- Email: [email protected]
Invalid arguments against ABC: Reply to A.R. Templeton
Update experiments (Table 1) using in total 1213 women only from Western societies. Given that the world female population might be around three billion belonging to the most diverse communities, it is courageous to make inferences on human evolutionary ecology based on such a single-cohort sample. Second, the age varies between 16 and 39 years, masking many obvious aspects of age-related variability (e.g. adolescence; see also [4,5]). For example, the authors do not consider that fertile ovulation drops remarkably with age. In addition, the degree of awareness of the fertile mid-phase in a 16-year-old woman could not be as it is in a 39-year-old woman. Getting information about conscious intentions of maternity (e.g. by checking with ovulation sticks or other commercially adopted procedures) might be an important variable to consider. Finally, in the double-choice tests the age of the women changes, but the selection of stimulus faces solely represents young men [1]. A properly designed allocation of different male stimuli according to age and other features seems more realistic. As long ago as 1982, quail (Coturnix japonica) partner preference was being assessed with multiple choice tests [9], while behavioural biologists are increasingly aware that animals can base their preferences additionally on personality traits [10]. Why shouldn’t human mate preference also be based on personality traits? We are aware that our criticisms could be valid for almost every experiment in human physiology or every clinical trial, but physiologists do not jump so easily to particular speculations. Based on a set of limited data and designs, Alvergne and Lummaa present women as the unique depositary of the decision process for the genetic quality of their offspring, giving the impression that women seem able to choose for a pregnancy-shot the best genetic bachelor based on his ‘attractiveness’ and for the boring long-term shot the fathering–caring man, brilliantly resolving the dual sexuality dilemma. Apparently, for men it is enough simply to smell whether or not a woman is
Trends in Ecology and Evolution Vol.25 No.9
ovulating in order to decide to remain enchanted and make their job as a pollinator ‘wasp’. Does it not count that men have plenty of sex with non-ovulating women as well? Overall, some of our criticisms apply generally to those evolutionary psychology studies that tend to generate easy conclusions with limited sample diversity and size, generic or simple stimulus design, as well as limited and rather specific measures. Although the paper by Alvergne and Lummaa definitely rests on some shaky and far from ideal data, it seems this might be the only kind of data available on the topic, and the authors do acknowledge their weaknesses. References 1 Alvergne, A. and Lummaa, V. (2009) Does the contraceptive pill alter mate choice in humans? Trends Ecol. Evol. 25, 171–179 2 Sherman, B.M. and Korenman, S.G. (1975) Hormonal characteristics of the human menstrual cycle throughout reproductive life. J. Clin. Inv. 55, 699–706 3 Treloar, A.E. et al. (1967) Variation of the human menstrual cycle through reproductive life. Int. J. Fertil. 12, 77–126 4 Jung-Hoffmann, C. and Kuhl, H. (1987) Divergent effects of two low-dose oral contraceptives on sex hormone-binding globulin and free testosterone. Am. J. Obstet. Gynecol. 156, 199–203 5 Wiegratz, I. et al. (2003) Effect of four different oral contraceptives on various sex hormones and serum-binding globulins. Contraception 67, 25–32 6 Metcalf, M.G. and Mackenzie, J.A. (1980) Incidence of ovulation in young women. J. Biosoc. Sci. 12, 345–352 7 Katz, E. (1988) The luteinized unruptured follicle and other ovulatory dysfunctions. Fertil. Steril. 50, 839 8 Qublan, H. et al. (2006) Luteinized unruptured follicle syndrome: incidence and recurrence rate in infertile women with unexplained infertility undergoing intrauterine insemination. Hum. Reprod. 21, 2110–2113 9 Bateson, P. (1982) Preferences for cousins in Japanese quail. Nature 295, 236–237 (http://www.nature.com/nature/journal/v295/n5846/abs/ 295236a0.html) 10 Groothuis, T.G.G. and Carere, C. (2005) Avian personalities: characterization and epigenesis. Neurosci. Biobehav. Rev. 29, 137–150
0169-5347/$ – see front matter ß 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.tree.2010.06.004 Trends in Ecology and Evolution 25 (2010) 489–490
Letters Response
Invalid arguments against ABC: Reply to A.R. Templeton Katalin Csille´ry1, Michael G.B. Blum1, Oscar E. Gaggiotti2 and Olivier Franc¸ois1 1 Laboratoire Techniques de l’Inge´nierie Me´dicale et de la Complexite´, Centre National de la Recherche Scientifique UMR5525, Universite´ Joseph Fourier, 38706 La Tronche, France 2 Laboratoire d’Ecologie Alpine, Centre National de la Recherche Scientifique UMR5553, Universite´ Joseph Fourier, 38041 Grenoble, France
Templeton’s letter [1] contains a reformulation of his previous arguments against some of the works cited in our review [2–7], and refers to the core of our article only marginally. Templeton’s main objection to ABC is that it can produce posterior probabilities that are not ‘true’ Corresponding author: Csille´ry, K. ([email protected]).
