Euphytica 36 (1987) 109-l 15

ANALYSIS OF COMPETITIVE ABILITY AMONG GENOTYPES OF PERENNIAL RYEGRASS.

II. EFFECT UPON DRY MATTER PRODUCTION

J. HILL’, KENNETH MATHER* and P. D. S. CALIGAR13*

‘Welsh Plant Breeding Station, Aberystwyth, Dyfed, SY23 3EB, UK *Department of Genetics, University of Birmingham, Birmingham, B15 2TT, UK

3Scottish Crop Research Institute, Pentlandlield, Roslin, Midlothian, EH25 9RF, UK

Received 26 March 1986

INDEX WORDS

Lolium perenne, perennial ryegrass, competition, competitive pressure, competitive response, productivity.

SUMMARY

An analysis of the effects of competition upon the dry matter production per plant (after square root trans- formation) revealed no significant differences between the two genotypes of perennial ryegrass (Lolium perenne) used as regards the pressures which they exerted upon each other. Their response to these pressures differed significantly however. Using these estimates of the pressure and response parameters it was shown that the impact of intra-genotypic competition upon these two genotypes was considerably greater than that of inter-genotypic competition. In general this will be true whenever the pressure and response para- meters take the same sign. Intensity of competition increased linearly with tigour of growth in both cutting regimes, though changes in vigour had a significantly greater effect upon the intensity of competition under frequent cutting.

INTRODUCTION

In a previous paper (HILL et al., 1987) the effects of competition upon the survival of three morphologically contrasting genotypes (B, C and E) of perennial ryegrass (Lolium perenne) were analysed. No significant differences existed between two large- leaved, erect genotypes, C and E, either in respect of the pressures which they exerted or in their response to such pressures. By contrast, genotype B, a short-leaved, pro- strate type, differed significantly from one or both the others for pressure and response. Differences between the genotypes were more pronounced under an infrequent (R) rather than a frequent (F) cutting regime. This interaction was caused by the rapid elimination of genotype B from most of its duocultures under the R regime, where it was more responsive to the pressures exerted upon it by the other two genotypes.

The present paper assesses the effects of competition upon the dry matter yield of genotypes C and E over four successive years. Full details of the experimental and analytical techniques were given in the previous paper (HILL et al., 1987).

*Present address: Department of Agricultural Botany, Plant Science Laboratories, University of Reading, Whiteknights, Reading RG6 2AS, UK.

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1. HILL, K. MATHER AND P. D. S. CALIGARI

Table 1, Estimates of the regression parameters and the competition values derived therefrom for dry matter per plant (as measured by &) under frequent (F) and infrequent (R) cutting regimes (all entries ~10~).

Year C E

brn hi ccc CCE b, bd CEE CEC

- 55.43 -114.41 - 97.06 - 30.75

- 9.74 - 7.29 -66.02

1.97

55.43 114.41 97.06 30.75

F regime 45.69 - 35.15 9.49 35.15 44.64

107.12 - 57.58 1.91 57.58 59.49 31.04 - 71.71 6.26 71.71 77.97 32.72 - 15.68 -29.44 15.68 -13.76

1 -104.77 -11.06 104.77 2 -135.90 -40.57 135.90 3 -114.15 -21.35 114.15 4 -109.16 -19.69 109.16

R regime 93.71 - 74.24 21.56 74.24 95.80 95.33 -105.39 10.49 105.39 115.88 92.80 -104.53 -21.10 104.53 83.43 89.47 ~ 65.47 -19.65 65.47 45.82

RESULTS AND DISCUSSION

Using genotypes C and E as indicator in turn, Table 1 sets out the estimates of the regression coefficients b, and bd obtained from the complete data set (after square root transformation), together with the competition values derived therefrom. Taking the first year’s data under the F regime as an example, ccc = -b, = 55.43, ccE = bd - 6, = -9.74 - (-55.43) = 45.69, and so on. From the previous paper we may write ccc = C + a + r + i = 55.43 ccE = C - a + r - i = 45.69 cEc = C + a - r - i = 44.64 cEE = ? - a - r + i = 33.15, from which? = 451225, a = 4.805, r = 5.335 and i = 0.065. Values of these parameters obtained for each year and averaged over the four years are given separately for each cutting regime in Table 2. Alongside are given the sums (a + r) and differences (r - a) of the associate (pressure) and response parameters together with estimates of e, the expression of the character by either genotype C or E at the reference density of 20 plants. As mentioned in the previous paper, error variances for these estimates are derived from two sources, namely half the differences between the duplicate values of & (M.S.E.), and the mean square deviation of the observed results from their expected values calculated from the fitted regression lines (M.S.D.). These variances are homogeneous over the whole experiment except for genotype E in year 4 under the F regime, where M.S.D. significantly exceeds M.S.E. Clearly the model breaks down here, due no doubt to the cumulative effects of virus upon genotype E alluded to in the previous paper. In estimating the error variation appropriate to each cutting regime this value of M.S.D. has therefore been omitted, though the corresponding estimate of M.S.E. has been retained since it is independent of the analytical model used. The two basic estimates of error, each obtained by pooling the relevant M.S.D. and M.S.E. are I’, = 0.038243 based on 61 d.f. for the F regime and V, = 0.058804 based on 80 d.f. for the R regime. The lower number of d.f. for the error variance in the F regime results from the omission of the M.S.D. for genotype E in year four

