Jan Krzymański, Krystyna Krótka
Instytut Hodowli i Aklimatyzacji Roślin – Państwowy Instytut Badawczy, Oddział w Poznaniu Autor korespondencyjny – J. Krzymański, e-mail: krzym@nico.ihar.poznan.pl
DOI: 10.5604/12338273.1101404
Competition between plants on adjacent plots
in the field trial on the winter oilseed rape
(Brassica napus
L.)
2. An attempt to eliminate the impact
of competition between plants growing
on neighboring plots on the seed yield
from the plot by statistical calculations
Konkurencja pomiędzy roślinami z sąsiednich poletek
w doświadczeniu polowym z rzepakiem ozimym
2. Próba wyeliminowania wpływu konkurencji między roślinami
rosnącymi na sąsiadujących poletkach na plon nasion z poletka
na drodze obliczeń statystycznych
Key words: winter rapeseed, seed yield, soil variability, plant competition, regression analysis,
variation analysis, expected heritability and genetic gain Summary
The results of field trials with winter oilseed rape are biased by the effects of competition between plants growing on adjacent plots. We tried to remove the impact of these effects using analysis of regression. The proposed formula for calculating the concomitant variable needed the knowledge of real values of seed yields of tested objects. In the first stage of the calculations these real values has been replaced by the best available their approximations represented by the averages of seed yield for examined objects. Then in the process of iterations more and more accurate approximations of the actual yielding values of the objects were got. Regression analysis with so calculated concomitant variables allowed adjusting the impact of competition between plants growing on adjacent plots. This method makes it possible to increase the precision of the experiment at the same time.
Conclusions — Adjustment of the effects of competition among plants growing on adjacent plots
into field trial changed the ranking of examined breeding objects and significantly increased the accuracy of their ratings. It also allows you to estimate the possible to obtain breeding progress in terms of seed yield of winter oilseed rape when the selection shall be made on the basis of field experiment conducted in several localities.
Słowa kluczowe: plon nasion, zmienność glebowa, konkurencja roślin, analiza regresji, analiza wariancji, przewidywana odziedziczalność i postęp genetyczny
Streszczenie
Wyniki doświadczeń polowych dotyczące plonów nasion rzepaku ozimego są obciążone efektami konkurencji pomiędzy roślinami rosnącymi na sąsiadujących poletkach. Wpływ tych efektów starano się usunąć stosując analizę regresji. Zaproponowano odpowiedni wzór na obliczanie zmiennej towarzyszącej. We wzorze tym konieczna jest znajomość rzeczywistych plonów nasion badanych obiektów. Na pierwszym etapie obliczeń te rzeczywiste wartości zastąpiono najlepszymi znanymi ich przybliżeniami, to jest średnimi wartościami plonów obiektów. Następnie w procesie iteracji uzyskiwano coraz dokładniejsze przybliżenia rzeczywistych plenności badanych obiektów. Analiza
regresji z tak obliczonymi zmiennymi towarzyszącymi pozwala skorygować wpływ konkurencji
między roślinami z sąsiadujących poletek. Metoda ta pozwala zwiększyć precyzję doświadczeń, co wpływa jednocześnie na skuteczność selekcji.
Wprowadzenie korekty wpływu konkurencji między roślinami rosnącymi na sąsiednich poletkach w doświadczeniu polowym zmieniło ranking badanych rodów oraz zwiększyło znacznie precyzję ich
oceny. Umożliwia także oszacowanie możliwego do uzyskania postępu hodowlanego w zakresie
plonu nasion rzepaku ozimego, gdy selekcję przeprowadza się na podstawie doświadczenia polowego założonego w kilku miejscowościach.
Introduction
The field trials comparing the variety or strains of oilseed rape are carried out in Poland by using plots with area 12 m2 or 15 m2 depending on your tools for field trial cultivation. Row distances are typically 30 cm, and the plots consist of four or five rows with a length of 10 m. Paths between the test plots are 40–50 cm wide depending on the width of the wheels of used plots drills and harvesters. Because the plants of winter oilseed rape spreading strongly (Niemczyk 2009) they covers these paths and extends the length of the plot of approximately 60–80 cm. Real yielding area of plot is greater than the theoretical by 13% to 21.5% depending on the width of the paths between the plots used in the field trial. The results of seed yield from trials are higher of about these values as compared with the seed yields from plantations. If the tested objects occupy the free spaces in the same manner we would have to deal with systematic error, raising the height of the seed yield of these objects equally. This would not influence the ranges of objects compared in the experiment (field trial). But tested objects occupy the free spaces between the test plots on differentiated ways. It depends on their earliness, maturity class, how to promote and spread the branches and leaves, the height of plants, the vigor of plants etc. In this way competition between plants on the boundary rows of adjacent plots is created. This competition affects the results of the evaluation of tested objects according their seed yields. As has been shown in previous studies this competition affects mainly the first boundary row, but it may also affects seed yield from the next row although to a much lesser degree (Krzymański 1985). Disorders resulting from competition of plants growing on boundary rows ofadjacent plots in trial can have a clear impact on the results of the seed yield evaluation of objects compared in the field trial.
In a previous publication it has been shown (Krzymański et al. 2012), that effects resulting from competition between plants growing on the nearest neighbor plots are competing with effects caused by soil variability occurring inside the block. Concomitant variable calculated as the average seed yield of two nearest neighbor plots does not allow to identify and eliminate separately the impact of plant competition on the seed yield of examined objects, or to remove the effects of variation of soil fertility inside the block. To solve this problem it was suggested to estimate the seed yield by harvesting the seeds only from the middle rows of the plot omitting the edge rows.
In present work we try to estimate only the impact of effects caused by the competition of plants growing on neighboring plots. Efforts were made to identify and eliminate the impact of these effects using the statistical calculations.
Materials and methods
Methods of calculation
In conducted research data ordering and conversion was carried out on Excel worksheets. The programs contained in the package "Data Analysis" in Microsoft Excel 2007 were used to calculate regression, correlation, and analysis of variance. Some parts of the calculation were made using the macros. Tested objects in addition to the sequence numbers (a = 1 to 25) had numbers derived from randomisation of experiment (i = 1 to 25). Both of these numbers allowed to arrange the objects according to the needs of statistical elaboration stages.
The significances of differences in the analysis of variance were estimated with F test of Snedecor. In the case of significant interactions between seed yield and localities, the average mean of square for interaction was used in the calculation of the F values rather than the average mean square of the error. It was connected with the target of experiments. So the breeder as well as the Office for variety licensing are interested in prediction of yield of tested varieties that can be obtained in the region of cultivation, rather than in a single experiment in one location (localities are random sample that represents expected crop area.).
In the study regression analyses were used. Data used in regression analysis cannot contain the variability coming from different environments in which the field trials were conducted. Therefore, the yield of seeds from each plot was corrected to eliminate the influences of the variability among localities and the variability among replications. Elimination of the variability among blocks was
made for each plot by subtracting the average block value and adding the average total value according to the following formula:
y’(ijl) = y(ijl) – y(.jl) + y(...) (1)
where:
y(ijl) = seed yield from plot (raw data) — plon nasion uzyskany z poletka (plon surowy) y’(ijl) = corrected seed yield after elimination of variability connected with
localities and replications — skorygowany plon nasion z poletka po usunięciu
zmienności związanej z powtórzeniami i miejscowościami,
y(.jl) = mean for block — średnia blokowa, y(...) = total mean — średnia całkowita,
i = position of object in block — pozycja obiektu w bloku, j = position of block in locality — pozycja bloku w miejscowości, l = locality — miejscowość,
n = number of objects in block (replication) — ilość obiektów w bloku (powtórzeniu). This correction removes also the variability coming from localities.
