the sum of the slopes

18 of the two linear regression lines will equal two (since the mean of their slopes equals one).

19 Given that R2 is a simple function of slope, when two regression estimates have equal

20 deviations from regression, i.e., the same "goodness of fit," the one with the greater slope will

21 have a proportionately greater R2 as well. For this reason alone, R2 is of dubious value for

22 comparing the fit of regression estimates of different treatments. If the purpose of MSA were







9
1 to arrive at statistics for regression lines or to do tests on those statistics, such as testing the

2 significance of the difference of the slope from zero, these mathematical anomalies would be

3 important. They are, however, of little concern since the purpose of MSA should not be to

4 generate statistics but to get as accurate a picture as possible of the underlying "structure" of the

5 treatment-by-environment interaction to determine if different treatments are specifically adapted

6 to different environments, i.e., if there are different recommendation domains.

7 When there are more than two treatments, the kind of scatter plot in Figure la, with all

8 data points plotted together, is often too cluttered to be of use. A better way to check the fit of

9 a proposed regression estimate is to plot the data and then superimpose the regression line for

10 each treatment separately, as in Figure 2. In Figure 2a it is evident that the simple linear

11 regression prediction overestimates yield of S35 in the range 0 < EI < 500 (as expected) and

12 underestimates yield in the range 500 < El < 2000. In general, though, the estimate is

13 reasonably good, i.e., deviations from predicted yields are more or less symmetrical about the

14 regression line, through the entire range where EI > 1000. An alternative method of checking

15 for goodness of fit is to plot deviations from regression against the environmental index.

16 It would appear, then, that some sort of curved response, bowing upward in the case of

17 S35 and downward for locals, would be a better estimate of the response of yields across EIs

18 than is a straight line. How does one find the best curved response? Two alternatives, the

19 response of yield calculated as a quadratic function of EI, and as a quadratic function of El with

20 the Y-intercept restricted to pass through zero, were calculated. The three models were

21 essentially equal; for S35, R2 for the quadratic function was 0.842 and for the constrained

22 quadratic function was 0.839, compared to 0.842 for the linear model. While R2 is of little







10
1 value for comparing regressions of different treatments in MSA, as explained above, it can be

2 valuable for comparing different regression models for a given treatment. Visual comparison

3 of graphs of the three regression lines also showed little advantage of the quadratic functions

4 over the simple linear one.

5 For the purpose of determining potential recommendation domains, the linear regressions

6 in Figure lb, then, are as good as any. Given that we know mathematically that the lines must

7 converge toward the origin at very low Els, we can still posit that S35 yields are greater than

8 yields of locals in low-yielding environments, but that this difference becomes much smaller in

9 high-yielding environments. Of particular significance is that the superiority of S35 represents

10 a large difference in proportional terms (50-100% increases) in low-yielding environments, but

11 represents only a small proportional difference in high-yielding ones.

12

13 Linear regression by year

14 Was it necessary to do four years of testing to arrive at this result? Could the same

15 relationship of S35 and locals yields have been seen using MSA with only one or two years of

16 testing? Had MSA been done on the results of the first year's tests in 1984, the simple linear

17 regressions on El would appear practically the opposite of those over all four years. The 1984

18 data result in regression lines that converge near zero (as expected logically), but that diverge

19 at high Els (Figure 3b). It is not at all apparent from the data points plotted together on El

20 (Figure 3a) that a quadratic response, converging toward El = 0, would have been chosen over

21 a straight line response. In addition, R2 values for the quadratic and constrained quadratic

22 functions are practically no different than that of the linear function. Predicted yields from these







11
1 two estimates indicate, despite a high-end convergence, that S35 would be greatly superior to

2 locals across the range 500 < EI < 3000 (Figure 4a), rather than in a more restricted, lower

3 range, as seen in the 1984-87 data set (Figure la).

4 The key to the difference between the regressions of the 1984 data and of the entire data

5 set is the range and distribution of environments (Els) on which the regression is done. For all

6 four years there is a wide, evenly distributed range of Els from almost zero to 3500, with broad

7 concentrations from 500 to almost 3000 (Figure lb). The range of Els in 1984 is much more

8 weighted toward low values, concentrated from 500 to 1500, but with a relatively high

9 proportion less than 500 and very few above 2000. Taking into account these differences in the

10 distribution of the sample of environments, it can be hypothesized that the primarily linear

11 response of yields across a range of environments weighted toward low- and average-yielding

12 Els diverges as El increases, while the response across a range of environments weighted toward

13 average- and high-yielding Els converges as El increases (Figure 4b). This hypothetical picture

14 of the response appears to fit the plotted data for all four years (Figure la) better than any of

15 the standard regression functions proposed. This sort of segmented response can be estimated

16 using a segmented linear models technique available in some sophisticated statistical software

17 packages. It is possible, of course, that the yield of one treatment, e.g., of the locals in our

18 present example, could intersect the X axis at an EI value well above zero (and therefore equal

19 zero from that point downward to El = 0). When there are only two treatments, the slope of

20 the other treatment would equal two from that point down to EI = 0.