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Table 2. Estimates of the competition parameters, C, n, r and i, the dry matter yield per plant of genotypes C and E at their reference density (after square root transformation) ec and e& and the error variances (V) of single entries. All entries are x lo3 except those for Ywhich are x 106.

Year C a r i a+r r-a ec eE

1 45.23 4.805 5.335 2 84.73 2.225 26.040 3 69.45 18.070 -5.395 4 16.34 -7.858 15.388

Mean 53.94 4.311 10.342 V 78.087

1 92.13 8.155 7.110 2 113.12 12.763 2.493 3 98.73 0.063 4.748 4 77.48 0.005 21.840

Mean 95.37 5.246 9.048 V 92.083

F regime 0.065 1.420

14.940 6.868

5.823

R regime -2.625

7.523 10.613

9.835

6.336

10.140 28.265 12.675

7.530

14.653 144.422

15.265 -1.045 15.255 -10.270

4.810 4.685 21.845 21.835

14.294 3.801 200.322 168.011

0.530 1183 1336 23.815 1417 1547

-23.465 1702 1040 23.245 1400 831

6.031 1426 1189 167.929 23483 25402

1457 1520 1891 2024 1506 1630 1578 1757

1608 1733 31663

already referred to, combined with the removal of the 5C/15E duoculture, which con- tained two abnormally large C plants that would otherwise have inflated the estimate of error variance.

Error variances for e, b,, bd, and the c values derived from them have been obtained by multiplying VE by the appropriate element in the J -’ matrix (MATHER et al., 1982) whilst the error variances for C, a, Y and i are the average of those for the four c values from which they have been calculated (MATHER & CALIGARI, 1983). Since a + r is estimated as i (cc- - c& its error variance is half the sum of the error variances of these two c values, and likewise for r - a which is calculated as f (cCE - cEc). One final point in connection with these variances, all of which are given in Table 2, is that the omission of the 5C/I5E duoculture in the F regime will obviously have a differential effect upon the precision of the two estimates of e under frequent cutting.

The x2 analyses of the data from Table 2 are presented in Table 3. Taking C under the F regime as an example, the departure of the overall mean from zero yields a xi testing whether competitive interactions occur within this regime. Because the multi- pliers of lo3 and lo6 used to simplify the presentation of the C and Vvalues respectively cancel out (see Table 2), this x2 may be calculated by multiplying the squared mean deviation by four and dividing by V, i.e. 53.942 x 4178.087 = 149.04, which is highly significant. There can be no doubt therefore that strong competition is operating with- in the F regime. Similarly the year to year variability may be calculated as [(45.232 + 84.732 + 69.45’ + 16.342) - (4 x 53.942)]/78.087. This gives a $ of 34.28, which, being highly significant, indicates that the strength of competition within the F regime varies between years. The R regime gave a similar overall picture, but the variability between years failed to reach formal significance. However, the variability between years may be explored further by partitioning the heterogeneity x: into three orthogon-

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Table 3. x2 tests of significance for the parameters set out in Table 2 (*P = 0.05-0.01; **P = O.OlLO.001; ***p = < 0.001).

Regime c a r i a+r r-a e, eE

F Deviation XT 149.040*** 0.952 5.479* 1.737 5.947* 0.866 346.374*** 222.518*** Heterogeneity Deviation x:

x: 34.248*** 4.379 6.974 1.751 1.802 9.009* 5.783 11.805** R 395.005*** 1.195 3.556 1.744 4.080* 0.344 326.648*** 379.314***

