Is Latitude Associated with Chronotype?

Daniel Vartanian

University of São Paulo

2025-02-03

Hi there! 👋

This presentation will provide an overview of the thesis objectives, main concepts, methods, and results. Together, we’ll uncover how environment factors can influence the cronotype.

We will cover the following topics:

1. Introduction
2. Methods
3. Results
4. Discussion
5. Conclusion

1. Introduction [5m]
2. Methods [5m]
3. Results [5m]
4. Discussion [5m]
5. Conclusion [5m]

Introduction

Question

This thesis focuses on the expression of sleep and circadian phenotypes (chronotypes), seeking to provide an answer to the following question related to human populations:

Is latitude associated with chronotype?

Chronotype

Temporal dimension of evolution.

Entrainment

Physiological global emergence.

An illustration depicting how the human circadian clock system regulate multiple aspects of metabolic physiology, such as: hormone secretion, core body temperature, resting metabolic rate, and plasma metabolite concentration.

The Latitude Hypothesis

URL: https://www.nature.com/articles/s41598-017-05797-w

Leocadio-Miguel et al. 

Sample: \(12,884\) Brazilian participants

Method: HO Questionnaire (Horne & Östberg, 1976)

\(\Delta \ \text{Adjusted} \ \text{R}^{2} = 0.388\%\) (Cohen’s \(f^2 = 0.004143174\))

Methods

MCTQ

The Two Process of Sleep Reg.

Illustration of the interaction between Process \(\text{S}\) (Homeostatic/Sleep-dependent process) and Process \(\text{C}\) (Circadian rhythm process) in sleep regulation.
The figure depicts two scenarios: One with \(17\) hours of wakefulness followed by \(7\) hours of sleep, and another, under sleep deprivation, with \(41\) hours of wakefulness followed by \(7\) hours of sleep. The hatched areas indicate periods of sleep, illustrating the exponential decline of Process \(\text{S}\).

Sample

Sample

The dataset used for analysis is made up of \(65,824\) Brazilian individuals aged 18 or older, residing in the UTC-3 timezone, who completed the survey between October 15th and 21st, 2017.

Geographical distribution of the sample used in the analysis (\(n = 65,824\)).
Each point represents a municipality, with its size proportional to the number of participants and its color indicating participant density. The sample includes Brazilian individuals aged 18 or older, residing in the UTC-3 timezone, who completed the survey between October 15th and 21st, 2017. The size and color scale are logarithmic (\(\log_{10}\)).

Hypothesis Test

The study tested whether latitude significantly improves model fit when predicting chronotype with nested models.

A restricted model (excluding latitude) with a full model (including latitude) was compared.

To ensure practical significance, a Minimum Effect Size (MES) criterion was applied, following the original Neyman-Pearson framework for hypothesis testing (Neyman & Pearson, 1928a, 1928b; Perezgonzalez, 2015).

The MES was set at Cohen’s threshold for small effects (\(f^2 = 0.02\), equivalent to \(\text{R}^2 = 0.01960784\)) (Cohen, 1988, p. 413). Thus, latitude was considered meaningful only if its inclusion accounted for at least \(1.960784\%\) of the variance in chronotype.

To balance the sample, a weighting procedure was applied to the data. The weights were calculated by cell weighting, using the sex, age group and Brazil’s state as reference.

Hypothesis Test

The hypothesis can be outlined as follows:

Null hypothesis (\(\text{H}_{0}\))

Adding latitude does not meaningfully improve the model’s fit. This implies that the change in adjusted \(\text{R}^{2}\) is negligible, or the F-test is not significant, given a type I error probability (\(\alpha\)) of \(0.05\).

Alternative Hypothesis (\(\text{H}_{a}\))

Adding latitude meaningfully improves the model’s fit. This implies that the change in adjusted \(\text{R}^{2}\) exceeds the expected Minimum Effect Size (MES), and the F-test is significant, given a type I error probability (\(\alpha\)) of \(0.05\).

\[ \begin{cases} \text{H}_{0}: \Delta \ \text{Adjusted} \ \text{R}^{2} \leq \text{MES} \quad \text{or} \quad \text{F-test is not significant} \ (\alpha \geq 0.05) \\ \text{H}_{a}: \Delta \ \text{Adjusted} \ \text{R}^{2} > \text{MES} \quad \text{and} \quad \text{F-test is significant} \ (\alpha < 0.05) \end{cases} \]

Results

Chronotype Distribution

Distribution of the local time of the sleep-corrected midpoint between sleep onset and sleep end on work-free days (MSF_sc), a proxy for chronotype.
Chronotypes are categorized into quantiles, ranging from extremely early (\(0 |- 0.11\)) to extremely late (\(0.88 - 1\)).

