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Clocks in the Wild: Entrainment to Natural Light

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Supplementary Material

1 SUPPLEMENTARY FIGURES

20 24 28

1 [h]

E S E 365

Day of Year

Berlin A = 4

A

20 24 28

1 [h]

E S E 365

Berlin A = 6

B

20 24 28

1 [h]

E S E 365

Berlin A = 8

C

20 24 28

1 [h]

E S E 365

Berlin A = 10

D

-12 -6 0 6 12

[h]

Figure S1. Entrainment region decreases with increasing clock amplitude.Entrainment regions and color-coded phases of entrainmentψforφ= 52.51, a latitude corresponding to Berlin, for four different free running amplitudesAof the internal clock (i.e. the Poincar´e oscillator), namelyA= 4,6,8and10in panels A-D, respectively.

20 24 28

1 [h]

E S E 365

Day of Year

Berlin

= 0.01h1

A

20 24 28

1 [h]

E S E 365

Berlin

= 0.1h1

B

20 24 28

1 [h]

E S E 365

Berlin

= 0.5h1

C

-12 -6 0 6 12

[h]

Figure S2. Entrainment region decreases with increasing radial relaxation rate.Entrainment regions and color-coded phases of entrainment ψ for φ = 52.51, a latitude corresponding to Berlin, for three different radial relaxation rates λ of the internal clock (i.e. the Poincar´e oscillator), namely λ= 0.01h−1,0.1h−1and0.5h−1in panels A-C, respectively.

1

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Supplementary Material

1 E S E S

Day of Year

90 60 30 0 30 60 90

Latitude [degree]

Equator Antarctic Circle Arctic Circle

A

0 5 10 15 20

Daily Insolation[

kW m2

]

20 24 28

1

[h]

E S E S

Day of Year

= 52.51 Sun Tracking

C

1 E S E S

Day of Year

90 60 30 0 30 60 90

Latitude [degree]

Equator Antarctic Circle Arctic Circle

B

0.0 0.3 0.6

SD of Daily Irradiance [

kW m2]

Figure S3. Sun tracking enhances the perceived daily insolation and leads to a robust entrainment at winter season.A) Daily insolation for different latitudes and times of year in case of a Sun tracking light perceiving surface. B) Standard deviation of the solar irradiance, calculated over a complete day (24h), for different latitudes and times of year in case of a Sun tracking light perceiving surface. C) Entrainment regions and color-coded phases of entrainmentψ forφ = 52.51, a latitude corresponding to Berlin, in case that the circadian clock perceives light analogously to a Sun tracking surface. Compare Figures 3 B and D as well as Figure 4 C of themain text.

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