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# Early childhood investment impacts social decision-making four decades later

## Abstract

Early childhood educational investment produces positive effects on cognitive and non-cognitive skills, health, and socio-economic success. However, the effects of such interventions on social decision-making later in life are unknown. We recalled participants from one of the oldest randomized controlled studies of early childhood investment—the Abecedarian Project (ABC)—to participate in well-validated interactive economic games that probe social norm enforcement and planning. We show that in a repeated-play ultimatum game, ABC participants who received high-quality early interventions strongly reject unequal division of money across players (disadvantageous or advantageous) even at significant cost to themselves. Using a multi-round trust game and computational modeling of social exchange, we show that the same intervention participants also plan further into the future. These findings suggest that high quality early childhood investment can result in long-term changes in social decision-making and promote social norm enforcement in order to reap future benefits.

## Introduction

Early childhood investment improves the development of disadvantaged children through affecting a variety of cognitive and non-cognitive skills, often translating into better outcomes during adulthood1,2,3. The Abecedarian Project (ABC)—one of the world’s oldest high-quality experiments of early childhood intervention—enrolled newborns from low-income, multi-risk families in Orange County, North Carolina, between 1972 and 1977, and provided intensive early childhood education intervention from the first few months of life until school entry. Follow-up studies have provided mounting evidence for positive cognitive4, educational5, economic6, and physical health7 outcomes into adulthood for participants who were exposed to this intervention. However, possible effects of early childhood interventions on social decision-making strategies have not yet been investigated in this population. This is an important issue as certain social decision-making strategies could benefit an individual, including later financial, educational, social, and health outcomes. One such strategy is to choose actions that enforce social norms such as equality. Social norm enforcement, which often entails a cost8, is thought to be motivated by the fact that it can result in long-term positive effects on cooperation9 and thus lead to future benefit—outweighing the immediate cost—for the individual. Since the development of social decision-making styles can be traced back to early childhood10,11, it is therefore essential to investigate if early childhood intervention can impact social decision-making later in adulthood. In the current study, we used two economic games to probe decision-making during social interactions in ABC participants at ages 39–45: the ultimatum game (UG) particularly effective at measuring enforcement of social norms of equality and fairness12 and the multi-round trust game (MRT) measuring the process of cooperation forming/rupture through iterated social exchanges13,14.

In the UG aimed at probing social decision-making related to norm enforcement, one player (Proposer) has to decide how to split a sum of money with another player (Responder). The Responder’s acceptance results in each party receiving the allocated money whereas rejection results in both receiving no money15. The UG builds a context in which players have to make trade-offs between self-interest and social norms of equality—rejections being a way to punish behaviors that transgress such social norms16. A prominent hypothesis for explaining such behavior is the Fehr–Schmidt inequality aversion model, which proposes that people use a utility function that expresses preferences for equality and away from inequality, in both disadvantageous (i.e., Responder gets less than the Proposer) and advantageous (i.e., Responder gets more than the Proposer) situations17. The Fehr–Schmidt model is consistent with the fact that rejection of disadvantageous (low) offers has been consistently observed across studies15,18. However, behavior towards advantageous offers is more variable19,20,21. A recent study found participants rejected both disadvantageous and advantageous offers more than equal offers when playing the UG as a third party not involved in the distributive outcome. In contrast, when playing as Responders whose own benefit was affected by their choices, these same participants did not reject advantageous offers more than equal offers22. This finding suggests that even if individuals aspire to promote and enforce an “equal world”, self-interest can often overcome inequality aversion.

### Statistics

Statistics were implemented using SPSS software (IBM SPSS Statistics Version 21.0, IBM Corp.). For all analyses, the significance level was set at 0.05 and Greenhouse–Geisser correction non-sphericity was used when appropriate. Post hoc comparisons were evaluated using two-tailed pairwise tests with Bonferroni correction. Partial eta-squared (η2p) values were provided to demonstrate effect size where appropriate43.