21 Comparing the simple linear responses of S35 and locals on El for 1985, 1986 and 1987

22 to those for 1984 and for 1984-87, and to the hypothetical two-phase response, there is







12

1 considerable evidence of the importance of the range and distribution of environments. In 1985,

2 when environments were evenly and broadly distributed over a range from 500 to 3000, with

3 only one or two either above or below this range, the responses were essentially parallel, with

4 only the slightest convergence toward high Els (Figure 5). With a similar range and distribution

5 of El in 1986, the responses of S35 and locals to environment were practically identical. In

6 1987, when'distribution of El was weighted even more toward the high end of the range, and

7 with only one environment with El < 1000, the response lines were very similar, with a slight

8 cross-over in the high range of EI.

9 From comparisons of MSA by year, the hypothesis of different linear responses across

10 different ranges of EI, illustrated in Figure 4b, can be refined. It can be hypothesized, for

11 example, that in a range of low-yielding environments the linear responses of S35 and locals on

12 EI converge toward 0, that in a middle range of environments the slopes of the regression lines

13 are more or less parallel, and that in a high range the lines would converge toward very high

14 Els. This hypothesis is strongly supported by doing MSA on selected, overlapping low-,

15 middle-, and high-EI subsets of the four-year, 239-observation data set (Table 2).

16 It should be clear that the number of tests (or years of tests) needed to get of good picture

17 of the variety-by-environment interaction will depend on how representative the sample of test

18 environments is -of the entire population of environments, across years and locations, for which

19 recommendations are to be made. In this case, in a region where year effects such as rainfall

20 and date of seeding (often highly dependent on the onset of rains) are extremely important

21 determinants of overall mean yields, one or two years of data may not be sufficiently

22 representative.









1 Characterizing environments and determining recommendation domains

2 Using the entire data set, which is the largest and presumably most representative sample

3 of environments, regressions of El on date of seeding were done to see how much of the

4 variability in average yields could be accounted for by date of seeding. For the 1984-1986 data,

5 El was regressed on rainfall occurring during the 90 days after seeding; these data were

6 unavailable for the 1987 tests. The results of these regressions are presented in Table 3. Over

7 all four years' data, as well as in the subsets for 1984, 1985, and 1984-85 combined, average

8 yields (EI) were found to be inversely related to number of days planting followed 1 January.

9 This relationship accounted for 17 percent of the variability in yields over all four years, and

10 for almost as much in the 1984-85 subset. It accounted for only three percent of the variability

11 of yields in 1984, no doubt because such a high proportion of tests that year were seeded late.

12 The relationship between El and rainfall is not consistent from one data set to another

13 (Table 3), and the percentage of variability in yields due to rainfall is much less than that due

14 to date of seeding. Farmers do have some idea of average rainfall over all years; they also

15 know that some regions are generally higher yielding than others. They never know, of course,

16 what the rainfall in any given year will be, but recommendations could conceivably be made to

17 farmers on the basis of knowledge of average rainfall in their area. From the results of

18 regression of El on rainfall, however, such recommendations for S35 versus local varieties

19 would not be warranted.









1 Analysis of results by recommendation domain

2 Farmers can and do, however, make choices among alternative technologies at the time

3 of seeding in function of their knowledge of the effects of date of seeding. The linear

4 regressions of S35 and locals on EI over four years, and the inverse relationship of El and date

5 of seeding, led to the delineation, for this study, of two potential recommendation domains, an

6 early-seeded one (date of seeding before 26 June) and a late-seeded one (date of seeding after

7 25 June). Analysis of variance and mean separations within each of these domains indicated a

8 mere 10 percent increase in yields from S35 compared to locals in the early-seeded domain, but

9 a 48 percent increase in the late-seeded domain (Table 4). Combined analysis of variance

10 indicated a significant (a = 0.05) treatment-by-domain interaction. Over all test sites, i.e., for

11 only a single recommendation domain, S35 resulted in only a 21 percent increase in yields; this

12 may seem considerable, but in many cases it may not be enough to offset other characteristics

13 of S35 which farmers find less appealing than for the local varieties (taste, cooking qualities,

14 resistance to bird and other pest damage, etc.).

