Among colours people cannot tell apart, modelled bees and blue tits split flowers from backgrounds more often

Two surfaces can look the same colour to a person and differ sharply to a bee, which sees ultraviolet. We asked where such hidden differences fall among 728 measured Australian surfaces: 221 flower petals and 507 rocks, bark and leaves. Each observer was modelled with the receptor-noise-limited model and published receptor curves. Among pairs a modelled human cannot separate, modelled bees and blue tits separate flower-background pairs more often than background-background pairs, and the separation ratio exceeded its label-shuffle 95th percentile in every condition tested: two noise models on the first set, and two on a second set of Californian flowers against North American soil and leaf litter.c1 The size of the ratio did not travel: for the bee it was 2.04 with Weber noise and 1.67 with photon noise added on the first set, and 45.6 on the second set, where the backgrounds are brown and alike.c2 A preregistered instrument check failed under both noise models: the model resolves finer wavelength steps than bees show in behaviour, so only the direction of the effect is claimed.c3

Each animal's colour vision rests on a few receptor classesDefinition: receptor class vision science One kind of light-sensitive cell in the eye, defined by the wavelengths it responds to. Humans have three cone classes, bees three including one for ultraviolet, blue tits four. Excludes the rods used in dim light, and the nerve cells that compare receptor signals. full definition. People have three cone classes, the honeybee three with one in the ultraviolet, and the blue tit four with one in the ultraviolet. Two surfaces can give the same signals in a person's cones and different signals in a bee's, so the bee tells apart what the person cannot.

The standard way to compute such differences is the receptor-noise-limited modelDefinition: receptor-noise-limited model visual ecology The model of Vorobyev and Osorio in which two colours can be told apart when the difference in log receptor signals is large compared with the noise in each receptor class. Brightness differences are left out. Excludes models of colour appearance, and any effect of pattern, motion or learning. full definition of Vorobyev and Osorio [1]. It treats colour as coded by comparisons between receptor classes and sets the threshold by the noise in each class. A distance of one just-noticeable difference (JND)Definition: just-noticeable difference (JND) psychophysics The unit of colour distance in the receptor-noise-limited model. A distance of 1 is treated as the threshold, so pairs at or below 1 count as indistinguishable for that observer. Excludes a measured threshold for a real animal on a real task. full definition is the threshold. The model was built to predict colour thresholds for animals whose eyes have been measured but whose thresholds have not.

The link between flower colour and pollinator vision has a long record. Chittka and Menzel [2] analysed 180 flower reflectance spectraDefinition: reflectance spectrum optics and visual ecology The share of light a surface reflects at each wavelength, here measured from 300 to 700 nm, which includes the ultraviolet below 400 nm. Excludes the colour a viewer sees, which also depends on the light and the eye. full definition and found that sharp steps in reflectance fall where bee-like insects discriminate best; their calculations of the best set of three receptors for telling flower colours apart matched the receptors measured in many Hymenoptera. Dorin, Shrestha, Garcia, Burd and Dyer [3] measured the surface set used here, flowers with rocks, minerals, bark and leaves from Australia, and found that the share of flowers with sharp spectral steps was an order of magnitude above the share among background samples. They argued that insect colour vision is older than flowers and was shaped by flight among rocks and plants, and that flowers evolved colours that stand out against that background.

This paper asks a narrower question that the model can answer directly. Among the pairs of surfaces a person cannot tell apart, does a modelled bee or blue tit tell apart flower-background pairs more often than background-background pairs? Searches we ran on 9 November 2026 found the work above and no direct count of this kind; that is what the searches returned, not proof that none exists.

The first study was written as a preregistrationDefinition: preregistration research method (metascience) A dated written plan for a study, fixed and hash-locked before any result is seen: the question, the data, the statistic, the controls, the forecasts and the kill conditions. Excludes a plan revised after looking at the outcome, and a protocol written only for the record after the run. full definition on 29 October 2026 and locked at 01:27:38 UTC on 30 October. Before the lock, the code was run only on scrambled data, with every spectrum permuted across wavelength and the group labels permuted, and only keys, counts and timings were printed. The model was checked against its published closed forms on random numbers, to 4 times 10 to the power -16. No statistic of a real spectrum seen through any observer was computed before the lock.