490
probabilities [2–4]. The argument is as follows. Suppose that we want to test the hypothesis that some parameter q takes a given value q0 from a continuum, for example from the interval [0,1]. A model that assumes q = q0 must have a probability that is less than or equal to the probability of a more general model, e.g. one that assumes that q lies between 0 and 1. According to Templeton, a method that
Update contradicts the above statement violates the constraints of formal logic, and thus produces incorrect probabilities. Templeton uses the study of Fagundes et al. as an example for an incorrect analysis, where q represents the rate of interbreeding between modern and archaic human populations [5]. To re-evaluate Templeton’s argument in a simpler setting, let us consider a coin tossing experiment where q is the probability of observing a Head. Suppose that we want to test the null hypothesis (H0) that the coin is fair q = 0.5. Under the alternative hypothesis (H1), we assume that q can take any random values between 0 and 1. In a Bayesian framework, H0 and H1 represent non-overlapping events and our assumptions about the distribution of q are formulated conditionally on these separate events. Let us now calculate the posterior probabilities of the two hypotheses. We give equal prior weights to H0 and H1. The coin is flipped 20 times, and we observe 9 ‘heads’. A short computation shows that the posterior probability of H0 is 3.3637 times greater than the posterior probability of H1. The above exact calculation of probabilities highlights that Templeton’s criticism of ABC is, in fact, a criticism of the general rules of Bayesian inference. According to Templeton, H0 and H1 would be nested events. However, in a proper Bayesian framework, such as the one we used in the above coin tossing experiment, the two hypotheses represent non-nested events. Templeton’s letter also includes a ‘‘coherent correction’’ to ABC. He suggests that data should be simulated only under the general model to obtain the posterior distribution of the parameter. Then, he constructs a hypothesis test using the 95% credible interval for the parameter. In the coin tossing example, his suggestion amounts to testing if the 95% credible interval of q contains 0.5. This simple alternative to a Bayesian model choice was proposed earlier by Lindley [8]. An example of the application of Lindley’s method is given in Beaumont and Balding [9], who
Trends in Ecology and Evolution
Vol.25 No.9
developed a Bayesian algorithm to scan genomes for signatures of natural selection. More generally, Lindley’s method is often applied by statisticians to alleviate the computational burden of Markov chain Monte Carlo algorithms, even though it is not fully Bayesian. Nevertheless, the Bayes factor is often preferred in the literature [10]. In the context of ABC, Csille´ry et al. [7] suggested the use of methods based on posterior predictive distributions because Bayes factors are not properly defined when regression-based algorithms are used. One point where Csille´ry et al. [6] and Templeton could agree is that computing model complexity and evaluating alternative models still require further research. References 1 Templeton, A.R. (2010) Correcting approximate Bayesian computation. Trends Ecol. Evol. 25, 488–489 2 Templeton, A.R. (2009) Statistical hypothesis testing in intraspecific phylogeography: NCPA versus ABC. Mol. Ecol. 18, 319–331 3 Templeton, A.R. (2010) Coalescent-based, maximum likelihood inference in phylogeography. Mol. Ecol. 19, 431–435 4 Templeton, A.R. (2010) Coherent and incoherent inference in phylogeography and human evolution. Proc. Natl. Acad. Sci. U. S. A. 107, 6376–6381 5 Beaumont, M.A. et al. (2010) In defence of model-based inference in phylogeography. Mol. Ecol. 19, 436–446 6 Fagundes, N.J.R. et al. (2007) Statistical evaluation of alternative models of human evolution. Proc. Natl. Acad. Sci. U. S. A. 104, 17614–17619 7 Csille´ry, K. et al. (2010) Approximate Bayesian computation (ABC) in practice. Trends Ecol. Evol. 25, 410–418 8 Lindley, D.V. (1965) Introduction to Probability and Statistics from a Bayesian Viewpoint, Cambridge University Press 9 Beaumont, M.A. and Balding, D.J. (2004) Identifying adaptive genetic divergence among populations from genome scans. Mol. Ecol. 13, 969– 980 10 Kass, R.E. and Raftery, A.E. (1995) Bayes factors. J. Am. Stat. Assoc. 90, 773–795
0169-5347/$ – see front matter ß 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.tree.2010.06.011 Trends in Ecology and Evolution 25 (2010) 490–491
Letters Response
Response to Carere et al. Human mate preference: inconsistency between data and interpretations Alexandra Alvergne1,2 and Virpi Lummaa1 1 2
Department of Animal and Plant Sciences, University of Sheffield, Sheffield, S10 2TN, UK Department of Anthropology, University Collage London, London, WC1H 0BW, UK
We would first like to thank Carere et al. [1] for their interest and for providing us with an opportunity to discuss our paper [2], since further debate on this topic with scientists from different fields, such as behavioural physiology, will have a strong benefit for future research. Additionally, we assume their comments could be representative of a community generally sceptical about evolCorresponding author: Alvergne, A. ([email protected]).
