Origine, fonctions et évolution de l'iridescence chez les oiseaux : exemple chez les colibris

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Origine, fonctions et évolution de l’iridescence chez les oiseaux : exemple chez les colibris

Hugo Gruson

To cite this version:

Hugo Gruson. Origine, fonctions et évolution de l’iridescence chez les oiseaux : exemple chez les colibris. Agricultural sciences. Université Montpellier, 2019. English. �NNT : 2019MONTG046�.

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,ǨȢȢ˃ɧǨɷ ƂǝŔȊ˃ŸƟʙɷ õǝŔȊʙɧŔȢǨŔ ƂȲȊȲȜŸǨƂŔ

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žǨȢƌ

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êƟ࢙

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ÚɧȲɷȲɝȲƂƟɧŔ

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êƂǨƟȢƂƟ

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žƟȊȲɝɷǨʄʄŔƂʙɷ ʙȢƌʙȊŔʄʙɷ

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°Ȣ ʄǝƟ ȲɧǨNJǨȢ ȲLJ ɷɝƟƂǨƟɷ Ÿ˃ ȜƟŔȢɷ ȲLJ ȢŔʄʙɧŔȊ ɷƟȊƟƂʄǨȲȢ࡬ Ȳɧ ʄǝƟ ɝɧƟɷƟɧʶŔʄǨȲȢ ȲLJ LJŔʶȲʙɧƟƌ ɧŔƂƟɷ ǨȢ ʄǝƟ ɷʄɧʙNJNJȊƟ LJȲɧ ȊǨLJƟࡲ

õǝƟ ƌƟɷƂƟȢʄ ȲLJ ȜŔȢ࡬ ŔȢƌ ɷƟȊƟƂʄǨȲȢ ǨȢ ɧƟȊŔʄǨȲȢ ʄȲ ɷƟ˂

žƟʄǝȲƌɷ ǨȢ DƂȲȊȲNJ˃ ŔȢƌ DʶȲȊʙʄǨȲȢ ?iiTb,ff/QBXQ`;fRyXRRRRfky9R@

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DƂȲȊȲNJ˃ ’ƟʄʄƟɧɷ

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,ǝǨɧȲ˂ǨɝǝǨŔ ȊǨȢƟŔɧǨɷ

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%ƟǝŔʶǨȲɧŔȊ DƂȲȊȲNJ˃

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ÚŔʄʄƟɧȢ áƟƂȲNJȢǨʄǨȲȢ

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,ǝɧ˃ɷȲƂȲƂƂ˃˂ ƂʙɝɧƟʙɷ ĸƟǨʄɷƂǝɧǨLJʄ LJʠɧ ĸƟȊȊLJȲɧɷƂǝʙȢNJ ʙȢƌ žǨȄɧȲɷȄȲɝǨɷƂǝƟ ȢŔʄȲȜǨƟ

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áƟʶ êʙǨɷɷƟ ĸȲȲȊ

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ŠȲʙɧȢŔȊ ȲLJ õǝƟ áȲ˃ŔȊ êȲƂǨƟʄ˃ wȢʄƟɧLJŔƂƟ ?iiTb , ff/QBXQ`;fRyXRyN3f`bB7XkyRkXyRR3 kk9NRN3R

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DƂȲȊȲNJ˃ ŔȢƌ DʶȲȊʙʄǨȲȢ

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DʶȲȊʙʄǨȲȢŔɧ˃ %ǨȲȊȲNJ˃

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DƂȲȊȲNJǨƂŔȊ žȲȢȲNJɧŔɝǝɷ

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õƟƂʄȲƂȲɧǨɷ ƌǨȲɝʄǝŔȊȜʙɷ

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õǝƟ ȜƟɧǨƂŔȢ ¢ŔʄʙɧŔȊǨɷʄ

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,ŔȊȲɝʄƟɧ˃˂

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ÚɧȲƂƟƟƌǨȢNJɷ ȲLJ ʄǝƟ ĸȲȲȊȲNJ࢙

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cƟȲNJɧŔɝǝǨƂ wȢLJȲɧȜŔʄǨȲȢ êƂǨƟȢƂƟ

ƂʄŔ °ɧȢǨʄǝȲȊȲNJǨƂŔ

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,ŔȊ˃ɝʄƟ ŔȢȢŔ ŠȲʙɧȢŔȊ ȲLJ ,ȲȜɝŔɧŔʄǨʶƟ Úǝ˃ɷǨȲȊȲNJ˃

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êƂǨƟȢƂƟ ?iiTb,

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ȜȲȢȲNJɧŔɝǝ ȲLJ ʄǝƟ õɧȲƂǝǨȊǨƌŔƟ࡬ Ȳɧ LJŔȜǨȊ˃ ȲLJ ǝʙȜȜǨȢNJ࢙ŸǨɧƌɷ

