physiological constraints on long-term population cycles: a...

1

Physiological Constraints on Long-Term Population Cycles: A Broad-Scale View

David M. Anderson1,3 & James F. Gillooly2

1Department of Biology, University of Florida. Email: [email protected]

2Department of Biology, University of Florida. Email: [email protected]

3To whom correspondence should be addressed:

David M. Anderson

220 Bartram Hall. PO Box 118525

Gainesville, FL 32611-8525

Tel: 303-990-0387, Email: [email protected]

_____________________________________________________________________________________________

APPENDIX

Appendix part I begins on the next page.

Appendix part II begins on page 42.

Evolutionary Ecology Research — Volume 18 (2017)

Keywords: macroecology, metabolic theory, population dynamics, climate change, global warming, scaling

Evolutionary-Ecology.com/data/3111Appendix.pdf

Constraints on Long-term Population Cycles Anderson & Gillooly

1

Appendix 1

Cycle period, body mass, temperature, generation time, and covariate data with sources.

____________________________________________________________________________________________________________

* Median period per species. For species with an even number of observations, we report the larger period adjacent to the median.

† Bird or mammal temperatures noted with superscript “c” are class-level estimates, whereas those without superscripts are species-

specific estimates (ref. 5). The column labeled (AT) includes average annual temperature data for insects, whereas the column labeled

(GST) includes average growing season temperature for insects. ‡ Statistical significance was attributed to the cycle period by the original author using the method indicated

3. Blank fields correspond

to cycle periods for which statistical support was not assessed. sig = statistically significant, n.s. = not statistically significant. § Methods are abbreviated as follows: Spect = Spectral analysis. Auto = Autocorrelation analysis. Subj = average time between peaks

or troughs in abundance. Wave = wavelet analysis. TPT = Kendall’s turning point test. Cos = cosine test.

Species Period

(years) Mass (g)

Temp.

℃†

(AT)

Temp.

℃†

(GST)

Gen.

Time

(days)

Series

Length

(years)

Lat. Signif.‡

Method§ Ref.

Period

Ref.

M.

Ref.

T.

Ref.