It was assumed that the effects of competition between plants growing on the nearest neighbor plots should be correlated to differences in yields from these plots. It suggested the necessity of using a new concomitant variable computed as the difference between the average of the yields of the two neighboring plots and seed yield of the plot:
x(ijl) = [y’((i-1)jl + y’((i+1)jl)]/2 – y’(ijl) = [y((i-1)jl) + y((i+1)jl)]/2 – y(ijl) (2)
Concomitant variable calculated according formula 2 included not only the effects of competition between plants growing on neighboring plots but also effect resulting from differences in real values of yielding abilities of objects growing on these adjacent plots. It was necessary to make some improvements of this concomitant variable. To eliminate this impact the new concomitant variable x was proposed. It should eliminate effect of differences in true yielding values of adjacent objects. To make such elimination the knowledge of these true yielding values of objects was necessary. However, these real yielding values for the objects were unknown but its best estimates available at the time were their averages calculated by all the replications (means for objects). Therefore, on the first stage the appropriate amendment was proposed for formula 2 using these averages. This should allow to eliminate impacts resulting from differences in real yielding values of adjacent objects. The following new formula for the calculation of the concomitant variable x was received:
x(ijl) = {[y’((i-1)jl + y’((i+1)jl)]/2 – y’(ijl)} – {[y’((i-1)..) + y’((i+1)..)]/2 – y’(i..)} (3a)
This formula can be converted as follows:
x(ijl) = {[y’((i-1)jl) – y’((i-1)..)] + [y’((i+1)jl) – y’((i+1)..)]}/2 – [y’(ijl) – y’(i..)] (3b)
where:
y’(ijl) = corrected plot yield (after removal the variation among the blocks) —
skorygowany plon z poletka (po usunięciu zmienności pomiędzy blokami),
y'((i-1)..); y'(i..); y'((i + 1)..) are average calculated from all replications for objects that are
marked as y'((i-1) jl) ; y'(ijl) and y’((i + 1) jl) in the j-block j and l-locality,
y'((i-1)..); y'(i..); y'((i + 1)..) are average calculated from all replications for objects that are
marked as y'((i-1)jl); y'(ijl) and y’((i+1)jl) in the j-block j and l-locality.
So the proposed concomitant variable x(ijl) (according to formula 3b) in the
first approximation is equal to the average of the yields of two plots adjacent on both sides to the plot minus plot yield but everything calculated on the deviations from the object averages.
New values for seed yields of the objects corrected by regression in analysis of the covariance were better approximations of the real values of the objects and using these values the new concomitant variables x1 could be calculated. These variables were used in the next analysis of variance to obtain the next approximation of the actual yields of objects, which will be used to calculate the next following concomitant variables x2 and similarly, x3, x4, .... Each such iteration step should yield a new average object values approximating more and more to the real values of object yielding ability. This process could be repeated (iterate) until obtaining stabile object ranking, or to obtain set up maximum differences of object averages between successive iterations. This iteration method should lead to a convergence of results-what are the conditions for its use.
Above described method should lead to the elimination of the competition effects between plants growing on adjacent plots and let calculate the actual yielding abilities of objects on the assumption that the regression coefficients for individual objects do not differ significantly. So the calculated seed yields of tested objects should respond to production results which you can expect on the plantations of these objects. However, this does not eliminate the systematic error resulting from incorrect determination of the yielding area of plot which was discussed before in introduction.
To demonstrate the benefits of a correction of the results of field trials through the analysis of regression/covariation with proposed concomitant variables the analyses of variance were performed for raw seed yields from plots and for seed yields adjusted with regression. The analyses were done using program “two-factor with replication" analysis of variance ("Data Analysis" for Excel 2007).
The expected effectiveness of the selection for objects was estimated on the basis of expected values of mean squares from the analysis of variation. Calculations were made for both data: raw and adjusted with regression. Heritability and expected genetic gain were calculated for the selection carried out on the basis of the object averages according to the method suggested by Allard (1966).
Problem of the plots on the ends of blocks (edge plots on replications)
The plots at the beginning and at the end of the block (replication) have only the seed yield for only one neighboring plot. These plots you can either skip in the calculation (option B) or concomitant variable (the value of x(ijl)) can be calculatedusing only one value for neighboring plot (option A) as follows:
x(1jl) = {[y’(1jl + y’(2jl)]/2 – y’(1jl)} – {[y’(1..) + y’(2..)]/2 – y’(1..)} (4a)
and
x(njl) = {[y’((n-1)jl + y’(njl)]/2 – y’(njl)} – {[y’((n-1)..) + y’((n..)]/2 – y’(n..)} (4b)
Then sum of x for block is 0, as well as the total sum and average of x are also equal to 0
∑x(ij.) = 0; ∑x(...) = 0 and x(…) = 0
Materials
The statistical analyses of the results of field trials (experiments) were done using data from two preliminary trials with breeding materials of winter oilseed rape to verify the effectiveness of the proposed method. In the previous study (Krzymański et al. 2012) four field trials were investigated and show different behavior of objects according to their origin. The biggest differences in the behavior of oilseed rape were found in experiments 1 and 2 so these data were chosen to presented study. Breeding strains from the three winter oilseed rape breeding tested in the first experiment (DW1), showed the advantage of competition effects between the plants from adjacent plots, while in the second experiment (DW2), in which the experimental hybrids from only one winter oilseed rape hybrid breeding were examined, the advantage over the competition effects showed the effects due to soil fertility variation inside the blocks.
Each field experiment concerned the 25 breeding strains or experimental hybrid of winter oilseed rape and trials were conducted in six localities in 2009/2010. These were: Borowo (N 52o07’, E 16o47’), Bąków (N 50o58’, E 18019’), Kończe-wice (N 53o
11’, E 18o34'), Łagiewniki (N 51o46’, E 17o14'), Małyszyn (N 52o44’, E 15o10'), Strzelce (N 52o19’, E 19o24’). All of them are situated in the Western and Central part of the Poland. The weather during the growing period for winter oilseed rape in 2009/2010 was unfavorable for the development of crop and seed production. These adverse conditions reduced and differentiated crop seeds among localities.
Field trials were sown in a complete randomized block design in four replications. The size of the four-row plots amounted to 12 m2 (length 10 m, width 1.2 m, the distance between the rows 30 cm, the distance between the boundary rows of adjacent plots are 40 cm or 50 cm depending on the locality). Air dry 9% of moisture seed yields of plots determined after harvesting in kg/plot have been converted into dt/ha.
Two sets of 600 threes of data and two sets of 552 threes of data (without boundary plots) were obtained using equations (1, 3a, 4a and 4b). Each threes of data represents the raw yield of seed from the plot (y), the seed yield of plot after elimination of block and locality variations (y’) and the value of the proposed concomitant variable (x). These data were used in iteration process to calculate the linear regression equations, adjusting the raw data with the use of regression coefficient and concomitant variable and variance analyses of corrected data. Then new set of concomitant variability was calculated.
The authors express their gratitude for sharing raw results of seed yields from the field experiments to mgr Maria Ogrodowczyk, dr Henryk Woś, dr Grzegorz Budzianowski, dr Roman Biliński and Jolanta Zagierska. Experiments have been made within the framework of breeding programs conducted by Plant Breeding Companies Strzelce and Smolice of IHAR group. These data have been used for the practical verification of the proposed method for statistical analysis of field experiment carried out in several localities.