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oƟȊǨȲƌȲ˂Ŕ ȊƟŔƌŸƟŔʄƟɧǨ oƟ࢙

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ŠȲʙɧȢŔȊ ȲLJ ʄǝƟ °ɝʄǨƂŔȊ êȲƂǨƟʄ˃ ȲLJ ȜƟɧǨƂŔ ?iiTb,ff/QBXQ`;fRyXRje9fCPaX8yXyyRyy8

õǝƟ ßʙŔɧʄƟɧȊ˃

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Úǝ˃ɷǨ࢙

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DʙɧƟȜŔ ǝƟƂŔŸƟ %ƟǝŔʶǨȲɧŔȊ DƂȲȊȲNJ˃ ?iiTb,ff/QBXQ`;fRyXRyNjf#2?2+Qf`KyN9

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,ƟȊȊʙȊȲɝǝŔNJŔ Ȋ˃ʄǨƂŔ êƂǨƟȢʄǨ˩Ƃ áƟɝȲɧʄɷ ?iiTb , f f /QB X Q`; f Ry X Ryj3 f b`2TRNNye

áƟɝȲɧʄɷ ȲȢ ÚɧȲNJɧƟɷɷ ǨȢ Úǝ˃ɷǨƂɷ ?iiTb,ff/QBXQ`;fRyXRy33fyyj9@9338fdRfdfyde9yR

ÚɧȲƂƟƟƌǨȢNJɷ ȲLJ ʄǝƟ ¢ŔʄǨȲȢŔȊ ƂŔƌƟȜ˃ ȲLJ êƂǨƟȢƂƟɷ

?iiTb,ff/QBXQ`;fRyXRydjfTMbXN8XR8X39ky NedReNk

ÚȊŔʄ˃ƂƟɧƂʙɷ ƟȊƟNJŔȢɷ êƂǨƟȢʄǨ˩Ƃ áƟɝȲɧʄɷ ?iiTb,ff/QBXQ`;fRyXRyj3fb`2T9R998

ÚŔȊƟȲŸǨȲȊȲNJ˃ ?iiTb,ff/QBXQ`;fRyXRyRdfT#XkyR9X9

ÚɧȲNJɧƟɷɷ ǨȢ %ǨȲɝǝ˃ɷǨƂɷ ŔȢƌ žȲȊƟƂʙȊŔɧ

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ÚɧȲƂƟƟƌǨȢNJɷ ȲLJ ʄǝƟ áȲ˃ŔȊ êȲƂǨƟʄ˃ %࡫ %ǨȲȊȲNJǨƂŔȊ êƂǨƟȢƂƟɷ

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Úǝ˃ɷ࢙

ǨȲȊȲNJǨƂŔȊ ĸȲȲȊȲNJ˃ ?iiTb,ff/QBXQ`;fRyXRy3efT?vbxQQHXjeXkXjyR889je

¢ŔʄʙɧƟ ,ȲȜȜʙȢǨƂŔʄǨȲȢɷ ?iiTb, ff/QBXQ`;fRyXRyj3fM+QKKbee99

%ƟǝŔʶǨȲɧŔȊ DƂȲȊȲNJ˃

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°ɝʄǨƂɷ D˂ɝɧƟɷɷ

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ŠȲʙɧȢŔȊ ȲLJ ʶǨŔȢ %ǨȲȊȲNJ˃ ?iiTb,ff/QBXQ`;fRyXRRRRfDXReyy@y93sXkyRkXy8eeeXt

%ƟǝŔʶǨȲʙɧŔȊ ÚɧȲƂƟɷɷƟɷ

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ڒ°ê °¢D ?iiTb,ff/QBXQ`;fRyXRjdRfDQm`MHXTQM2Xyy8Ndd9

õǝƟ ĤǨȊɷȲȢ %ʙȊȊƟʄǨȢ

ŸǨȲá˂Ǩʶ

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ÚɧȲƂƟƟƌǨȢNJɷ ȲLJ ʄǝƟ áȲ˃ŔȊ êȲƂǨƟʄ˃ %࡫ %ǨȲȊȲNJǨƂŔȊ êƂǨƟȢƂƟɷ

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%ƟǝŔʶǨȲɧŔȊ DƂȲȊȲNJ˃ ?iiTb,ff/QBXQ`;fRyXRyNjf#2?2+Qf`Tyd9

ɧƂǝǨȊȲƂǝʙɷ ŔȊƟ˂ŔȢƌɧǨ êƟȊŔɷɝǝȲɧʙɷ ɷŔɷǨȢ õǝƟ ,ȲȢƌȲɧ ?iiTb,ff/QBXQ`;fRyXkjydfRjeeejj