GT

Birds

Bonasa umbellus 8 532.0 41.5c

120.0 29 n.s. Spect 1-3 4 5 6

Bonasa umbellus 9.9 532.0 41.5c 120.0 25 n.s. Spect 7, 2, 3 4 5 6

Bonasa umbellus 11*

532.0 41.5c

120.0 35 sig Spect 8, 2, 3 4 5 6

Bonasa umbellus 14.7 532.0 41.5c

120.0 33 n.s. Spect 1-3 4 5 6

Bonasa umbellus 16 532.0 41.5c

120.0 42 n.s. Spect 1-3 4 5 6

Branta bernicla 15* 1464.0 40.5 730.0 47 n.s. Spect 9, 3 5 5 4

Callipepla squamata 5 191.0 41.5c

363.5 24 sig Spect 10 4 5 4

Callipepla squamata 6.3* 191.0 41.5

c 363.5 24 sig Spect 10 4 5 4

Callipepla squamata 12.5 191.0 41.5c

363.5 24 sig Spect 10 4 5 4

Colinus virginianus 5 173.3 41.5c

364.2 24 sig Spect 10 4 5 4

Colinus virginianus 5 173.3 41.5c

364.2 24 sig Spect 10 4 5 4


2

Colinus virginianus 6.3* 173.3 41.5

c 364.2 24 sig Spect 10 4 5 4

Colinus virginianus 8.9 173.3 41.5c

364.2 31 n.s. Spect 11, 3 4 5 4

Colinus virginianus 12.5 173.3 41.5c

364.2 24 sig Spect 10 4 5 4

Cyanistes caeruleus 12.6* 11.2 41.5

c 365.0 31 n.s. Spect 12, 3 4 5 4

Falcipennis canadensis 6.67* 460.0 42 365.0 19 n.s. Spect 1-3 5 5 4

Lagopus lagopus 4 620.0 41.7 364.2 13 n.s. Spect 7, 3 5 5 4

Lagopus lagopus 10*

620.0 41.7 364.2 30 Subj 13 5 5 4

Lagopus lagopus 12.6 620.0 41.7 364.2 41 n.s. Spect 14, 3 5 5 4

Lagopus lagopus

scoticus 5.6 625.0 41.5

c 364.2 50 n.s. Spect 15, 2, 3 3 5 4

Lagopus lagopus

scoticus 5.67 625.0 41.5

c 364.2 52 sig Spect 16, 3 3 5 4

Lagopus lagopus

scoticus 6 625.0 41.5

c 364.2 112 sig Spect 15, 2, 3 3 5 4

Lagopus lagopus

scoticus 6 625.0 41.5

c 364.2 97 n.s. Spect 15, 2, 3 3 5 4

Lagopus lagopus

scoticus 6.08 625.0 41.5

c 364.2 57 sig Spect 16, 3 3 5 4

Lagopus lagopus

scoticus 6.26 625.0 41.5

c 364.2 56 sig Spect 16, 3 3 5 4

Lagopus lagopus

scoticus 8 625.0 41.5

c 364.2 75 n.s. Spect 15, 2, 3 3 5 4

Lagopus lagopus

scoticus 9.04

* 625.0 41.5

c 364.2 79 n.s. Spect 15, 2, 3 3 5 4

Lagopus lagopus

scoticus 11.11 625.0 41.5

c 364.2 77 sig Spect 15, 2, 3 3 5 4

Lagopus lagopus

scoticus 11.3 625.0 41.5

c 364.2 72 sig Spect 15, 2, 3 3 5 4

Lagopus lagopus

scoticus 18.9 625.0 41.5

c 364.2 99 n.s. Spect 15, 2, 3 3 5 4

Lagopus lagopus

scoticus 23 625.0 41.5

c 364.2 95 sig Spect 15, 2, 3 3 5 4

Lagopus lagopus

scoticus 23 625.0 41.5

c 364.2 87 sig Spect 15, 2, 3 3 5 4


3

Lagopus lagopus

scoticus 25.3 625.0 41.5

c 364.2 59 sig Spect 15, 2, 3 3 5 4

Lagopus lagopus

scoticus 35 625.0 41.5

c 364.2 107 sig Spect 17, 3 3 5 4

Lagopus mutus 11.9 420.0 42.3 363.5 75 n.s. Spect 7, 2, 3 5 5 4

Lagopus mutus 12* 420.0 42.3 363.5 55 sig Spect 18, 3 5 5 4

Lagopus mutus 15.4 420.0 42.3 363.5 81 n.s. Spect 15, 2, 3 5 5 4

Perdix perdix 34* 405.5 41.5

c 364.2 141 sig Spect 16, 3 4 5 4

Tetrao tetrix 6.1 1085.0 41.5c

455.1 39 sig Spect 19, 3 4 5 4


455.1 14 n.s. Spect 20, 2, 3 4 5 4

Tetrao tetrix 8* 1085.0 41.5

c 455.1 32 n.s. Spect 19, 3 4 5 4


455.1 28 n.s. Spect 16, 2, 3 4 5 4

Tetrao urogallus 15.43* 2943.0 41.5

c 911.0 81 sig Spect 15, 2, 3 4 5 4

Mammals

Alces alces 19 325000.0 38.6 711.6 28 Subj 21, 22 5 5 4

Alces alces 20* 325000.0 38.6 711.6 Subj 23, 24 5 5 4

Alces alces 21 325000.0 38.6 711.6 41 sig Spect 25 5 5 4

Apodemus sylvaticus 2.17* 18.5 36.7 71.0 20.5 sig Spect 26, 2, 3 5 5 4

Arvicola amphibius 3.56 92.0 37.5 51.0 37 n.s. Spect 27 5 5 4

Arvicola amphibius 5 92.0 37.5 51.0 20 n.s. Spect 27 5 5 4

Arvicola amphibius 5 92.0 37.5 51.0 25 sig Spect 27 5 5 4

Arvicola amphibius 5 92.0 37.5 51.0 25 n.s. Spect 27 5 5 4

Arvicola amphibius 5.4* 92.0 37.5 51.0 27 sig Spect 27 5 5 4


4

Arvicola amphibius 6.2 92.0 37.5 51.0 31 sig Spect 27 5 5 4

Arvicola amphibius 6.75 92.0 37.5 51.0 54 sig Spect 27 5 5 4



Capra hircus 6* 18000.0 39.5 446.5 19 Subj 28 5 5 4

Castor canadensis 7.56* 19930.0 36.4

c 648.2 sig Spect 29, 30 4 5 4

Cervus canadensis 10.2* 265000.0 36.4

c 912.5 41 n.s. Spect 31, 3 32 5 33

Dicrostonyx

groenlandicus 3.67

* 59.6 38.4

40.0 12 Subj 34 5 5 4

Erethizon dorsatus 22 10500.0 37.5 933.8 133 sig Wave 35 5 5 4

Erethizon dorsatus 45.7* 10500.0 37.5 933.8 120 sig Spect 36, 2, 3 5 5 4

Eutamias minimus 7* 45.8 37 365.0 22 Cos 37 5 5 4

Ictidomys

tridecemlineatus 8

* 205.4 35.7 354.0 22 Cos 37 5 5 4

Lemmus lemmus 3 80.0 37.8 24.0 9 n.s. Spect 38, 2, 3 5 5 4

Lemmus lemmus 3.5* 80.0 37.8 24.0 Subj 39, 22 5 5 4

Lemmus lemmus 3.6 80.0 37.8 24.0 41 sig Spect 40, 3 5 5 4

Lepus americanus 8.4 1581.0 39.8 259.4 Subj 41, 24 5 5 4

Lepus americanus 8.8 1581.0 39.8 259.4 33 n.s. Spect 1-3 5 5 4


Lepus americanus 10.3* 1581.0 39.8 259.4 56 sig Spect 42, 2, 3 5 5 4

Lepus americanus 10.7 1581.0 39.8 259.4 61 sig Spect 43, 3 5 5 4


Lepus californicus 6.33*

2300.0 39.2 243.4 19 Subj 44, 45 5 5 4


5

Lepus europaeus 10.45 3673.0 38.3 227.7 45 sig Spect 46, 30 5 6 4

Lepus europaeus 11.4*

3673.0 38.3 227.7 31 n.s. Spect 16, 3 5 6 4