Results and their discussion
The problem of the plots at the edges of replications
A plot at the beginning and at the end of the block (replication) had data for only one neighboring plot. On the other side was a plot sown to protect the formation of edge effects. Its seed yield was disturbed by these effects and was not collected. It was possible either to omit in calculation the plots on the ends of blocks (edge plots on replications) (option B) or calculate the concomitant variables (the values of x(ijl)) according to the equations of 4a and 4b by using only
one neighboring plot (Option A). In the first case, we had a more accurate calculation of the concomitant variable; however we get incomplete blocks, which made very difficult the further statistical analysis of the results. In the second case, we maintain the complete blocks design of experiment but calculation of regressions coefficient may be less accurate. Calculations have been carried out for both data sets in order to determine what effect on the regression coefficient had the concomitant variable values calculated according to the equations 4a and 4b.
Regression analyses between proposed concomitant variables x and corrected seed yields from plots y’ were made for both experiments and for both sets of data (options: A and B – with and without data for boundary plots in replications). The results of the regression analyses for both experiments is shown in Figures 1 and 2 and Tables 1 and 2.
A B
Fig. 1. The relationship between the proposed concomitant variable x and corrected yield of seeds from the plot y’.. Experiment 1, Objects: experimental varieties from breeding
programs conducted in Bąków, Borowo and Małyszyn. Calculation with whole set of data
for plots (A) and without data for border plots in replications (B) — Zależność między
proponowaną zmienną towarzyszącą x a skorygowanym plonem nasion z poletka y’. Doświadczenie 1, obiekty: rody z hodowli prowadzonych w Bąkowie, Borowie i Małyszynie. Obliczenia z całym zestawem danych dla poletek (A) oraz bez danych dla poletek brzegowych w powtórzeniach (B).
A B
Fig. 2. The relationship between the proposed concomitant variable x and corrected yield of seeds from the plot y’. Experiment 2, Objects: experimental hybrids from breeding project conducted in Borowo. Calculation with whole set of data for plots (A) and without data for border plots in replications (B) — Zależność między proponowaną zmienną towarzyszącą x
a skorygowanym plonem nasion z poletka y’. Doświadczenie 2, próbne mieszańce z hodowli prowadzonej w Borowie. Obliczenia z całym zestawem danych dla poletek (A) oraz bez danych dla poletek brzegowych w powtórzeniach (B).
Table 1
Analysis of variance for regression between the proposed concomitant variable x and
corrected yield of seeds from the plot y’. Experiment 1, Objects: experimental varieties from breeding programs in Bąków, Borowo and Małyszyn — Analiza wariancji dla regresji
między proponowaną zmienną towarzyszącą x a skorygowanym plonem nasion z poletka y’. Doświadczenie 1, obiekty: rody z hodowli prowadzonych w Bąkowie, Borowie i Małyszynie
Calculation for full set of data (with border plot in replications – A)
Obliczenia z całością danych dla poletek (z poletkami brzegowymi w powtórzeniach – A)
Source of variation Źródło zmienności Degrees of freedom Stopnie swobody Sum of squares Suma kwadratów Mean square
Średni kwadrat Statystyka F Statistic F
Probability level of error — Poziom prawdopodobieństwa dla błędu Regression Regresja 1 13424.93 13424.93 1471.685 2.3E-163 Random deviation Odchylenia losowe 598 5455.045 9.122148 Total — Suma 599 18879.98 Coefficients
Współczynniki Wartość Value
Standard error Błąd standardowy T-test Probability level of error Poziom prawdo-podobieństwa dla błędu Confidence interwal Przedział ufności a 40.59433 0.12330 329.224 0 (40.3522÷40.8365) b -0.66830 0.01742 -38.3626 2.3E-163 (-0.7025÷-0.63409)
Statistics of regression — Statystyki dla regresji
— coefficient of correlation — współczynnik korelacji = 0.843248 — coefficient of determination — współczynnik determinacji = 0.711067
Calculation for data set without border plots in replications (B)
Obliczenia bez danych dla poletek brzegowych w powtórzeniach (B)
Source of variation Źródło zmienności Degrees of freedom Stopnie swobody Sum of squares Suma kwadratów Mean square
Średni kwadrat Statystyka F Statistic F
Probability level of error — Poziom prawdopodobieństwa dla błędu Regression Regresja 1 13110.2 13110.2 1461.93 5.1E-157 Random deviation Odchylenia losowe 550 4932.26 8.96775 Total — Suma 551 18042.49 Coefficients
Współczynniki Wartość Value
Standard error Błąd standardowy T-test Probability level of error Poziom prawdo-podobieństwa dla błędu Confidence interwal Przedział ufności a 40.5558 0.12746 318.177 0 (40.305÷40.806) b -0.6663 0.01743 -38.2352 5.1E-157 (-0.7005÷-0.6632)
Statistics of regression — Statystyki dla regresji
— coefficient of correlation — współczynnik korelacji = 0.852426 — coefficient of determination — współczynnik determinacji = 0.726631
Table 2 Analysis of variance for regression between the proposed concomitant variable x and corrected yield of seeds of the plot y’. Experiment 2, Objects: experimental hybrids from breeding program in Borowo — Analiza wariancji dla regresji między proponowaną
zmienną towarzyszącą x a skorygowanym plonem nasion z poletka y’. Doświadczenie 2, obiekty: próbne mieszańce z hodowli prowadzonej w Borowie)
Calculation for full set of data (with border plot in replications – A)
Obliczenia z całością danych dla poletek (z poletkami brzegowymi w powtórzeniach – A)
Source of variation Źródło zmienności Degrees of freedom Stopnie swobody Sum of squares Suma kwadratów Mean square
Średni kwadrat Statystyka F Statistic F
Probability level of error — Poziom prawdopodobieństwa dla błędu Regression Regresja 1 8638.771 8638.771 611.775 1.46E-93 Random deviation Odchylenia losowe 598 8444.257 14.12083 Total — Suma 599 17083.03 Coefficients
Współczynniki Wartość Value
Standard error Błąd standardowy T-test Probability level of error Poziom prawdo-podobieństwa dla błędu Confidence interwal Przedział ufności a 44.68859 0.15341 291.3011 0 44.3873÷44.9899 b -0.69197 0.027976 -24.7341 1.46E-93 -0.74692÷-0.63703
Statistics of regression — Statystyki dla regresji
— coefficient of correlation — współczynnik korelacji = 0.711121 — coefficient of determination — współczynnik determinacji = 0.505693
Calculation for data set without border plots in replications (B)
Obliczenia dla danych bez danych dla poletek brzegowych w powtórzeniach (B)
Source of variation Źródło zmienności Degrees of freedom Stopnie swobody Sum of squares Suma kwadratów Mean square
Średni kwadrat Statystyka F Statistic F
Probability level of error — Poziom prawdopodobieństwa dla błędu Regression Regresja 1 8396.238 8396.238 632.0968 1.94E-93 Random deviation Odchylenia losowe 550 7305.733 13.28315 Total — Suma 551 15701.97 Coefficients
Współczynniki Wartość Value
Standard error Błąd standardowy T-test Probability level of error Poziom prawdo-podobieństwa dla błędu Confidence interwal Przedział ufności a 44.7215 0.155128 288.288 0 44.4168÷45.0262 b -0.69019 0.027452 -25.1415 1.94E-93 -0.74412÷-0.63627
Statistics of regression — Statystyki dla regresji
— coefficient of correlation — współczynnik korelacji = 0.731249 — coefficient of determination — współczynnik determinacji = 0.534725
Then testing was performed on the homogeneity of regression coefficients calculated for the data of the options/variants (A) and (B). The results of the calculations were presented in Table 3.
Table 3 Comparison of regression parameters calculated for a full set of data (A) and after removal of the plots at the beginning and at the end of the block (replication) (B) — Porównanie
parametrów regresji obliczonej dla pełnego zestawu danych (A) oraz po usunięciu danych dla poletek na początku i na końcu bloku (powtórzenia) (B).
