Appendix ESM 1. Study lakes and selected limnological characteristics. ‘X’ indicates if the lake was retained in multivariate ordinations (> 40 midge subfossil specimens recovered) or in the thermal regime logistic regression inference model. SA = surface area; DOC = dissolved organic carbon; Zmax = lake maximum depth; RDA = redundancy analysis.

Lake / SA / DOC / Zmax / Lake retained in
(ha) / (µmol L-1) / (m) / Midge RDA / thermal regime inference model
109 / 14.9 / 495 / 10.1 / X / X
110 / 5.3 / 593 / 13.1 / X / X
115 / 6.5 / 1040 / 1.5 / X / X
122 / 12.2 / 1000 / 12.8 / X / X
127 / 4.9 / 690 / 4.7 / X / X
150 / 11.8 / 820 / 7.3 / X
152 / 5.3 / 680 / 6.1 / X
164 / 20.3 / 920 / 7.1 / X
226NE / 8.3 / 589 / 14.7
304 / 3.6 / 788 / 6.7
375 / 23.2 / 475 / 26.8
378 / 24.3 / 680 / 18.1 / X / X
382 / 36.9 / 640 / 13.3 / X / X
435 / 5.7 / 590 / 2.4 / X / X
436 / 8.6 / 940 / 5.0 / X
437 / 10.0 / 980 / 1.2 / X / X
438 / 17.0 / 770 / 4.0 / X / X
442 / 16.0 / 600 / 17.8
470 / 5.7 / 1020 / 1.7 / X / X
523 / 35.0 / 1180 / 4.0 / X / X
626 / 27.9 / 540 / 11.2 / X / X
627 / 35.5 / 580 / 8.2 / X
628 / 24.0 / 780 / 3.3 / X / X
632 / 1.2 / 1247 / 1.2 / X / X
640S / 16.0 / 1180 / 12.0 / X / X
641 / 30.0 / 980 / 13.4 / X / X
645 / 7.0 / 1120 / 8.2 / X
651 / 6.0 / 1180 / 5.5 / X
652 / 10.0 / 660 / 4.1 / X / X
661 / 1.3 / 1573 / 1.0 / X / X
663 / 40.0 / 980 / 8.0
679 / 4.7 / 1930 / 2.0 / X / X
938 / 19.2 / 433 / 5.9 / X / X
Dixie / 30.0 / 330 / 15.0 / X / X
Earngey / 60.0 / 450 / 18.0 / X / X
George / 80.0 / 690 / 28.5
Isabel / 35.0 / 840 / 15.0 / X / X
Island / 50.0 / 800 / 4.5 / X / X
Little Joe / 16.0 / 790 / 13.0 / X / X
Petursson / 15.0 / 820 / 9.5 / X
Tower / 14.0 / 830 / 9.5 / X

Appendix ESM 2. Location of Experimental Lakes Area in central North America.

Appendix ESM 3. Statistics of ‘best’ lake depth (Zmax) inference models.

Model type / RMSE1 / r2* / RMSEP1 / r2(jack)* / Max bias2
Weighted-averaging regression, with inverse deshrinking (WAinv) / 0.462 / 0.764 / 0.578 / 0.631 / 1.073
Weighted-averaging partial least squares regression, first component (WAPLS-1) / 0.462 / 0.764 / 0.577 / 0.632 / 1.071
Partial least squares regression, first component (PLS-1) / 0.446 / 0.780 / 0.533 / 0.686 / 0.771
Modern Analogue Technique, weighted, closest 5 matches, squared Chi-squared distance (WMAT) / 0.606 / 0.596 / 0.606 / 0.596 / 0.760

1RMSE = root mean squared error; RMSEP = root mean squared error of prediction

2Max bias = maximum bias in residuals, jack-knifed model

*r2 = “apparent” r2, r2(jack) = jack-knifed (cross-validated) r2

Appendix ESM 4. Common taxa (at least ≥ 2% in 2 lakes) in the 35 lake training set, taxon code, maximum % abundance in training set (Max %), effective number of occurrences (Hill’s N2), and beta coefficient in the jack-knifed PLS lake depth inference model (Beta-C1-X). Taxa are listed in rank order of increasing beta coefficient.

Taxon / Taxon Code / Max % / N2 / Beta-C1-X
Tanytarsina undifferentiated / TANYTA / 82.0 / 33.1 / -0.104
Polypedilum / POLYPE / 11.8 / 23.8 / -0.087
Psectrocladius (Monopsectrocladius) / PSECTM / 19.1 / 18.6 / -0.081
Pagastiella / PAGAST / 9.6 / 14.6 / -0.075
Microtendipes / MICROT / 15.3 / 26.3 / -0.068
Procladius / PROCLD / 19.0 / 28.3 / -0.058
Cladopelma / CLADOP / 6.4 / 21.3 / -0.053
Psectrocladius undifferentiated / PSECTU / 3.6 / 15.7 / -0.037
Endochironomus / ENDOCH / 19.1 / 6.9 / -0.024
Chironomus / CHIRON / 11.8 / 24.7 / -0.020
Glyptotendipes/Dicrotendipes / GLYDICR / 8.6 / 12.2 / -0.009
Psectrocladius (Psectrocladius) / PSECTP / 6.6 / 21.8 / -0.005
Zalutschia / ZALUTS / 8.8 / 26.0 / 0.004
Psectrocladiusseptrionalis / PSECTS / 3.7 / 3.5 / 0.005
Tribelos / TRIBEL / 4.9 / 19.9 / 0.006
Dicrotendipes / DICROT / 4.7 / 20.8 / 0.013
Pseudochironomus / PSEUDO / 3.6 / 15.4 / 0.014
Parakiefferiella sp B / PARAKB / 6.3 / 23.2 / 0.015
Cryptochironomus / CRYPTC / 2.5 / 12.0 / 0.018
Tribe Pentaneurini undifferentiated / OPENTA / 8.4 / 21.8 / 0.022
Taxon CD / CD / 3.8 / 4.8 / 0.022
Cricotopus/Orthocladius / CRICOR / 10.7 / 19.8 / 0.024
Lauterborniella/Zavreliella / LAUTER / 5.5 / 12.4 / 0.027
Glyptotendipes / GLYPTO / 12.6 / 31.7 / 0.028
Synorthocladius / SYNORTH / 3.6 / 6.2 / 0.030
Stempellina / STMPLA / 10.7 / 15.3 / 0.043
Stempellinella/Zavrelia / STMPLL / 6.5 / 23.2 / 0.063
Heterotrissocladius undifferentiated / HTRTRS / 13.2 / 22.1 / 0.084
Chaoborus undifferentiated / CHAOBO / 66.2 / 20.2 / 0.104
Sergentia / SERGE / 32.8 / 11.6 / 0.135
Corynoneura/Thienemanniella / CORYTH / 23.3 / 23.0 / 0.162

Appendix ESM 5. Bias-reduced logistic regression model of thermal regime. Probability of mixing: > 0.5 = stratification; < 0.5 = polymixis. The short vertical lines along the x-axes are the placement of the 26 sites in the regression model along the PCA axis 1 score gradient. Dotted lines are the 95% confidence limits of the model.

Appendix ESM 6. Passive ordination of L240 stratigraphic samples (triangles) within training set samples (circles).