ŠȲʙɧȢŔȊ ȲLJ D˂ɝƟɧǨȜƟȢʄŔȊ %ǨȲȊȲNJ˃

žƟʄǝȲƌɷ ǨȢ DƂȲȊȲNJ˃ ŔȢƌ DʶȲȊʙʄǨȲȢ ?iiTb,ff/QBXQ`;f RyXRRRRfky9R@kRysXRjRd9

ŠȲʙɧȢŔȊ ȲLJ õǝƟ áȲ˃ŔȊ êȲƂǨƟʄ˃ wȢʄƟɧLJŔƂƟ ?iiTb,ff/QBXQ`;fRyXRyN3f`bB7XkyRRXy98e

ÚɧȲƂƟƟƌǨȢNJɷ ȲLJ ʄǝƟ ¢ŔʄǨȲȢŔȊ ƂŔƌƟȜ˃ ȲLJ êƂǨƟȢƂƟɷ

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DʶȲȊʙʄǨȲȢ

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%ƟǝŔʶǨȲɧŔȊ DƂȲȊȲNJ˃

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wŸǨɷ ?iiTb,ff/QBXQ`;fRyX

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%ƟǝŔʶǨȲɧŔȊ DƂȲȊȲNJ˃ ?iiTb,ff/QBXQ`;fRyX RyNjf#2?2+Qf`ByRk

ŸǨȲá˂Ǩʶ ?iiTb,

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oƟȊǨƂȲȢǨʙɷ ƟɧŔʄȲ ŠȲʙɧȢŔȊ

ȲLJ D˂ɝƟɧǨȜƟȢʄŔȊ %ǨȲȊȲNJ˃ ?iiTb , f f /QB X Q`; f Ry X Rk9k f D2# X Rje8kj kdk9djR3

ŠȲʙɧȢŔȊ ȲLJ D˂ɝƟɧǨȜƟȢʄŔȊ %ǨȲȊȲNJ˃ Rk9yN8yR

ê˃ɷʄƟȜŔʄǨƂ %ǨȲȊȲNJ˃ ?iiTb,

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,ʙɧɧƟȢʄ %ǨȲȊȲNJ˃

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õǝƟ ʙȄ ?iiTb,ff/QBXQ`;fRyX RyNjfmFfRkkXjXdNj

%ƟǝŔʶǨȲɧŔȊ DƂȲȊȲNJ˃ ŔȢƌ êȲƂǨȲŸǨȲȊȲNJ˃ ?iiTb , f f /QB X Q`; f Ry X Ryyd f byyke8 @ yRy @ RRj8 @ 8 3de

,ŔȊ˃ɝʄƟ ŔȢȢŔ ŠȲʙɧȢŔȊ ȲLJ D˂ɝƟɧǨȜƟȢʄŔȊ %ǨȲȊȲNJ˃

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¢ŔʄʙɧƟ ,ȲȜȜʙȢǨƂŔʄǨȲȢɷ ?iiTb, ff/QBXQ`;fRyXRyj3fb9R9ed@yR3@y83N3@3

ŸǨȲá˂Ǩʶ ?iiTb,ff/QBXQ`;fRyXRRyRf93N9RN

õǝƟ ʙȄ

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DʶȲȊʙʄǨȲȢ

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%Ǩɧƌ ,ȲȊȲɧŔʄǨȲȢ࡬ ġȲȊʙȜƟ ࠃ࡫ žƟƂǝŔȢǨɷȜɷ ŔȢƌ žƟŔɷʙɧƟ࢙

ȜƟȢʄɷ

õǝƟ ,ȲȢƌȲɧ ?iiTb,ff/QBXQ`;fRyXkjydfRjed8dd

DʶȲȊʙʄǨȲȢ ?iiTb,ff/QBXQ`;fRyX

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ÚɧȲƂƟƟƌǨȢNJɷ ȲLJ ʄǝƟ áȲ˃ŔȊ êȲƂǨƟʄ˃ %࡫ %ǨȲȊȲNJǨƂŔȊ êƂǨƟȢƂƟɷ

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DʶȲȊʙʄǨȲȢ

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ŠȲʙɧȢŔȊ ȲLJ ,ȲȜɝŔɧŔʄǨʶƟ Úǝ˃ɷǨȲȊȲNJ˃ ?iiTb,ff/QBXQ`;fRyXRyydfbyyj8N@yy3@yjN8@k

ŠȲʙɧȢŔȊ ȲLJ ,ȲȜɝŔɧŔʄǨʶƟ Úǝ˃ɷǨȲȊȲNJ˃ ?iiTb,ff/QBXQ`;fRyXRyydfbyyj8N@yyN@y9d9@x

ÚɧȲƂƟƟƌǨȢNJɷ ȲLJ ʄǝƟ áȲ˃ŔȊ êȲƂǨƟʄ˃ %࡫ %ǨȲȊȲNJǨƂŔȊ êƂǨƟȢƂƟɷ ?iiTb, ff/QBXQ`;fRyXRyN3f`bT#XkyRRXRddd kRNdee3j