The locked file names the data, the observers and their noise values with a grade for each source, the model, the measures, the hypotheses with their pass rules and kill conditionsDefinition: kill condition research method (our usage, after Popper's falsification) A rule written in the preregistration that, when met, decides against the claim with no room for judgement after the run. Excludes reasons found after the run for setting a result aside. full definition, the controlsDefinition: control statistics and experimental design A version of the data with the structure under test removed (for example shuffled or pooled), scored the same way as the real data, so the real score has something to beat. Excludes a comparison with a different dataset or with a published number. full definition and the multiple-testing plan. This paper reports hypothesis H2, the flower test, with its secondary H2b and the instrument check V0. The same run tested other hypotheses about the information each observer carries; those are reported in the findings ledger and are not part of this paper.

H2 reads: among pairs one observer X cannot separate, the share another observer Y separates is larger for flower-background pairs than for background-background pairs. It was tested for four pairs of observers: human then bee, human then blue tit, dog then bee, and dog then blue tit. The kill condition: a ratio at or below 1, or inside the label-shuffle range. Each conditional share needs at least 20 pairs.

A second study, written after the first and locked at 02:40:37 UTC on 30 October, added photon noiseDefinition: photon noise physics of light detection The random variation in how many photons a receptor absorbs, which every real receptor has and which matters most when the catch is small. Added here as a term that falls with the catch. Excludes noise in the nerve cells after the receptors. full definition to the model, reran the instrument check, and repeated H2 on the first set and on a second set of surfaces. Its preregistration was hash-locked in the same way. Its result narrows this finding and is reported here as the replication.

Set 1 is the 728 reflectance spectra of Dorin and colleagues [4], under CC0: 346 rocks and minerals, 96 bark, sticks and dry plant material, 65 green leaves, 153 insect-pollinated and 68 bird-pollinated flower petals, measured from 300 to 700 nm. The files were fetched from the Zenodo mirror of the Dryad deposit, because the Dryad file interface needed a token; the archive hashes equal those Dryad publishes.

Human cones are the CIE 2006 two-degree cone fundamentals, and the light is CIE standard illuminant D65, both under CC BY-SA 4.0 [5]. Bee, dog and blue tit receptor curves, blue tit ocular media and two natural lights come from the data inside the pavo 2.10.0 R package [6], under GPL version 2 or later; they were read with a pure-Python reader and no package code was run.

Set 2, used only in the replication, joins 512 flower spectra from Californian serpentine seeps (LeCroy and colleagues [7], CC0) with 41 eastern North American forest-floor backgrounds: 20 soils, 10 dry litter and 11 wet litter samples (Kraemer and Adams [8], CC0). Flowers and backgrounds come from different deposits and places.

For a surface with reflectance $R$ under light $I$, the quantum catchDefinition: quantum catch vision science The number of photons a receptor class absorbs from a surface, the sum over wavelength of reflectance times light times the receptor's sensitivity, here divided by the catch from a perfect white under the same light. Excludes the brightness a viewer reports. full definition of receptor class $i$ with sensitivity $S_i$ is

summed over wavelength $\lambda$ in photon units. With von Kries adaptationDefinition: von Kries adaptation colour science Scaling each receptor class's catch by its catch from a white under the same light, a simple model of how eyes adjust to the colour of the light. Excludes adaptation that mixes signals between receptor classes. full definition, $q_i$ is $Q_i$ divided by the catch from a perfect white, and the receptor signal is $f_i=\ln q_i$. For two surfaces, let $d_i$ be the difference in $f_i$. For an observer with three receptor classes and noise $e_1$, $e_2$, $e_3$, the colour distance in JND is

Two- and four-class observers use the general form of the same model [1]. Brightness differences are left out.

In the first study each receptor's noise is a Weber fractionDefinition: Weber fraction psychophysics and vision science The noise in one receptor class as a fixed share of its signal, the same at every light level. We call a model with only this noise the Weber model. Excludes photon noise, which grows in relative size as the catch falls. full definition, a fixed share of its signal. The human values are 0.063, 0.028 and 0.020 for the short, middle and long cones, from a long-cone fraction of 0.02 and relative cone densities of 1 to 5 to 10. The bee values are 0.13, 0.06 and 0.12. The blue tit uses 0.1 for its long-wave class with relative densities 0.37 to 0.70 to 0.99 to 1. The dog uses 0.05 for its long-wave class with densities 1 to 9. The preregistration grades these sources: the human densities and fraction are from memory with low confidence, the bee and blue tit values from memory of published sources with moderate confidence, and the dog value assumed.

The replication adds photon noise:

where $w_i$ is the Weber fraction above, $q_i$ the catch, and $N_i$ the photon catch from the white per receptor and integration time. $N_i$ is $N$ scaled by each class's relative density, with $N$ set to 10,000. That value is an order-of-magnitude memory with low confidence. Noise is evaluated at the mean catch of the pair.