15 Analysis of risk of low yields showed that in both early- and late-seeded domains, the

16 chance of an unacceptably low yield depended almost entirely on the difference between means

17 and very little on differences in the variability in yields on which the means were calculated

18 (Figure 6).

19

20 Ex post verification of proposed recommendation domains

21 How well do the proposed early- and late-seeded recommendation domains match the

22 known patterns in the adoption of S35 in the Center North Zone of North Cameroon? In all but







15
1 one of the nine latest-seeded SODECOTON sectors (based on average seeding dates of the tests

2 from 1984 to 1987), S35 adoption has been either good or very good (Table 5). Correspondence

3 of late average date of seeding to known acceptability and adoption of S35 was not apparent

4 using just the 1984 subset of tests to calculate the mean seeding date, but was apparent using the

5 1984 and 1985 tests combined.

6

7 Conclusions and Implications for MSA of On-Farm Trials

8 While it is true that this study benefitted much from hindsight, it indicated that when use

9 of modified stability analysis is not overly reliant on stability, regression statistics, or "good"

10 and "poor" environments, it can be of great value in determining specific adaptation to groups

11 of farm environments and in delineating recommendation domains based on characteristics which

12 can be identified before planting. Had MSA--with appropriate environmental characterization--

13 been done on the data from the 1984-87 North Cameroon trials, for example, a recommendation

14 of S35 only for seeding after 20 or 25 June might have led to increased efficiency in extension

15 efforts and perhaps to improved adoption. The same results might even have been obtained by

16 analysis only of the first two years' (1984-85) data.

17 Although this example was based on MSA with only two treatments, the very simplicity

18 of the data--combined with an exceptionally large number of locations and years--is useful in

19 illustrating the importance of several key procedures in MSA. The first of these is the plotting

20 of data points on EI before attempting to find the best regression fit. In many cases, a hand-

21 drawn approximation of the response will give as good a picture of the treatment-by-EI

22 interaction as will any easily derived regression function.







16
1 This study also highlighted the crucial importance of ensuring that the sample of on-farm

2 trial environments is truly representative of the total population of environments for which

3 recommendations will eventually be made. Representativeness may be relatively easy to judge

4 in some agroecosystems, as with a study recently done in the rainforest zone in Brazil, where

5 the dominant determinant of mean yields was soil fertility, determined by land use type (Singh,

6 1990). In others, however, where important environmental determinants of yield are very

7 unpredictable across locations or across seasons, particular and careful attention must be paid.

8 MSA should not just end at the level of "good" and "poor" environments. Where

9 environmental characteristics can be quantified, their relation to El can be assessed with linear

10 regression. When they cannot, e.g., for land use type, soil texture class, geographical region

11 or zone, etc., correspondence with El can be done by ranking environments from low to high

12 EI and looking for patterns in the ranking of the non-quantifiable variable(s).

13 Once recommendation domains are tentatively identified on the basis of treatment-by-

14 environment interactions in the regression portion of MSA, analysis of treatment performance

15 within each domain should be done. In this study, only ANOVA and risk analysis by domain

16 were performed; in cases where socioeconomic trial data have been collected, any number of

17 socioeconomic analyses are possible. In fact, when evaluation criteria other than yield are

18 important to farmers, these criteria should be used for the determination of recommendation

19 domains (Hildebrand and Poey, 1985), as well as for the analyses by domain.









1 Acknowledgements

2 The analyses presented here were done on data extracted from results of trials done by

3 researchers and extension personnel in IRA and SODECOTON in North Cameroon. In

4 particular, they were designed and implemented by the SAFGRAD (1984, 1985) and the Testing

5 and Liaison Unit (1986, 1987) sections of IRA's Agronomic Research Center in Maroua,

6 Cameroon. Funding for much of the work of these on-farm test sections was furnished by

7 USAID, through the SAFGRAD Accelerated Crop Production Officer Project and the National

8 Cereals Research and Extension project. The analyses were done, with permission, while the

9 first author was employed by the International Institute of Tropical Agriculture, and later

10 comprised part of his Ph.D. dissertation at the University of Florida. Appreciation is extended

11 to all concerned in these institutions and projects.