### Rejection rate and emotion rating in UG

Our analyses focus on the participants’ social behavior towards inequality. Specifically, we tested the interaction between equality and treatment on rejection rate by a (3 × 3) Group (ABC Intervention vs. ABC Control vs. Roanoke Control) × Equality (Disadvantageous Unequal (offers < 10) vs. Equal (offers = 10) vs. Advantageous Unequal (offers > 10)) analyses of covariance (ANCOVA) with Gender as the covariate in the MHM type to take account of the gender unbalance within MHM type. As offers higher than $10 were rarely displayed for in the MLM type, a (3 × 2) Group (ABC Intervention vs. ABC Control vs. Roanoke Control) × Equality (Disadvantageous Unequal (offers < 10) vs. Equal (offers = 10)) ANCOVA with Gender as the covariate was used for the MLM type. Gender was included as a covariate in the analyses to control for the difference in gender composition in the three groups. Further, the rejection rates for each offer were calculated for each participant—making it possible to precisely describe social behavior from highly disadvantageous, to highly advantageous inequality. Because of the different distribution of offers between MHM and MLM (Fig. 2a and Supplementary Fig. 1a) resulting in small number of offers for certain amounts depending on the conditioning type, different offer sizes were evaluated for MHM and MLM. For each participant with MHM type, offers lower than$8 and offers higher than $12 were respectively pooled together. For each participant with MLM type, offers lower than$5 were pooled together and offers higher than $10—rarely displayed—were not included into the behavioral data analysis in MLM type. For each conditioning type, differences in rejection rates were analyzed using a (3 × 7) Group × Offer Size ANCOVA with Gender as the covariate to take account of the gender unbalance within MLM type. Differences in emotion ratings were analyzed using a similar approach: a Group × Equality ANCOVA and an Offer Size × Group ANCOVA with Gender as the covariate for each type of conditioning. Model-based analyses for behaviors in UG. We assumed that the participants’ behavior could be modeled by their aversion to offers that deviate from equality and fitted each participant’s behaviors to a Fehr–Schmidt inequality aversion model (FS model)17. As previous studies using the UG have shown that people have internal norms (expectations on money allocation) which can be updated based on the history of offers16,44,45, we also fitted the behavioral data to two types of adaptation models, a Bayesian observer model44 and a Rescorla–Wagner model33,46 to test if they outperformed the FS model. In the FS inequality aversion model, the utility of each offer at each round was represented by the Fehr–Schmidt inequality aversion utility function. $$U(s_i) = s_i - \alpha \max \left\{ {10 - s_i,0} \right\} - \beta \;{\mathrm {max}}\{ s_i - 10,0\} .$$ (1) Here, U(si) represents the utility of the offer si at round i. This value is discounted by the difference between the amount allocated (offer) to the Responder (si) and an even split ($10). The disutility associated with inequality is controlled by two parameters: α or “envy” (α[0,10]) which represents the participant’s unwillingness of the participant to accept unequal offers disadvantageous to him/her; β or “guilt” (β[0,10]) which represents his/her unwillingness to accept unequal offers advantageous to him/her.

The probability of accepting each offer was modeled using a softmax function:

$$p_{{\mathrm{accept}}} = \frac{{e^{u \ast \gamma }}}{{1 + e^{u \ast \gamma }}}.$$
(2)

Here, γ is the softmax inverse temperature parameter where the lower γ is, the more diffuse and variable the choices are (γ[0,1]).

Under the Bayesian observer model44 (BO model), we assumed that each participant believed that the offers were sampled from a Gaussian distribution with uncertain mean and variance, and performed Bayesian update after receiving a new offer. Specifically, each participant was assumed to have a prior on the distribution of the offers (s), with mean μ and variance σ2, denoted as s~N(μ,σ2). Since μ and variance σ2 were mixed together, the prior of offers (s) was assumed as p(μ,σ2). The prior was updated following Bayes’ rule once the participant received a new offer. The posterior was given by

$$p(\mu \,\sigma ^2|s_i) = \frac{{p(s|\mu ,\sigma ^2)p(\mu |\sigma ^2)}}{{p(s_i)}}.$$
(3)

For convenience we assumed a conjugate prior of μ and σ2:

$$p(\mu ,\,{\mathrm{\sigma }}^2) = p(\mu ,|\sigma ^2)\,p({\mathrm{\sigma }}^2),$$
(4)

with

$$p(\mu |\sigma ^2) = {\mathrm {Normal}}(\hat \mu ,\hat \sigma ^2/k)$$
(5)
$$p(\sigma ^2) = {\mathrm{Inv}} - \chi ^2(\nu ,\hat \sigma ^2).$$
(6)

We set the initial value of the hyperparameters k, ν and $${\hat{\mathrm \sigma }}^2$$ as

$$k_0 = 4,\;\nu _0 = 10,\;\hat \sigma _0^2 = 4$$

Two variations of the BO models were tested. The first assumed equality as a fixed initial norm for all participants, $$\hat \mu _0 = 10$$. The second assumed that the initial norm could vary between participants, hence $$\hat \mu _0$$ was individually fitted using each participant’s responses ($$\hat \mu _0 \in \left[ {0,20} \right]$$).

