Using A Priori Contrasts for Multivariate Repeated-Measures ANOVA to Analyze Thermoregulatory Responses of the (Parantechinus apicalis; Marsupialia, ) Author(s): Philip C. Withers and Christine E. Cooper Reviewed work(s): Source: Physiological and Biochemical Zoology, Vol. 84, No. 5 (September/October 2011), pp. 514-521 Published by: The University of Chicago Press Stable URL: http://www.jstor.org/stable/10.1086/661637 . Accessed: 22/11/2011 19:59

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TECHNICAL COMMENT

Using A Priori Contrasts for Multivariate Repeated-Measures ANOVA to Analyze Thermoregulatory Responses of the Dibbler (Parantechinus apicalis; Marsupialia, Dasyuridae)

Philip C. Withers* physiological variables to a categorical factor and are especially Christine E. Cooper useful for repeated-measures ANOVA designs common to many Biology M092, University of Western , physiological studies. Stirling Highway, Crawley, 6009, Australia; and Department of Environment and Agriculture, Curtin University, P.O. Box U1987 , Western Australia 6845, Australia Introduction Accepted 5/16/2011; Electronically Published 8/24/2011 A priori contrasts provide a powerful tool to evaluate expected patterns with a categorical factor for ANOVA (Cohen 2008), Online enhancement: Excel file. univariate repeated-measures ANOVA (Potvin et al. 1990; Park et al. 2009), and multivariate repeated-measures ANOVA (Rencher 2002), because they examine specific hypotheses using an appropriate contrast matrix (e.g., Bock 1975; Hand and ABSTRACT Taylor 1987). For example, a simple contrast tests whether a Physiological studies often involve the repeated measurement control category is different from each other category. For or- of individuals over a range of ordered categorical conditions, dered categorical data, a Helmert contrast tests whether a - for example, varying ambient temperature. We illustrate here egory is different from all subsequent categories pooled to- the use of a priori contrasts for multivariate repeated-measures gether; a reverse-Helmert contrast tests whether a category is ANOVA by analyzing the thermal responses of various physi- different from all previous categories pooled. For ordered nu- Њ ological variables for a small , the dibbler (Parantech- meric categories (e.g., ambient temperature Ta measured in C), inus apicalis). Our analyses showed that conform closely a polynomial contrast examines whether there is a linear, qua- to the Scholander-Irving model of endothermy. Body tempera- dratic, or other polynomial relationship. A priori contrasts can 0.24ЊCat be more powerful than the overall ANOVA hypothesis (that all ע ture was constant at low air temperatures, was 36.3 thermoneutrality (30ЊC), and increased at 35ЊC. Metabolic rate means are equal) because they address more specific hypotheses decreased with increasing ambient temperature to a basal rate of than general post hoc tests and because they address fewer Ϫ1 Ϫ1 Њ ע 0.619 0.036 mL O2 g h at 30 C; it extrapolated closely to specific uncorrelated hypotheses (e.g., experimental groups dif- thermoneutral body temperature. Increased oxygen demand at fer from a control group, or there is a linear relationship for lower ambient temperature was met by increased respiratory ordered categories). However, contrast tests have not been minute volume, achieved by increased respiratory frequency and widely embraced by comparative physiologists despite their use- tidal volume; oxygen extraction was constant at about 19%. Evap- fulness for examining specific patterns in physiological data sets orative water loss and wet and dry thermal conductance increased and especially their particular value in overcoming the issue of markedly at high ambient temperatures but not sufficiently to an absence of post hoc tests for repeated-measures ANOVA. maintain constant body temperature. Relative water economy Many physiological studies involve the repeated measure- was similar to that of other small , increasing linearly ment of individuals subjected to different categorical treatments at lower air temperatures with a point of relative water economy on an ordered scale, for example, measurement of a physio- of 20.3ЊC. We conclude that a priori contrasts provide a statis- logical variable at different ambient temperatures. Multivariate tically appropriate and powerful analysis that can be used rou- repeated-measures analysis of variance (MANOVAR) is an ap- tinely to statistically describe the pattern of response of propriate statistical analysis for such data, with the repeated

measure (e.g., Ta) being the multivariate factor (Potvin et al. 1990; Rencher 2002; Park et al. 2009). However, a major lim- * Corresponding author; e-mail: [email protected]. itation of MANOVAR is that it does not have formal compar-