Coefficient
Współczynnik A B Difference Różnica Test jednorodności Homogeneity test
Experiment 1 — Doświadczenie 1 b -0.6683 0.6663 0.0020 t* = -0.0281 p = 0.978 F** = 0.0540 p = 0.816 Experiment 2 — Doświadczenie 2 b -0.6920 -0.6902 -0.0018 t* = -0.0454 p = 0.964 F** = 0.0248 p = 0.875 * Steel R.G.D., Torrie J.H. 1960, pp. 173-174
** Steel R.G.D., Torrie J.H. 1960, pp. 319-320, Eland R. 1964 p. 337
The results in Table 3 show that the regression coefficients calculated without data for plots at the ends of the blocks (replications) (B) do not differ significantly from the results for the full set of data (A) where the value of x for plots at the ends of the replications have been calculated according to the formulas 4a or 4b, it means with the use the yield of only one neighboring plot. These differences are highly not significant statistically, and so both regressions can be thought of as homogeneous.
In the following researches the calculations were carried out using the complete set of 600 x, y and y' values and concomitant variables x, x1, x2, x3.... obtained in the process of iteration.
Calculation of successive concomitant variables with iteration method
and their impact on the object averages
Verification of the proposed method for statistical analysis of results of field experiments carried out in several localities in the randomized block design was continued using the raw results of seed yields harvested from the plots. The calculations were carried out for both experiments: 1 (DW1 – with the breeding strains from the three breeding) and 2 (DW2 – with experimental hybrids from one breeding). The data for the calculations consisted of, as described earlier, 600 threes values of y, y' and x. The values of the concomitant variable x have been calculated in accordance with the formula 3a. Average values for objects have been used initially to create the second section of equation. After doing a regression
analysis between values y' and x and after the correction of y with the use of obtained regression coefficient the new values of adjusted average values for objects were calculated. These average values were used in the next cycle to calculate the new concomitant variables and after next regression analysis new object averages were calculated. This cycle has been repeated ten times. Results for sequence of calculations of object averages for experiment DW1 were summarized in Table 4, and for the experiment DW2 in Table 5. The average values of objects fluctuated less and less during the iterative process progress. This process was shown at the bottom of the tables with the following values:
— the sum of the changes in the absolute value (modules) of object averages, — the average of the changes in absolute values (modules) of the object averages, — the maximum change of object averages,
— the minimum change of object averages.
The course of these changes were also shown as graphs on Figures 3 (DW1) and 4 (DW2) where the following changes in relation to the initial values were presented. Figures 5 (DW1) and 6 (DW2) were showing how to change the ranking of object averages on the following stages of iteration. Figures 5a (DW1) and 6a (DW2) shown the changes of the object averages occurring during iterative process of calculation of the following concomitant variables. On these figures it could be seen how individual objects differently responded on elimination the effects linked to competition between plants growing on adjacent plots in field trial. This phenomenon could be best track on the well-known standard varieties Chagall and Castille. Lush, well branching and high Chagall variety maintained its position with small changes. While lower, more delicate and less branching the Castille variety regained its position in the course of correcting the effects of plant competition.
Changes to the object averages occurring during iterative process of calculation the concomitant variable were varied for individual objects, but after ten iterations all reached constant values within the limits of the permissible error. Average object values obtained after the removal of the influence of competition between plants on the test plots should reflect the real ability to seed yielding in terms of monoculture (on plantations).
Comparison of the results of seed yield: calculated on the basis
of the raw data of seed yields from the plots and after their adjustment
by means of regression
Study concerned the seed yielding ability of the new experimental varieties and hybrids of double improved (double low or “00”) winter oilseed rape. They constituted an attitude to carry out the selection and choose the best to further stages of breeding or for license application. Presented calculations concerned the yields of air dry seeds (9% moisture content) converted from kg/plot to dt/ha.