DƂȲȊȲNJ˃ ŔȢƌ DʶȲȊʙʄǨȲȢ ?iiTb,ff/QBXQ`;fRyX Ryykf2+2jXRN8y

ŠȲʙɧȢŔȊ ȲLJ õǝƟ áȲ˃ŔȊ êȲƂǨƟʄ˃ wȢʄƟɧLJŔƂƟ ?iiTb,ff/QBXQ`;fRyXRyN3f`bB7XkyRRX yey3 kkydk99d

ÚɧȲƂƟƟƌǨȢNJɷ ȲLJ ʄǝƟ áȲ˃ŔȊ êȲƂǨƟʄ˃ %࡫ %ǨȲȊȲNJǨƂŔȊ êƂǨƟȢƂƟɷ ?iiTb , ff/QBXQ`;fRyXRyN3f`bT#XkyRkXRk38

ŠȲʙɧȢŔȊ ȲLJ D˂ɝƟɧǨȜƟȢʄŔȊ %ǨȲȊȲNJ˃ Rky3Nkyd

ġǨɷǨȲȢ áƟɷƟŔɧƂǝ ?iiTb ,

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ɝŔʄʙɧŔ ǨɧǨɷ ࡲ ǨȊǨŔ

°ɝʄǨƂɷ D˂ɝɧƟɷɷ ?iiTb,ff/QBXQ`;fRyXRje9fP1XRNXyy83Rd

ŠȲʙɧȢŔȊ ȲLJ D˂ɝƟɧǨȜƟȢʄŔȊ %ǨȲȊȲNJ˃

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ŠȲʙɧȢŔȊ ȲLJ °ɝʄǨƂɷ ࡫ ÚʙɧƟ ŔȢƌ ɝɝȊǨƟƌ °ɝʄǨƂɷ

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ŠȲʙɧȢŔȊ ȲLJ õǝƟ áȲ˃ŔȊ êȲƂǨƟʄ˃ wȢʄƟɧLJŔƂƟ ?iiTb,ff/QBXQ`;fRyXRyN3f`bB7X kyRdXyN93 kNeeN3Nk

êƂǨƟȢʄǨ˩Ƃ áƟɝȲɧʄɷ

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,ǝŔɧǨƌȲʄƟȊȊŔ ŔȜŸǨʄŔ ɧʄǝɧȲɝȲƌ êʄɧʙƂʄʙɧƟ ॻ 5ƟʶƟȊȲɝȜƟȢʄ ?iiTb,ff/QBXQ`;fRyXRyRefDXb/XkyReXRyXyy3

%Ŕʄʄʙɷ ɝǝǨȊƟȢȲɧ ŠȲʙɧȢŔȊ ȲLJ wȢɷƟƂʄ êƂǨƟȢƂƟ

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ŠȲʙɧȢŔȊ ȲLJ DʶȲȊʙʄǨȲȢŔɧ˃ %ǨȲȊȲNJ˃ ?iiTb,ff/QBXQ`;fRyXRRRRfD2#XRkR38

o˃ƌɧȲŸǨȲȊȲNJǨŔ ?iiTb,ff/QBXQ`;fRyXRyydfbRyd8y@yRj@R88d@v

ڒ°ê °¢D ?iiTb,ff

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õǝƟ ,ȲȢƌȲɧ

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žȲɧɝǝȲ ɧǝƟʄƟȢȲɧ

ŠȲʙɧȢŔȊ ȲLJ õǝƟ áȲ˃ŔȊ êȲƂǨƟʄ˃ wȢʄƟɧLJŔƂƟ ?iiTb,ff/QBXQ`;fRyXRyN3f`bB7Xkyy9Xyyye Re39NR8k

ŠȲʙɧȢŔȊ ȲLJ ,ȲȜɝŔɧŔʄǨʶƟ Úǝ˃ɷǨȲȊȲNJ˃ % ?iiTb , f f /QB X Q`; f Ry X Ryyd f byyjey@yRk@yedd@9