Physiological and Biochemical Zoology 84(5):514–521. 2011. ᭧ 2011 by The ison tests equivalent to ANOVA post hoc tests (e.g. Tukey, University of Chicago. All rights reserved. 1522-2152/2011/8405-1014$15.00. Dunnett, Student-Newman-Keuls, etc). Consequently, it is dif- DOI: 10.1086/661637 ficult to statistically discern the pattern of the effect of a sig- Technical Comment 515

nificant repeated factor (e.g., the pattern of a Ta effect for a Respirometry physiological variable) within the MANOVAR model. The re- cent physiological literature includes various approaches to this Metabolic rate (oxygen consumption, Vo2; carbon dioxide pro- problem. Some repeated-measures studies simply do not eval- duction, Vco2) and EWL were measured by flow-through res- uate the pattern of the repeated measure (e.g., Beaupre and pirometry for individuals that had been fasted for 20 h before Zaidan 2001; Gomez et al. 2006), and some use a Bonferroni- the commencement of experiments. Dibblers were measured type adjustment for multiple comparison tests (e.g., Rezende for 5–9 h at each Ta during their inactive phase (day) until et al. 2004; Berg and Biewener 2008; Park et al. 2009; Wu et Vo2,Vco2, and EWL were stable and minimal; individuals were al. 2009; Dunlap et al. 2010) or post hoc ANOVA tests that do measured at only one Ta per day and not more frequently than not account for repeated measurements (e.g., McLean and every 3 days. Observations of dibblers in the metabolic chamber Speakman 2000; Gilmour et al. 2001; Zerm et al. 2004; Zhao by video indicated when dibblers were resting and asleep; these and Cao 2009; Dupont-Prinet et al. 2010). periods were easily identified in the continuous traces of phys- We illustrate here the use of a priori contrasts, by examining iological data and used for analysis, so we are confident that the thermoregulatory responses of the dibbler (Parantechinus our values are for resting, inactive dibblers. Tb was measured apicalis), a 40–100-g endangered dasyurid marsupial charac- when dibblers were removed from the chamber at the end of terized by a white eye ring and freckled fur (Woolley 2008). the experiment, using a plastic-tipped thermocouple (con- The dibbler’s current distribution is restricted to three small nected to a Radio Spares 611–234 thermocouple meter) in- islands near Jurien, Western Australia, and a few scattered serted ∼1.5 cm into the cloaca. mainland sites on the south coast of Western Australia, where Mass flow controllers (Aalborg GFC17 and Cole-Palmer it inhabits dense heath on sandy soils (Menkhorst and Knight 32708-26) regulated the flow of ambient air at a constant rate 2004; Cronin 2008; Woolley 2008). We characterize body tem- of 500–700 mL minϪ1 through cylindrical glass chambers (500 perature, metabolic rate, thermal conductance, respiratory ven- mL), located in a temperature-controlled cabinet. Individuals Њ Њ tilation, evaporative water loss, and relative water economy over were measured at each ambient temperature (Ta:9.4,15.3, a range of ambient temperatures and then examine the various 19.9Њ, 25.3Њ, 30.8Њ, and 35.3ЊC) in random for indepen- patterns of Ta effects below and above thermoneutrality using dence of data from the order of measurement. Excurrent air a priori contrasts and MANOVAR (Rencher 2002), based on passed over a thin-film-capacitance relative humidity (RH) and the typical responses of (e.g., McNab 1980; Withers Ta probe (Vaisala HMP45A), with a subsample passing through 1992) and more specifically of other dasyurid marsupials (e.g., a column of Drierite (W. A. Hammond Drierite) and then an Dawson and Wolfers 1978; Morton and Lee 1978; Geiser 1986; oxygen analyzer (Sable Systems FoxBox or Servomex 574) and Geiser and Baudinette 1988; Hallam and Dawson 1993; Lar- a carbon dioxide analyzer (Sable Systems FoxBox or CA-2A). combe 2002; Schmidt et al. 2009; Cooper and Withers 2010; The data were recorded by a PC every 20 s throughout the Warnecke et al. 2010). We use polynomial contrasts to examine experimental period using custom-written Visual Basic (v6) linear changes with Ta, as might be expected for metabolic rate software, via the serial port of the Sable Systems FoxBox or a