1 References
2
3
4 Freeman, G. H. 1973. Statistical methods for the analysis of genotype-environment interaction.
5 Heredity 31:339-354.
6
7 Hildebrand, Peter E. 1984. Modified stability analysis of farmer managed on-farm trials.
8 Agron. J. 76:272-274.
9
10 Hildebrand, Peter E., and Federico Poey. 1985. On-farm agronomic trials in farming systems
11 research and extension. Lynne Rienner Publishers, Inc. Boulder, Colorado.
12
13 Hildebrand, Peter E. 1990. Modified stability analysis and on-farm research to breed specific
14 adaptability for ecological diversity. p. 169-180. In Manjit S. Kang (ed.) Genotype-by-
15 environment interaction and plant breeding. Proc. Symposium on Genotype-by-
16 Environmental Interaction and Plant Breeding, 12-13 Feb. 1990, Louisiana State
17 University, Baton Rouge.
18
19 Johnson, Jerry J. 1988. Final report of on-farm testing within IRA Maroua 1984-87. Institute
20 of Agronomic Research, Maroua, Cameroon.
21
22 Russell, J. T. 1991. Yield and yield stability of pure and mixed stands of sorghum [Sorghum
23 bicolor (L.) Moench] varieties in North Cameroon. Ph.D. diss. University of Florida,
24 Gainesville. Diss. Abstr. Int. 52-10B:5028.
25
26 Singh, Braj K. 1990. Sustaining crop phosphorus nutrition of highly leached oxisols of the
27 Amazon Basin of Brazil through use of organic amendments. Ph.D. diss. University of
28 Florida, Gainesville. Diss. Abstr. Int. 52-01B:0005.
29
30 Testing and Liaison Unit, Maroua. 1986. Annual Report. National Cereals Research and
31 Extension Project, Cameroon.
32
33 Testing and Liaison Unit, Maroua. 1987. Annual Report. National Cereals Research and
34 Extension Project, Cameroon.
35










Table 1.


Summary of on-farm variety test results (from Testing and Liaison Unit, 1986;
Testing and Liaison Unit, 1987; and Johnson, 1988)


Seasonal Mean
Yieldt (ka/ha) Rainfall Seeding
Year Test Group. 535 Local S.E. (mm) Date


1984 North (42 Sites) 1070 598 99 393 3 July
Central (46 Sites) 1573 829 109 359 6 July

1985 Early-Seeded (42 Sites) 1866 1721 Ns 118 504 14 June
Late-Seeded (16 Sites) 1416 1156 160 515 28 June

1986 All (38 Sites) 2164 2128 NS 145 621 22 June

1987 All (35 Sites) 1889 1825 Ns 123 604 19 June


t Yields of varieties for a year and test group are significantly
different (*) or not significant (Ns) at the 5% level, by Fisher's
Protected LSD test.










Table 2.


Regressions of yields of S35 and locals on three overlapping segments of the
range of EI, 1984-87.


EI<1000 500
S35 Locals S35 Locals S35 Locals

Intercept 10 -10 144 -144 253 -253

b 1.31 0.68 1.05 0.95 0.93 1.06

Mean 769 389 1104 722 1992 1733











Regressions of El (S35 and locals) on
1984-87, 1984, 1985, and 1984-85.


date of seeding (DOS) and on rainfall*,


a) 1984-87


Intercept
b
R2
p


b) 1984


c) 1985


Intercept
b
R2
P


Intercept
b
R2
P


d} 1984-85


Intercept
b
R2
p


DOS

5979
-25.4
0.17
0.0001


DOS

3140
-11.4
0.03
0.022


DOS

5470
-22.6
0.13
0.006


DOS

5209
-22.0
0.17
0.0001


Rainfall*

864
1.3
0.07
0.0003


Rainfall

645
1.04
0.03
0.088


Rainfall

2483
-1.6
0.09
0.02


Rainfall

1034
0.63
0.01
0.126


t Date of seeding = days after 1 January.

$ Rainfall = mm, 1-90 days after seeding.

S 1987 excluded from regression of El on rainfall since rainfall data in
this data set was aggregated over the entire year.


Table 3.










Table 4.


Mean grain yields,t 1984-87 data, over all locations, and by recommendation
domain based on date of seeding.


Over All Locations Seeded Before 26 June Seeded After 25 June
Variety (239 Environments) (138 Environments) (101 Environments)

--------------------------------kg/ha--------------------------

S35 1670 a 1832 a 1448 a

Locals 1379 b 1672 b 979 b


LSD(~o 85.6 111.2 128.1


t Means within a column followed by different letters are significantly
different at the 5% level, by Fisher's Protected LSD test.











Table 5.


Correspondence of average test date of seeding, by sector, and sectors where S35
had actually been adopted, 1984-87 data.