Hypothesis Test

Restricted Model
(Based on Leocadio-Miguel et al. (2017))

• Predictors (\(4\)):
  Age, Sex, Longitude, and the Average Monthly Global Horizontal Irradiance (GHI) at the time of questionnaire completion.
• $^2_{} = $
• \(\text{F}(4, 65818) = 1531.808\)
• \(p\text{-value} < 1e-05\)

Components of solar irradiance. \(G_{0}\) = Extraterrestrial irradiance. \(G_{n}\) = Direct normal irradiance. \(G_{dif}\) = Diffuse horizontal irradiance. \(G_{dir}\) = Direct horizontal irradiance. \(G\) = Global horizontal irradiance. \(G_{i}\) = Inclined plane irradiance.

In particular, it was used the Global Horizontal Irradiance (GHI) data, which is the total amount of irradiance received from above by a surface horizontal to the ground.

Hypothesis Test

Full Model A
(Based on Leocadio-Miguel et al. (2017))

• Predictors (\(8\)):
  [restricted predictors] + Average Annual Global Horizontal Irradiance (GHI), Daylight Duration for the Nearest March Equinox, June and December solstices
• $^2_{} = $
• \(\text{F}(8, 65814) = 794.12\)
• \(p\text{-value} < 1e-05\)

Full Model B

• Predictors (\(5\)):
  [restricted predictors] + Latitude
• $^2_{} = $
• \(\text{F}(5, 65817) = 1233.588\)
• \(p\text{-value} < 1e-05\)

Hypothesis Test

All coefficients were statistically different from zero (\(p\text{-value} < 0.05\)). Assumption checking and residual diagnostics primarily relied on visual inspection, as formal assumption tests (e.g., Anderson-Darling) are often not recommended for large samples (Shatz, 2024). All validity assumptions were met, and no serious multicollinearity was found among the predictor variables.

An ANOVA for nested models revealed a significant reduction in the residual sum of squares in both tests (A \(\text{F}(4, 65814) = 51.71\), \(p\text{-value} < 1e-05\)) (B \(\text{F}(1, 65817) = 37.325\), \(p\text{-value} < 1e-05\)).

However, similarly to Leocadio-Miguel et al. (2017), when estimating Cohen’s \(f^2\) effect size (\(f^2 = 0.004143174\)), the results were below the MES (i.e., negligible) (A \(f^2 = 0.0031428, 95\% \ \text{CI}[0, 0.012203]\)) (B \(f^2 = 0.0005671, 95\% \ \text{CI}[0, 0.0095426]\)).

Sunrise times for the nearest March and September equinoxes, as well as the June and December solstices, were excluded due to high multicollinearity. Daylight duration for the September equinox was excluded for its collinearity with daylight duration during the March equinox.

Discussion

Chronotype versus Latitude

Boxplots of mean MSF_sc values aggregated by \(1°\) latitude intervals, illustrating the relationship between latitude and chronotype. MSF_sc represents the local time of the sleep-corrected midpoint between sleep onset and sleep end on work-free days, a proxy for chronotype. Higher MSF_sc values indicate later chronotypes. The × symbol points to the mean. The orange line represents a linear regression. The differences in mean/median values across latitudes are minimal relative to the Munich ChronoType Questionnaire (MCTQ) scale.

Chronotype Geo. Distribution

Geographical distribution of MSF_sc values by Brazilian state, illustrating how chronotype varies with latitude in Brazil. MSF_sc is a proxy for chronotype, representing the midpoint of sleep on work-free days, adjusted for sleep debt. Higher MSF_sc values correspond to later chronotypes. The color scale was not transformed and it has as limits the first and third quartile (interquartile range). Differences in mean MSF_sc values across states are small and fall within a narrow range relative to the scale of the Munich ChronoType Questionnaire (MCTQ), limiting the significance of these variations.

Chronotype Geo. Distribution

Respondent level by categorical chronotype.

The p-value Problem

Large samples and sensitivity

Is a difference of \(0.00001\) valid?

Statistical ritual versus Statistical thinking

Confirmation bias

Comparison of a 95% of confidence level (\(\alpha = 0.05\)) and an n-dependent p-value curve. The parameter \(n_{\alpha}\) represents the minimum sample size to detect statistically significant differences among compared groups. The parameter \(n_{\gamma}\) represents the convergence point of the p-value curve. When the p-value curve expresses practical differences, the area under the red curve (\(A_{p(n)}\)) is smaller than the area under the constant function \(\alpha = 0.05\) (\(A_{\alpha = 0.05}\)) when it is evaluated between \(0\) and \(n_{\gamma}\).

