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### Description

**Introduction**

Long-term field experiments are a valuable research infrastructure to provide information about plant × environment interaction and nutrient use. The ‘Eternal Rye’ trial at the University of Halle-Wittenberg, Germany, was established by Julius Kühn in 1878 and is the world’s second oldest long-term fertilization trial. During the long history of the trial, the rye varieties changed at irregular intervals (3-50 years). While such changes are unavoidable during the long duration of the trial, they strongly influence the grain yield. In this study, different approaches are compared to identify and quantify the varietal effect over time in order to evaluate the isolated effect of the fertilization treatments.

**Materials and Methods**

*Field trial set-up*

The field trial is located in Halle/Saale, Saxony-Anhalt, Germany (https://ltehub.landw.uni-halle.de/eternal-rye). It consists of a continuous cultivation of winter rye with six fertilization treatments. The treatments include the application of farmyard manure, mineral fertilizers (PK, NPK), a combination of mineral and organic fertilization (NPK+FM), organic fertilization, which was ended in 1952 to analyze the after-effects, and an unfertilized control. The treatments are not replicated.

The rye varieties harvested were Saaleroggen (1879-1921), Petkuser (1922-1971), Danae (1972-1974), Dankowski Zlote (1975-1981), Janos (1982-1986), Pluto (1987-1992), Amando (1993-1999), Nikita (2000-2012), and Conduct (2013-2023).

*Factorization of grain yield*

Factorized grain yields show the deviation of the grain yield of each individual treatment from the annual mean grain yield across all treatments. The factorized grain yield $f_ty$ was calculated as

$f_ty=x_ty/x ̅_y$

where $t$ is the treatment, $y$ is the year, $x_ty$ is the grain yield for a given treatment and year, and $x̅_y$ is the mean grain yield of all treatments in a given year. A value >1 marks a yield higher than the annual average, whereas a value <1 indicates below-average yield. Due to the annual calculation of the mean value, the breeding progress is not considered and the differences between the treatments become clear.

*Adjusted grain yield*

In another approach the yield of all earlier used varieties is adjusted for the varietal effect by relating it to the yield level of the most recent variety. For each year this adjustment was calculated as

$Y_j=((Y_i-Y ̅_1 )⋅s_2)/s_1 +Y ̅_2$

where $Y_j$ is the adjusted annual yield, $Y_i$ is the annual yield that needs to be adjusted, $Ȳ_1$ and $s_1$ are the mean yield and the standard deviation of the previously used variety across all years, $Ȳ_2$ and $s_2$ are the mean grain yield and the standard deviation of the most recent variety (Chmielewski, 2023).

*Linear models*

To quantify the influence of both treatment and variety on the grain yield, variance component analyses were calculated, using both fixed and random models. Additionally, linear models were used describe the timely development of grain yield within the period of one variety.

**Results and discussion**

During periods with no varietal change (e.g. 1878-1921 and 1922-1971) negative trends in grain yield were detectable. With the introduction of new varieties, grain yield increases, due to breeding progress (Laidig et al., 2021). In recent years, the overall level of grain yield increased considerably, even in the completely unfertilized plot.

The factorization allowed to determine the deviation of yield in the six treatments from the annual mean yield. Annual recalculation of the mean yield helps to quantify differences within one specific year.

Adjusting the grain yield of previously used varieties helped to minimize the influence of the variety on the yield, hence it became possible to analyze the long-term effects of the fertilization under the influence of the given meteorological conditions of each year.

A variance component analysis was calculated in random models, eta squared (η²) in fixed models, showing that the influence of variety was smaller than of the treatment but still significant.

With the help of linear models, we aim to find a tool to describe the trend of grain yield development within one variety as well as the increase and change of trend after introducing a new variety to the trial. The analyses are not yet concluded but preliminary results are promising.

**References**

CHMIELEWSKI, F.-M. (2023) personal communication.

LAIDIG, F., et al. (2021) Long-term breeding progress of yield, yield-related, and disease resistance traits in five cereal crops of German variety trials. Theoretical and Applied Genetics 134, 3805–3827.

Keywords | Long-term experiment ; variety effect ; linear model |
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