Is It the Heat, or the Virus?

Case file 01Vineyard mystery

Which route fits?

Heat · virus · gene response

Heat?Vine response

Choose a route to reveal the split.

Two routes, one response

Route	Model path
Through the virus	Heat acts through viral titer before reaching the gene response
Direct	Heat acts directly on the gene response

How the split is calculated

The analysis fits M ~ X and Y ~ X + M. The indirect effect is $ab$ ; the direct effect is $c'$ . Their ratio gives the mediated share.

I used 2,000 bootstrap resamples to estimate uncertainty.

Vineyard result

MBF1c: 61.8% through virus · 38.2% direct
Gene screen: 39 mediators / 2,000 genes

61.8% describes MBF1c—not every heat response in the vineyard.

Same method, new scale

Role in the model	Grapevine study	Farming re-application
Starting variable	Seasonal temperature	Year
Possible go-between	Viral titer	Harvested area
Measured outcome	Gene expression	Crop production

Case file 02The method goes travelling

More farmland or better harvests?

63 years · 10 crops · one route split

Which crop was most land-driven?

Explore a crop

1961–2023

Sugarcane

Expansion dominated

Nearly all of the modeled production trend travelled through expansion of harvested area.

4.50×

production

3.01×

harvested area

Modeled route split

97.2%

through harvested area

Bootstrap interval
86.0–110.8%

97% land

Through harvested area Remaining direct pathway

Modeled global trends—not causal proof.

Crop comparison

Growth-route portfolio

Different crops reached growth through very different routes

Sugarcane’s modeled trend was almost entirely land-driven; rice growth was dominated by the productivity route.

Sugarcane97.2% via land

Land expansion

Maize72.8% via land

Land expansion

Cassava59.8% via land

Land expansion

Productivity route

Banana48.6% via land

Land expansion

Productivity route

Rice12.5% via land

Productivity route

Harvested-area routeRemaining direct route

Source: FAOSTAT world totals, 1961–2023. Shares come from observational mediation models with 2,000 bootstrap resamples; they are not causal proof.

Evidence detail

Crop	Via harvested area	Bootstrap interval	Remaining route
Sugarcane	97.2%	86.0–110.8%	2.8%
Maize	72.8%	66.4–78.9%	27.2%
Cassava	59.8%	51.9–69.0%	40.2%
Banana	48.6%	22.3–78.8%	51.4%
Rice	12.5%	5.5–23.0%	87.5%

When the split breaks

Growth strategy matrix

More output did not always require more land

Potato, barley, and wheat produced more while using roughly the same or less land; soybean combined the strongest production and land expansion.

Soybean

Production 13.80× · Land 5.78×

Efficient

Sugarcane

Production 4.50× · Land 3.01×

Land-led

Wheat

Production 3.57× · Land 1.07×

Efficient

Potato

Production 1.43× · Land 0.77×

Efficient

Source: FAOSTAT world totals, 1961–2023. Values compare the final year with 1961 and describe global observational trends.

Evidence detail

Crop	Production growth	Area growth	Interpretation
Tomato	6.72×	3.04×	Output outpaced land
Soybean	13.80×	5.78×	Output outpaced land
Sugarcane	4.50×	3.01×	Land-intensive growth
Maize	6.04×	2.00×	Output outpaced land
Cassava	4.77×	3.44×	Land-intensive growth
Banana	6.09×	2.79×	Output outpaced land
Rice	3.73×	1.46×	Output outpaced land
Wheat	3.57×	1.07×	Output outpaced land
Potato	1.43×	0.77×	More output, less land
Barley	1.97×	0.84×	More output, less land

Signal	Crops
Land route exceeds total	Soybean · Tomato
Land route opposes trend	Wheat
More output, less land	Potato · Barley

Limits of the comparison

The crop analysis separates observational trends; it does not prove that land change caused production change. Breeding, irrigation, policy, trade, and region also changed over time. Mediation shows how a modeled effect divides—it cannot choose the causal story by itself.

Watch the method

See the signal split

Two short videos

Method overview1:16

Text alternative

A visual introduction to causal mediation. One response is separated into a direct path and an indirect path that travels through a mediator, using the vineyard heat-virus-gene question and the crop land-production comparison.

Splitting a trend1:23

Text alternative

A step-by-step visual explanation of the signal split, the roles of the starting variable, mediator, and response, and why bootstrap uncertainty and causal caution are necessary when interpreting the result.