Development of an improved - PDF document

Development of an improved Combined-O
Development of an improved Combined-Over-Year Uniformity Criterion Adrian Roberts & Kristian Kristensen Presentation •Introduction – DUS Testing & COYU •Flaws with current COYU •Consideration of potential improvements •Implementation of an improved

COYU Funded by UK & Danish Governm
COYU Funded by UK & Danish Governments and the Community Plant Variety Office Thanks to David Nutter, BioSS and UPOV TWC colleagues Introduction Plant Breeder’ Right PBR – protection for plant varieties International Convention for the Protection of New V

arieties of Plants •72 members â
arieties of Plants •72 members •International Union for the Protection of New Varieties of Plants (UPOV) •To be granted rights, a variety must be distinct, uniform and stable (DUS) DUS Distinct: differs from all other known varieties by one or more important botanical ch

aracteristics, such as height, maturity,
aracteristics, such as height, maturity, colour, etc. Uniform: plant characteristics are consistent from plant to plant within the variety Stable: plant characteristics are genetically fixed UPOV guidance  EU/national procedures New varieties compared to existing vari

eties in trials over two or three cycle
eties in trials over two or three cycles •Usually one location Characteristics defined in advance for a crop •Generally not performance characters •Qualitative or quantitative •Quite numerous (e.g. Pea ~ 20) DUS assessment DUS assessment Evaluation is character

-by-character •not multivariate
-by-character •not multivariate Must be distinct from every variety but only for one character in each Needs to be uniform in all characters considered Key methods for quantitative characteristics COYD – Combined Over-Years Distinctness criterion •Based

on ANOVA on trial x variety means â€
on ANOVA on trial x variety means •Applied character-by-character •Explained further in following talk COYU – Combined Over-Years Uniformity criterion •Uniformity based on within-plot SDs averaged over replicates •Uniformity compared to uniformity of

existing (reference) varieties in tria
existing (reference) varieties in trial •Adjustment for any relationship between uniformity and level of expression and for year effects COYU introduction Uniformity represented by log (SD+1) Often there’ a relationhip etween variaility and level of expression â

†’ adjutment for any relationhip ï
†’ adjutment for any relationhip etween uniformity and level of expression and for year effects Adjusted log SD of candidate compared to log SDs of comparable varieties COYU introduction Well established method Described more fully in UPOV document TGP/8 htt

p://www.upov.int/edocs/tgpdocs/en/tgp_8_
p://www.upov.int/edocs/tgpdocs/en/tgp_8_1.pdf Available in DUST software COYU method 1.Calculate within-plot SDs for each variety in each year. 2.Logarithm transform SDs after adding 1. 3.Estimate the relationship between the log SD and mean in each year using

moving averages. * 4.Adjust log
moving averages. * 4.Adjust log SDs based on the estimated relationships. 5.Average adjusted log SDs over years. 6.Calculate maximum allowable SD using an estimate of the variability in the uniformity of comparable varieties derived from ANOVA on the variety-by-yea

r table of adjusted log SDs. * 7
r table of adjusted log SDs. * 7.Compare the adjusted log SDs of candidate varieties with the maximum allowable SD. Log SD Adjustment Variability of measurements often depends on level of expression •So an adjustment is used to compensate •Currently the method used is 9

-Point Moving Average Log SD Adjus
-Point Moving Average Log SD Adjustment Variability of measurements often depends on level of expression •So an adjustment is used to compensate •Currently the method used is 9-Point Moving Average Log SD Adjustment Variability of measurements often depends on level o

f expression •So an adjustment is u
f expression •So an adjustment is used to compensate •Currently the method used is 9-Point Moving Average Steps: 1.Order log SDs (Y) by mean expression (X) to get Y(1), Y(2), …. Y(n) 2.Let the trend value Ti be the mean of the 9 values Y(i-4), Y(i-3, …

, Yi4 3.For X values ranked
, Yi4 3.For X values ranked 1 and 2, Ti is the mean of the first 3 values. 4.For the X value ranked 3, Ti is the mean of the first 5 values. 5.For the X value ranked 4, Ti is the mean of the first 7 values. 6.Similar for highest ranked X values. Log SD Adjustment