Lepus timidus 5.3 3000.0 39.7 265.9 19 n.s. Spect 45, 2, 3 5 5 4

Lepus timidus 8 3000.0 39.7 265.9 21 n.s. Spect 47, 2, 3 5 5 4

Lepus timidus 10.45* 3000.0 39.7 265.9 sig Spect 19, 30 5 5 4

Lepus timidus 12 3000.0 39.7 265.9 47 n.s. Spect 16, 3 5 5 4

Lepus timidus 13.3 3000.0 39.7 265.9 31 sig Spect 45, 2, 3 5 5 4

Macropus fuliginosus 9.5* 30700.0 37.2 689.4 39 n.s. Spect 48, 3 5 5 4

Macropus rufus 17.3* 35730.0 35.9 517.0 40 n.s. Spect 48, 3 4 6 4

Microtus agrestis 2.5 28.0 37.6 36.0 9 Subj 49, 50 5 5 4

Microtus agrestis 2.5 28.0 37.6 36.0 6 Subj 50 5 5 4

Microtus agrestis 3 28.0 37.6 36.0 13 Subj 50 5 5 4







Microtus agrestis 4* 28.0 37.6 36.0 28 Subj 51, 52 5 5 4



Microtus agrestis 4 28.0 37.6 36.0 7 Subj 38, 50 5 5 4


6






Microtus arvalis 3.56 20.0 37 38.0 12 n.s. Spect 55, 2, 3 5 5 4

Microtus arvalis 4* 20.0 37 38.0 28 Subj 54 5 5 4

Microtus arvalis 8.7 20.0 37 38.0 38 n.s. Spect 55, 2, 3 5 5 4

Microtus californicus 3.2* 44.0 38.8 23.8 17 Subj 56 5 5 4

Microtus ochrogaster 1.25* 46.7 37.9 47.0 5.25 Subj 57 5 5 4

Microtus oeconomus 4.5* 33.7 38.4 36.7 19 Subj 50 5 5 4

Microtus

pennsylvanicus 4 38.9 38.5 30.2 16 Subj 58 5 5 4

Microtus

pennsylvanicus 4

* 38.9 38.5 30.2 Subj 59 5 5 4

Myocastor coypus 2.67* 7290.0 38 159.8 10 sig Spect 60, 3 5 5 4

Myodes glareolus 2 20.8 36.4c

47.0 6 Subj 61, 50 4 5 4

Myodes glareolus 2.3 20.8 36.4c

47.0 12 Subj 50 4 5 4


47.0 9 Subj 62, 50 4 5 4


47.0 28 n.s. Spect 26, 2, 3 4 5 4


47.0 17 Subj 50 4 5 4


47.0 7 Subj 38, 50 4 5 4


47.0 9 Subj 49, 50 4 5 4


47.0 9 Subj 50 4 5 4


7

Myodes glareolus 3* 20.8 36.4

c 47.0 15 Subj 50 4 5 4


47.0 11 Subj 50 4 5 4


47.0 12 Subj 63, 50 4 5 4


47.0 17 Subj 50 4 5 4


47.0 7 Subj 38, 50 4 5 4


47.0 7 Subj 38, 50 4 5 4


47.0 8 Subj 64, 50 4 5 4


47.0 6 Subj 50 4 5 4


47.0 28 n.s. Spect 65, 3 4 5 4

Myodes rufocanus 4.5 27.5 36.4c

85.9 34 sig Spect 3 4 5 4

Myodes rufocanus 4 40.0 36.4c

85.9 8 Subj 66, 50 4 5 4

Myodes rufocanus 4* 40.0 36.4

c 85.9 6 Subj 67, 50 4 5 4


85.9 19 Subj 50 4 5 4


85.9 40 Subj 50 4 5 4

Myodes rutilus 3 25.0 36.4c

121.7 6 Subj 67, 50 4 5 4

Myodes rutilus 3.43* 25.0 36.4

c 121.7 8 n.s. Spect 38, 2, 3 4 5 4

Myopus schisticolor 3*

26.4 39 29.0 15 Subj 68 5 5 4

Odocoileus virginianus 24 58590.0 39 309.0 34 Subj 69, 22 5 5 4

Odocoileus virginianus 46.7* 58590.0 39 309.0 107 sig Spect 70, 3 5 5 4

Ondatra zibethicus 6.42 1005.0 37.4 174.5 44 sig Spect 71, 30 5 5 4

Ondatra zibethicus 7 1005.0 37.4 174.5 43 n.s. Spect 1-3 5 5 4

Ondatra zibethicus 7.3 1005.0 37.4 174.5 34 n.s. Spect 1-3 5 5 4


8

Ondatra zibethicus 8* 1005.0 37.4 174.5 39 n.s. Spect 1-3 5 5 4

Ondatra zibethicus 10.2 1005.0 37.4 174.5 79 n.s. Spect 72, 2, 3 5 5 4

Ondatra zibethicus 10.9 1005.0 37.4 174.5 93 sig Spect 72, 2, 3 5 5 4

Oryctolagus cuniculus 11.2 2000.0 39 185.6 65 n.s. Spect 16, 3 5 5 4

Oryctolagus cuniculus 11.4* 2000.0 39 185.6 31 n.s. Spect 16, 3 5 5 4

Peromyscus

maniculatus 3.5

* 22.8 36.6 60.0 8 Subj 73 5 5 4

Poliocitellus franklinii 5 607.0 36.6 327.0 31 Subj 74 5 5 4

Poliocitellus franklinii 10* 607.0 36.6 327.0 22 Cos 37 5 5 4

Rangifer tarandus 25.6 101300.0 39.2 695.2 39 sig Spect 75 4 5 4

Rangifer tarandus 34.7 101300.0 39.2 695.2 30 n.s. Spect 75 4 5 4

Rangifer tarandus 36 101300.0 39.2 695.2 32 sig Spect 75 4 5 4





Rangifer tarandus 52.6* 101300.0 39.2 695.2 47 sig Spect 75 4 5 4





Rangifer tarandus 20 147700.0 39.2 695.2 20 Subj 76, 24 24 5 4

Rangifer tarandus 38.5 147700.0 39.2 695.2 40 Subj 77 24 5 4


9

Sus scrofa 7.94 135000.0 39 334.0 100 sig Spect 78, 30 4 6 4

Sus scrofa 8.13* 135000.0 39 334.0 100 sig Spect 78, 30 4 6 4

Tamias striatus 8* 87.4 38.2 169.6 22 Cos 37 5 5 4

Tamiasciurus

hudsonicus 11

* 228.3 38.7 342.1 22 Cos 37 5 5 4

Ursus americanus 43* 70000.0 38.3 1278.0 129 sig Spect 70, 3 5 5 4

Insects

Acleris gloverana 14.25* 0.0322 6.3 9.6 365.0 58 49.4 Subj 79 80 81 82

Acleris variana 8* 0.0277 4.6 12.1 365.0 12 46.3 Auto 83, 84 85 81 83

Aphis fabae 2* 0.0011 10.1 13.6 18.0 5 51.3 Subj 86 87 81 88

Aphis glycines 2* 0.0001 10.1 17.4 8.0 8 40.4 Subj 89 90 81 91

Aphis nasturtii 6.1* 0.0005 4.1 11.9 16.1 54 46.3 Spect 92 87 81 93

Bupalus piniarius 6.9 0.0648 8 11.3 365.0 37 56.3 Spect 94, 30 95 81 96

Bupalus piniarius 8* 0.0648 8 11.3 365.0 60 56.3 Auto 97, 84 95 81 96

Cerapteryx graminis 7* 0.2124 0.73 7.8 365.0 11 64.6 Subj 98, 22 99 81 100

Choristoneura biennis 32* 0.0843 1.7 8.5 730.0 127 54.6 Spect 101 102 81 101

Choristoneura

fumiferana 26 0.0956 -1.5 8.8 365.0 175 58.8 Subj 103 104 81 105

Choristoneura

fumiferana 35 0.0956 2.8 10.8 365.0 210 47.1 Subj 105, 84 104 81 105

Choristoneura

fumiferana 36

* 0.0956 -0.54 9.4 365.0 55 50.4 n.s. Auto 106 104 81 105

Choristoneura

fumiferana 39.5 0.0956 2.9 10.1 365.0 450 47.9 Subj 107 104 81 105

Choristoneura

