Genotype by environment interaction: why lines change rank

Every breeder has seen it. A line tops the trial at one station and sits in the middle at the next. Is it noise, or is the line really different there?

Often it's real. It's called genotype by environment interaction, or G×E, and it's one of the main reasons variety testing takes so many sites and years. This article explains it in plain terms, with reaction norms to make it visible, and covers what you can do about it.

The simple model

A plot's yield can be split into parts:

yield = average + line + environment + line × environment + plot error

The line part is what a line brings everywhere. The environment part is what a site-year does to every line: a dry year at a sandy site pulls everything down. The line × environment part is what's left over: how this particular line did in this environment, beyond what the first two predict.

If that last part is small, you can rank lines once and the ranking holds. If it's large, the best line depends on where and when you grow it.

Three kinds of G×E

Here is a made-up example with two lines at two sites, in tonnes per hectare.

Line A wins at the dry site by 0.6. Line B wins at the wet site by 0.7. The lines swap ranks. This is a crossover interaction, and it's the kind that changes decisions.

Now imagine Line B had yielded 4.1 at the wet site instead. Line A would win at both sites: by 0.6 at the dry site and by 1.0 at the wet one. The gap changes but the order holds. That's a scale interaction, sometimes called non-crossover. It matters for estimates, but it rarely changes which line you keep.

If the gap were the same at both sites, there would be no interaction at all.

Reaction norms

A reaction norm is a line's performance plotted against the environment. Put the environments along the bottom, ordered from poor to good, and draw one line per genotype.

• Parallel lines mean no G×E.
• Lines that fan out mean a scale interaction: some lines respond more to good conditions.
• Lines that cross mean a crossover interaction: ranks change.

The usual way to order environments is by their site mean, the average of all lines there. Regressing each line on the site mean gives its Finlay–Wilkinson slope. A slope near 1 means the line responds like the average line. Above 1, it gains more than most in good environments and falls further behind in poor ones. Below 1, it's steadier, but it may leave yield behind when conditions are good.

Read the slope together with the line's mean. A steady line with a low mean isn't much use.

Why lines change rank

G×E usually comes from stress hitting lines at different stages, or from something present at one site and not another.

• Timing. An early line can flower before a July heat wave. A later line catches it right at flowering. In another year the late line may catch rain the early one misses.
• Disease. A resistant line only shows its value where the disease turns up. At a clean site, a susceptible line with higher yield potential can win.
• Lodging. Tall lines may lodge in a wet year on rich soil and stand fine in a dry one.
• Soil. Acid, saline or poorly drained ground favours the lines that tolerate it.
• Day length. Lines that respond differently to day length shift their heading dates between sites at different latitudes, and that moves everything after heading too.

Timing is worth dwelling on. The same calendar week means different things at different sites. A dry June hurts most where the crop is flowering in June. At a cooler site the crop might still be weeks from flowering. If you compare weather by calendar date, you miss this. Compare it by crop stage instead: rain in the month before heading, heat in the two weeks around flowering, heat during grain fill.

Real pattern or one odd year?

Not all G×E is equally useful. It helps to split it in two.

• Line × site that repeats every year. One station has acid soil, or gets stripe rust most years. You can plan around this, and even breed for it.
• Line × year, and line × site × year. The weather of one particular season. You mostly can't predict it. You can only test across enough years to average it out.

A rank change seen once is weak evidence; one that shows up at the same site year after year is a pattern.

What G×E does to heritability

G×E also tells you how to spend your plots. A common formula for heritability on a line-mean basis across sites is:

H² = σ²g / (σ²g + σ²ge / s + σ²e / (s × r))

Here s is the number of sites, r the reps per site, σ²g the genetic variance, σ²ge the G×E variance and σ²e the plot error.

Take made-up values: σ²g = 1, σ²ge = 1 and σ²e = 2.

• One site with three reps: H² = 1 / (1 + 1 + 0.67) = 0.38.
• Three sites with one rep each: H² = 1 / (1 + 0.33 + 0.67) = 0.50.

The same number of plots, spread over more sites, gives a more reliable ranking. More reps only shrink the plot error term. More sites shrink both terms. When G×E is large, more sites beat more reps.

Tools that help

Beyond the Finlay–Wilkinson slope, two biplots are widely used for multi-site trials.

• GGE biplot. Shows which line won where. Sites that share a winner group together, which hints at mega-environments: parts of your region that want different varieties.
• AMMI. Separates the main effects from the interaction, then breaks the interaction into a few patterns. Lines near the centre of the interaction axes are the stable ones.

Both work from the table of line means at each site. Neither says why a line does well somewhere. For that you need to bring in the environment itself.

Explaining G×E with the weather

If you measure the right weather at the right crop stage, you can model each line's response to it. Instead of a reaction norm on the site mean, you get one on heat at flowering, say, or rain before heading. Then you can ask how a line would do at a site across many seasons it was never tested in, by running it on that place's past weather.

The catch is data. You need many site-years, good daily weather for each, and heading dates to line the windows up. You also need a way to give new lines a response before they've seen many environments. Relatives help here: a new line borrows its relatives' response until it has records of its own.

How Crossling does it

For a multi-location trial, Crossling's results put the locations side by side (site mean, CV and heritability), so a weak site stands out. They give G×E and heritability across locations, the Finlay–Wilkinson stability chart, the GGE biplot's "which won where" view, and AMMI.

The Outlook page goes a step further, with a reaction norm model learned from your program's own trials and weather.

• Each site-season's weather becomes a handful of covariates: rain in the first weeks, in the month before heading, around flowering and in grain fill; daytime heat before heading, around flowering and in grain fill; days over 30 °C around flowering and in grain fill; frost nights after the crop came up; and warmth over the season.
• The windows are set by when the crop headed there that year, from the heading model, not by calendar date.
• Each line's response to the weather is learned through its relatives (pedigree, and DNA where you have it), so a new line borrows its relatives' response.
• For each station, every line is run on each of the past years' weather there. You get its expected value, what a bad year brings, and how much its rank moves between years.
• It shows which weather moves the site average most, and which lines cope with heat.
• It's tested by leaving each site-season out and predicting it, beside the same model without the weather, so it says plainly whether the weather adds anything on your data.

The model starts once a trait has been measured at five site-seasons. It can only explain the G×E that weather captures. Disease pressure and soil differences between sites aren't in it.

Try the demo to see a three-station spring wheat program's multi-site results, or create an account and add your own trials.