After receiving si, at round i, these values were updated as

$$k_i = k_{i - 1} + 1,v_i = v_{i - 1} + 1,$$
(7)
$$\hat \mu _i = \hat \mu _{i - 1} + \frac{1}{{k_i}}(s_i - \hat \mu _{i - 1}),$$
(8)
$$\nu _i\hat \sigma _i^2 = \nu _{i - 1}\hat \sigma _{i - 1}^2 + \frac{{k_{i - 1}}}{{k_i}}(s_i - \hat \mu _{i - 1})^2.$$
(9)

We define the prevailing norm as μi−1 at round i, and the utility of the offer is given by

$$U(s_i) = s_i - \alpha \max \;\left\{ {\mu _{i - 1} - s_i,0} \right\} - \beta \;\max\{ s_i - \mu _{i - 1},0\} .$$
(10)

Here, α represents the unwillingness of the participant to accept offers lower than his/her norm (α[0,10]). β represents the unwillingness to accept offers higher than him/her norm (β[0,10]).

The probability of accepting each offer was

$$p_{{\mathrm{accept}}} = \frac{{e^{u \ast \gamma }}}{{1 + e^{u \ast \gamma }}},$$
(2)

where γ[0,1].

The Rescorla–Wagner (RW) model assumed that each participant had internal norms which were updated by the RW rule:33,46

$$x_i = x_{i - 1} + \varepsilon (s_i - x_{i - 1}).$$
(11)

Here xi represents the norm at round i and ε is the norm adaptation rate (ε[0,1]), which represents the extent to which the norm was influenced by the difference (i.e., norm prediction error) between the current offer si and the preceding norm xi−1. A low ε indicates a lower impact of the norm prediction error on norm updating whereas a high ε indicates a high impact. Similar to the BO model, two variations of the RW model were tested based on the initial norm x0: a fixed initial norm based on equality (x0 = 10) and variable initial norms across participants. The utility of an offer at round i is given by

$$U(s_i) = s_i - \alpha \,{\mathrm{max}} \,\left\{ {x_{i - 1} - s_i,0} \right\} - \beta \,{\mathrm{max}}\{ s_i - x_{i - 1},0\} .$$
(12)

Similar to BO model, α here represents the unwillingness of the participant to accept offers lower than his/her norms (α[0,10]). β represents the unwillingness to accept offers higher than him/her norms (β[0,10]).

The probability of accepting each offer was

$$p_{{\mathrm{accept}}} = \frac{{e^{u \ast \gamma }}}{{1 + e^{u \ast \gamma }}},$$
(2)

where γ[0,1].

All models were then fitted to the behavioral data individually, which estimated the values of α, β, γ, and $$\hat \mu _0$$ or x0 for variable starting norm models for each subject by maximizing the log likelihood of choices over 60 trials. Then model comparison was implemented by calculating the Bayesian information criterion score (BIC) for each model for each participant. The model with the lowest mean BIC is considered the winning model since it has the maximal model evidence (Supplementary Table 4). The estimated parameters from the winning model were compared among the three groups of participants with an ANCOVA with Gender as a covariate. Post hoc comparisons were evaluated using Bonferroni correction. The ranges of the free parameters in models presented above were based on previous work44. We tested other ranges that resulted in slightly worse model fitting and did not significantly affect the results presented here.

### Model-based analyses for behaviors in MRT

The foundation of players’ payoff assessment was also based on the Fehr–Schmidt inequality aversion model17, but the envy term of the equation was omitted for the MRT. To distinguish the guilt parameter in the MRT from the one in the UG, the guilt parameter in the MRT is called inequality aversion, which quantifies the tendency to try and reach a fair outcome with values of {0, 0.4, 1}.