,ŔȊȲƟȢŔɷ ȢǨƂȲŸŔɧǨƂŔ ƌʶŔȢƂƟƌ

°ɝʄǨƂŔȊ žŔʄƟɧǨŔȊɷ ?iiTb,ff/QBXQ`;fRyXRyykf/QKXkyRdyRkR3

`ʙȢƂʄǨȲȢŔȊ DƂȲȊȲNJ˃ ?iiTb , f f /QB X Q`; f Ry X RRRR f Rje8 @ k9j8XRky3e

%ǨȲȊȲNJǨƂŔȊ áƟʶǨƟʺɷ ?iiTb,ff/QBXQ`;fRyXRRRRf#`pXRkkjy

õ˃ʄȲ ŔȊŸŔ ÚʙȊɷŔʄɧǨ˂ ɝƟɧɷɝǨƂǨȊȊŔʄŔ

êʄɧǨ˂ ŔȊŸǨʄŔɧɷǨɷ °ɧȢǨʄȲȊȲNJǪŔ ¢ƟȲʄɧȲɝǨƂŔȊ

õǝƟ ĤǨȊɷȲȢ ŠȲʙɧ࢙

ȢŔȊ ȲLJ °ɧȢǨʄǝȲȊȲNJ˃ ?iiTb,ff/QBXQ`;fRyXRedefyk@Ry8

cȊȲŸŔȊ ,ǝŔȢNJƟ

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oƟȊǨŔȢNJƟȊʙɷ ’ȲɝǝȲɝǝȲ࢙

ɧʙɷ ĸƟǨʄɷƂǝɧǨLJʄ LJʠɧ ĸƟȊȊLJȲɧɷƂǝʙȢNJ ʙȢƌ žǨȄɧȲɷȄȲɝǨɷƂǝƟ ȢŔʄȲȜǨƟ ?iiTb,ff/QBXQ`;fRyXRyydf

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oŔȢƌŸȲȲȄ ȲLJ ʄǝƟ %Ǩɧƌɷ ȲLJ ʄǝƟ ĤȲɧȊƌ ȊǨʶƟ

`ʙȢƂʄǨȲȢŔȊ DƂȲȊȲNJ˃ ?iiTb ,

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%ǨȲȊȲNJ˃

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ÚǝǨȊȲɷȲɝǝǨƂŔȊ õɧŔȢɷŔƂʄǨȲȢɷ ȲLJ ʄǝƟ áȲ˃ŔȊ êȲƂǨƟʄ˃ %࡫

%ǨȲȊȲNJǨƂŔȊ êƂǨƟȢƂƟɷ ?iiTb , f f /QB X Q`; f Ry X RyN3 f `bi# X kyRe X y8je

ŠȲʙɧȢŔȊ ȲLJ žȲɧɝǝȲȊȲNJ˃ ?iiTb, ff/QBXQ`;fRyXRyykfDKQ`Xkyj9d k89kdN8R

õǝƟ êƂǨƟȢƂƟ ȲLJ ¢ŔʄʙɧƟ ?iiTb,ff/QBXQ`;fRyXRyydfbyyRR9@yRd@R9NN@3

ŠȲʙɧȢŔȊ ȲLJ õǝƟ áȲ˃ŔȊ êȲƂǨƟʄ˃ wȢʄƟɧLJŔƂƟ ?iiTb,ff/QBX Q`;fRyXRyN3f`bB7Xkyy3Xy98NX7Q+mb RNR9R9jy

%ǨȲȊȲNJ˃ ’ƟʄʄƟɧɷ

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DƂȲȊȲNJ˃ ’ƟʄʄƟɧɷ

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%ƟǝŔʶǨȲɧŔȊ DƂȲȊȲNJ˃ ?iiTb,ff/QBXQ`;fRyXRyNjf#2?2+Qf`vyRe

DʶȲȊʙʄǨȲȢ ?iiTb,ff/QBX

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õǝƟ ȜƟɧǨƂŔȢ ¢ŔʄʙɧŔȊǨɷʄ ?iiTb,ff/QBXQ`;f RyXRy3efdy9dd9

õǝƟ ȜƟɧǨƂŔȢ ¢ŔʄʙɧŔȊǨɷʄ

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%ǨȲȊȲNJ˃ ’ƟʄʄƟɧɷ

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õǝƟ ȜƟɧǨƂŔȢ ¢ŔʄʙɧŔȊǨɷʄ ?iiTb,ff/QBXQ`;fRyXRy3efee8yjR

žŔʄƟɧǨŔȊɷ õȲƌŔ˃࡫ ÚɧȲƂƟƟƌǨȢNJɷ

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cɧŔɝǝǨʙȜ ɷŔɧɝƟƌȲȢ

ŠȲʙɧȢŔȊ ȲLJ D˂ɝƟɧǨȜƟȢʄŔȊ %ǨȲȊȲNJ˃ ?iiTb,ff/QBXQ`;fRyX Rk9kfD2#Xy9R9j9 ky9j83k9

ÚɧȲƂƟƟƌǨȢNJɷ ȲLJ ʄǝƟ áȲ˃ŔȊ êȲƂǨƟʄ˃ ȲLJ ’ȲȢƌȲȢ %࡫ %ǨȲȊȲNJǨƂŔȊ êƂǨƟȢƂƟɷ ?iiTb,ff/QBXQ`;fRyXRyN3f