O bj ect m ean ch an ges w ith th e i ter at io n pr og res s i n cal cu lat io n o f c onc om ita nt acco m pan yi ng v ar iab le ( ex per im en t 1 D W 1) Zm iany śr ed ni ch obi ek tow yc h w m iar ę pos tę pu ite rac yj ne go pr oc es u obl ic zan ia zm ie nne j t ow ar zy sz ąc ej (doś w iadc ze ni e 1 D W 1) O bj ec t O bi ek t R aw Su ro w e C or re ct ed re gr es si on w ith su bs eq ue nd c ha ng es o f c on co m ita nt v ar iab le K or yg ow an e r eg res ją w ra z z k ol ej ny m i z m ia na m i z m ie nn ej to w ar zys zą ce j C ov ar . 1 C ov ar . 2 C ov ar . 3 C ov ar . 4 C ov ar . 5 C ov ar . 6 C ov ar . 7 Co va r. 8 C ov ar . 9 C ov ar . 1 0 C ov B K 8 /0 8 41 .5 63 1 40 .9 82 9 40 .6 49 1 40 .4 58 2 40 .3 49 5 40 .2 87 5 40 .2 51 9 40 .2 31 1 40 .2 18 7 40 .2 11 3 40 .2 06 8 40 B K 1 1/ 08 40 .6 23 9 39 .7 16 3 39 .2 23 1 38 .9 52 7 38 .8 02 7 38 .7 17 9 38 .6 68 8 38 .6 39 6 38 .6 21 8 38 .6 10 7 38 .6 03 6 38 B K 2 0/ 08 37 .5 16 7 37 .3 11 1 37 .2 09 2 37 .1 58 1 37 .1 31 6 37 .1 17 1 37 .1 08 4 37 .1 02 8 37 .0 98 9 37 .0 96 1 37 .0 94 0 37 B K 2 2/ 08 39 .2 02 8 39 .1 80 6 39 .2 16 4 39 .2 59 9 39 .2 95 4 39 .3 20 6 39 .3 37 2 39 .3 47 8 39 .3 54 4 39 .3 58 5 39 .3 60 9 39 B K 2 3/ 08 41 .5 19 6 41 .1 95 9 41 .0 17 9 40 .9 21 6 40 .8 70 4 40 .8 43 3 40 .8 28 9 40 .8 21 3 40 .8 17 3 40 .8 15 1 40 .8 13 9 40 B K 2 5/ 08 40 .3 87 0 40 .4 29 9 40 .5 12 5 40 .5 91 6 40 .6 54 4 40 .7 00 4 40 .7 32 5 40 .7 54 5 40 .7 69 4 40 .7 79 5 40 .7 86 3 40 B K 2 6/ 08 41 .5 96 5 41 .2 95 9 41 .1 66 3 41 .1 17 8 41 .1 05 6 41 .1 08 1 41 .1 15 2 41 .1 22 9 41 .1 29 6 41 .1 34 9 41 .1 39 0 41 B O 7 -7 7 40 .3 91 9 39 .6 82 1 39 .2 66 5 39 .0 22 2 38 .8 78 4 38 .7 93 7 38 .7 43 7 38 .7 14 1 38 .6 96 5 38 .6 86 0 38 .6 79 8 38 B O 8 -1 37 42 .0 80 7 41 .5 30 9 41 .2 48 6 41 .1 04 7 41 .0 31 9 40 .9 95 2 40 .9 76 8 40 .9 67 4 40 .9 62 6 40 .9 60 1 40 .9 58 7 40 B O 1 34 1/ 106 42 .8 50 6 42 .6 51 4 42 .5 18 3 42 .4 37 3 42 .3 91 8 42 .3 68 0 42 .3 56 7 42 .3 52 1 42 .3 50 9 42 .3 51 2 42 .3 52 1 42 B O 1 34 1/ 3/ 06 40 .5 63 8 41 .1 22 8 41 .4 17 9 41 .5 71 0 41 .6 48 9 41 .6 87 8 41 .7 07 0 41 .7 16 3 41 .7 20 7 41 .7 22 7 41 .7 23 6 41 B O 1 55 2/ 7/ 06 41 .1 55 9 41 .2 98 2 41 .3 37 5 41 .3 31 7 41 .3 10 1 41 .2 86 1 41 .2 65 0 41 .2 48 2 41 .2 35 5 41 .2 26 3 41 .2 19 7 41 B O 1 56 6/ 3/ 06 39 .4 97 6 40 .7 16 4 41 .4 37 3 41 .8 61 4 42 .1 09 9 42 .2 56 0 42 .3 42 5 42 .3 94 4 42 .4 25 8 42 .4 45 2 42 .4 57 3 42 B O 1 89 9-1/0 8 35 .9 48 7 36 .7 66 7 37 .2 11 0 37 .4 52 9 37 .5 85 3 37 .6 58 6 37 .7 00 0 37 .7 24 0 37 .7 38 2 37 .7 46 8 37 .7 52 2 37 M A 2 21 39 .0 33 6 38 .7 83 6 38 .6 86 4 38 .6 58 2 38 .6 58 4 38 .6 68 0 38 .6 79 2 38 .6 88 9 38 .6 96 6 38 .7 02 3 38 .7 06 5 38 M A 2 22 41 .8 90 0 41 .9 39 8 41 .9 11 6 41 .8 58 0 41 .8 03 6 41 .7 57 5 41 .7 22 0 41 .6 95 8 41 .6 77 1 41 .6 64 1 41 .6 55 2 41 M A 2 23 39 .7 81 4 39 .9 51 5 39 .9 52 0 39 .9 02 0 39 .8 47 1 39 .8 01 6 39 .7 67 6 39 .7 43 5 39 .7 26 8 39 .7 15 4 39 .7 07 6 39 M A 2 24 40 .3 95 8 40 .2 72 1 40 .2 01 0 40 .1 63 4 40 .1 44 9 40 .1 36 6 40 .1 33 2 40 .1 32 0 40 .1 31 8 40 .1 31 9 40 .1 32 1 40 M A 2 25 42 .3 27 4 42 .5 51 2 42 .7 36 9 42 .8 66 6 42 .9 49 0 42 .9 98 1 43 .0 26 0 43 .0 41 1 43 .0 48 8 43 .0 52 5 43 .0 54 0 43 M A 2 26 40 .2 75 3 40 .6 03 7 40 .8 18 8 40 .9 61 5 41 .0 56 2 41 .1 19 1 41 .1 60 6 41 .1 88 1 41 .2 06 1 41 .2 18 0 41 .2 25 7 41 M A 2 27 39 .3 91 1 39 .4 47 8 39 .4 58 0 39 .4 52 3 39 .4 43 2 39 .4 34 9 39 .4 28 5 39 .4 24 0 39 .4 20 8 39 .4 18 8 39 .4 17 4 39 M A 2 28 43 .7 21 4 43 .6 35 0 43 .5 04 2 43 .3 85 0 43 .2 92 4 43 .2 25 8 43 .1 79 7 43 .1 48 6 43 .1 27 8 43 .1 14 0 43 .1 04 9 43 M A 2 29 40 .4 56 6 40 .5 63 1 40 .5 75 2 40 .5 60 9 40 .5 44 2 40 .5 31 7 40 .5 23 8 40 .5 19 5 40 .5 17 3 40 .5 16 5 40 .5 16 3 40 C AS TI LL E 40 .2 55 9 40 .9 06 1 41 .3 17 5 41 .5 73 6 41 .7 31 1 41 .8 27 4 41 .8 86 2 41 .9 22 2 41 .9 44 4 41 .9 58 2 41 .9 66 7 41 C HAGAL L 42 .4 30 8 42 .3 23 3 42 .2 65 2 42 .2 35 7 42 .2 22 2 42 .2 17 4 42 .2 16 9 42 .2 18 2 42 .2 20 2 42 .2 22 2 42 .2 23 9 42 Su m o f d iff er en ce m od ul s Su m a m od uł ów ró żn ic 8. 73 26 4. 90 58 2. 94 05 1. 78 38 1. 09 94 0. 68 50 0. 43 01 0. 27 18 0. 17 37 0. 11 28 0. M ea n of d iff er en ce m od ul s Śr ed ni a m od uł ów ró żn ic 0. 34 93 0. 19 62 0. 11 76 0. 07 14 0. 04 40 0. 02 74 0. 01 72 0. 01 09 0. 00 69 0. 00 45 0. M ax im um d iffe re nc e M ak sy m al na ró żn ic a 1. 21 88 0. 72 09 0. 42 41 0. 24 85 0. 14 61 0. 08 65 0. 05 18 0. 03 15 0. 01 94 0. 01 21 0. M in im um d iffe re nc e Mi ni m al na ró żn ic a 0. 02 23 0. 00 05 0. 00 56 0. 00 02 0. 00 24 0. 00 05 0. 00 11 0. 00 11 0. 00 01 0. 00 02 0.
C han ges in o bj ect m ean s w ith th e i ter at io n p ro gr es s i n cal cu lat io n o f co nco m itan t v ar iab le ( ex per im en t 2 D W 2) Zm iany śr ed ni ch obi ek tow yc h w m iar ę pos tę pu it er ac yj ne go pr oc es u obl ic zan ia zm ie nne j t ow ar zy sz ąc ej (doś w iadc ze ni e 2 D W 2) O bj ec t O bi ek t R aw Su ro w e C or re ct ed re gr es si on w ith su bs eq ue nd c ha ng es o f c on co m ita nt v ar iab le K or yg ow an e r eg res ją w ra z z k ol ej ny m i z m ia na m i z m ie nn ej to w ar zys zą ce j C ov ar . 1 Co va r. 2 C ov ar . 3 C ov ar . 4 C ov ar . 5 C ov ar . 6 C ov ar . 7 C ov ar . 8 C ov ar . 9 C ov ar . 1 0 C ov 2 0 8 D E0 03 70 42 .1 26 9 41 .4 82 7 41 .1 92 2 41 .0 80 3 41 .0 41 2 41 .0 28 3 41 .0 24 3 41 .0 23 1 41 .0 22 8 41 .0 22 7 41 .0 22 7 41 2 0 8 D E0 03 72 48 .1 59 0 47 .8 63 5 47 .7 29 0 47 .6 79 9 47 .6 65 7 47 .6 63 5 47 .6 64 6 47 .6 66 1 47 .6 67 3 47 .6 68 2 47 .6 68 7 47 TY 10 C2 5. 65 46 .2 46 9 46 .5 28 8 46 .7 32 6 46 .8 53 8 46 .9 19 8 46 .9 54 6 46 .9 72 7 46 .9 82 1 46 .9 87 0 46 .9 89 6 46 .9 90 9 46 TY 10 C2 7. 