This model of MRT includes six other parameters: (1) planning horizon, which quantifies number of steps to likely plan ahead with values of {1, 2, 3, 4}; (2) theory of mind (ToM), which quantifies the number of mentalization steps with values of {0, 2, 4}; (3) inverse temperature, which quantifies the randomness of the choice preference with values of {1/4, 1/3, 1/2, 1}; (4) risk aversion, which quantifies the value of money kept over money potentially gained with values of {0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8}; (5) irritability, which quantifies tendency to retaliate on repayments worse than expected with values of {0, 0.25, 0.5, 0.75, 1.0}; and (6) irritability Belief, which quantifies the initial belief of likelihood of the partner being irritable with values of {0, 1, 2, 3, 4}. The values for the parameters were selected based on previous work23. The whole collection of parameters that best characterize an individual player are determined by maximizing the likelihood of their choices (over a grid of possible values). See ref. 23 for a detailed description of the model. Since these seven parameters from the model were ordinal variables, the tests of group effects for each parameter were conducted with independent-samples Kruskal–Wallis H tests. Post hoc comparisons were evaluated using two-tailed Mann-Whitney U-tests with Bonferroni correction.

### Code availability

The code used to analyze data in the current study is available from the corresponding author on request.

### Reporting Summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

## Data availability

The datasets generated and/or analyzed during the current study are available from the corresponding author on request. A reporting summary for this article is available as a Supplementary Information.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## References

1. 1.

Nores, M. & Barnett, W. S. Benefits of early childhood interventions across the world:(under) investing in the very young. Econ. Educ. Rev. 29, 271–282 (2010).

2. 2.

Barnett, W. S. Effectiveness of early educational intervention. Science 333, 975–978 (2011).

3. 3.

Heckman, J. J. Skill formation and the economics of investing in disadvantaged children. Science 312, 1900–1902 (2006).

4. 4.

Ramey, C. T. et al. Persistent effects of early childhood education on high-risk children and their mothers. Appl. Dev. Sci. 4, 2–14 (2000).

5. 5.

Campbell, F. A. et al. Adult outcomes as a function of an early childhood educational program: an Abecedarian Project follow-up. Dev. Psychol. 48, 1033 (2012).

6. 6.

Masse, L. N. & Barnett, W. S. in Cost-Effectiveness and Educational Policy (eds. Levin H. M. & McEwan P. J.) 157–173 (Eye on Education, Inc., Larchmont, NY, 2002).

7. 7.

Campbell, F. A. et al. Early childhood investments substantially boost adult health. Science 343, 1478–1485 (2014).

8. 8.

Fehr, E. & Fischbacher, U. Social norms and human cooperation. Trends Cogn. Sci. 8, 185–190 (2004).

9. 9.

Brosnan, S. F. & de Waal, F. B. Evolution of responses to (un) fairness. Science 346, 1251776 (2014).

10. 10.

Piaget, J. The Moral Judgment of the Child (The Free, New York, 1965).

11. 11.

Fehr, E., Bernhard, H. & Rockenbach, B. Egalitarianism in young children. Nature 454, 1079–1083 (2008).

12. 12.

Fehr, E. & Camerer, C. F. Social neuroeconomics: the neural circuitry of social preferences. Trends Cogn. Sci. 11, 419–427 (2007).

13. 13.

King-Casas, B. et al. Getting to know you: reputation and trust in a two-person economic exchange. Science 308, 78–83 (2005).

14. 14.

King-Casas, B. et al. The rupture and repair of cooperation in borderline personality disorder. Science 321, 806–810 (2008).

15. 15.

Güth, W., Schmittberger, R. & Schwarze, B. An experimental analysis of ultimatum bargaining. J. Econ. Behav. Organ. 3, 367–388 (1982).

16. 16.

Montague, P. R. & Lohrenz, T. To detect and correct: norm violations and their enforcement. Neuron 56, 14–18 (2007).

17. 17.

Fehr, E. & Schmidt, K. M. A theory of fairness, competition, and cooperation. Q. J. Econ. 114, 817–868 (1999).

18. 18.

Sanfey, A. G., Rilling, J. K., Aronson, J. A., Nystrom, L. E. & Cohen, J. D. The neural basis of economic decision-making in the ultimatum game. Science 300, 1755–1758 (2003).