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’ǨNJǝʄ࡫ êƂǨƟȢƂƟ ॻ ɝɝȊǨƂŔʄǨȲȢɷ ?iiTb , ff/QBXQ`;fRyXRyj3fHbXkyR8XRe

ŠȲʙɧȢŔȊ ȲLJ D˂ɝƟɧǨȜƟȢʄŔȊ %ǨȲȊȲNJ˃

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%ǨȲȊȲNJǨƂŔȊ ŠȲʙɧȢŔȊ ȲLJ ʄǝƟ ’ǨȢȢƟŔȢ êȲƂǨƟʄ˃

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õǝƟ ,ȲȢƌȲɧ

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žƟʄ࢙

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rsfs.royalsocietypublishing.org

Research

Cite this article:Gruson H, Andraud C, Daney de Marcillac W, Berthier S, Elias M, Gomez D.

2018 Quantitative characterization of iridescent colours in biological studies: a novel method using optical theory.Interface Focus9:

20180049.

http://dx.doi.org/10.1098/rsfs.2018.0049

Accepted: 11 October 2018

One contribution of 11 to a theme issue ‘Living light: optics, ecology and design principles of natural photonic structures’.

Subject Areas:

biomaterials, biophysics, environmental science

Keywords:

iridescence, structural colours, thin-film interferences, hummingbirds, Lepidoptera, visual signals

Author for correspondence:

Hugo Gruson

e-mail: hugo.gruson@normalesup.org

Electronic supplementary material is available online at https://dx.doi.org/10.6084/m9.

figshare.c.4275911.

Quantitative characterization of iridescent colours in biological studies: a novel method using optical theory

Hugo Gruson

, Christine Andraud

, Willy Daney de Marcillac

, Serge Berthier

, Marianne Elias

and Doris Gomez

1CEFE, Univ Montpellier, CNRS, Univ Paul Vale´ry Montpellier 3, EPHE, IRD, Montpellier, France

2CRC, MNHN, Ministe`re de la Culture et de la Communication, CNRS, Paris, France

3INSP, Sorbonne Universite´, CNRS, Paris, France

4ISYEB, CNRS, MNHN, EPHE, Sorbonne Universite´, Paris, France

HG, 0000-0002-4094-1476; ME, 0000-0002-1250-2353; DG, 0000-0002-9144-3426

Iridescent colours are colours that change with viewing or illumination geometry. While they are widespread in many living organisms, most evolutionary studies on iridescence do not take into account their full com- plexity. Few studies try to precisely characterize what makes iridescent colours special: their angular dependency. Yet, it is likely that this angular dependency has biological functions and is therefore submitted to evolution- ary pressures. For this reason, evolutionary biologists need a repeatable method to measure iridescent colours as well as variables to precisely quan- tify the angular dependency. In this study, we use a theoretical approach to propose five variables that allow one to fully describe iridescent colours at every angle combination. Based on the results, we propose a new measure- ment protocol and statistical method to reliably characterize iridescence while minimizing the required number of time-consuming measurements.

We use hummingbird iridescent feathers and butterfly iridescent wings as test cases to demonstrate the strengths of this new method. We show that our method is precise enough to be potentially used at intraspecific level while being also time-efficient enough to encompass large taxonomic scales.

1. Introduction

Most interactions between organisms, whether between different species (inter- specific) or different individuals of the same species (intraspecific), involve communication. Communication can have different purposes (e.g. warning, camouflage, display) and use different channels (e.g. olfactory, acoustic, visual) [1]. In particular, colour is a specific kind of communication channel that can be produced through two non-mutually exclusive mechanisms: pigmentary col- ours are generated by the selective absorption of some wavelengths by special molecules called pigments while structural colours are generated by the physical interaction of light with matter, causing dispersion, diffraction or interferences [2].

Among structural colours, iridescent colours change depending on the illumi- nation or observation angle. They can be produced by interferences of light after reflection by a thin-film or multilayer structure, or diffraction on a grating. Irides- cent colours are present in many taxa, and particularly widespread among bony fishes (Actinopterygii), insects, as well as some birds (see detailed review in table 1 for studies on each one of these taxa). Iridescent colours seem to be involved in many important biological processes [123] and their angular depen- dency is likely under selection to produce complex visual signals [74,87,115,124].

In some cases, however, angular dependency may be selected against [125]. In all those cases, the study of the evolution of iridescent colours requires a precise quantification of the angular dependency. However, the inherent physical com- plexity of iridescent colours has hampered the development of quantitative methods to fully describe them in the angle space.