65 45 .3 40 2 44 .8 24 8 44 .5 89 5 44 .4 95 6 44 .4 59 9 44 .4 45 9 44 .4 40 1 44 .4 37 4 44 .4 36 0 44 .4 35 2 44 .4 34 8 44 M R 2 52 6 43 .1 36 5 42 .5 99 2 42 .3 95 9 42 .3 41 4 42 .3 36 4 42 .3 43 1 42 .3 50 1 42 .3 55 2 42 .3 58 4 42 .3 60 3 42 .3 61 5 42 M R 2 55 5 44 .4 45 8 44 .1 79 7 44 .0 82 1 44 .0 57 1 44 .0 55 5 44 .0 59 1 44 .0 62 6 44 .0 65 2 44 .0 66 9 44 .0 67 9 44 .0 68 5 44 M R 2 55 6 44 .4 00 6 43 .8 67 6 43 .5 73 2 43 .4 27 7 43 .3 57 8 43 .3 23 4 43 .3 06 0 43 .2 96 7 43 .2 91 7 43 .2 89 0 43 .2 87 4 43 M R 2 57 3 46 .5 05 4 46 .0 60 4 45 .8 22 2 45 .7 11 4 45 .6 63 1 45 .6 42 5 45 .6 33 8 45 .6 30 1 45 .6 28 7 45 .6 28 1 45 .6 27 9 45 M R 2 65 2 43 .9 14 7 43 .6 83 4 43 .5 44 7 43 .4 72 9 43 .4 37 9 43 .4 21 3 43 .4 13 4 43 .4 09 6 43 .4 07 8 43 .4 07 0 43 .4 06 6 43 M R 2 66 2 43 .1 73 3 43 .0 88 7 43 .0 46 9 43 .0 28 8 43 .0 21 7 43 .0 19 4 43 .0 18 9 43 .0 19 1 43 .0 19 5 43 .0 19 9 43 .0 20 2 43 M R 2 68 8 43 .9 84 1 44 .1 72 4 44 .2 07 5 44 .1 94 2 44 .1 75 4 44 .1 61 8 44 .1 53 6 44 .1 49 1 44 .1 46 7 44 .1 45 5 44 .1 45 0 44 M R 2 69 2 44 .0 57 3 43 .4 95 0 43 .2 90 2 43 .2 36 3 43 .2 29 8 43 .2 33 9 43 .2 38 2 43 .2 41 1 43 .2 42 7 43 .2 43 5 43 .2 43 9 43 M R 2 69 8 44 .6 60 9 45 .2 61 4 45 .5 35 6 45 .6 43 4 45 .6 82 4 45 .6 95 8 45 .7 00 3 45 .7 01 6 45 .7 01 8 45 .7 01 8 45 .7 01 7 45 M R 2 69 9 46 .4 77 2 46 .6 47 3 46 .7 91 4 46 .8 84 8 46 .9 38 7 46 .9 68 5 46 .9 84 8 46 .9 93 6 46 .9 98 5 47 .0 01 2 47 .0 02 7 47 M R 2 70 0 45 .4 57 8 46 .0 16 8 46 .3 18 3 46 .4 65 7 46 .5 36 6 46 .5 71 7 46 .5 89 8 46 .5 99 5 46 .6 04 8 46 .6 07 7 46 .6 09 4 46 M R 2 71 1 45 .1 99 1 46 .1 87 5 46 .6 13 0 46 .7 65 6 46 .8 13 0 46 .8 25 5 46 .8 27 7 46 .8 27 4 46 .8 26 8 46 .8 26 3 46 .8 26 0 46 M R 271 5 48 .0 15 2 48 .3 09 0 48 .4 19 5 48 .4 51 5 48 .4 57 8 48 .4 57 7 48 .4 56 7 48 .4 55 9 48 .4 55 4 48 .4 55 2 48 .4 55 1 48 M R 2 71 9 45 .6 00 7 46 .1 50 1 46 .3 81 3 46 .4 55 9 46 .4 71 5 46 .4 69 5 46 .4 64 1 46 .4 59 5 46 .4 56 2 46 .4 54 1 46 .4 52 8 46 M R 2 72 9 40 .4 31 5 41 .2 97 7 41 .7 32 0 41 .9 21 4 41 .9 98 8 42 .0 30 1 42 .0 42 7 42 .0 47 9 42 .0 50 0 42 .0 50 9 42 .0 51 2 42 M R 2 73 7 42 .4 69 8 41 .1 17 9 40 .4 48 3 40 .1 60 7 40 .0 45 0 39 .9 99 1 39 .9 80 6 39 .9 73 0 39 .9 69 7 39 .9 68 2 39 .9 67 5 39 M R 2 74 2 44 .8 63 7 44 .5 45 0 44 .3 81 9 44 .3 08 5 44 .2 76 8 44 .2 62 9 44 .2 56 5 44 .2 53 3 44 .2 51 6 44 .2 50 7 44 .2 50 2 44 M R 2 56 0 40 .7 64 8 40 .4 36 0 40 .2 59 6 40 .1 74 5 40 .1 34 3 40 .1 14 7 40 .1 04 7 40 .0 99 4 40 .0 96 5 40 .0 94 9 40 .0 93 9 40 Vi sb y 47 .9 39 4 48 .2 46 4 48 .3 91 1 48 .4 52 5 48 .4 78 3 48 .4 90 0 48 .4 95 7 48 .4 98 8 48 .5 00 6 48 .5 01 6 48 .5 02 2 48 C as tille 45 .6 94 3 46 .7 54 4 47 .2 75 4 47 .4 95 7 47 .5 81 7 47 .6 13 9 47 .6 25 7 47 .6 29 8 47 .6 31 2 47 .6 31 5 47 .6 31 5 47 C ha ga ll 44 .1 49 4 44 .3 98 8 44 .4 61 0 44 .4 55 0 44 .4 35 3 44 .4 18 5 44 .4 07 1 44 .4 00 1 44 .3 96 0 44 .3 93 6 44 .3 92 2 44 Su m o f d iff er en ce m od ul s Su m a m od uł ów ro żn ic 12 .2 28 2 5. 77 63 2. 40 01 0. 97 67 0. 43 01 0. 21 06 0. 10 78 0. 05 73 0. 03 09 0. 01 70 0. M ea n o f d iff er en ce m od ul s Śr ed ni a m od uł ów ró żn ic 0. 48 91 0. 23 11 0. 09 60 0. 03 91 0. 01 72 0. 00 84 0. 00 43 0. 00 23 0. 00 12 0. 00 07 0. M ax im um d iffe re nc e M ak sy m al na ró żn ic a 1. 35 20 0. 66 96 0. 28 76 0. 11 57 0. 04 59 0. 01 85 0. 00 97 0. 00 53 0. 00 29 0. 00 17 0. M in im um d iffe re nc e M in im al na ró żn ic a 0. 08 47 0. 03 51 0. 00 60 0. 00 16 0. 00 01 0. 00 05 0. 00 02 0. 00 03 0. 00 00 0. 00 00 0.
Ex pe rim en t 1 D W 1 — D oś wi adc ze ni e 1 D W 1 Ex pe rim en t 2 D W 2 — D oś wi adc ze ni e 2 D W 2 Fi g. 3 a nd 4. C ha ng es i n t he obj ec t m ea ns du ring t he pr og re ss i n i te ra tion pr oc es s o f t he co nco m ita nt v ar iab le cal cu Zm iany śr edni ch obi ek to wy ch w m ia rę pos tę pu ite rac yj ne go ob lic zani a zm ie nne j t ow ar zy sz ąc ej — [d t/h a]
Ex pe rim en t 1 D W 1 — D oś w ia dcz en ie 1 D W 1 Ex pe rim en t 2 D W 2 — D oś w ia dcz en ie 2 D W 2 Fi g. 5 a nd 6 . C ha ng es i n th e ran ki ng o f ob ject m ean s w ith t he pr og res s in it er at io n pr oces s of co nco m itan t var iab le cal cu Zm iany rank ingu śr edni ch obi ek tow yc h w m iar ę pos tę pu ite rac yj ne go obl ic zani a zm ie nne j t ow ar zy sz ąc ej R atin g: 2 5 th e hig he st y ie ld , 1 th e lo w es t y ie ld — O ce na: 2 5 naj wy żs zy pl on, 1 naj ni żs zy pl on
Ex pe rim en t 1 D W 1 — D oś w ia dcz en ie 1 D W 1 Ex per im en t 2 D W 2 — D oś w ia dcz en ie 2 D W 2 Fi g. 5 a and 6 a C ha ng es o f o bj ect m ea n v al ue s w ith th e p ro gr es s i n iter at io n p ro ces s o f co nco m ita nt v ar iab le cal cu lat io n — Zm śr edni ch obi ek tow yc h w m iar ę pos tę pu ite rac yj ne go obl ic zani a zm ie nne j t ow ar zy sz ąc ej — S ee d yie ld in d t/ha — P lon nas ion w
Experiment 1 (DW1)
Variance analysis was performed for two factors (strains × locality) with replications (4) and average yields of seeds for the tested breeding strains were calculated. The calculations were made on the raw yields of plots (A), and after the correction of the effects of competition among plants from adjacent plots (B) using regression after the calculation of the concomitant variable by 10 iterations. The results of the analyses of variance were presented in Tables 6 and 8.
