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Supplemental Information

Nonlinear temperature effects on multifractal complexity of metabolic rate

The data shows individual time series for 18 mice assigned at random to seven different temperature treatments. Given that experimental records differed in total length, data in the matrix have been padded with "nan" codes. For every time series, we provide the original experimental code, individual body mass measured after metabolic rate recording, and environmental temperature at which the metabolic rate signal was registered.

DOI: 10.7287/peerj.preprints.2404v1/supp-1

Supplementary Figure 1: Temperature effects on long range scaling exponent αDFA in metabolic rate fluctuations

The figure shows the average DFA scaling exponent αDFA calculated as a function of experimental temperature for (a) Linear DFA de-trending, (b) quadratic polynomial de-trending and (c) cubic de-trending. Average scaling exponents corresponding to exponent for raw r(VO2) data within the 10 < s < 100 scaling regime are shown with filled circles, while filled squares show the scaling exponents for the raw r(VO2) data within the 100 < s < 1024 scaling regimes are shown with. Open circles and squares show the scaling exponents for these two respective scaling regimes when data are shuffled.

DOI: 10.7287/peerj.preprints.2404v1/supp-2

Supplementary Figure 2:Effects of de-trending polynomial order on the generalized fluctuation function of r(VO2) measured at 0ºC

The figure shows the average generalized fluctuation function Fq(s) vs. time scale s in log-log plots for r(VO2) fluctuations using different de-trending orders. Figures in the top row show average results calculated for the raw time series measured at Ta= 0ºC when data are detrended using (a) a linear function, (b) a quadratic polynomial and (c) a cubic polynomial. The bottom row shows the results for the shuffled time series when the data are detrended using (d) a linear function, (e) a quadratic polynomial and (f) a cubic polynomial. Open circles show the observed Fq(s) values for different values of q, with q = 8, 4, 2,1,0, -1,-2, -4, and -8 (from the top to the bottom). All curves are shifted vertically for clarity. The straight lines are best piecewise linear regression fits to the Fq(s) functions. Dashed straight lines with slope h=0.5 are shown below the data in each figure to allow qualitative comparison with the uncorrelated case.

DOI: 10.7287/peerj.preprints.2404v1/supp-3

Supplementary Figure 3: Effects of de-trending polynomial order on the generalized fluctuation function of r(VO2) measured at 5ºC

The figure shows the average generalized fluctuation function Fq(s) vs. time scale s in log-log plots for r(VO2) fluctuations using different de-trending orders. Figures in the top row show average results calculated for the raw time series measured at Ta= 5ºC when data are detrended using (a) a linear function, (b) a quadratic polynomial and (c) a cubic polynomial. The bottom row shows the results for the shuffled time series when the data are detrended using (d) a linear function, (e) a quadratic polynomial and (f) a cubic polynomial. Open circles show the observed Fq(s) values for different values of q, with q = 8, 4, 2,1,0, -1,-2, -4, and -8 (from the top to the bottom). All curves are shifted vertically for clarity. The straight lines are best piecewise linear regression fits to the Fq(s) functions. Dashed straight lines with slope h=0.5 are shown below the data in each figure to allow qualitative comparison with the uncorrelated case.

DOI: 10.7287/peerj.preprints.2404v1/supp-4

Supplementary Figure 4: Effects of de-trending polynomial order on the generalized fluctuation function of r(VO2) measured at 10ºC

The figure shows the average generalized fluctuation function Fq(s) vs. time scale s in log-log plots for r(VO2) fluctuations using different de-trending orders. Figures in the top row show average results calculated for the raw time series measured at Ta= 10ºC when data are detrended using (a) a linear function, (b) a quadratic polynomial and (c) a cubic polynomial. The bottom row shows the results for the shuffled time series when the data are detrended using (d) a linear function, (e) a quadratic polynomial and (f) a cubic polynomial. Open circles show the observed Fq(s) values for different values of q, with q = 8, 4, 2,1,0, -1,-2, -4, and -8 (from the top to the bottom). All curves are shifted vertically for clarity. The straight lines are best piecewise linear regression fits to the Fq(s) functions. Dashed straight lines with slope h=0.5 are shown below the data in each figure to allow qualitative comparison with the uncorrelated case.