&

We reviewed all studies that performed reflectance measurements of biological samples with iridescent colours produced by a multilayer or a thin-film structure in table 1.

We notice two main trends: (i) many studies measure irides- cence at a single fixed angle (first row in table 1). In these studies, authors generally remain cautious and warn they are not attempting to measure angle dependency. However, the multilayer or thin film producing iridescent colours may not be parallel to the sample surface [67,80,96,102,109], and the angle between them and the sample surface may vary between species or even between individuals of the same species [105].

Hence, even though the angle of the measuring optical fibres relative to the macroscopic is constant, the angle relative to the structures is not. This jeopardizes any biological interpret- ation of differences between samples because the effects of many different parameters are intertwined.

(ii) Other studies take measurements at multiple angles but few attempt to precisely quantify angle dependency (‘Literature review’ folder in electronic supplementary material). Even when angle dependency is quantified, variables never stem from a theoretical approach, which leads to a large diversity of custom variables for each author. This heterogeneity in the methods, variable naming and sign conventions has likely hin- dered the spread of new concepts and results among researchers working on iridescence in living organisms.

Osorio & Ham [110] and Meadows et al. [114] started to address this heterogeneity in measurement methods and advocated for the use of a goniometer to reliably measure colour in a controlled angle configuration. However, they did not propose a detailed protocol or statistical tools to study angu- lar dependency. Here, we use the optical laws that govern iridescence to propose a set of parameters to characterize

angle dependency of brightness, hue and saturation of irides- cent colours. Next, we confirm the validity of these equations for complex biological structures using two highly different groups of organisms well known for their iridescent colours:

Trochilidae (hummingbirds) and Lepidoptera (i.e. butterflies and moths), including the iconic Morpho butterflies that harbour large wings with bright iridescent blue colours. The standard framework we propose here makes iridescent colours comparable across taxa and across studies, opening up new perspectives in the study of their biological functions.

2. Model

2.1. Choice of colour variables

Since we want to produce a general method that would not depend on any specific vision system, we use variables directly derived from spectra, without computing vision models. We define brightness Bas the average reflectance over a range between the minimal (lmin) and maximal (lmax) wavelengths (B2in Montgomerie [126]), saturation Sas the full width at half maximum reflectance and hue H as the wavelength at which reflectance is maximal (H1 in Montgomerie [126]).

These three variables are represented in figure 1 and are the most common measures of brightness, hue and saturation in studies about iridescence (see the literature review in the electronic supplementary material).

2.2. Assumptions and equations

Our method relies on three assumptions that greatly simplify the equations for brightness, hue and saturation in the angle Table 1.Review of the methods used in the literature to study iridescent colours from multilayer or thin-film structures. The criteria we used for studies to be included in the table were the following: (i) at least one quantitative reflectance measurement using a spectrometer, (ii) functioning with white light (no monochromatic illumination), and (iii) the patch measured had to be described as iridescent in the article. A more detailed version of this table, with all angle configurations and colour variables used for each study is available in the electronic supplementary material. The terms ‘constant illumination’, ‘constant collection’, ‘constant angle bisector’ and ‘constant span’ are defined in figure 3d.

no. measurements fibre configuration (no. studies) birds arthropods others

single measurement single fixed angle (53) [3 – 33] [34 – 48] bony fishes [49]; mammals [50];

plants [51 – 54]

single measurement relative to the structure orientation (6)

— [55 – 60] —

multiple measurements along a single line

constant illumination (5) [61] [62 – 64] bacteria [65]

constant collection (2) [66] [67] —

constant angle bisector (16) [68 – 78] [79 – 83] —

constant span (16) [84 – 87] [88 – 96] bony fishes [97]; lizards [98,99]

multiple measurement lines

multiple constant illuminations (4) [100] [101,102] bacteria [103]

multiple constant collections (1) [104] —

multiple constant spans (1) [105] —

constant illumination and bisector (3) — [106,107] bacteria [108]

multiple illumination and bisector (1) — [109] —

constant illumination and span (3) [110,111] [112] —

constant span and bisector (6) [113 – 115] [116 – 118] gastropods [119]

constant illumination, span and bisector (4) [120,121] [102,122] —

rsfs.royalsocietypublishing.orgInterfaceFocus9:20180049

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space. See appendix A for mathematical proofs of the equations and the role of each one of these assumptions:

(1) Small angles (less than or equal to 30⁸). Outside of this range, the signal due to iridescence is often very low and all that remains is the effect of the underlying pigments, which can be measured through traditional methods.

For all thin films, and in some multilayers (depending on chemical composition), it is possible to consider angles up to 45⁸, as illustrated in the electronic supplementary material. This may help in producing more repeatable parameter estimates. For instance, a 45⁸angle can corre- spond to a viewer standing next to the viewed iridescent patch illuminated from above. Many previous studies have in this way mimicked the position of the bird relative to the sun in their measurements [66,87,98,105,114,118].