occidentalis 25 0.1140 10.9 16.6 365.0 389 34.6 sig Spect 108 109 81 110

Choristoneura

occidentalis 26 0.1140 4.3 9.9 365.0 258 50.4 Subj 111 109 81 111


10

Choristoneura


Choristoneura

occidentalis 29

* 0.1140 2.3 7.0 365.0 252 50.4 Subj 111 109 81 111

Choristoneura


Choristoneura

occidentalis 37 0.1140 3.2 9.1 365.0 397 37.1 sig Spect 112 109 81 110

Choristoneura


Choristoneura pinus 5 0.0200 5.7 14.5 365.0 25 45.4 n.s. Spect 113 114 81 115


Choristoneura pinus 5 0.0200 5.43 14.0 365.0 28 45.4 sig Spect 113 114 81 115








Choristoneura pinus 6* 0.0200 4.1 13.1 365.0 31 46.3 sig Spect 113 114 81 115




Choristoneura pinus 10 0.0200 -0.5 10.0 365.0 50 54.6 sig Spect 116 114 81 115



11






Coloradia pandora 27* 0.8565 6.1 10.7 730.0 622 43.8 Subj 117 118 81 117

Dendroctonus frontalis 8* 0.0018 18.9 24.2 60.8 41 31.3 Subj 119-121 122 81 121

Dendroctonus

ponderosae 17.5

* 0.0108 0.16 6.4 365.0 70 52.9 Subj 123 124 81 125

Dendrolimus pini 9.66* 0.6291 9.4 13.0 365.0 41 52.1 sig Spect 126, 30 127 81 30

Diprion pini 17 0.0750 10.7 14.8 365.0 48.8 Subj 128, 22 129 81 96

Diprion pini 17 0.0750 10.7 14.8 365.0 27.4 48.8 Subj 128, 22 129 81 96

Diprion pini 18* 0.0750 10.7 14.8 365.0 22 48.8 Subj 128, 22 129 81 96

Diprion pini 23.5 0.0750 10.7 14.8 365.0 50 48.8 Subj 128, 22 129 81 96

Drepanosiphum

platanoides 2

* 0.0016 10.1 13.6 91.3 18 51.3 Auto 130, 120 131 81 131

Epinotia tedella 6.5* 0.0137 8.2 12.6 365.0 33 55.4 Auto 84, 132 133 81 134

Epirrita autumnata 9.4 0.0780 0.2 6.2 365.0 68 65.4 Subj 135 136 81 136

Epirrita autumnata 9.85* 0.0780 4 8.3 365.0 28 46.3 Subj 137, 30 136 81 136

Epirrita autumnata 10 0.0780 0.2 6.2 365.0 13 65.4 Auto 138, 84 136 81 136

Exapate duratella 9* 0.0236 4 8.3 365.0 27 46.3 Subj 139, 137 140 81 140

Grapholita molesta 1.04* 0.0111 16.1 18.8 52.3 5 -27.1 Spect 141 142 81 141

Heterocampa guttivitta 11.2* 0.2278 6.5 14.9 365.0 67.2 42.1 Subj 143, 144 145 81 145

Hyphantria cunea 8* 0.1810 1.9 10.8 365.0 22 48.8 Auto 146, 84 147 81 146


12

Lambdina fiscellaria

lugubrosa 8.8

* 0.2278 5.83 10.5 365.0 44 49.6 Subj 148, 144 149 81 150

Leucoptera caffeina 2* 0.0006 18.3 18.3 40.6 7 -2.9 Subj 151, 152 153 81 152

Leucoptera myricki 2* 0.0006 18.3 18.3 45.6 7 -2.9 Subj 151, 152 153 81 152

Loxostege sticticalis 10.75 0.0843 4.9 15.5 182.5 50 43.8 Subj 154 155 81 156

Loxostege sticticalis 11.9* 0.0843 -0.4 9.6 182.5 162 58.8 Subj 157 155 81 156

Lymantria dispar 4.91 0.7650 12 18.1 365.0 31 39.6 Wave 158 159 81 160

Lymantria dispar 5.84 0.7650 13.8 19.4 365.0 46 36.3 Wave 158 159 81 160

Lymantria dispar 8 0.7650 10.3 16.6 365.0 57 44.6 sig Spect 161 159 81 160

Lymantria dispar 8 0.7650 11 16.6 365.0 66 44.6 sig Spect 161 159 81 160


Lymantria dispar 9 0.7650 8.5 13.6 365.0 29 43.8 Auto 162, 84 159 81 160

Lymantria dispar 9.8 0.7650 10.1 15.9 365.0 36 47.9 sig Spect 161 159 81 160

Lymantria dispar 9.8* 0.7650 10.2 15.9 365.0 51 47.9 sig Spect 161 159 81 160

Lymantria dispar 9.83 0.7650 8 15.0 365.0 79 42.1 Wave 158 159 81 160




Lymantria dispar 12.5 0.7650 8.6 14.5 365.0 57 52.9 sig Spect 161 159 81 160

Lymantria dispar 13 0.7650 9 14.6 365.0 49 48.8 sig Spect 161 159 81 160

Lymantria fumida 7* 0.4675 13.8 15.7 365.0 35 36.3 Subj 163, 144 164 81 163

Macrosiphum

euphorbiae 3.9

* 0.0003 4.1 11.9 16.1 54 46.3 sig Spect 92 165 81 166

Malacosoma

californicum 8.3

* 0.1440 5.83 10.5 365.0 50 49.6 Subj 167 168 81 169


13

Malacosoma disstria 9 0.2894 7.6 11.5 365.0 16 48.8 Auto 167 170 81 170

Malacosoma disstria 9 0.2894 -3.2 5.9 365.0 65 53.8 Subj 171 170 81 170

Malacosoma disstria 10 0.2894 1.6 9.5 365.0 132 53.8 Subj 172 170 81 170

Malacosoma disstria 10 0.2894 -0.5 9.0 365.0 95 50.4 Subj 173, 171 170 81 170

Malacosoma disstria 13* 0.2894 1.9 10.5 365.0 65 47.9 Subj 171 170 81 170

Malacosoma disstria 15.5 0.2894 1.2 11.1 365.0 129 51.3 Subj 174 170 81 170

Malacosoma disstria 20 0.2894 1 10.4 365.0 43 53.8 Subj 175, 174 170 81 170

Malacosoma disstria 20 0.2894 1.6 9.5 365.0 129 53.8 Subj 172, 174 170 81 170

Malacosoma disstria 20 0.2894 1.3 8.2 365.0 47 54.6 Subj 176 170 81 170

Myzocallis boerneri 2 0.0008 10.1 13.7 83.4 17 52.9 n.s. Auto 177 178 81 177

Myzocallis boerneri 2* 0.0008 10.1 13.7 83.4 17 52.9 n.s. Auto 177 178 81 177

Nepytia freemani 11.3* 0.0544 5.83 10.5 365.0 45.2 49.6 Subj 179, 144 180 81 181

Operophtera brumata 7* 0.0293 9.4 13.0 365.0 19 52.9 Auto 182, 84 183 81 180

Orygia pseudotsugata 7 0.1452 6.7 11.6 365.0 18 44.6 Auto 184, 84 118 81 185


Orygia pseudotsugata 8* 0.1452 13.2 18.5 365.0 11 33.8 Auto 184, 84 118 81 185


Orygia pseudotsugata 9 0.1452 7.6 13.6 365.0 47.9 Subj 144 118 81 185

Panolis flammea 6.19* 0.1452 7.4 12.6 365.0 20 49.6 sig Spect 186, 30 187 81 30

Pristiphora erichsonii 26.6* 0.0323 -3.6 5.9 365.0 308 53.8 Subj 188, 22 189 81 190