utionary psychology, and it is therefore crucial to correct misleading points if we are to attract scientists from all fields to solve the question we raised. First, Carere et al.’s title ‘Human mate preference: inconsistency between data and interpretations’ is not correct. To date, there is no evidence against the hypothesis that hormonal contraceptives affect mate preferences in humans, and the fact that all ten previous studies point in the same direction deserves interest, given the 491
Trends in Ecology and Evolution Vol.25 No.9
ovulating in order to decide to remain enchanted and make their job as a pollinator ‘wasp’. Does it not count that men have plenty of sex with non-ovulating women as well? Overall, some of our criticisms apply generally to those evolutionary psychology studies that tend to generate easy conclusions with limited sample diversity and size, generic or simple stimulus design, as well as limited and rather specific measures. Although the paper by Alvergne and Lummaa definitely rests on some shaky and far from ideal data, it seems this might be the only kind of data available on the topic, and the authors do acknowledge their weaknesses. References 1 Alvergne, A. and Lummaa, V. (2009) Does the contraceptive pill alter mate choice in humans? Trends Ecol. Evol. 25, 171–179 2 Sherman, B.M. and Korenman, S.G. (1975) Hormonal characteristics of the human menstrual cycle throughout reproductive life. J. Clin. Inv. 55, 699–706 3 Treloar, A.E. et al. (1967) Variation of the human menstrual cycle through reproductive life. Int. J. Fertil. 12, 77–126 4 Jung-Hoffmann, C. and Kuhl, H. (1987) Divergent effects of two low-dose oral contraceptives on sex hormone-binding globulin and free testosterone. Am. J. Obstet. Gynecol. 156, 199–203 5 Wiegratz, I. et al. (2003) Effect of four different oral contraceptives on various sex hormones and serum-binding globulins. Contraception 67, 25–32 6 Metcalf, M.G. and Mackenzie, J.A. (1980) Incidence of ovulation in young women. J. Biosoc. Sci. 12, 345–352 7 Katz, E. (1988) The luteinized unruptured follicle and other ovulatory dysfunctions. Fertil. Steril. 50, 839 8 Qublan, H. et al. (2006) Luteinized unruptured follicle syndrome: incidence and recurrence rate in infertile women with unexplained infertility undergoing intrauterine insemination. Hum. Reprod. 21, 2110–2113 9 Bateson, P. (1982) Preferences for cousins in Japanese quail. Nature 295, 236–237 (http://www.nature.com/nature/journal/v295/n5846/abs/ 295236a0.html) 10 Groothuis, T.G.G. and Carere, C. (2005) Avian personalities: characterization and epigenesis. Neurosci. Biobehav. Rev. 29, 137–150
0169-5347/$ – see front matter ß 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.tree.2010.06.004 Trends in Ecology and Evolution 25 (2010) 489–490
Letters Response
Invalid arguments against ABC: Reply to A.R. Templeton Katalin Csille´ry1, Michael G.B. Blum1, Oscar E. Gaggiotti2 and Olivier Franc¸ois1 1 Laboratoire Techniques de l’Inge´nierie Me´dicale et de la Complexite´, Centre National de la Recherche Scientifique UMR5525, Universite´ Joseph Fourier, 38706 La Tronche, France 2 Laboratoire d’Ecologie Alpine, Centre National de la Recherche Scientifique UMR5553, Universite´ Joseph Fourier, 38041 Grenoble, France
Templeton’s letter [1] contains a reformulation of his previous arguments against some of the works cited in our review [2–7], and refers to the core of our article only marginally. Templeton’s main objection to ABC is that it can produce posterior probabilities that are not ‘true’ Corresponding author: Csille´ry, K. ([email protected]).