19. 19.

Güth, W., Schmidt, C. & Sutter, M. Fairness in the mail and opportunism in the internet: a newspaper experiment on ultimatum bargaining. Ger. Econ. Rev. 4, 243–265 (2003).

20. 20.

Blake, P. et al. The ontogeny of fairness in seven societies. Nature 528, 258–261 (2015).

21. 21.

Hennig-Schmidt, H., Li, Z.-Y. & Yang, C. Why people reject advantageous offers—non-monotonic strategies in ultimatum bargaining: evaluating a video experiment run in PR China. J. Econ. Behav. Organ. 65, 373–384 (2008).

22. 22.

Civai, C., Crescentini, C., Rustichini, A. & Rumiati, R. I. Equality versus self-interest in the brain: differential roles of anterior insula and medial prefrontal cortex. Neuroimage 62, 102–112 (2012).

23. 23.

Hula, A., Vilares, I., Lohrenz, T., Dayan, P. & Montague, P. R. A model of risk and mental state shifts during social interaction. PLoS Comput. Biol. 14, e1005935 (2018).

24. 24.

Watkins, C. J. & Dayan, P. Q-learning. Mach. Learn. 8, 279–292 (1992).

25. 25.

Ramey, C. T. & Smith, B. J. Assessing the intellectual consequences of early intervention with high-risk infants. Am. J. Ment. Defic. 81, 318–324 (1977).

26. 26.

Sparling, J. & Lewis, I. Learningames for the First Three Years: A Guide to Parent-Child Play (Walker & Co., Palo Alto, CA,1979).

27. 27.

Ramey, C. T., Bryant, D. M., Sparling, J. J. & Wasik, B. H. Project CARE: a comparison of two early intervention strategies to prevent retarded development. Top. Early Child. Spec. Educ. 5, 12–25 (1985).

28. 28.

Ramey, C. & Campbell, F. in Frontiers of Knowlege in Mental Retardation. Vol. 1 (eds. Mittler, P. and de Jong Lancaster, J. M.) 47–57 (MTP Press, 1981).

29. 29.

Campbell, F. A. & Ramey, C. T. Effects of early intervention on intellectual and academic achievement: a follow‐up study of children from low‐income families. Child Dev. 65, 684–698 (1994).

30. 30.

Güth, W. & Napel, S. Inequality aversion in a variety of games—an indirect evolutionary analysis. Econ. J. 116, 1037–1056 (2006).

31. 31.

Bolton, G. E. & Zwick, R. Anonymity versus punishment in ultimatum bargaining. Games Econ. Behav. 10, 95–121 (1995).

32. 32.

Gmytrasiewicz, P. J. & Doshi, P. A framework for sequential planning in multi-agent settings. J. Artif. Intell. Res. 24, 49–79 (2005).

33. 33.

Sutton, R. S. & Barto, A. G. Reinforcement Learning: An Introduction. Vol. 1 (MIT Press Cambridge, 1998).

34. 34.

Camerer, C. F., Ho, T.-H. & Chong, J.-K. A cognitive hierarchy model of games. Q. J. Econ. 119, 861–898 (2004).

35. 35.

Nowak, M. A., Page, K. M. & Sigmund, K. Fairness versus reason in the ultimatum game. Science 289, 1773–1775 (2000).

36. 36.

Cappelen, A. W., List, J. A., Samek, A. & Tungodden, B. The Effect of Early Education on Social Preferences (National Bureau of Economic Research, 2016).

37. 37.

Kosse, F., Deckers, T., Schildberg-Hörisch, H. & Falk, A. The formation of prosociality: causal evidence on the role of social environment. IZA Discussion Paper No. 9861 (2016).

38. 38.

Bahry, D. L. & Wilson, R. K. Confusion or fairness in the field? Rejections in the ultimatum game under the strategy method. J. Econ. Behav. Organ. 60, 37–54 (2006).

39. 39.

Tracer, D. Selfishness and fairness in economic and evolutionary perspective: an experimental economic study in Papua New Guinea. Curr. Anthropol. 44, 432–438 (2003).

40. 40.

Henrich, J. et al. Costly punishment across human societies. Science 312, 1767–1770 (2006).