DOI: 10.7287/peerj.preprints.2404v1/supp-5

Supplementary Figure 5:Effects of de-trending polynomial order on the generalized fluctuation function of r(VO2) measured at 15ºC

The figure shows the average generalized fluctuation function Fq(s) vs. time scale s in log-log plots for r(VO2) fluctuations using different de-trending orders. Figures in the top row show average results calculated for the raw time series measured at Ta= 15ºC when data are detrended using (a) a linear function, (b) a quadratic polynomial and (c) a cubic polynomial. The bottom row shows the results for the shuffled time series when the data are detrended using (d) a linear function, (e) a quadratic polynomial and (f) a cubic polynomial. Open circles show the observed Fq(s) values for different values of q, with q = 8, 4, 2,1,0, -1,-2, -4, and -8 (from the top to the bottom). All curves are shifted vertically for clarity. The straight lines are best piecewise linear regression fits to the Fq(s) functions. Dashed straight lines with slope h=0.5 are shown below the data in each figure to allow qualitative comparison with the uncorrelated case.

DOI: 10.7287/peerj.preprints.2404v1/supp-6

Supplementary Figure 6:Effects of de-trending polynomial order on the generalized fluctuation function of r(VO2) measured at 20ºC

The figure shows the average generalized fluctuation function Fq(s) vs. time scale s in log-log plots for r(VO2) fluctuations using different de-trending orders. Figures in the top row show average results calculated for the raw time series measured at Ta= 20ºC when data are detrended using (a) a linear function, (b) a quadratic polynomial and (c) a cubic polynomial. The bottom row shows the results for the shuffled time series when the data are detrended using (d) a linear function, (e) a quadratic polynomial and (f) a cubic polynomial. Open circles show the observed Fq(s) values for different values of q, with q = 8, 4, 2,1,0, -1,-2, -4, and -8 (from the top to the bottom). All curves are shifted vertically for clarity. The straight lines are best piecewise linear regression fits to the Fq(s) functions. Dashed straight lines with slope h=0.5 are shown below the data in each figure to allow qualitative comparison with the uncorrelated case.

DOI: 10.7287/peerj.preprints.2404v1/supp-7

Supplementary Figure 7: Effects of de-trending polynomial order on the generalized fluctuation function of r(VO2) measured at 25ºC

The figure shows the average generalized fluctuation function Fq(s) vs. time scale s in log-log plots for r(VO2) fluctuations using different de-trending orders. Figures in the top row show average results calculated for the raw time series measured at Ta= 25ºC when data are detrended using (a) a linear function, (b) a quadratic polynomial and (c) a cubic polynomial. The bottom row shows the results for the shuffled time series when the data are detrended using (d) a linear function, (e) a quadratic polynomial and (f) a cubic polynomial. Open circles show the observed Fq(s) values for different values of q, with q = 8, 4, 2,1,0, -1,-2, -4, and -8 (from the top to the bottom). All curves are shifted vertically for clarity. The straight lines are best piecewise linear regression fits to the Fq(s) functions. Dashed straight lines with slope h=0.5 are shown below the data in each figure to allow qualitative comparison with the uncorrelated case.

DOI: 10.7287/peerj.preprints.2404v1/supp-8

Supplementary Figure 8: Effects of detrending polynomial order on the generalized fluctuation function of r(VO2) measured at 30ºC

The figure shows the average generalized fluctuation function Fq(s) vs. time scale s in log-log plots for r(VO2) fluctuations using different detrending orders. Figures in the top row show average results calculated for the raw time series measured at Ta= 30ºC when data are detrended using (a) a linear function, (b) a quadratic polynomial and (c) a cubic polynomial. The bottom row shows the results for the shuffled time series when the data are detrended using (d) a linear function, (e) a quadratic polynomial and (f) a cubic polynomial. Open circles show the observed Fq(s) values for different values of q, with q = 8, 4, 2,1,0, -1,-2, -4, and -8 (from the top to the bottom). All curves are shifted vertically for clarity. The straight lines are best piecewise linear regression fits to the Fq(s) functions. Dashed straight lines with slope h=0.5 are shown below the data in each figure to allow qualitative comparison with the uncorrelated case.

DOI: 10.7287/peerj.preprints.2404v1/supp-9

Supplementary Figure 9: Effects of temperature and detrending polynomial order on the breakpoint δ of the generalized fluctuation function Fq(s)

Top to bottom rows show the results for Ta=0ºC to Ta=30ºC respectively. Left hand, central and right hand columns show the results for linear, quadratic and cubic de-trending polynomials respectively. In all figures, black lines show the smoothed conditional mean estimate of the breakpoint, while red lines show the smoothed conditional mean estimates for shuffled data.