490
probabilities [2–4]. The argument is as follows. Suppose that we want to test the hypothesis that some parameter q takes a given value q0 from a continuum, for example from the interval [0,1]. A model that assumes q = q0 must have a probability that is less than or equal to the probability of a more general model, e.g. one that assumes that q lies between 0 and 1. According to Templeton, a method that
Update contradicts the above statement violates the constraints of formal logic, and thus produces incorrect probabilities. Templeton uses the study of Fagundes et al. as an example for an incorrect analysis, where q represents the rate of interbreeding between modern and archaic human populations [5]. To re-evaluate Templeton’s argument in a simpler setting, let us consider a coin tossing experiment where q is the probability of observing a Head. Suppose that we want to test the null hypothesis (H0) that the coin is fair q = 0.5. Under the alternative hypothesis (H1), we assume that q can take any random values between 0 and 1. In a Bayesian framework, H0 and H1 represent non-overlapping events and our assumptions about the distribution of q are formulated conditionally on these separate events. Let us now calculate the posterior probabilities of the two hypotheses. We give equal prior weights to H0 and H1. The coin is flipped 20 times, and we observe 9 ‘heads’. A short computation shows that the posterior probability of H0 is 3.3637 times greater than the posterior probability of H1. The above exact calculation of probabilities highlights that Templeton’s criticism of ABC is, in fact, a criticism of the general rules of Bayesian inference. According to Templeton, H0 and H1 would be nested events. However, in a proper Bayesian framework, such as the one we used in the above coin tossing experiment, the two hypotheses represent non-nested events. Templeton’s letter also includes a ‘‘coherent correction’’ to ABC. He suggests that data should be simulated only under the general model to obtain the posterior distribution of the parameter. Then, he constructs a hypothesis test using the 95% credible interval for the parameter. In the coin tossing example, his suggestion amounts to testing if the 95% credible interval of q contains 0.5. This simple alternative to a Bayesian model choice was proposed earlier by Lindley [8]. An example of the application of Lindley’s method is given in Beaumont and Balding [9], who
Trends in Ecology and Evolution
Vol.25 No.9
developed a Bayesian algorithm to scan genomes for signatures of natural selection. More generally, Lindley’s method is often applied by statisticians to alleviate the computational burden of Markov chain Monte Carlo algorithms, even though it is not fully Bayesian. Nevertheless, the Bayes factor is often preferred in the literature [10]. In the context of ABC, Csille´ry et al. [7] suggested the use of methods based on posterior predictive distributions because Bayes factors are not properly defined when regression-based algorithms are used. One point where Csille´ry et al. [6] and Templeton could agree is that computing model complexity and evaluating alternative models still require further research. References 1 Templeton, A.R. (2010) Correcting approximate Bayesian computation. Trends Ecol. Evol. 25, 488–489 2 Templeton, A.R. (2009) Statistical hypothesis testing in intraspecific phylogeography: NCPA versus ABC. Mol. Ecol. 18, 319–331 3 Templeton, A.R. (2010) Coalescent-based, maximum likelihood inference in phylogeography. Mol. Ecol. 19, 431–435 4 Templeton, A.R. (2010) Coherent and incoherent inference in phylogeography and human evolution. Proc. Natl. Acad. Sci. U. S. A. 107, 6376–6381 5 Beaumont, M.A. et al. (2010) In defence of model-based inference in phylogeography. Mol. Ecol. 19, 436–446 6 Fagundes, N.J.R. et al. (2007) Statistical evaluation of alternative models of human evolution. Proc. Natl. Acad. Sci. U. S. A. 104, 17614–17619 7 Csille´ry, K. et al. (2010) Approximate Bayesian computation (ABC) in practice. Trends Ecol. Evol. 25, 410–418 8 Lindley, D.V. (1965) Introduction to Probability and Statistics from a Bayesian Viewpoint, Cambridge University Press 9 Beaumont, M.A. and Balding, D.J. (2004) Identifying adaptive genetic divergence among populations from genome scans. Mol. Ecol. 13, 969– 980 10 Kass, R.E. and Raftery, A.E. (1995) Bayes factors. J. Am. Stat. Assoc. 90, 773–795
0169-5347/$ – see front matter ß 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.tree.2010.06.011 Trends in Ecology and Evolution 25 (2010) 490–491
Letters Response
Response to Carere et al. Human mate preference: inconsistency between data and interpretations Alexandra Alvergne1,2 and Virpi Lummaa1 1 2
Department of Animal and Plant Sciences, University of Sheffield, Sheffield, S10 2TN, UK Department of Anthropology, University Collage London, London, WC1H 0BW, UK
We would first like to thank Carere et al. [1] for their interest and for providing us with an opportunity to discuss our paper [2], since further debate on this topic with scientists from different fields, such as behavioural physiology, will have a strong benefit for future research. Additionally, we assume their comments could be representative of a community generally sceptical about evolCorresponding author: Alvergne, A. ([email protected]).
utionary psychology, and it is therefore crucial to correct misleading points if we are to attract scientists from all fields to solve the question we raised. First, Carere et al.’s title ‘Human mate preference: inconsistency between data and interpretations’ is not correct. To date, there is no evidence against the hypothesis that hormonal contraceptives affect mate preferences in humans, and the fact that all ten previous studies point in the same direction deserves interest, given the 491