title: Analyses of Developmental Rate Isomorphy in Ectotherms: Introducing the Dirichlet Regression.
abstract: Temperature drives development in insects and other ectotherms because their metabolic rate and growth depends directly on thermal conditions. However, relative durations of successive ontogenetic stages often remain nearly constant across a substantial range of temperatures. This pattern, termed 'developmental rate isomorphy' (DRI) in insects, appears to be widespread and reported departures from DRI are generally very small. We show that these conclusions may be due to the caveats hidden in the statistical methods currently used to study DRI. Because the DRI concept is inherently based on proportional data, we propose that Dirichlet regression applied to individual-level data is an appropriate statistical method to critically assess DRI. As a case study we analyze data on five aquatic and four terrestrial insect species. We find that results obtained by Dirichlet regression are consistent with DRI violation in at least eight of the studied species, although standard analysis detects significant departure from DRI in only four of them. Moreover, the departures from DRI detected by Dirichlet regression are consistently much larger than previously reported. The proposed framework can also be used to infer whether observed departures from DRI reflect life history adaptations to size- or stage-dependent effects of varying temperature. Our results indicate that the concept of DRI in insects and other ectotherms should be critically re-evaluated and put in a wider context, including the concept of 'equiproportional development' developed for copepods.
authors.affiliation: Department of Ecosystem Biology, Faculty of Science, University of South Bohemia, České Budějovice, Czech Republic; Department of Ecology and Biosystematics, Institute of Entomology, Biology Centre of the Czech Academy of Sciences, vvi, České Budějovice, Czech Republic.
authors.forename: David S
authors.initials: DS
authors.lastname: Boukal
authors.affiliation: Department of Biology, Faculty of Education, University of South Bohemia, České Budějovice, Czech Republic; Department of Ecology and Biosystematics, Institute of Entomology, Biology Centre of the Czech Academy of Sciences, vvi, České Budějovice, Czech Republic.
authors.forename: Tomáš
authors.initials: T
authors.lastname: Ditrich
authors.affiliation: Department of Entomology, Faculty of Biology, St. Petersburg State University, St. Petersburg, Russia.
authors.forename: Dmitry
authors.initials: D
authors.lastname: Kutcherov
authors.affiliation: Department of Ecology and Biosystematics, Institute of Entomology, Biology Centre of the Czech Academy of Sciences, vvi, České Budějovice, Czech Republic.
authors.forename: Pavel
authors.initials: P
authors.lastname: Sroka
authors.affiliation: Department of Ecology and Biosystematics, Institute of Entomology, Biology Centre of the Czech Academy of Sciences, vvi, České Budějovice, Czech Republic; Department of Zoology, Faculty of Science, University of South Bohemia, České Budějovice, Czech Republic.
authors.forename: Pavla
authors.initials: P
authors.lastname: Dudová
authors.affiliation: Department of Biology, Faculty of Education, University of South Bohemia, České Budějovice, Czech Republic.
authors.forename: Miroslav
authors.initials: M
authors.lastname: Papáček
mesh_terms: D000818:Animals; D007313:Insecta / Q000254:growth & development*; D008018:Life Cycle Stages; D008954:Models, Biological; D015233:Models, Statistical; D013696:Temperature