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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: We show that these conclusions may be due to the caveats hidden in the statistical methods currently used to study DRI.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.

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Related in: MedlinePlus

Possible mechanisms leading to DRI violation.Left column shows development rates of three hypothetical life stages, early (blue dotted line), intermediate (orange dashed line) and late (green line), and the overall rate of development (thick grey); grey rectangles highlight the thermal range (T1, T2) in which the overall rate of development increases almost linearly with temperature; time units are omitted. Right column shows the corresponding relative duration of each stage in the (T1, T2) range. (a) DRI; (b) violation of DRI due to shifted, stage-dependent temperature optima; (c) violation of DRI due to progressively limiting, temperature-dependent metabolic scope for growth in individual stages; (d) violation of DRI due to limiting metabolic scope for growth in the intermediate stage. Even more severe DRI violation outside the (T1, T2) range in panels (b)–(d) is omitted for clarity. See text for further details.
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pone.0129341.g001: Possible mechanisms leading to DRI violation.Left column shows development rates of three hypothetical life stages, early (blue dotted line), intermediate (orange dashed line) and late (green line), and the overall rate of development (thick grey); grey rectangles highlight the thermal range (T1, T2) in which the overall rate of development increases almost linearly with temperature; time units are omitted. Right column shows the corresponding relative duration of each stage in the (T1, T2) range. (a) DRI; (b) violation of DRI due to shifted, stage-dependent temperature optima; (c) violation of DRI due to progressively limiting, temperature-dependent metabolic scope for growth in individual stages; (d) violation of DRI due to limiting metabolic scope for growth in the intermediate stage. Even more severe DRI violation outside the (T1, T2) range in panels (b)–(d) is omitted for clarity. See text for further details.

Mentions: Temperature drives development of ectotherms. Within an ecologically relevant thermal range, the entire development from egg to adult is faster at higher temperatures because they enhance the development rate through increased metabolic rate [1]. Moreover, previous studies found that temperature does not affect the proportion of time spent in any given non-diapausing developmental stage, at least within the thermal range for which the rate of development increases linearly with temperature (Fig 1a). This concept is called ‘equiproportional development’ (EPD) in the copepod literature, where it was first described by Corket and McLaren [2] and formalized by Corket [3], and ‘developmental rate isomorphy’ (DRI) in the insect literature, where it was first proposed by van Rijn et al. [4] and formalized by Jarošík et al. [5]. Although EPD has a longer history, considers a wider thermal range beyond the near linear part of the response in development rate and has been extended to situations when food is limiting [6–8], we primarily use the term DRI as our focus in this paper is on temperature-dependent development in insects under conditions of food satiation.


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)

Possible mechanisms leading to DRI violation.Left column shows development rates of three hypothetical life stages, early (blue dotted line), intermediate (orange dashed line) and late (green line), and the overall rate of development (thick grey); grey rectangles highlight the thermal range (T1, T2) in which the overall rate of development increases almost linearly with temperature; time units are omitted. Right column shows the corresponding relative duration of each stage in the (T1, T2) range. (a) DRI; (b) violation of DRI due to shifted, stage-dependent temperature optima; (c) violation of DRI due to progressively limiting, temperature-dependent metabolic scope for growth in individual stages; (d) violation of DRI due to limiting metabolic scope for growth in the intermediate stage. Even more severe DRI violation outside the (T1, T2) range in panels (b)–(d) is omitted for clarity. See text for further details.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0129341.g001: Possible mechanisms leading to DRI violation.Left column shows development rates of three hypothetical life stages, early (blue dotted line), intermediate (orange dashed line) and late (green line), and the overall rate of development (thick grey); grey rectangles highlight the thermal range (T1, T2) in which the overall rate of development increases almost linearly with temperature; time units are omitted. Right column shows the corresponding relative duration of each stage in the (T1, T2) range. (a) DRI; (b) violation of DRI due to shifted, stage-dependent temperature optima; (c) violation of DRI due to progressively limiting, temperature-dependent metabolic scope for growth in individual stages; (d) violation of DRI due to limiting metabolic scope for growth in the intermediate stage. Even more severe DRI violation outside the (T1, T2) range in panels (b)–(d) is omitted for clarity. See text for further details.
Mentions: Temperature drives development of ectotherms. Within an ecologically relevant thermal range, the entire development from egg to adult is faster at higher temperatures because they enhance the development rate through increased metabolic rate [1]. Moreover, previous studies found that temperature does not affect the proportion of time spent in any given non-diapausing developmental stage, at least within the thermal range for which the rate of development increases linearly with temperature (Fig 1a). This concept is called ‘equiproportional development’ (EPD) in the copepod literature, where it was first described by Corket and McLaren [2] and formalized by Corket [3], and ‘developmental rate isomorphy’ (DRI) in the insect literature, where it was first proposed by van Rijn et al. [4] and formalized by Jarošík et al. [5]. Although EPD has a longer history, considers a wider thermal range beyond the near linear part of the response in development rate and has been extended to situations when food is limiting [6–8], we primarily use the term DRI as our focus in this paper is on temperature-dependent development in insects under conditions of food satiation.

Bottom Line: We show that these conclusions may be due to the caveats hidden in the statistical methods currently used to study DRI.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