41. 41.

Cozzolino, P. J. Trust, cooperation, and equality: a psychological analysis of the formation of social capital. Br. J. Soc. Psychol. 50, 302–320 (2011).

42. 42.

Lang, P. J. in Technology in Mental Health Care Delivery Systems (eds. Sidowski, J. B., Johnson, J. H. & Williams, T. A.) (Ablex, Norwood, NJ, 1980).

43. 43.

Cohen, J. Eta-squared and partial eta-squared in fixed factor ANOVA designs. Educ. Psychol. Meas. 33, 107–112 (1973).

44. 44.

Xiang, T., Lohrenz, T. & Montague, P. R. Computational substrates of norms and their violations during social exchange. J. Neurosci. 33, 1099–1108 (2013).

45. 45.

Gu, X. et al. Necessary, yet dissociable contributions of the insular and ventromedial prefrontal cortices to norm adaptation: computational and lesion evidence in humans. J. Neurosci. 35, 467–473 (2015).

46. 46.

Rescorla, R. & Wagner, A. in Classical Conditioning. II: Current Research and Theory (Appleton-Century-Crofts, New York, 1972).

## Acknowledgements

We thank Laura Bateman and Carrie Bynum for their assistance. Our extreme gratitude also goes out to the families and individuals who have participated in this work over these many years. This work was funded by a Principal Research Fellowship from the Wellcome Trust (to P.R.M.), Virginia Tech (to P.R.M. and S.L.R.), and the FRQ-S and CIHR (to S.H.). P.F. is receipt of a National Institute for Health Research (NIHR) Senior Investigator Award (NF-SI-0514-10157). P.F. was in part supported by the NIHR Collaboration for Leadership in Applied Health Research and Care (CLAHRC) North Thames at Barts Health NHS Trust. The views expressed are those of the authors and not necessarily those of the NHS, the NIHR, or the Department of Health. P.D. was funded by the Gatsby Charitable Foundation; he is currently at Max Planck Institute for Biological Cybernetics, Tuebingen, Germany.

## Author information

### Author notes

1. These authors contributed equally: Yi Luo, Sébastien Hétu.

### Affiliations

1. #### Virginia Tech Carilion Research Institute, Roanoke, VA, 24016, USA

• Yi Luo
• , Sébastien Hétu
• , Terry Lohrenz
• , Sharon Landesman Ramey
• , Libbie Sonnier-Netto
• , Jonathan Lisinski
• , Stephen LaConte
•  & Craig Ramey
2. #### Université de Montréal, Montreal, QC, H3C 3J7, Canada

• Sébastien Hétu
3. #### Austrian Institute of Technology, 1210, Vienna, Austria

• Andreas Hula
4. #### Wellcome Trust Centre for Neuroimaging, University College London, 12 Queen Square, London, WC1E 6BT, UK

• Peter Dayan
• , Tobias Nolte
5. #### Gatsby Computational Neuroscience Unit, University College London, London, WC1E 6BT, UK

• Peter Dayan
6. #### Anna Freud National Centre for Children and Families, 21 Maresfield Gardens, London, NW3 5SD, UK

• Tobias Nolte
•  & Peter Fonagy
7. #### Research Department of Clinical, Educational and Health Psychology, University College London, Gower Street, London, WC1E 6BT, UK

• Peter Fonagy
8. #### Psychiatry Department, Virginia Tech Carilion School of Medicine, Roanoke, VA, 24016, USA

• Elham Rahmani

### Contributions

Y.L., S.H., T.L., and P.R.M. designed the ultimatum game and the multi-round trust game experiment; C.R. and S.R. designed the ABC experiment and follow-up; Y.L., S.H., S.L.R., C.R., L.S. and P.R.M. performed research; Y.L., S.H., T.L., A.H., P.D., J.L., T.N., P.F., and P.R.M analyzed data; Y.L., S.H., T.L., A.H., P.D., S.L.R., J.L., S.L., C.R., T.N., P.F., E.R. and P.R.M. discussed the results; Y.L., S.H., T.L. and P.R.M. wrote the manuscript. A.H., P.D., S.L., T.N., S.L.R., E.R. and C.R. provided important comments and suggestions that significantly contributed to the manuscript.

### Competing interests

The authors declare no competing interests.