Quadricalcarifera

punctatella 9

* 0.3000 13.8 19.2 365.0 84 36.3 Auto 191 192 81 191

Sphinx pinastri 13.33* 1.4490 8.7 13.5 365.0 60 52.9 Subj 126, 22 193 81 194


14

Tanytarsus gracilentus 6.67* 0.0017 4.4 7.1 182.5 20 65.6 Subj 195 196 197 196

Thaumetopoea

pityocampa 7 0.6900 10.9 14.1 365.0 32 48.8 sig Spect 198 199 81 200

Thaumetopoea


Thaumetopoea


Thaumetopoea


Thaumetopoea

pityocampa 8

* 0.6900 5.3 9.7 365.0 32 44.6 sig Spect 198 199 81 200

Thaumetopoea


Thaumetopoea


Thaumetopoea


Thaumetopoea


Thrips imaginis 1* 0.0001 15.4 19.1 15.1 6 -34.5 n.s. Auto 201, 202 203 81 204

Zeiraphera diniana 8 0.0215 5.3 9.7 365.0 20 44.6 Auto 139, 84 205 81 205

Zeiraphera diniana 8.7 0.0215 1 5.1 365.0 1173 46.3 sig Spect 206 205 81 205


Zeiraphera diniana 9* 0.0215 4 8.3 365.0 29 46.3 Auto 139, 84 205 81 205



Zooplankton

Brachionus calyciflorus 0.011 1.540E-06 25 0.83 0.090 Spect 208 209 210 211




15

Brachionus calyciflorus 0.0452 1.540E-06 25 0.83 0.093 Spect 210, 212 209 210 211

Brachionus calyciflorus 0.0548* 1.540E-06 25 0.83 0.132 Spect 208 209 210 211





Brachionus plicatilis 0.1096* 2.800E-07 20 2.17 3.288 sig Wave 213 214 213 215

Brachionus rubens 0.0275* 3.000E-07 20 2.00 0.123 Subj 216 214 216 217

Daphnia magna 0.1389* 1.812E-03 25 9.37 0.641 Subj 218 219 218 220

Daphnia obtusa 0.126* 1.880E-05 14 10.00 0.611 sig TPT 221, 222 223 221 223

Daphnia pulicaria 0.0822 5.000E-05 19 7.07 0.071 sig TPT 224, 222 225 224 225

Daphnia pulicaria 0.1732 5.000E-05 15 7.07 1.326 sig Spect 226 225 226 225


Daphnia pulicaria 0.2608* 5.000E-05 15 7.07 1.688 sig Spect 226 225 226 225



Eurytemora affinis 0.1096* 5.500E-06 20 9.20 3.288 sig Wave 213 227 213 228

Protists

Dictyostelium discoideu 0.0055 8.400E-10 25 0.33 0.022 Subj 229 209 229 230

Dictyostelium discoideu 0.0123* 8.400E-10 25 0.33 0.074 Subj 229 209 229 230

Dictyostelium discoideu 0.0123 8.400E-10 25 0.33 0.074 Subj 229 209 229 230

Didinium nasutum 0.0178 2.000E-07 22 0.30 0.110 TPT 231 231 231 231


16

Didinium nasutum 0.0288 2.000E-07 22 0.30 0.110 TPT 231 231 231 231

Didinium nasutum 0.0166 7.350E-07 27 0.50 0.099 Subj 232 209 232 232

Didinium nasutum 0.0178* 7.350E-07 27 0.50 0.321 Subj 232 209 232 232





Tetrahymena pyriformis 0.0082 2.000E-08 25 0.10 0.041 Subj 235 235 229 236


Tetrahymena pyriformis 0.0132* 2.000E-08 20 0.10 0.085 Subj 237 235 237 236


Woodruffia metabolica 0.0179* 1.180E-07 25 0.42 0.233 Subj 238 209 238 238

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1

Electronic Supplement 2 ______________________________________________________________________________

Supplementary Figures

Figure S1: Effect of the insect body temperature estimate (i.e., mean annual temperature vs. mean

growing season temperature) on the mass and temperature dependence of period within insects.

Figure S2: Effect of the insect body temperature estimate (i.e., mean annual temperature vs. mean

growing season temperature) on the mass and temperature dependence of period across all taxa.

Supplementary Tables

Table S1: Summary of multiple linear regression results assessing the effects of body mass,

temperature, and latitude on insect cycle periods.

Table S2: Results of ordinary nonparametric bootstrapping procedure.

Table S3: The distribution of methodological covariates within and across taxonomic groups.

Table S4: Results of ANCOVA analyses evaluating the effect of covariate 1 (i.e., statistical

methodology used to determine cycle period) on the OLS-fitted parameter estimates presented in

Table 1 of the main text.

Table S5: OLS parameter estimates within levels of covariate 1 (i.e., statistical methodology).

Table S6: Results of ANCOVA analyses evaluating the effect of covariate 2 (i.e., statistical

significance attributed to cycle period) on the OLS-fitted parameter estimates presented in Table 1

of the main text.

Table S7: OLS parameter estimates within levels of covariate 2 (i.e., statistical significance).

Table S8: Results of ANCOVA analyses evaluating the effect of covariate 3 (i.e., the number of

cycles observed in the time series) on the OLS-fitted parameter estimates presented in Table 1 of

the main text.

Table S9: OLS parameter estimates within levels of covariate 3 (i.e., the number of cycles

observed).

Table S10: Summary of OLS and PGLS analyses for Model 1 and Model 2 within taxonomic

groups without grouping (i.e., we do not group zooplankton and protists or mammals and birds).


2

Figure S1: Effect of the estimate for insect body temperature (i.e., mean annual temperature vs. mean growing

season temperature) on the body mass and temperature dependence of cycle period within insects. Panels (a, b)

show the body mass (a) and temperature (b) dependence of cycle period with mean growing season

temperature. Panels (c, d) show the body mass (c) and temperature (d) dependence of cycle period with mean

annual temperature. Cycle periods were corrected for body mass and temperature using the values of E and b

estimated for the respective group and temperature estimate (see methods). All lines were determined by OLS

regression, and all slopes are significantly different from zero.


3

Figure S2: Effect of the estimate for insect body temperature (i.e., mean annual temperature vs. mean growing

season temperature) on the body mass and temperature dependence of cycle period across all taxa. Panels (a,

b) show the body mass (a) and temperature (b) dependence of cycle period with mean growing season

temperatures as insect body temperatures. Panels (c, d) show the body mass (c) and temperature (d)

dependence of cycle period with mean annual temperatures as insect body temperatures. Cycle periods were

corrected for body mass and temperature using the values of E and b estimated for the respective group and

temperature estimate (see methods). All lines were determined by OLS regression, and all slopes are

significantly different from zero.