A human-blind pairDefinition: human-blind pair our usage, after the metamer of colour science A pair of surfaces whose modelled colour distance for the human trichromat is at most 1 JND, so the model says a person cannot tell them apart by colour. Dog-blind pairs are defined the same way. Excludes pairs a person cannot tell apart by brightness, which the model does not test. full definition is a pair with $S\le 1$ for the human model. Among the human-blind pairs, let $P_{\mathrm{FB}}$ be the share of flower-background pairs with $S>1$ for the second observer, and $P_{\mathrm{BB}}$ the same share among background-background pairs. The separation ratioDefinition: separation ratio our usage Among pairs one observer cannot separate, the share of flower-background pairs a second observer separates divided by the share of background-background pairs it separates. 1 means flowers gain nothing over the background. Excludes how far apart the pairs are for the second observer. full definition is

Dog-blind pairs are treated the same way. Flower-flower pairs are not counted.

H2b compares, for each flower, the median bee distance to all backgrounds between insect- and bird-pollinatedDefinition: insect- and bird-pollinated pollination ecology The dataset's labels for flowers whose recorded pollinators are insects only or birds only. Excludes flowers visited by both, which the dataset does not include in these groups. full definition flowers, with a one-sided label-permutation p value. Named examples were listed among human-blind flower-background pairs, with each surface's UV shareDefinition: UV share our usage A surface's mean reflectance below 400 nm divided by its mean reflectance from 400 to 700 nm. Excludes whether the ultraviolet forms a pattern on the petal. full definition.

The instrument checkDefinition: instrument check our usage; a known-answer test of the model against behaviour A preregistered test in which the model must reproduce published behavioural measurements, here the smallest wavelength step each observer can detect. If it fails, only ranks and ratios from the model are used. Excludes a test of the model against its own output, and a planted check on synthetic data. full definition, V0, asks the model for the smallest step in wavelength between two pure spectral lights that reaches 1 JND, in steps of 0.1 nm. In the first study the human minimum had to lie between 0.5 and 5 nm and the bee minimum between 1.5 and 12 nm, against behavioural values of about 1 to 2 nm for people and 4 to 5 nm for bees. In the replication the rules were tightened to a factor of 2 of the behavioural values at named wavelengths, for example a human step between 3 and 12 nm at 640 nm and a bee minimum between 2.25 and 9 nm. The behavioural values come from secondary sources and memory; the primary papers were not in hand. If V0 fails, absolute sizes from the model are not used.

The control for H2 is a label shuffleDefinition: label shuffle statistics (permutation test) A control that randomly reassigns the flower and background labels over the same surfaces, here 500 times, and recomputes the separation ratio, which shows how large it gets when the labels carry no meaning. Excludes a shuffle of the spectra themselves. full definition: the flower and background labels are permuted over the same surfaces 500 times and the ratio recomputed. The null distributionDefinition: null distribution statistics The spread of scores a control gives over many random draws. Its 95th percentile is the bar a real score must clear. Excludes a theoretical distribution assumed rather than drawn from the data. full definition of the ratio has a mean near 1, as it should. A real ratio must exceed the shuffle's 95th percentile. The p value from drawsDefinition: p value (from draws) statistics The share of control draws scoring at or above the real score, with one added to the count and to the number of draws, so it is never zero. Excludes a p value from a textbook formula that assumes a distribution. full definition is the share of shuffles at or above the real ratio, counted with one added to both counts, so with 500 draws the smallest possible value is 0.002. The p values were then put through the Benjamini-Hochberg correctionDefinition: Benjamini-Hochberg correction statistics, multiple testing A rule that adjusts a set of p values so that, among the tests called significant, the expected share of false calls stays at or below a chosen rate q, here 0.05. Excludes the stricter Bonferroni rule, which bounds the chance of any false call. full definition: over 7 tests in the first study and 14 in the replication.

Two code checks stand in for a planted checkDefinition: planted check research method; called a positive control in experimental science Data built so that the right answer is known, run through the same analysis before the real data, to show that the analysis can see the effect when it is there. Excludes any check made on the real data, which cannot show what the analysis misses. full definition. The model's distances agreed with the published closed forms for two and three receptor classes to 4 times 10 to the power -16 on random inputs, and pavo's D65 equalled the CIE D65 to within 8 times 10 to the power -6. The instrument check is the known-answer test against behaviour. No surface set with a planted flower effect was run.

