How to walk on statistical mandalas as a population ecologist

Popul Ecol (2016) 58:3–8 DOI 10.1007/s10144-015-0532-z SPECIAL FEATURE: PREFACE Bayesian, Fisherian, error, and evidential statistical approaches for population ecology How to walk on statistical mandalas as a population ecologist Yukihiko Toquenaga1 Received: 8 September 2015 / Accepted: 30 November 2015 / Published online: 21 December 2015 Ó The Society of Population Ecology and Springer Japan 2015 Abstract We population ecologists who are believed to be good at dealing with statistics often get confused about what kinds of statistical methods we should apply to our nuisance data. There are a couple of conflicting paradigms and many associated methods in statistics. Classical frequentists’ approaches that have dominated in science have been severely criticized by the newcomers: Bayesian and evidential statistics. But, both newcomers also have weak points. Researchers devoted to different statistical approaches are seeking soft landing places where they can compromise each other. Key aspects of statistical inference are discriminating model selection and parameter estimation. Likelihood and Fisher information play important roles in both processes. As an overview of the compromise processes, here I will introduce three contributing papers by M. L. Taper, J. M. Ponciano, R. M. Dorazio, and K. Yamamura for the special feature entitled ‘‘Bayesian, Fisherian, error, and evidential statistical approaches for population ecology.’’ This special feature is based on a symposium held in Tsukuba, Japan, on 11 October 2014 This manuscript was submitted for the special feature based on a symposium in Tsukuba, Japan, held on 11 October 2014. & Yukihiko Toquenaga 1 Faculty of Life and Environmental Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8572, Japan Keywords Bayesian
Evidential
Fisherian
Frequentist
Model selection
Parameter estimation Introduction When a non-native-English-speaking scientist submits his/ her manuscript to an international ecological journal, he/ she often asks English proofreading of a professional or of his/her native-English-speaking colleague. However, interestingly, there are few authorized systems to encourage proofreading of statistical methods. One reason for this trend might be that statistical methods have no authorized standards as does scientific English. Statistical practices, and in some cases paradigms, are quite different among scientific fields. Population ecologists, who are believed to be relatively better at statistics than ecologists specializing in other fields, also have to consider which statistical methods and paradigms they should apply to their own researches. Are we population ecologists actually good at statistics? I would say no. Most of us only specialize in specific statistical methods and paradigms. That would be why Dr. Takashi Saitoh who was the president of the Society of Population Ecology asked Dr. Kohji Yamamura and myself to organize a special feature on statistics of population ecology from a broad perspective. In this introductory review, I briefly list questions and concerns about statistics that I have felt during my career as a population ecologist. I first discuss the dominance of classical frequentist approaches in chronological order for which they appeared for me personally, then I briefly discuss the two newcomers, Bayesian and evidential statistics, and finally, I introduce the three contributing articles for this special feature. This special feature is based on a symposium held in Tsukuba, Japan, on 11 October 2014. 123 4 Dominance of classical frequentist approaches The vast majority of textbooks on statistics in the library of my university in the middle of the 1980s were, and might still be, classified as classical frequentist statistics. Here ‘‘classical frequentist’’ refers to non-Bayesian or non-evidential, and mainly consists of null-hypothesis testing and P value worship approaches that assume normal distributions of original or transformed target variables. As other students of population ecology, I had to start learning classical statistics when I was a graduate student. I have always wondered why regressions and ANOVA-type methods have two steps: significance tests of explanatory variables for the data variation as a whole followed by significance tests for parameters or means of sub-units. Even for a simple one-way ANOVA test for three categories, once we detect a significant difference among the three categories, we cannot simply claim that the largest mean value for a category is larger than those of the other two categories. I was taught that we had to perform appropriate post hoc tests even when the plot of mean values clearly showed the difference. The former step is model fitting, and the latter one is parameter estimation. These two steps sometimes invoke different statistical methods, e.g., model fitting with information criteria, such AIC or BIC, and parameter estimation with Bayesian methods. The former requires post hoc tests to compare parameters of the best models, but the latter can spontaneously compare multiple parameters after obtaining their posterior probabilities by checking the overlap of their posterior distributions. post hoc tests are a variant of multiple comparison (Hsu 1998). Multiple comparison per se does not inherently mean post hoc tests, and there are relevant a priori tests of multiple comparison. The difference between post hoc and a priori comparison is the epistemological attitude towards data collection by researchers. If one designed the comparison before his/her data collection, the test is a priori but it should be treated as post hoc if one did the comparison after his/her data collection. This epistemological difference would affect the complicatedness of calculating appropriate variances in the comparison. Much simpler methods of post hoc comparison, for example the Bonferroni test or its variants (Holm 1979; Moran 2003), often require some kind of programming skills, so one would preferably be able to claim, ‘‘I did design the comparison beforehand!’’ My supervisor, Dr. Koichi Fujii, mastered statistics under Dr. Robert R. Sokal who is the author of the famous textbook, Biometry (Sokal and Rohlf 1981), which has a good flavor of classical statistics. My friends believed that I would become an obedient successor of this ‘‘normal distribution empire.’’ Then Dr. Nobuhiro Minaka who taught 123 Popul Ecol (2016) 58:3–8 statistics at various institutes and universities at that time, secretly sent me his image of a statistical mandala at the end of the 1980s (Fig. 1). I was very excited about this mandala because with it I learned that there were options other than the ‘‘normal distribution empire.’’ Moreover, those other options were extremely attractive. After that, Dr. Mark L. Taper visited my laboratory as a post-doctoral fellow of the National Science Foundation, USA, and introduced me to the bossa nova (...truncated)