N Sector Mean DOS
(Days after 1 Jan.)


10 Bidzar 168.2
10 Lara 169.7
7 Ardaf 169.3
10 Dziguilao 169.8
10 Guidiguis 170.3
11 Karhay I 170.4
13 Gobo 170.4
11 Moutouroua 171.9
14 Mokong 172.0
11 Sorawel 172.9
10 Dana 173.4
9 Mayo Oulo 174.8
14 Zongoya 176.9
10 Karhay II 177.1
8 Kourgui 178.4 **
7 Koza 178.7 **
9 Moulvoudaye 179.1 *
12 Hina 179.7
10 Yoldeo 180.0 *
10 Meme 181.8 **
10 Mindif 183.1 *
8 Dogba 183.1 *
13 Bogo 184.0 *


** Sectors with very good S35 adoption
* Sectors with good S35 adoption













a

5000


4000


3000


2000


1000


0







b


5000


Plot of Sorghum Yields on El, 1984-87


0 500 1000 1500 2000 2500 3000 3500 4000
El (kg/ha)

S35 + Locals


Linear Regression on El, 1984-87


Grain Yield (kg/ha)


0 500 1000 1500 2000 2500
El (kg/ha)


3000 3500 4000


- S35 ...- Locals o Environments


Figure 1. Yields of S35 and locals plotted (a) and regressed (b) on environmental index
(EI), 1984-1987 data.













Linear Regression, S35 on El, 1984-87

Grain Yield (kg/ha)


0 500 1000 1500 2000 2500 3000 3500 4000
El (kg/ha)

S35 observations linear



Linear Regression, Locals on El, 1984-87

Grain Yield (kg/ha)


-1000 '
0 500 1000 1500 2000 2500 3000 3500 4000
El (kg/ha)

+ Locals observations linear






Figure 2. Linear regressions on El of S35 (a) and locals (b) superimposed on plotted data
points, 1984-1987 data.













S35 and Locals Observations, 1984

Grain Yield (kg/ha)


0 500 1000 1500 2000 2500
El (kg/ha)

S35 + Locals



Linear Regressions, 1984

Grain Yield (kg/ha)


3000 3500


0 500 1000 1500 2000 2500 3000 3500
El (kg/ha)

S35 Locals o Environments


Yields of S35 and locals plotted (a) and regressed (b) on EI, 1984 data.


Figure 3.
















Regressions Compared, 1984


Grain Yield (kg/ha)


0 500 1000 1500 2000
El (kg/ha)


2500 3000 3500


- S36 quad.
- Locale quad.


- 835 ln.
- Looals lin.


---- S35 cons.
---- Locals oons.


Hypothetical Response to El, 1984-87


Grain Yield (kg/ha)


0 500 1000 1500 2000 2500 3000 3500 4000
El (kg/ha)


S35 -- Locals


Figure 4. Linear, quadratic, and constrained quadratic regressions compared for 1984 data
(a), and a hypothesis concerning the response on EI for all four years (b).


annhl


---7


3000


2000


1000


0


-1000


R-squares 335:
Linear: 0.8332 '
Quadratic: 0.8375 --
Constrained: 0.8371







><* oo 00 oo coooMeaa SsB of0 9 o0 o o o o

1 1 1 1 1 1


~---














S35 and Locals Observations, 1985

Grain Yield (kg/ha)


a


4000



3000



2000



1000



0


]


1


3000 3500


Grain Yield (kg/ha)
4000


3000 S35: b-0.98
Locals: b-1.02

2000 -


1000


0
0 O 00C 0OO m O 00OW0 C m o WC00 0


0 500 1000


1500 2000
El (kg/ha)


2500


3000 3500


- S35 -- Locals 0 Environments


Yields of S35 and locals plotted (a) and regressed (b) on EI, 1985 data.


3 500 10


.4 +


440 .++ ++ .

+ + +


4--
.4t*^^- +


++^+
1 II I I I


Figure 5.


100 1500 2000 2500
El (kg/ha)

+ Locals S35



Linear regressions, 1985


(














Risk, Late-Seeded Domain, 1984-87


400 800 1200 1600
Grain Yield (kg/ha)

Locals, late-seeded -- 835, late-seeded


2000


Risk, Early-Seeded Domain, 1984-87


Risk (%)


1200
Grain Yield (kg/ha)


1600


800


2000


Locals, early-seeded -~- S35, early-seeded


Figure 6. Means and lower confidence limits for late-seeded (a) and early-seeded (b)
recommendation domains.


0 *


5 *





/ *
5 ______*----------0---- --- --
IC '* p




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