4

Table S1 Summary of multiple linear regression results assessing the effects of body mass, temperature, and latitude on insect cycle periods. We assess the temperature dependence with both mean annual temperature (MAT) and mean growing season temperature (MGST). We limit our analysis to northern hemisphere populations to give an approximately even sample across latitude (4 populations from the southern hemisphere were excluded). Lower and upper bounds of the 95% CI are noted within parentheses. ** denotes P < 0.01

Model: 𝐥𝐧 𝛒 = 𝐥𝐧(𝐈𝐨) + 𝐛𝐥𝐧 𝐌 + 𝐄 𝟏𝐤

𝟏𝐓− 𝟏

𝐓𝟐𝟎℃+ 𝒄 ∗ 𝑳𝒂𝒕𝒊𝒕𝒖𝒅𝒆

n ln(IA) P b P E P c P R2 Insect MAT

114 8.1 (7.3, 8.9)

** 0.16 (0.11, 0.21)

** 0.47 (0.28, 0.66)

** -0.01 (-0.03, 0.01)

0.33 0.36

Insect MGST

114 8.5 (7.6, 9.4)

** 0.15 (0.10, 0.20)

** 0.60 (0.34, 0.86)

** -0.01 (-0.03, 0.01)

0.24 0.34


5

Table S2. Results of ordinary nonparametric bootstrapping procedure. This procedure is performed for OLS parameter estimates. ‘Bias’ is the difference between the OLS estimate and the average estimate of 10,000 random samples of cycle periods. Given are the original OLS parameter estimates presented in Table 1 of the main text, followed by the bias and standard error in these estimates as calculated by the bootstrapping procedure.

Model 1: 𝐥𝐧 𝛒 = 𝐥𝐧 𝐈 + 𝛉 𝐥𝐧 𝛕

ln(I) Bias Std. error θ Bias Std. error All groups 3.3 3 ∗ 10JK 0.11 0.88 −5 ∗ 10JN 0.02

Insects 4.9 −6 ∗ 10JS 0.55 0.56 1 ∗ 10JS 0.09 Zooplankton & Protists 2.7 −1 ∗ 10JK 0.10 0.66 2 ∗ 10JK 0.06

Mammals & Birds 5.0 −2 ∗ 10JK 0.16 0.58 2 ∗ 10JN 0.04

Model 2: 𝐥𝐧 𝛒 = 𝐥𝐧(𝐈𝐨) + 𝐛𝐥𝐧 𝐌 + 𝐄 𝟏𝐤

𝟏𝐓− 𝟏

𝐓𝟐𝟎℃

ln(IA) Bias Std. error

b Bias Std. error

E Bias Std. error

All groups 7.6 5 ∗ 10JU 0.04 0.31 −2 ∗ 10JN 0.01 0.65 −3 ∗ 10JN 0.02 Insects 7.6 2 ∗ 10JK 0.17 0.17 9 ∗ 10JU 0.02 0.48 −2 ∗ 10JN 0.09

Zoop. & Protists 5.6 2 ∗ 10JS 0.45 0.20 1 ∗ 10JK 0.03 0.77 3 ∗ 10JK 0.17 Mam. & Birds 6.5 −1 ∗ 10JK 0.09 0.24 3 ∗ 10JN 0.02 N/A N/A N/A


6

Table S3. The distribution of methodological covariates within and across groups.

Group Statistical Methodology*

n Statistical significance†

n # Cycles observed‡

n

Insects Spectral 53 Sig. 35 > 3 88 Subjective 43 n.s. 11 < 3 29 Auto 23 Unknown 73 Unknown 2 Other 0

Zooplankton & Protists

Spectral 16 Sig. 10 > 3 28 Subjective 16 n.s. 0 < 3 8 Auto 0 Unknown 26 Other 4

Mammals & Birds

Spectral 104 Sig. 58 > 3 98 Subjective 58 n.s. 46 < 3 63 Auto 0 Unknown 63 Unknown 6 Other 5

All groups Spectral 173 Sig. 103 > 3 214 Subjective 117 n.s. 57 < 3 100 Auto 23 Unknown 162 Unknown 8 Other 9

* Spectral = spectral or global wavelet analysis. Subjective = average time between peaks or troughs in abundance, Auto = autocorrelation analysis, Other = other methods (e.g., Kendall’s turning point test, Cosine analysis). † Sig. = p – value < 0.05, n.s. = p - value > 0.05, unknown = no test of statistical significance was used. ‡ “> 3” = Length of time series / cycle period is greater than 3. “< 3” = Length of time series / period is less than 3. Unknown = Length of times series is unknown.


7

Table S4. Results of ANCOVA analyses evaluating the effect of covariate 1 (i.e., statistical methodology used to determine cycle period) on the OLS-fitted parameter estimates presented in Table 1 of the main text. Across all groups, autocorrelation was included in the “other” category.

Group

Model 1:

𝐥𝐧 𝛒 = 𝐥𝐧 𝐈 + 𝛉 𝐥𝐧 𝛕

Model 2:

𝐥𝐧 𝛒 = 𝐥𝐧(𝐈𝐨) + 𝐛𝐥𝐧 𝐌 + 𝐄𝟏𝐤𝟏𝐓−

𝟏𝐓𝟐𝟎℃

ln(I) θ ln(IA) b E

All groups FS,KYZ = 15.9 p < 0.001

FS,KYZ = 2.1 p = 0.12

FS,KYK = 0.03 p = 0.97

FS,KYK = 1.9 p = 0.14

FS,KYK = 6.5 p = 0.002

Insects FS,YYK = 22.4 p < 0.001

FS,YYK = 5.2 p = 0.01

FS,YY] = 10.8 p < 0.001

FS,YY] = 1.1 p = 0.34

FS,YY] = 3.8 p = 0.03


FS,K] = 3.0 p = 0.06

FS,K] = 1.9 p = 0.17

FS,S^ = 4.3 p = 0.02

FS,S^ = 0.000 p = 0.99

FS,S^ = 1.5 p = 0.24

Mammals & Birds

FS,YZY = 1.7 p = 0.19

FS,YZY = 0.2 p = 0.80

FS,YZY = 9.0 p < 0.001

FS,YZY = 0.11 p = 0.89

N/A


8

Table S5. OLS-fitted parameter estimates within levels of covariate 1 (i.e., statistical methodology). Lower and upper bounds of the 95% CI for each parameter estimate are noted in parentheses. (***) indicates p < 0.001, (**) indicates p < 0.01, (*) indicates p < 0.05, and (.) indicates p < 0.1.


