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Analyses of Developmental Rate Isomorphy in Ectotherms: Introducing the Dirichlet Regression.

Boukal DS, Ditrich T, Kutcherov D, Sroka P, Dudová P, Papáček M - PLoS ONE (2015)

Bottom Line: However, relative durations of successive ontogenetic stages often remain nearly constant across a substantial range of temperatures.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.

View Article: PubMed Central - PubMed

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.

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.

No MeSH data available.


Related in: MedlinePlus

Examples of results of Dirichlet regression for (a) Acilius and (b) Loxostege.Acilius: best fitting model (f+tF, grey solid line) compared to DRI (model const, black dashed lines); Loxostege: dataset with average clutch data, 21–27°C and different population origin (B = Buryatia, K = Krasnodar, H = Hebei), best fitting DRI model (f, black dashed lines) compared to model f+t (black solid lines). Box and whisker plots of raw data: horizontal line = median, box = first to third quartiles, line = data within 1.5 times the interquartile range; dots = outliers. Non-feeding stages labelled with asterisk.
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pone.0129341.g002: Examples of results of Dirichlet regression for (a) Acilius and (b) Loxostege.Acilius: best fitting model (f+tF, grey solid line) compared to DRI (model const, black dashed lines); Loxostege: dataset with average clutch data, 21–27°C and different population origin (B = Buryatia, K = Krasnodar, H = Hebei), best fitting DRI model (f, black dashed lines) compared to model f+t (black solid lines). Box and whisker plots of raw data: horizontal line = median, box = first to third quartiles, line = data within 1.5 times the interquartile range; dots = outliers. Non-feeding stages labelled with asterisk.

Mentions: Inclusion of an additional factor, sometimes in interaction with temperature, led to a significantly improved model in all remaining species and datasets: sex in Cloeon and Acilius (although the differences between male and female Acilius were minor), photoperiod in Amara, Gastrophysa and Leptinotarsa, and geographic origin in Loxostege (Fig 2 and Tables 1 and 2). Other model variants involving the factor and temperature usually provided a similarly good fit of the data (bold values in Tables 1 and 2) and their predictions were similar to the best-fitting model (details not shown).


Analyses of Developmental Rate Isomorphy in Ectotherms: Introducing the Dirichlet Regression.

Boukal DS, Ditrich T, Kutcherov D, Sroka P, Dudová P, Papáček M - PLoS ONE (2015)

Examples of results of Dirichlet regression for (a) Acilius and (b) Loxostege.Acilius: best fitting model (f+tF, grey solid line) compared to DRI (model const, black dashed lines); Loxostege: dataset with average clutch data, 21–27°C and different population origin (B = Buryatia, K = Krasnodar, H = Hebei), best fitting DRI model (f, black dashed lines) compared to model f+t (black solid lines). Box and whisker plots of raw data: horizontal line = median, box = first to third quartiles, line = data within 1.5 times the interquartile range; dots = outliers. Non-feeding stages labelled with asterisk.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4482627&req=5

pone.0129341.g002: Examples of results of Dirichlet regression for (a) Acilius and (b) Loxostege.Acilius: best fitting model (f+tF, grey solid line) compared to DRI (model const, black dashed lines); Loxostege: dataset with average clutch data, 21–27°C and different population origin (B = Buryatia, K = Krasnodar, H = Hebei), best fitting DRI model (f, black dashed lines) compared to model f+t (black solid lines). Box and whisker plots of raw data: horizontal line = median, box = first to third quartiles, line = data within 1.5 times the interquartile range; dots = outliers. Non-feeding stages labelled with asterisk.
Mentions: Inclusion of an additional factor, sometimes in interaction with temperature, led to a significantly improved model in all remaining species and datasets: sex in Cloeon and Acilius (although the differences between male and female Acilius were minor), photoperiod in Amara, Gastrophysa and Leptinotarsa, and geographic origin in Loxostege (Fig 2 and Tables 1 and 2). Other model variants involving the factor and temperature usually provided a similarly good fit of the data (bold values in Tables 1 and 2) and their predictions were similar to the best-fitting model (details not shown).

Bottom Line: However, relative durations of successive ontogenetic stages often remain nearly constant across a substantial range of temperatures.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.

View Article: PubMed Central - PubMed

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.

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.

No MeSH data available.


Related in: MedlinePlus