Heterogeneity x$ 7.092 1.296 2.485 1.219 0.743 3.259 3.607 4.454

F + R Deviation x: 523.953*** 2.147 8.837** 3.475 9.722* 1.151 667.693*** 598.289*** F - R Difference x: 40.347*** 0.021 0.039 0.006 0.001 0.059 2.403 20.744***

al comparisons testing for the presence of linear, quadratic and cubic components of change over the four years. For the F regime the results show significant linear (XT = 6.66) and quadratic (x! = 27.46) components, but no evidence of a cubic element. Under the R regime only the quadratic component is significant (x: = 4.84). Thus although changes in the strength of competition are much less evident in the R regime, the component which is greatest in the F regime is nevertheless detectable under infre- quent cutting. Combining the results for the two regimes (F + R) yields an even greater x:, thereby confirming that the C values are reinforcing each other. Interestingly the difference (F - R) is also highly significant, indicating that competition is more intense under the R regime. The error variance for these two latter tests is calculated as 3 (78.087 + 92.083) = 85.085.

Considering the remaining parameters, although only one of the eight individual a values is negative, thus suggesting that genotype C is perhaps exerting greater pres- sure than E, these differences are in fact non-significant throughout. By contrast the response parameter (r) is signilicantly positive in the F regime, though it just fails to attain formal significance under the R regime. Overall F + R is highly significant, leaving no doubt that genotype C displays the greater response to any competitive pressures exerted upon it, whilst the non-significant xi for F - R indicates homogenei- ty over cutting regimes.

As regards i, the interaction between a and r, the x2 tests are generally non-signili- cant, though the combined deviation from zero (F + R) approaches significance. Clearly, the use of a multiplicative model, as advocated by MATHER & CALIGARI (1983) for the first year’s data when genotype B was included, would not have materially affected the validity of our conclusions.

Not surprisingly, the a + r and r - a values confirm the findings of a and r taken separately, with the former being significant under both cutting regimes, whereas the latter are generally non-significant throughout. There is, however, evidence of hetero- geneity amongst r - a within the F regime, due to the large negative value it takes in the third year. Since no such heterogeneity exists in the R regime, too much weight should not be given to this particular result.

Turning to ec and eE, the expression of the character at the reference density of 20 plants; under the R regime the two parameters behave similarly, with both deviating significantly from zero and neither showing heterogeneity over years, though this is a point to which we will return later. Under the F regime, however, eE presents compli- cations in that for the third and fourth years its value is significantly lower than ec.

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COMPETITIVE ABILITY OF PERENNIAL RYEGRASS

F 125*

Y2 0

loo--

75.

50..

2s.-

J PO00

I 1250 1500 1750 2000

B Fig. 1. The relation between C, measuring the overall competitive interactions, and 2, the average expression of dry matter yield per plant (after square root transformation) for genotypes C and E at their reference density. The two regressions, representing the F (open circles) and R (solid circles) cutting regimes over the four years Y 1 to Y4, were calculated independently of each other.

This anomalous behaviour is probably due to the viral infection referred to in the previous paper. Caution requires therefore that eB be omitted from the analyses for these two years. From the remaining values it is apparent that e, and eE rise to a peak during the second and third years, falling back thereafter. A comparison of eE and ec from the six unbiassed estimates of eE - ec indicates that though eE > ec throughout, this difference is not significant. Furthermore, an analysis of the ec values for both cutting regimes reveals that no significant differences exist between F and R. If, however, we confine our attention to the first two years data, when both eE and ec can be analysed, the difference between the two cutting regimes attains signifi- cance, suggesting that the e values are indeed lower under frequent cutting.

Finally the variation displayed by the e values over years may also be analysed. Complete data are available for ec in both cutting regimes, but only in the R regime for eE. Yearly variation amongst the sum of these three values was tested against an error variance calculated as f (V,, + V,,, + v&) = 28936.3. The heterogeneity xi measuring variability between years just failed to reach significance. However, as with the c values, the analysis was taken a stage further by using the three orthogonal components of the cubic regression of e on years. Neither the linear nor cubic compo- nents proved to be significant, but the quadratic component has a xi of 4.68 with

Euphytica 36 (1987) 113

J. HILL, K. MATHER AND P. D. S. CALIGARI

P = 0.03, a result which has a striking similarity to those obtained from the analyses of the C values, particularly under the R regime. This similarity bears closer examina- tion because it points to the conclusion that the more vigorous the growth, as measured by e, the stronger the competition between the two genotypes, a conclusion which is perhaps not wholly unexpected. The relation between C, our measure of the overall competitive interactions in the system, and Z = f (ec + eJ is illustrated in Fig. 1. Years three and four under the F regime are also included since the anomalous behav- iour of a genotype should not of itself disturb any relationship which might exist be- tween intensity ofcompetition and vigour. Within both cutting regimes there is a signif- icant linear regression of C on Z, with the slope of b, (0.190) being significantly greater than bR (0.0428). But, whereas under the F regime the linear model tits the data satisfac- torily (xi = 0.48, P = 0.8), under the R regime significant variation remains about the fitted line (~2’ = 9.25, P = 0.01). This is due solely to the point for year four (Fig. l), the removal of which reduces the residual variation to insignificance ($ = 0.12, P = 0.73), yet leaves the slope of the fitted line virtually unchanged.