Variability of measurements often depe
Variability of measurements often depends on level of expression •So an adjustment is used to compensate •Currently the method used is 9-Point Moving Average Log SD Adjustment Variability of measurements often depends on level of expression •So an adjustment is used to

compensate •Currently the method u
compensate •Currently the method used is 9-Point Moving Average Maximum allowable SD 1-way ANOVA on adjusted log SDs of comparable varieties •candidates excluded & with year as classifying factor Gives variance of adjusted logSDs over comparable varieties (adjust

ed for year), V Maximum allowable SD
ed for year), V Maximum allowable SD 1-way ANOVA on adjusted log SDs of comparable varieties •candidates excluded & with year as classifying factor Gives variance of adjusted logSDs over comparable varieties (adjusted for year), V Maximum allowable (adjusted) log SD is

given by: where Mr is the me
given by: where Mr is the mean of the adjusted log SDs for the comparable varieties, k is the number of years, r is the number of comparable varieties and tp is the one-tailed Student t-value for probability p with degrees of freedom as for V. Concern with

current COYU method In a 2008 UPOV te
current COYU method In a 2008 UPOV technical working paper (TWC/26/17: Kristensen and Meyer), it was shown that the variance in the expression is underestimated. This leads to rejection of more varieties than expected In practice, this seems to be partially compensated for by use o

f smaller probability levels than usual
f smaller probability levels than usual •Typical probability level for COYD is 1% •Typical probability level for COYU is 0.1% Concern with current COYU method Simulation examples in a 2009 UPOV paper (TWC/27/15: Kristensen and Roberts), rejection rate was more than 2 times

expected (with probability value set at
expected (with probability value set at 0.05). Looked at effect of: •Number of reference varieties, 10 or 50 •Underlying relationship, none or linear •Size of variety by year interaction Three years, 10 candidates, probability level 0.05, 500 sims Concern with current

COYU method Simulation examples in a
COYU method Simulation examples in a 2009 UPOV paper (TWC/27/15: Kristensen and Roberts), rejection rate was more than 2 times expected (with probability value set at 0.05). Set No Assumptions in simulations Method No reference varieties, r Variety,V2/ Slope,  In

terac-tion,YV2 No adjust-men
terac-tion,YV2 No adjust-ment Moving average 1 50 0/0 0 0.045 0.111 2 10 0/0 0 0.050 0.121 3 50 125/0.1 0 0.111 0.111 4 10 125/0.1 0 0.121 0.119 5 50 0/0 100 0.045 0.117 6 10 0/0 100 0.050 0.123 7 50 12

5/0.1 100 0.093 0.108 8 10 1
5/0.1 100 0.093 0.108 8 10 125/0.1 100 0.099 0.116 Work on improving COYU Need to improve on the moving average adjustment method But want to keep the framework the same •Easier to gain acceptance in UPOV •Others welcome to propose more radical changes! S

o considered various alternative methods
o considered various alternative methods of adjustment •Needs to fit relationships between variation and level of expression well •No bias problem Methods of adjustment considered Polynomial: linear, quadratic … Flexible: many alternatives available including, •L

OESS •Proposed as part on improvem
OESS •Proposed as part on improvements to COYU in Büsche, Piepho & Meyer (2007) •Cubic smoothing spline •Fix degrees of freedom Looked at linear, quadratic, cubic regression and cubic smoothing spline with 3 and 4 degrees of freedom •Assess fit and rejection rat

es Examples of fitting Lolium peren
es Examples of fitting Lolium perenne (perennial ryegrass) Amenity with 44-80 varieties per year Forage with 34-77 varieties per year Germany, Netherlands and United Kingdom 10 years of data for most countries and characteristics 9 characteristics Brassica napus L.