Group/Cov. lvl. n ln(I) P θ P All groups

Spectral 173 3.3 3.0, 3.7 *** 0.85 0.79, 0.91 *** Subj 117 3.3 3.1, 3.5 *** 0.93 0.88, 0.98 *** Other 32 2.8 2.3, 3.2 *** 0.90 0.81, 0.99 ***

Insects Spectral 53 6.0 4.8, 7.1 *** 0.35 0.15, 0.55 *** Auto 23 3.3 2.2, 4.4 *** 0.81 0.61, 1.0 *** Subj 43 4.7 3.7, 5.7 *** 0.67 0.49, 0.84 *** Other 0 N/A N/A

Zoop. & Protists Spectral 16 2.9 2.4, 3.3 *** 0.79 0.42, 1.2 *** Auto 0 N/A N/A Subj 16 2.3(1.9, 2.6) *** 0.45(0.23, 0.66) *** Other 4 2.7 2.0, 3.3 *** 0.46(0.10, 0.81) ***

Mam. & Birds Spectral 104 5.1 4.4, 5.9 *** 0.56 0.43, 0.69 *** Auto 0 N/A N/A Subj 58 5.1 4.7, 5.6 *** 0.53 0.43, 0.63 *** Other 5 7.6 1.7, 13.5 * 0.08 −0.96, 1.1


𝟏𝐓− 𝟏

𝐓𝟐𝟎℃

n ln(IA) P b P E P

All groups Spectral 173 7.5 7.4, 7.6 *** 0.30 0.28, 0.32 *** 0.57 0.50, 0.64 *** Subj 117 7.6 7.5, 7.7 *** 0.31 0.29, 0.32 *** 0.72 0.66, 0.78 *** Other 32 7.7 7.5, 7.9 *** 0.34 0.31, 0.38 *** 0.65 0.53, 0.76 ***

Insects Spectral 53 7.1 6.6, 7.5 *** 0.20 0.13, 0.27 *** 0.73 0.45, 1.01 *** Auto 23 7.6 7.0, 8.2 *** 0.22 0.15, 0.29 *** 0.51 0.25, 0.76 *** Subj 43 8.5 7.8, 9.3 *** 0.20 0.10, 0.30 *** 0.22 −0.04, 0.48 . Other 0 N/A N/A N/A

Zoop. & Protists Spectral 16 3.5 −2, 8.9 −0.02 −0.5, 0.4 1.45 0.17, 2.7 * Auto 0 N/A N/A N/A Subj 16 4.6 3.4, 5.8 *** 0.16 0.10, 0.23 *** 0.32 −0.4, 1.02 Other 4 5.0 −13, 22 0.17 −1.1, 1.5 0.86 −6.5, 8.2

Mam. & Birds Spectral 104 6.7 6.4, 7.04 *** 0.22 0.17, 0.26 *** N/A Auto 0 N/A N/A N/A Subj 58 6.4 6.3, 6.6 *** 0.21 0.18, 0.23 *** N/A Other 5 7.3 6.2, 8.4 *** 0.15 −0.07, 0.36 N/A


9

Table S6. Results of ANCOVA analyses evaluating the effect of covariate 2 (i.e., statistical significance attributed to cycle period) on the OLS-fitted parameter estimates presented in Table 1 of the main text.

Group

Model 1:


Model 2:


𝟏𝐓𝟐𝟎℃

ln(I) θ ln(IA) b E All groups FS,KYZ = 1.9

p = 0.15 FS,KYZ = 11.5 p < 0.001

FS,KYK = 0.64 p = 0.53

FS,KYK = 9.6 p < 0.001

FS,KYK = 4.9 p = 0.008

Insects FS,YYK = 7.8 p = 0.001

FS,YYK = 2.1 p = 0.13

FS,YY] = 3.6 p = 0.03

FS,YY] = 1.3 p = 0.27

FS,YY] = 1.1 p = 0.32


FY,KS = 2.8 p = 0.10

FY,KS = 0.0003 p = 0.99

FY,K] = 3.3 p = 0.08

FY,K] = 0.35 p = 0.56

FY,K] = 1.3 p = 0.27

Mammals & Birds

FS,YZY = 4.8 p = 0.01

FS,YZY = 3.9 p = 0.02

FS,YZY = 8.0 p < 0.001

FS,YZY = 2.6 p = 0.08

N/A


10

Table S7. OLS-fitted parameter estimates within levels of covariate 2 (i.e., statistical significance). Lower and upper bounds of the 95% CI for each parameter estimate are noted in parentheses. (***) indicates p < 0.001, (**) indicates p < 0.01, (*) indicates p < 0.05, and (.) indicates p < 0.1.



n.s. 57 5.6 4.8, 6.4 *** 0.44 0.29, 0.59 *** Sig. 103 3.0 2.5, 3.6 *** 0.91 0.81, 1.0 *** unknown 162 3.3 3.1, 3.5 *** 0.90 0.86, 0.94 ***

Insects n.s. 11 3.8 1.5, 6.0 ** 0.70 0.28, 1.1 ** Sig. 35 6.5 5.0, 8.1 *** 0.26 −0.01, 0.5 . unknown 73 4.9 4.02, 5.8 *** 0.59 0.43, 0.74 ***

Zoop. & Protists n.s. 0 N/A N/A Sig. 10 3.2(2.0, 4.3) *** 0.54(−0.08, 1.2) unknown 26 2.5(2.2, 2.9) *** 0.53(0.27, 0.79) ***

Mam. & Birds n.s. 46 6.1 5.3, 6.9 *** 0.36 0.21, 0.50 *** Sig. 58 4.6 3.5, 5.8 *** 0.67 0.47, 0.87 *** unknown 63 5.2 4.8, 5.6 *** 0.51 0.43, 0.60 ***


𝟏𝐓− 𝟏

𝐓𝟐𝟎℃

n ln(IA) P b P E P

All groups n.s. 57 7.6 7.4, 7.8 *** 0.22 0.16, 0.27 *** 0.31 0.16, 0.45 *** Sig. 103 7.5 7.4, 7.6 *** 0.31 0.28, 0.34 *** 0.56 0.47, 0.65 *** unknown 162 7.6 7.5, 7.7 *** 0.31 0.30, 0.33 *** 0.70 0.65, 0.75 ***

Insects n.s. 11 3.0 −1.9, 8.0 −0.15 −0.6, 0.29 1.9 0.49, 3.4 * Sig. 35 7.7 7.0, 8.4 *** 0.13 0.02, 0.24 * 0.31 −0.14, 0.77 *** unknown 73 7.7 7.3, 8.2 *** 0.14 0.08, 0.22 *** 0.45 0.26, 0.63 ***

Zoop. & Protists n.s. 0 N/A N/A N/A Sig. 10 3.8 −0.06, 7.6 . 0.01 −0.3, 0.32 1.1 −0.04, 2.3 . unknown 26 5.2 3.6, 6.7 *** 0.19 0.11, 0.28 *** 0.31 −0.64, 1.3

Mam. & Birds n.s. 46 7.1 6.7, 7.5 *** 0.14 0.08, 0.21 *** N/A Sig. 58 6.6 6.2, 7.1 *** 0.24 0.18, 0.30 *** N/A unknown 63 6.5 6.3, 6.6 *** 0.21 0.18, 0.24 *** N/A


11

Table S8. Results of ANCOVA analyses evaluating the effect of covariate 3 (i.e., the number of cycles observed in the time series) on the OLS-fitted parameter estimates presented in table 1 of the main text.