The p-value Problem

SMALL EFFECT SIZE: \(f^2 = .02\). Translated into \(\text{R}^{2}\) or partial \(\text{R}^{2}\) for Case 1, this gives \(.02 / (1 + .02) = .0196\). We thus define a small effect as one that accounts for 2% of the \(\text{Y}\) variance (in contrast with 1% for \(r\)), and translate to an \(\text{R} = \sqrt{0196} = .14\) (compared to .10 for \(r\)). This is a modest enough amount, just barely escaping triviality and (alas!) all too frequently in practice represents the true order of magnitude of the effect being tested. (p. 413)

[…] in many circumstances, all that is intended by “proving” the null hypothesis is that the ES [Effect Size] is not necessarily zero but small enough to be negligible […]. (p. 461)

Nonrealistic Models

Conclusion

Answer

I suggest that it is the aim of science to find satisfactory explanations, of whatever strikes us as being in need of explanation.

This study, using what is arguably one of the largest datasets on chronotype, found no evidence supporting the latitude hypothesis in humans.

Closing remarks

This thesis was presented to the School of Arts, Sciences and Humanities (EACH) at the University of São Paulo (USP) as a requirement for the degree of Master of Science by the Graduate Program in Complex Systems Modeling (PPGSCX).

I am deeply grateful to my advisor, Prof. Dr. Camilo Rodrigues Neto, for introducing me to complexity science in 2012, guiding my dissertation with patience, and demonstrating remarkable integrity in navigating a challenging supervisory transition.

Closing remarks

The presentation was created using the Quarto publishing system. All analyses presented are fully reproducible and were conducted using the R programming language.

To explore the code and repository for this thesis, click here. The research compendium is also accessible via The Open Science Framework by clicking here.

Financial support was provided by the Coordination for the Improvement of Higher Education Personnel (CAPES) (Grant number: 88887.703720/2022-00).

References

In accordance with the American Psychological Association (APA) Style, 7th edition.

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Thank you!

Appendices

(AP) Mimosa Pudica

Illustration of the circadian rhythm in leaf movement of the sensitive plant (Mimosa pudica) observed by Jacques d’Ortous de Mairan in 1729.

(AP) Entrainment

Illustration of a circadian rhythm entrained (Phase-advanced, indicated by a leftward shift) by a zeitgeber (Input).

(AP) Emergence

Stable macroscopic patterns arising from local interaction of agents (Epstein, 1999).

When the aggregate exhibits properties not attained by summation (Holland, 2014).

The behavior of each part don’t explain how they behave collectively.

Levels of description (Nicolis & Nicolis, 2012).

In mathematical terms, the interactions of interest are non-linear (Holland, 2014).

Emergence isn’t magic (Wilson, 2004).

You are dealing with an emergence phenomenon when there is no need to look under the hood (Krakauer, 2023).

(AP) Emergence

(AP) Emergence

An aggregate behavior emerges from the interactions of the parts (CAS) (Holland, 2012).

Illustrative example: Societies; immune cells.

A society is formed by individuals and their interactions. In this case, we are the agents and the society is the aggregate agent. And, as we know, we shape the society, but the society also shapes us.

(AP) Earth’s Rotation Axis

(AP) Corr. Matrix

Correlation matrix of main variables.

(AP) Chronotype Comparison

Brazil

Europe

• Left: Distribution of the local time of the sleep-corrected midpoint between sleep onset and sleep end on work-free days (MSF_sc), a proxy for chronotype. Chronotypes are categorized into quantiles, ranging from extremely early (\(0 |- 0.11\)) to extremely late (\(0.88 - 1\)).
• Right: Distribution of European chronotypes, as shown in Roenneberg et al. (2019) (for comparison).

(AP) Age versus Chronotype

Brazil

Europe

• Left: Relation between age and chronotype, divided by sex and aggregated by the mean. Chronotype is represented by the local time of the sleep corrected midpoint between sleep onset and sleep end on work-free days (MSF_sc), MCTQ proxy for measuring the chronotype. The gray line represents both sex. Vertical lines represent the standard error of the mean (SEM).
• Right: Distribution of European chronotypes by age, as shown in Roenneberg et al. (2007), for comparison.

(AP) Chronotype Geo. Dist.

Municipality level.

(AP) Chronotype Geo. Dist.

Respondent level by categorical chronotype.

(AP) Cohen’s Benchmarks

(AP) Directions for Fut. Research

WorldClim 2.1 in NetLogo (NetLogo/Scala-Java).