Table 6
Variance analyses for raw data and for data corrected with regression — Analizy wariancji
dla danych surowych i skorygowanych regresją
Experiment 1 DW1 — Doświadczenie 1 DW1
A – Variation analysis for raw data — Analiza wariancji dla danych surowych
Variability source
Źródło wariancji SS df MS F wartość p p-value Test F (0.05)
Localities — Miejscowości 74097.050 5 14819.41 716.0549 1.3E-211 2.234045
Strains — Rody 1616.288 24 67.34533 0.81071 0.717243 1.608437
Interaction — Interakcja 9968.353 120 83.06961 4.013817 7.81E-27 1.258759
Error — Błąd 9313.161 450 20.69591
Total — Razem 94994.850 599
B – Variation analysis for data corrected with regression Analiza wariancji dla danych poprawionych regresją Variability source
Źródło wariancji SS df MS F wp-value artość p
Test
F(0.05)
Regression — Regresja 13311.63 1 13311.63 97.45397 2.14E-21 3.857056
Residual — Resztkowy 81683.22 598 136.594
Total — Całkowita 94994.85 599
Localities — Miejscowości 74097.05 5 14819.41 1381.371 5.447E-270 2.23409
Strains — Rody 1506.715 24 62.7798 5.851933 1.1816E-15 1.54164
Interaction — Interakcja 1262.566 120 10.52138 0.980736 0.54197819 1.25884
Error — Błąd 4816.892 449 10.72804
Residual — Resztkowy 81683.22 598
For raw yields of seeds from plots interaction “strains × localities” proved to be statistically very significant. Taking this into account the differences in object averages of the examined strains proved to be statistically insignificant. There was no base to carry out effective selection.
Similar analysis carried out for regression adjusted seed yields from the plots showed the insignificant interactions between “strains × localities” and the differences among strains turned out to be very important and significant. So the adjustment of plot yields in addition to the removal of the effects of competition resulted in a solid foundation to carry out effective selection.
Table 7
Variance analyses for raw data and for data corrected with regression — Analizy wariancji
dla danych surowych i skorygowanych regresją
Experiment 2 DW2 — Doświadczenie 2 DW2
A – Variation analysis for raw data — Analiza wariancji dla danych surowych
Variability source
Źródło wariancji SS df MS F wartość p p-value Test F (0.05)
Localities — Miejscowości 73426.570 5 14685.31 873.7458 4.5E-229 2.234045
Strains — Rody 2337.427 24 97.39278 1.338396 0.154452 1.608437
Interaction — Interakcja 8732.195 120 72.76829 4.329563 8.06E-30 1.258759
Error — Błąd 7563.288 450 16.80731
Total — Razem 92059.480 599
B – Variation analysis for data corrected with regression Analiza wariancji dla danych poprawionych regresją Variability source
Źródło wariancji SS df MS F wp-value artość p
Test
F(0.05)
Regression — Regresja 7766.67 1 7766.67 55.09923 3.96E-13 3.85706
Residual — Resztkowy 84292.81 598 140.9579
Total — Całkowita 92059.48 599
Localities — Miejscowości 73426.57 5 14685.31 871.3919 1.7E-92 2.28985
Strains — Rody 3574.478 24 148.9366 8.837546 6.13E-17 1.60844
Interaction — Interakcja 2022.325 120 16.85271 1.435991 0.004662 1.25884
Error — Błąd 5269.437 449 11.73594
Residual — Resztkowy 84292.81 598
Table 8 shows the average seed yields for the tested strains in order of decreasing yields and the value of the lowest significant differences at confidence levels 0.05 and 0.01. The removal of the effects of competition among plants growing on the adjacent plots had changed not only the accuracy of the assessment of strains but also to their lineup (ranking).
Experiment 2 (DW2)
On the data of experiment 2 (DW2) a similar calculation was done as for the data from the experiment 1 (DW1). Their results were presented in Tables 7 and 9.
In previous work (Krzymański at al. 2012), it was found that in this experiment the soil variability inside the block dominated on the competition effects of plants growing on adjacent plots. Both two-factor ANOVA analyses of variance with replications so for the raw data (A) and for regression-adjusted data (B) showed:
— statistical significance of interaction “hybrids × localities” in both analysis, — slight differentiation in raw seed yields of hybrids but only at the level of
— very significant differentiation of hybrid yields after removing the effects of competition between plants growing on adjacent plots in field trial.
In this experiment, in which the influence of soil variability inside the block dominated, also removing the effects of competition had changed not only the accuracy of the assessment of hybrids but also changed their rank in order of decreasing yields.
Table 8 Mean values for obcjects calculated for raw data and for data corrected with regression
Średnie obiektowe obliczone z danych surowych i poprawionych regresją
Seed yield in dt/ha — Plon nasion w dt/ha Experiment 1 DW1 — Doświadczenie 1 DW1
Lp Strain Ród A raw data surowe dane Strain Ród B
regression corrected data dane skorygowane regresją
1 MA 228 43.72 MA 228 43.10 2 BO 1341/106 42.85 MA 225 43.05 3 CHAGALL 42.43 BO 1566/3/06 42.46 4 MA 225 42.33 BO 1341/106 42.35 5 BO 8-137 42.08 CHAGALL 42.23 6 MA 222 41.89 CASTILLE 41.97 7 BK 26/08 41.60 BO 1341/3/06 41.72 8 BK 8/08 41.56 MA 222 41.65 9 BK 23/08 41.52 MA 226 41.23 10 BO 1552/7/06 41.16 BO 1552/7/06 41.22 11 BK 11/08 40.62 BK 26/08 41.14 12 BO 1341/3/06 40.56 BO 8-137 40.96 13 MA 229 40.46 BK 23/08 40.81 14 MA 224 40.40 BK 25/08 40.79 15 BO 7-77 40.39 MA 229 40.52 16 BK 25/08 40.39 BK 8/08 40.20 17 MA 226 40.28 MA 224 40.13 18 CASTILLE 40.26 MA 223 39.70 19 MA 223 39.78 MA 227 39.42 20 BO 1566/3/06 39.50 BK 22/08 39.36 21 MA 227 39.39 MA 221 38.71 22 BK 22/08 39.20 BO 7-77 38.68 23 MA 221 39.03 BK 11/08 38.60 24 BK 20/08 37.52 BO 1899-1/08 37.76 25 BO 1899-1/08 35.95 BK 20/08 37.09 LSD — NIR p = 0.05 ns 1.821 LSD — NIR p = 0.01 ns 4.031
Table 9 Mean values for obcjects calculated for raw data and for data corrected with regression
Średnie obiektowe obliczone z danych surowych i poprawionych regresją
Seed yield in dt/ha — Plon nasion w dt/ha Experiment 2 DW2 — Doświadczenie 2 DW2
Lp Strain Ród A raw data surowe dane Strain Ród B
regression corrected data dane skorygowane regresją
1 2 08 DE00372 48.16 Visby 48.50 2 MR 2715 48.02 MR 2715 48.46 3 Visby 47.94 2 08 DE00372 47.67 4 MR 2573 46.51 Castille 47.63 5 MR 2699 46.48 MR 2699 47.00 6 TY10C25.65 46.25 TY10C25.65 46.99 7 Castille 45.69 MR 2711 46.83 8 MR 2719 45.60 MR 2700 46.61 9 MR 2700 45.46 MR 2719 46.45 10 TY10C27.65 45.34 MR 2698 45.70 11 MR 2711 45.20 MR 2573 45.63 12 MR 2742 44.86 TY10C27.65 44.43 13 MR 2698 44.66 Chagall 44.39 14 MR 2555 44.45 MR 2742 44.25 15 MR 2556 44.40 MR 2688 44.14 16 Chagall 44.15 MR 2555 44.07 17 MR 2692 44.06 MR 2652 43.41 18 MR 2688 43.98 MR 2556 43.29 19 MR 2652 43.91 MR 2692 43.24 20 MR 2662 43.17 MR 2662 43.02 21 MR 2526 43.14 MR 2526 42.36 22 MR 2737 42.47 MR 2729 42.05 23 2 08 DE00370 42.13 2 08 DE00370 41.02 24 MR 2560 40.76 MR 2560 40.09 25 MR 2729 40.43 MR 2737 39.97 LSD — NIR p = 0.05 4.777 2.299 LSD — NIR p = 0.01 6.315 3.039