(MR), ventilatory variables including respiratory rate (fR), tidal Pico Technology ADC11 A/D converter. A custom-written Vi- volume (VT) and minute volume (VI), and possibly evaporative sual Basic program was used for metabolic and hygric calcu- water loss (EWL). We use simple contrasts to compare ther- lations (after Withers 2001). moneutrality with the other Ta treatments and Helmert and Ventilatory data were measured by whole-body plethys- reverse-Helmert contrasts to identify a pattern of relative con- mography (Malan 1973; Withers 1977; Szewczak and Powell stancy but an increase at low or high Ta, as might be expected 2003), whereby pressure changes in the metabolic chamber due for body temperature (Tb), wet (Cwet) and dry (Cdry) thermal to respiration were detected with a custom-made pressure conductance, and possibly EWL. transducer (Motorola MPX2010 sensor). The voltage output from the pressure transducer was monitored using a Pico Tech- nology ADC11 A/D converter and was recorded on a PC every Material and Methods 15 ms for approximately 30 s using PicoScope. Between two and six sets of ventilatory data were obtained for an individual dibbler at each Ta, and a single mean was calculated for each

Eight dibblers (four male, four female) were studied at Perth ventilatory variable for each individual at each Ta. Ventilatory Zoo, Western Australia (31Њ58S, 115Њ51E), during August/Sep- measurements were made toward the end of each experiment, tember 2009. One individual was wild caught at Fitzgerald River when a low stable metabolic rate and video observation con- National Park (34Њ4S, 119Њ25E), and the others were captive- firmed that the dibbler was quiet and resting. A custom-written born descendants of other individuals from this location. Dib- Visual Basic program was used for ventilatory calculations (after blers were housed indoors in individual cages with a natural Malan 1973; Szewczak and Powell 2003). Ventilatory variables photoperiod and were fed a diet of minced meat, ground cat are presented at body temperature and pressure saturated biscuits, boiled eggs, and Wombaroo small- food, (btps) conditions. Oxygen extraction (Eo2) was calculated us- along with baby rats, crickets, and mealworms, with water ad ing the standard temperature and pressure dry (stpd) values lib. for Vo2 and VI at the time of ventilatory measurements, using 516 P. C. Withers and C. E. Cooper a fractional inspired oxygen content calculated as the mean of macro, based on Rencher (2002); this spreadsheet is available 0.2095 and the measured fractional excurrent oxygen at the in an Excel file in the online edition of Physiological and Bio- time of ventilatory measurements. chemical Zoology. Simple, Helmert and reverse-Helmert con- The FoxBox oxygen analyzer was two-point calibrated by its trast matrices were calculated after Bock (1975) and Hand and electronic zero function and dry ambient air (20.95%) and the Taylor (1987). Polynomial contrast matrices were calculated for