oleifera (oil seed rape - spring so
oleifera (oil seed rape - spring sown) Denmark 9 years with 64-113 varieties per year 9 characteristics Pisum sativum (field pea) Denmark 9 years with 82-154 varieties per year 6 characteristics Examples of fitting Selected examples follow For more, see UPOV p

aper TWC/29/22, 2011, Kristensen and Ro
aper TWC/29/22, 2011, Kristensen and Roberts http://www.upov.int/edocs/mdocs/upov/en/twc/29/twc_29_22.pdf 25 Examples Lolium perenne, Amenity Characteristic 02 Growth habit in autumn of year of sowing Purple = straight line Green = quadratic Blue = cubic Red = cubic spli

ne (4 df) 26 Examples Lolium p
ne (4 df) 26 Examples Lolium perenne, Forage Characteristic 14 Inflorescence: number of spikelets Purple = straight line Green = quadratic Blue = cubic Red = cubic spline (4 df) 27 Examples Lolium perenne, Amenity Characteristic 8 Time of infl

orescence emergence in 2nd year
orescence emergence in 2nd year Purple = straight line Green = quadratic Blue = cubic Red = cubic spline (4 df) 28 Example Brassica napus Characteristic 03 Purple = straight line Green = quadratic Blue = cubic Red = cubic spline (4 df) Conclusions from

review on real data Spline with 4 deg
review on real data Spline with 4 degrees of freedom appeared to perform best •Flexible enough to cope with more complex relationships •Not too wiggly when no relationship •Can be affected by influential points Rejection rates - simulations Firstly look at effect of:

•Number of reference varieties, 10 or
•Number of reference varieties, 10 or 50 •Underlying relationship, none or linear •Size of variety by year interaction Three years, 10 candidates, probability level 0.05, 500 sims More info in UPOV papers TWC/31/15 and TWC/28/27 Rejection rates - simulations First

ly look at effect of: •Number of re
ly look at effect of: •Number of reference varieties, 10 or 50 •Underlying relationship, linear, quadratic or sinusoidal Three years, 10 candidates, probability level 0.05, 10,000 sims for 50 refs & 100,000 for 10 refs More info in UPOV papers TWC/31/15 Conclusions from

simulations •Reasonable reject rat
simulations •Reasonable reject rates for splines for null and linear relationships •For less linear relationships, a spline with 4 degrees of freedom works better •Clearly there are limits when degrees of freedom fixed but more robust On the basis of these results, UPOV T

echnical Working Party supported develo
echnical Working Party supported development of alternative COYU using cubic smoothing spline with 4 degrees of freedom Formulation Formulation Formulation We need to fit separate relationships for each year Ideally the ANOVA and curve fitting would be carried out in one step (

Büsche, Piepho & Meyer,2007), e.g.
Büsche, Piepho & Meyer,2007), e.g. in a mixed model However the same result can be obtained by fitting curves to each year separately and combining the results •At least for balanced data •Needs care •Makes implementation much easier, especially with fixed degrees of f

reedom Software Development Code dev
reedom Software Development Code developed for R •Freeware – useful for wide distribution in UPOV members •Facilities for cubic smoothing splines •Can fix df •Can access smoother matrices etc. Other software •Module for widely distributed DUST software i

n development, based on R •GenStat
n development, based on R •GenStat and SAS use R code? Issues arising Key issues to deal with: •Unbalanced data •Choice of probability levels •When a new variety has a level of expression outside that seen in comparable varieties Unbalanced data In gen

eral, the same varieties will be tested
eral, the same varieties will be tested in all years However some countries use cyclic planting •Referenced varieties are planted 2 in 3 years Need to adapt current algorithm to allow for this Choice of probability levels New probability levels should be larger than for current

COYU How to choose? •Single va
COYU How to choose? •Single value? •Chosen to minimise effect on decisions? •in individual crops/country? Initial practical exercise •UPOV members Extrapolation What to do when a new variety has a level of expression outside that seen in comparable varieties

•R code has indicator to show cases
•R code has indicator to show cases •UPOV practical exercise will show how common this is •What to do? Future work •Unbalanced data •Release software for evaluation in R and DUST •Practical exercise •Consideration of technical issues •Adoption