The expected heritability and genetic gain calculated on the basis
of the variance analysis
Expected heritability and genetic gain in seed yield after selection of breeding strains or experimental hybrids were calculated on the basis of a two-factor with repetition ANOVA variance analysis. It was assumed that for further breeding the five best yielding objects were selected. However, it should be noted that these
estimates are too optimistic because despite the fact that they are based on the field trials made in four replications and carried out in six localities but only in just one year. This did not allow to remove the interaction of the “genotype × year” from of genetic variation. As it was shown (Krzymański at al. 1983) this interaction in case of winter oilseed rape had a bigger impact than the interaction of “genotypes × localities”. Heritability calculation was made according the method which has been proposed by Allard (1966). This method was based on the expected values of the mean squares from the analysis of variance. The results of the calculations have been presented in Table 10
Table 10 Expected genetic gain for selection of the best yielding five objects
Spodziewany postęp genetyczny przy selekcji najlepiej plonujących obiektów
Experiment Doświadczenie DW1 DW2 A raw data surowe dane B regression corrected data — dane skorygowane regresją A raw data surowe dane B regression corrected data — dane skorygowane regresją The best 5 breeding objects
5 najlepszych obiektów hodowlanych 43.7214 42.8506 43.43.0544 0988 48.48.0152 1590 48.4551 47.6691
42.3274 42.4649 46.5054 47.0035
42.0807 42.3531 46.4772 46.9916
41.8900 41.7240 46.2469 46.8258
Mean value of the best 5 objects Średnia 5 najlepszych obiektów.
42.5740 42.5391 47.2892 47.5298
Overall mean breeding objects
Średnia ogólna obiektów hodowlanych 40.5292 40.4635 44.5196 44.3950
Selection difference — Różnica selekcyjna 2.0448 2.0756 2.7696 3.1348
F 0.8107 5.8650 1.3384 8.8375
p 0.7172 1.2E-15 0.1545 6.1E-17
Heritability — Odziedziczalność h2 0.0000 0.8291 0.2528 0.8868
Expected genetic gain
Spodziewany postęp genetyczny:
in dt/ha — w dt/ha 0 1.7209 0.7003 2.7801
as % of overall mean
w % średniej ogólnej 0 4.2529 1.5729 6.2622
* Heritability calculated on the basis of the components of the mean squares with analysis
of variance — Odziedziczalność obliczana na podstawie składowych średnich kwadratów z analizy
wariancji (Allard 1966
Presented results of the calculations suggested significant benefits as a result of the elimination of competition effects among the plants growing on adjacent plots in field trial.
Compatibility of results obtained from field trials growing in different
localities
A measure of the effectiveness of the proposed method to eliminate variability resulting from plant competition growing on adjacent plots into trial is the statistical significance of the differences among tested objects and the expected genetic progress in selection process. Comparison of the correlation between object averages obtained in individual localities can also provide another measure of progress reached and the effectiveness derived with the proposed method. The calculated correlation coefficients between object averages for each individual locality were presented in Tables 11 (DW1) and 12 (DW2).
Table 11 Correlation coefficients between average seed yields in various localities
Współczynniki korelacji pomiędzy średnimi plonami nasion w różnych miejscowościach
Experiment 1 DW1 — Doświadczenie 1 DW1
Locality
Miejscowość Borowo Małyszyn Strzelce Kończewice Łagiewniki Bąków
A. Calculations made on raw field results Obliczenia dokonane na surowych wynikach polowych
Borowo 1 Małyszyn -0.143 1 Strzelce 0.199 0.151 1 Kończewice -0.238 0.548 -0.227 1 Łagiewniki 0.050 -0.196 0.025 -0.335 1 Bąków 0.583 0.026 0.516 -0.347 0.123 1 All localities Wszystkie miejscowości 0.272 0.645 0.236 0.675 0.114 0.276
B. Calculations made on data corrected with regression Obliczenia dokonane na danych poprawionych regresją
Borowo 1 Małyszyn 0.556 1 Strzelce 0.815 0.512 1 Kończewice 0.308 0.495 0.336 1 Łagiewniki 0.640 0.292 0.616 -0.159 1 Bąków 0.769 0.616 0.732 0.367 0.648 1 All localities Wszystkie miejscowości 0.869 0.769 0.853 0.594 0.597 0.887
r ≥ 0.396 significant at p = 0.05 and r ≥ 0.505 significant at p = 0.01 r ≥ 0,396 istotne przy p = 0,05 i r ≥ 0,505 istotne przy p = 0,01
Table 12 Correlation coefficients between average seed yields in various localities
Współczynniki korelacji pomiędzy średnimi plonami nasion w różnych miejscowościach
Experiment 2 DW2 — Doświadczenie 2 DW2
Locality
Miejscowość Borowo Małyszyn Strzelce Kończewice Łagiewniki Bąków
A. Calculations made on raw field results Obliczenia dokonane na surowych wynikach polowych
Borowo 1 Małyszyn 0.407 1 Strzelce 0.711 0.193 1 Kończewice -0.212 0.135 -0.452 1 Łagiewniki 0.527 0.408 0.532 -0.330 1 Bąków 0.616 0.277 0.635 -0.325 0.563 1 All localities Wszystkie miejscowości 0.666 0.686 0.443 0.399 0.551 0.526
B. Calculations made on data corrected with regression Obliczenia dokonane na danych poprawionych regresją
Borowo 1 Małyszyn 0.821 1 Strzelce 0.845 0.843 1 Kończewice 0.287 0.434 0.228 1 Łagiewniki 0.834 0.815 0.840 0.315 1 Bąków 0.909 0.808 0.862 0.293 0.853 1 All localities Wszystkie miejscowości 0.895 0.919 0.873 0.591 0.892 0.898
r ≥ 0.396 significant at p = 0.05 and r ≥ 0.505 significant at p = 0.01 r ≥ 0,396 istotne przy p = 0,05 i r ≥ 0,505 istotne przy p = 0,01
Comparing the results of the calculations presented in both tables you could see clearly that the removal of the competition effects of plants growing on adjacent plots into trial, had improved greatly the consistency of the results obtained in different localities.
Conclusions
Adjustment of the effects of competition among plants growing on adjacent plots into field trial changed the ranking of examined breeding objects and significantly increased the accuracy of their ratings. It also allows you to estimate the possible to obtain genetic progress in terms of seed yield of winter oilseed rape when the selection is made on the basis of field experiment conducted in several localities.References
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