(AP) Popper’s hypothetico-deductive method

The activity can be represented by a general schema of problem- solving by the method of imaginative conjectures and criticism, or, as I have often called it, by the method of conjecture and refutation. The schema (in its simplest form) is this:

flowchart LR
  A(P1) --> B(TT)
  B --> C(EE)
  C --> D(P2)

flowchart LR
  A(P) --> B(TT)
  B --> C(EE)
  C --> A

(AP) Popper’s hypothetico-deductive method

Here \(\text{P}_1\), is the problem from which we start, \(\text{TT}\) (the ‘tentative theory’) is the imaginative conjectural solution which we first reach, for example our first tentative interpretation. \(\text{EE}\) (‘error- elimination’) consists of a severe critical examination of our conjecture, our tentative interpretation: it consists, for example, of the critical use of documentary evidence and, if we have at this early stage more than one conjecture at our disposal, it will also consist of a critical discussion and comparative evaluation of the competing conjectures. \(\text{P}_2\) is the problem situation as it emerges from our first critical attempt to solve our problems. It leads up to our second attempt (and so on).

flowchart LR
  A(P1) --> B(TT)
  B --> C(EE)
  C --> D(P2)

(AP) Popper’s hypothetico-deductive method

The history of ideas teaches us very clearly that ideas emerge in logical or, if the term is preferred, in dialectical contexts. My various schemata such as

flowchart LR
  A(P1) --> B(TT)
  B --> C(EE)
  C --> D(P2)

may indeed be looked upon as improvements and rationalizations of the Hegelian dialectical schema: they are rationalizations because they operate entirely within the classical logical organon of rational criticism, which is based upon the so-called law of contradiction; that is to say, upon the demand that contradictions, whenever we discover them, must be eliminated. Critical error-elimination on the scientific level proceeds by way of a conscious search for contradictions.

(AP) Popper against positivism (or the problem of induction)

Notre activité intellectuelle est suffisamment excitée par le pur espoir de découvrir les lois des phénomènes, par le simple désir de confirmer ou d’infirmer une théorie. […] la philosophie positive est le véritable état définitif de l’intelligence humaine […] (Comte, 1892, pp. 9–10).

Why post-positivist?

• Anti-inductivist (deduction, satisfactory answers)
• Anti-verificationist (falsifiability as demarcation criterion)
• Anti-historicist (rebuttable presumptions)

(AP) Popper against positivism (or the problem of induction)

But I shall certainly admit a system as empirical or scientific only if it is capable of being tested by experience. These considerations suggest that not the verifiability but the falsifiability of a system is to be taken as a criterion of demarcation. In other words: I shall not require of a scientific system that it shall be capable of being singled out, once and for all, in a positive sense; but I shall require that its logical form shall be such that it can be singled out, by means of empirical tests, in a negative sense: it must be possible for an empirical scientific system to be refuted by experience.

(AP) Popper against positivism (or the problem of induction)

Everybody knows nowadays that logical positivism is dead. But nobody seems to suspect that there may be a question to be asked here—the question “Who is responsible?” or, rather, the question “Who has done it?”. (Passmore’s excellent historical article does not raise this question.) I fear that I must admit responsibility.

(AP) The 7 conclusions of Popper on science

1. It is easy to obtain confirmations, or verifications, for nearly every theory—if we look for confirmations.
2. Confirmations should count only if they are the result of risky predictions; that is to say, if, unenlightened by the theory in question, we should have expected an event which was incompatible with the theory—an event which would have refuted the theory.

(AP) The 7 conclusions of Popper on science

3. Every ‘good’ scientific theory is a prohibition: it forbids certain things to happen. The more a theory forbids, the better it is.
4. A theory which is not refutable by any conceivable event is nonscientific. Irrefutability is not a virtue of a theory (as people often think) but a vice.

(AP) The 7 conclusions of Popper on science

5. Every genuine test of a theory is an attempt to falsify it, or to refute it. Testability is falsifiability; but there are degrees of testability: some theories are more testable, more exposed to refutation, than others; they take, as it were, greater risks.
6. Confirming evidence should not count except when it is the result of a genuine test of the theory; and this means that it can be presented as a serious but unsuccessful attempt to falsify the theory. (I now speak in such cases of ‘corroborating evidence’).

(AP) The 7 conclusions of Popper on science

7. Some genuinely testable theories, when found to be false, are still upheld by their admirers—for example by introducing ad hoc some auxiliary assumption, or by re-interpreting the theory ad hoc in such a way that it escapes refutation. Such a procedure is always possible, but it rescues the theory from refutation only at the price of destroying, or at least lowering, its scientific status. (I later described such a rescuing operation as a ‘conventionalist twist’ or a ‘conventionalist stratagem’).

(AP) The 7 conclusions of Popper on science

One can sum up all this by saying that the criterion of the scientific status of a theory is its falsifiability, or refutability, or testability.