DOI: 10.7287/peerj.preprints.2404v1/supp-10

Supplementary Figure 10: Temperature effects on the goodness of fit of Renyi exponent spectra (τ(q)) to MMCM

The figure shows the average coeficient of determination (R2) for the fit of Renyi exponent spectra (τ(q)) to MMCM under different temperature treatments. Average R2 value in raw r(VO2) data is shown for (a) Linear de-trending, (b) quadratic polynomial de-trending and (c) cubic de-trending. Average R2 value in AAFT shuffled r(VO2) data is shown for (d) Linear de-trending, (e) quadratic polynomial de-trending and (f) cubic de-trending. Average R2 values for r(VO2) data within the 10 < s < 100 scaling regime are shown with filled circles, while open circles show average R2 values for r(VO2) data within the 100 < s < 1024 scaling regime.

DOI: 10.7287/peerj.preprints.2404v1/supp-11

Supplementary Figure 11: MF-DFA. Effect of quadratic de-trending on Multifractal Detrended Fluctuation Analysis of Mus musculus r(VO2) time series across different temperature treatments

The figure shows the effects of quadratic de-trending on the multifractal scaling analysis for all mice studied. Left, central and right hand column show the results for the generalized Hurst exponent spectra (h(q)), Renyi exponent spectra (τ(q)) and singularity spectra (f(α)). Each figure shows the smoothed conditional mean of the different spectra in dashed and continuous black lines, representing data for the first and second scaling regimes respectively. For shuffled data, dashed and continuous red lines show the smoothed conditional mean of the different spectra for the first and second scaling regimes respectively. For figures (c), (f), (i) and (o), the singularity spectra of the first regime corresponds to a single point, shown by a filled circle. The singularity spectra reveal that for temperatures in the range 0ºC < Ta < 10ºC the time scales in the 8 < s < 100 range present a monofractal scaling, while all remaining temperatures show a weak multifractal scaling. All data for the second scaling regime show strong multifractality.

DOI: 10.7287/peerj.preprints.2404v1/supp-12

Supplementary Figure 12: MF-DFA. Effect of cubic de-trending on Multifractal Detrended Fluctuation Analysis of Mus musculus r(VO2) time series across different temperature treatments

The figure shows the effects of cubic de-trending on the multifractal scaling analysis for all mice studied. Left, central and right hand column show the results for the generalized Hurst exponent spectra (h(q)), Renyi exponent spectra (τ(q)) and singularity spectra (f(α)). Each figure shows the smoothed conditional mean of the different spectra in dashed and continuous black lines, representing data for the first and second scaling regimes respectively. For shuffled data, dashed and continuous red lines show the smoothed conditional mean of the different spectra for the first and second scaling regimes respectively. For figures (c), (f), (i), (l), (o) and (u) the singularity spectra of the first regime corresponds to a single point, shown by a filled circle. The singularity spectra reveal that for all temperatures the time scales in the 8 < s < 100 range present either a monofractal scaling or a weak multifractal scaling. On the other hand, all data for the second scaling regime show strong multifractality.

DOI: 10.7287/peerj.preprints.2404v1/supp-13

Additional Information

Competing Interests

The authors declare that they have no competing interests.

Author Contributions

Fabio A Labra conceived and designed the experiments, analyzed the data, wrote the paper, prepared figures and/or tables, reviewed drafts of the paper.

Jose M Bogdanovich conceived and designed the experiments, performed the experiments, analyzed the data, contributed reagents/materials/analysis tools, wrote the paper, reviewed drafts of the paper.

Francisco Bozinovic conceived and designed the experiments, performed the experiments, contributed reagents/materials/analysis tools, wrote the paper, reviewed drafts of the paper.

Animal Ethics

The following information was supplied relating to ethical approvals (i.e., approving body and any reference numbers):

Care of experimental animals was in accordance with institutional guidelines, and experimental protocols followed were approved by the following review Boards:

Bioethics committee, Universidad Santo Tomás

Bioethics committee, Pontificia Universidad Católica de Chile

Bioethics committe, Chilean National Committee of Science and Technology (CONICYT)

All three review boards issued an approval letter, indicating the endorsement of animal care and experimental protocols.

Data Deposition

The following information was supplied regarding data availability:

The raw data has been supplied as a supplementary file.

Funding

This work was supported by grants from Fondo Nacional de Ciencia y Tecnología 1100729 to FAL and Fondo Nacional de Ciencia y Tecnología 1130015 and Fondo Basal FB-0002 to FB. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.


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