(2) The orientation of the layers within the multilayer struc- ture is affected by Gaussian noise. Many developmental processes are controlled by a large array of independent factors of small effect each, causing subsequent errors to often be Gaussian (due to the central limit theorem).

This assumption is also empirically supported by the results of Guret al.[127], who looked at the orientation of guanine crystals in neon tetra fishes (Paracheirodon innesi) using wide-angle X-ray scattering. Fitting a Cauchy distribution (fatter tail distribution) instead of a Gaussian distribution yields similar values of parameter estimates. For simplicity, we here only present the results with Gaussian noise.

(3) Multilayers are ideal, i.e. the optical thickness (layer thickness times optical index) of each layer is constant:

n1e1¼n2e2. This is a common assumption [36,54,67,97, 107,119,128–130] which is thought to be valid for most animal reflectors [131] because it produces the brightest and most saturated signals with a minimal number of layers (but see Schultz & Rankin [35] and Parkeret al.

[132] for beetles, Kinoshitaet al.[133] for neon tetra).

This set of assumptions allows us to formally derive simple analytic expressions of brightnessB, hueHand saturationS (figure 1) in the angle space (F_inc,F_col). All variables used in this study with their notations and their possible values are listed in table 2 and illustrated whenever possible in figure 2.

B(F_inc,F_col)¼Bmaxexp ((F_inc F_col)=2 t)²

2g²_B ^{, (A 4 bis)} H(F_inc,F_col)¼Hmaxcos g_HFincþFcol

2

(A 14 bis) and

S(F_inc,F_col)¼Smax: (2:1) Hereafter, we focus on brightnessBand hueHbecause satur- ation S is constant no matter the angle configuration. The brightnessB(Finc,Fcol) in the angle space is entirely defined by three parameters: Bmax, t and g_B. The tiltt is the angle between the multilayer structure and the sample surface (as illustrated in figure 2).Bmaxis the maximum reflectance pro- duced by the multilayer or thin-film structure, reached when the fibres are placed in a symmetrical configuration relative to the normal of the multilayer.g_Bis the parameter quantifying the disorder in the alignment of the multilayer structure. This disorder in the structure results in a reflected signal that is not purely specular but instead contains a diffuse component, meaning it can be seen at multiple angle configurations. For this reason, from a macroscopic point of view,g_Bis correlated with the angular dependency of brightness. Earlier studies used a binary classification of iridescent colours depending on the angle range at which the colour was visible (‘diffuse/

directional’ in Osorio & Ham [110], ‘wide-angle/flashing’

in Huxley [55], ‘limited view’ of Vukusic et al.[134]). This classification is positively correlated with 1/gB.

The hueH(F_inc,F_col) in the angle space is defined by two parameters: Hmax which is the hue at coincident geometry (when using a bifurcated probe for example) andg_His the angular dependency of hue.

The variations of brightness and hue in the angle space, according to equations (A 4) and (A 14), respectively, are represented in figure 3.

2.3. Angle and notation conventions

In the rest of this study, we measure the incoming light ray angles (u_iandF_inc) counter-clockwise and the outgoing light ray angles (u_randF_col) clockwise. For both incoming and out- going angles, the origin is the normal to the structures (u_iand u_r) or the normal to the sample (F_incandF_col). These conven- tions are represented in figure 2 where the direction of the arrows on angles represents the positive direction. The tilttcor- responds to the angle between the multilayer and the surface of the sample and is defined as t¼F_inc2u_i¼u_r2F_col (see appendix A for more details aboutt). In other words,tis posi- tive when the multilayer is tilted towards the illumination and negative otherwise (i.e.tis measured clockwise).

3. Methods

3.1. Study system: hummingbirds and butterflies

We used hummingbirds and butterflies (more precisely some Morpho and Papilio species) as study systems. Hummingbirds make an ideal example to test our framework for numerous reasons.

First, they belong to a speciose family where all species are irides- cent [135], which allows us to work on a large number of species that diverged fairly recently [136]. Upon visual examination, they display highly different types of iridescent colours, with either ‘dif- fuse’ (usually on dorsal patches) or ‘directional’ (usually on facial or hue H

R_max

R_max

brightness B saturation S

2

wavelength (l)

reflectance (R)

Figure 1.Graphical representation of the variables we used for hueH(wave- length at peak reflectanceR_max; calledH₁in Montgomerie [126]), brightness B(average of reflectance over the wavelength range of interest;B2in Mon- tgomerie [126]) and saturationS(full width at half maximum; no equivalent in Montgomerie [126]). (Online version in colour.)

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