Group

Model 1:


Model 2:


𝟏𝐓𝟐𝟎℃

ln(I) θ ln(IA) b E All groups FY,KY] = 8.1

p = 0.005 FY,KY] = 0.47 p = 0.50

FY,K]_ = 3.0 p = 0.09

FY,K]_ = 0.02 p = 0.90

FY,K]_ = 0.03 p = 0.89

Insects FY,YYK = 0.1 p = 0.74

FY,YYK = 0.000 p = 0.99

FY,YYY = 0.90 p = 0.35

FY,YYY = 0.001 p = 0.97

FY,YYY = 4.1 p = 0.047


FY,KS = 1.1 p = 0.30

FY,KS = 1.1 p = 0.30

FY,K] = 2.8 p = 0.11

FY,K] = 1.7 p = 0.20

FY,K] = 2.5 p = 0.12

Mammals & Birds

FY,YU^ = 21.7 p < 0.001

FY,YU^ = 33.1 p < 0.001

FY,YU^ = 9.9 p = 0.002

FY,YU^ = 11.7 p < 0.001

N/A


12

Table S9. OLS-fitted parameter estimates within levels of covariate 3 (i.e., the number of cycles observed in the time series). Lower and upper bounds of the 95% CI for each parameter estimate are noted in parentheses. (***) indicates p < 0.001, (**) indicates p < 0.01, (*) indicates p < 0.05, and (.) indicates p < 0.1.



< 3 100 3.4 2.9, 3.6 *** 0.89 0.83, 0.95 *** > 3 214 3.3 3.1, 3.5 *** 0.86 0.82, 0.91 ***

Insects < 3 29 5.0 3.3, 6.6 *** 0.56 0.28, 0.84 *** > 3 88 4.9 4.1, 5.8 *** 0.56 0.40, 0.71 ***

Zoop. & Protists < 3 8 2.9(2.3, 3.5) *** 0.41(−0.27, 1.1) > 3 28 2.7(2.4, 2.9) *** 0.70(0.55, 0.86) ***

Mam. & Birds < 3 63 4.1 3.5, 4.7 *** 0.79 0.68, 0.89 *** > 3 98 5.7 5.3, 6.2 *** 0.40 0.32, 0.49 ***


𝟏𝐓− 𝟏

𝐓𝟐𝟎℃

n ln(IA) P b P E P

All groups < 3 100 7.7 7.5, 7.8 *** 0.31 0.29, 0.33 *** 0.64 0.57, 0.72 *** > 3 214 7.5 7.5, 7.6 *** 0.31 0.30, 0.32 *** 0.65 0.60, 0.70 ***

Insects < 3 29 8.5 7.6, 9.3 *** 0.19 0.06, 0.32 ** 0.14 −0.20, 0.48 > 3 88 7.5 7.1, 7.8 *** 0.17 0.12, 0.22 *** 0.54 0.38, 0.70 ***

Zoop. & Protists < 3 8 −29 −80,29 −2.8 −8, 2.4 12.6 −9, 34 > 3 28 5.6 4.7, 6.6 *** 0.20 0.13, 0.27 *** 1.1 0.63, 1.5 ***

Mam. & Birds < 3 63 6.4 6.2, 6.7 *** 0.27 0.23, 0.30 *** N/A > 3 98 6.8 6.5, 7.1 *** 0.17 0.12, 0.22 *** N/A


13

Table S10: Summary of OLS and PGLS analyses for Model 1 and Model 2 within taxonomic groups without grouping (i.e., we do not group zooplankton and protists or mammals and birds). Lower and upper bounds of the 95% CI are noted within parentheses. ** denotes P < 0.01


n df ln(I) P 𝛉 P R2 Insects

PGLS 44 42 4.2 (2.6, 5.7) ** 0.74 (0.48, 1.00) ** 0.66 OLS 119 117 4.9 (4.2, 5.6) ** 0.56 (0.43, 0.70) ** 0.39

Zooplankton PGLS 7 5 3.2 (1.7, 4.6) 0.01 0.25 (-0.6, 1.1) 0.6 0.15 OLS 20 18 2.8 (2.3, 3.3) ** 0.66 (0.34, 0.99) ** 0.50

Protists PGLS 4 2 1.9 (1.6, 2.2) ** 0.20 (0.03, 0.37) 0.15 0.44 OLS 16 14 1.8 (1.2, 2.4) ** 0.12 (-0.28, 0.51) 0.54 0.03

Mammals PGLS 38 36 5.0 (3.2, 6.8) ** 0.58 (0.31, 0.85) ** 0.61 OLS 124 122 6.4 (6.2, 6.5) ** 0.24 (0.22, 0.26) ** 0.76

Birds

PGLS 11 9 5.7 (2.1, 9.3) 0.01 0.44 (-0.14, 1.01) 0.17 0.16 OLS 43 41 8.5 (6.2, 10.8) ** 0.05 (-0.45, 0.35) 0.81 0.001

Model 2: 𝐥𝐧 𝛒 = 𝐥𝐧(𝐈𝐨) + 𝐛𝐥𝐧 𝐌 + 𝐄 𝟏

𝐤𝟏𝐓− 𝟏

𝐓𝟐𝟎℃

n df ln(IA) P b P E P R2

Insects PGLS 44 41 8.2 (6.8, 9.5) ** 0.23 (0.08, 0.37) ** 0.41 (0.20, 0.61) ** 0.65 OLS 119 116 7.6 (7.3, 8.0) ** 0.17 (0.12, 0.21) ** 0.48 (0.34, 0.62) ** 0.48

Zooplankton PGLS 7 4 5.3 (2.0, 8.7) 0.04 0.15 (-0.1, 0.4) 0.3 0.55 (-0.4, 1.5) 0.3 0.39 OLS 20 17 5.5 (3.5, 7.6) ** 0.17 (-0.003, 0.3) 0.05 0.86 (0.23, 1.5) ** 0.59

Protists PGLS 4 1 2.4 (1.1, 3.8) 0.2 0.05 (-0.02, 0.12) 0.4 -0.22 (-0.6, 0.1) 0.45 0.88 OLS 16 13 3.4 (1.9, 4.8) ** 0.10 (0.02, 0.17) 0.02 0.16 (-0.5, 0.8) 0.6 0.37

Mammals PGLS 38 36 6.9 (5.3, 8.5) ** 0.16 (0.03, 0.30) 0.02 N/A* 0.43 OLS 124 122 6.4 (6.2, 6.5) ** 0.24 (0.22, 0.26) ** N/A* 0.76

Birds

PGLS 11 9 7.4 (5.5, 9.3) ** 0.19 (-0.14, 0.51) 0.3 N/A* 0.18 OLS 43 41 7.8 (6.6, 9.0) ** 0.07 (-0.13, 0.26) 0.5 N/A* 0.01

* We did not assess the body temperature dependence of cycle period in mammals and birds because species in these groups do not span a sufficient range of temperatures.

physiological constraints on long-term population cycles: a...

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