CONCLUSIONS

After making various allowances for the anomalous behaviour of genotype E under frequent cutting, it was shown that a linear relationship existed between dry matter production per plant, after square root transformation, and the number of plants of the indicator genotype omitted in monoculture or substituted in duoculture. Analyses of the pressure (a) and response (r) parameters revealed that no significant differences existed between the two genotypes for the former, but genotype C displayed a signiti- cantly greater response to the competitive pressures exerted upon it.

In the previous paper the pressure and response parameters were used to predict which component was likely to be the most successful in a mixed sward. These same parameters may also be used to assess the relative impact of intra- and inter-genotypic competition. Intra-genotypic competition within genotype C produces a competition value, ccc, of C + a + r + i, and within genotype E, cEE, of C - a - r + i. Half the difference, f (ccc - cEE) = u + r, measures the impact of intra-genotypic competi- tion on these two genotypes. Likewise, it can be shown that the impact of inter-geno- typic competition is equal to $ (c cE - cEc) or r - a. From Table 2 it is apparent that over the duration of this experiment differences between genotypes C and E are greater under intra- than inter-genotypic competition for both cutting regimes. Gener- ally speaking, whenever a and r have the same sign the impact of intra-genotypic com- petition will be greater since 1 u + r ) > 1 r - a 1, and vice versa when a and r have different signs.

Not surprisingly these results indicate that intensity of competition is positively re- lated to vigour of growth, as measured here by productivity. However, it is clear from Fig. 1 that the relationship is not straightforward, being either curvilinear or, more probably here, two interesecting regressions, one for each cutting regime. Signiticant differences exist between the two regressions, with change in vigour having a greater effect upon the intensity of competition under frequent cutting, that is when yields are lower. Such differences will undoubtedly reflect morphological and developmental changes engendered by the two cutting frequencies. Thus under frequent cutting, for

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example, complete light interception will never be achieved by any of the sward cano- pies, whereas under infrequent cutting it will during periods of rapid growth (RHODES,

1971). Once all the light has been intercepted then any further leaf production merely effects subtle changes in the distribution of light in relation to leaves of contrasting photosynthetic efficiency.

The results presented in these two papers illustrate clearly the competitive pressures individuals in a mixture exert both upon themselves and their neighbours and, perhaps more important, the response which they display to such pressures. Of more immediate practical interest, however, are the very different impacts intra- and inter-genotypic competition apparently have upon the individual (see also CONNELL, 1983), because this underlines the importance of evaluating those crops destined for use in mixtures under realistic conditions, a feature which has been conspicuously absent from many such breeding programmes hitherto. The techniques described here may in fact be used to assess the pressures and responses displayed by any number of associates and responders during the breeding and selection of potential mixtures. Moreover, the process can be streamlined considerably if i, the interaction between a and r is assumed to be absent because then just, two contrasting associates may be used to test any number of responders or vice-versa. Should interactions subsequently be detected then clearly a more detailed investigation would be called for. An investigation is now un- derway using mono- and duocultures of perennial ryegrass and white clover (Trifolium repens), where the duocultures are based upon components either with or without a previous history of coexistence, the aim being to ascertain whether improving com- patibility between components increases the productivity of the resultant mixture.

ACKNOWLEDGEMENTS

We thank Mr. T. Michaelson-Yeates and Mrs L. C. Hughes for technical assistance.

REFERENCES

CONNELL, J., 1983. On the prevalence and relative importance of interspecific competition: evidence from field experiments. Am. Nat. 122: 661-696.

HILL, J., K. MATHER &P. D. S. CALIGARI, 1987. Analysis of competitive ability among genotypes of peren- nial ryegrass. I. Effect upon survival. Euphytica 36: 99-107.

MATIIER, K. & P. D. S. CALIGARI, 1983. Pressure and response in competitive interactions. Heredity 51: 435454.

MATHER, K., J. HILL & CALIGARI, P. D. S., 1982. Analysis of competitive ability among genotypes of peren- nial ryegrass. Heredity 48: 421434.

RHODES, I., 1971. The relationship between productivity and some components of canopy structure in rye- grass (Lolium spp.) II. Yield, canopy structure and light interception. J. Agric. Sci., Camb. 77: 283-292.

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