A trait can be shaped by many genetic variants, but counting them is not enough: tiny contributors and powerful ones should not necessarily count the same. This paper turns that problem into one adjustable picture. Most traits are shaped by a diverse combination of genetic variants across the genome, rather than by almost a single genetic location.

But each variant’s contribution depends on both its effect size and its frequency in the population, creating a wide range of relative contributions. So a useful measure must capture not only how many variants contribute, but also how much each one contributes.

A previous approach proposed using mathematical averages to measure polygenicity, because those averages satisfy properties considered desirable for the task. Four particular averages were used to summarize how many variants contribute to genetic variation.

Here is the key idea: imagine judging a crowd by asking how many people would count if everyone had an equal voice. A loud few matter more when the rule emphasizes major contributors; quieter people matter more when it emphasizes minor contributors. The four measures that looked unrelated are actually four points along this continuum of effective numbers of contributing variants.

Measures that give more weight to minor variants produce higher polygenicity estimates, while measures emphasizing major variants are more conservative because they downweight many very small contributors. The connection also makes the mathematical parallel between the earlier measures and Hill numbers explicit.

It supports the conclusion that Hill numbers are the only averages of this type suitable for measuring polygenicity. Together, these examples show that Hill numbers unify the proposed measures and let them be understood by how much emphasis they place on major or minor variants.

The framework is not limited to four measures: it defines a continuous family, allowing researchers to plot a trait’s polygenicity profile across different levels of emphasis. A trait with equal contributions has a horizontal profile, while other genetic patterns have profiles that decline as the emphasis shifts toward major variants.

The contrast is stark: one profile stays flat, another falls smoothly, and a third drops almost immediately, revealing how differently contribution patterns respond to changing emphasis. The four focal measures correspond to four orders of the Hill numbers, revealing them as points along a continuum from emphasizing minor variants to emphasizing major variants.

The continuous family enables polygenicity profiles that facilitate comparisons across traits and provides a way to address variants with contributions that are vanishingly small. Two different lines of reasoning support Hill numbers as measures of polygenicity: among the proposed averages, only they measure polygenicity as an effective number of variants.

More broadly, they are the only diversity measures satisfying the replication principle together with five further conditions, providing a unified framework for measuring and understanding trait polygenicity. Hill numbers show that several apparently different ways to measure trait polygenicity are points on one continuum.

That makes comparisons clearer and lets researchers see whether a trait depends broadly on many variants or mainly on a few.