Among pairs a modelled human cannot separate, modelled bees and blue tits separate flower-background pairs more often than background-background pairs, and the separation ratio exceeded its label-shuffle 95th percentile in every condition tested: two noise models on the first set, and two on a second set of Californian flowers against North American soil and leaf litter.c1 In the first study, with Weber noise, the bee separated 0.98 of 1,108 human-blind flower-background pairs and 0.48 of 3,892 human-blind background pairs, a ratio of 2.04 against a shuffle 95th percentile of 1.08. The blue tit separated 0.99 against 0.45, a ratio of 2.22 against 1.09. Among dog-blind pairs the ratios were 1.45 for the bee and 1.16 for the blue tit, each above its shuffle percentile. All four had p 0.002 and passed the correction (Table 1).

H2b passed for the bee: the median bee distance from a flower to the backgrounds was 9.47 JND for insect-pollinated flowers and 6.83 for bird-pollinated flowers (p 0.002). It is not specific to bees. The human model also separates insect-pollinated flowers more (13.7 against 9.4, p 0.010), and for the blue tit the order reverses (9.65 against 10.16, p 0.79).

The named examples show what the count is made of. A petal of Hypericum pygmaeum against a dry, thin brown leaf sits 0.63 JND apart for the human model and 22.4 for the bee, with a UV share of 0.70 for the petal and 0.00 for the leaf. The reverse also occurs. The red, bird-pollinated Calothamnus graniticus sits 0.63 JND from fuchsite and 0.71 from white opal for the bee, and about 30 for the human model.

A preregistered instrument check failed under both noise models: the model resolves finer wavelength steps than bees show in behaviour, so only the direction of the effect is claimed.c3 With Weber noise the model's smallest step was 0.4 nm for the human, at 615 nm, and 0.3 nm for the bee, at 540 nm. Weber-only noise lets a receptor with a near-zero catch report changes that photon noise would bury. With photon noise the human minimum rose to 0.8 nm at 500 nm, which passes, but the human step at 640 nm was 2.2 nm against a required 3 to 12 nm. The bee minimum was 0.7 nm at 540 nm, outside both the required range and the required place. The model is still too fine for the bee.

The size of the ratio did not travel: for the bee it was 2.04 with Weber noise and 1.67 with photon noise added on the first set, and 45.6 on the second set, where the backgrounds are brown and alike.c2 With photon noise on set 1, more pairs became human-blind (2,201 flower-background and 9,185 background pairs), and the bee separated 0.96 against 0.58 of them. The blue tit's ratio fell from 2.22 to 1.50. Every one of the 12 replication ratios exceeded its shuffle percentile and passed the correction, with p 0.002 to 0.004. Figure 2 draws all 16 ratios against their shuffle ranges.

On set 2 the bee separated 0.98 of 1,374 human-blind flower-background pairs and only 0.022 of 465 background pairs. The 41 background spectra are brown and alike, so a bee separates few background pairs a human confuses. There the ratio measures how uniform the backgrounds are as much as anything about flowers.

The result agrees with Chittka and Menzel [2] and with Dorin and colleagues [3], who used this same surface set: flower colours stand apart from their backgrounds in ways insect vision can see. This paper puts a different number on it. Of the colour differences a person cannot see, a larger share falls between a flower and a background than between two backgrounds, for a modelled bee and a modelled blue tit. The control for chance holds that number up in every condition.

The size of the effect is a property of the model and the surfaces together. Photon noise made more pairs human-blind and cut the bee's ratio from 2.04 to 1.67. A second set of surfaces with uniform brown backgrounds pushed it to 45.6. None of these values is the ratio in a real meadow. The direction, flowers ahead of backgrounds, survived both changes, and that is the claim this paper makes.

The instrument check marks the limit. The model resolves wavelength steps finer than bees can in behaviour. A model that is too fine for the bee would separate pairs a real bee cannot, and we expect that error to raise both shares in the ratio. The shuffle shows that the labels carry the difference between the shares, but the absolute shares should not be read as what a bee sees. Each failed check here is an honest nullDefinition: honest null research method (our usage) A working test that found no effect beyond a stated bound, a forecast that failed, or an error of our own found and fixed, reported with the same weight as a positive result. Excludes a void run, and a result left unpublished because it was negative. full definition and is reported with the result.

H2b shows why care is needed with stories of design. Insect-pollinated flowers stand further from the backgrounds than bird-pollinated ones for the bee, and also for the human model. A colour that stands out for many eyes is not evidence of tuning to one.