Servomex with compressed N2 and dry ambient air. Carbon unequally spaced repeated measures (Robson 1959). The con- p Њ Њ Њ Њ dioxide analyzers were calibrated with compressed N2 and a trast matrices for our data set withTa 9.4 , 15.3 , 19.9 , 25.3 , Њ Њ certified gas mix (0.53% CO2). The calibration of the relative 30.8 , and 35.3 C are shown in Table 1. humidity probes was confirmed using 1% RH air (dried with Drierite) and 100% RH air (saturated; by breathing on the RH Results probe). Flowmeters were calibrated using a bubble flowmeter .( g (N p 8 5.1 ע Bubble-O-Meter). The plethysmography system was calibrated Mean body mass of the dibblers was78.3) by injecting known air volumes (0.3–0.5 mL) into the chamber There were mass differences between individuals (range 63.5– p ! and then accounting for the pressure decay characteristics (i.e., 99.3 g;F7, 40 204 ,P 0.001 ), but there was no change in mass p p mathematically converting the open-system measurement to a of individuals over the five measurements (F5, 3 6.25 , P closed system; see Szewczak and Powell 2003). 0.081). Respiratory exchange ratio (RER) was calculated as Observations of dibblers in the metabolic chamber indicated Ϫ1 Ϫ1 Њ Ϫ1 VCO22/VO , and Cwet (J g h C ) was calculated from met- that they rested and appeared to be asleep for most of the time, abolic heat production (MHP; converted from MR using the except for occasional short periods of activity (e.g., grooming) measured RER, by interpolation from Table 4.2 in Withers that corresponded to increased Vo2,Vco2 and EWL. The dib- Ϫ Ϫ1 Ϫ1 Њ Ϫ1 1992) asMHP/(TbaT ) . Cdry (J g h C ) was calculated blers were curled up with erect fur at low Ta, and their fur was Ϫ Ϫ as(MHP EHL)/(TbaT ) , where evaporative heat loss (EHL) more depressed and posture more stretched out as Ta increased. Ϫ1 ! waw converted from EWL assuming 2.4 J mg H2O (McNab None of the dibblers entered torpor, defined asVO2 75% of Ϫ1 Ϫ1 2002). Metabolic water production (MWP; mg g h )was basal metabolic rate (BMR) at any Ta (Geiser and Baudinette also calculated from MR using the measured RER after Withers 1988). Њ p Њ עЊ (1992). Relative water economy (RWE) was calculated as MWP/ Dibblers’ Tb ranged from36.3 0.2 C atTa 9 C to Њ p Њ עЊ EWL and the point of relative water economy (PRWE) as the 37.7 0.2 C atTa 35 C (Fig. 1). Individuals did not differ p p Ta at which RWE interpolated to 1. with respect to Tb (F7, 40 0.84 ,P 0.558 ), but there was a p p significant effect of Ta (F5, 3 13.1 ,P 0.030 ). Excluding the p Њ p p Ta4,435 C data removed the Ta effect (F 0.316 , P p Њ Statistics 0.855), suggesting a pattern of higher Tb atTa 35 C com- pared with all other T ’s. A priori contrasts supported this standard error, with N p 8 a ע Values are presented as mean pattern. Linear (P p 0.002 ), quadratic (P p 0.046 ), and cubic individuals. Basic statistical analyses were conducted with contrasts (P p 0.015 ) were significant whenT p 35Њ C data statistiXL (v1.8). Effects of T on physiological variables were a a were included, but not whenT p 35Њ C data were excluded examined using MANOVAR, with the eight dibblers as repli- a (P ≥ 0.379 ), indicating that theT p 35Њ C data differed from cates and T as the repeated measure (Rencher 2002). We ex- a a T at the other T ’s. Similarly, Helmert contrasts were significant amined various a priori contrasts, depending on the expected b a only for comparison ofT p 31Њ C withT p 35Њ C (P p T pattern, including linear, quadratic, and cubic polynomial aa a 0.004), and the only significant reverse Helmert contrast was contrasts, simple contrasts for comparing a specified group with p Њ ! for comparison ofTa 35 C with all of the lower Ta’s (P each other group, and Helmert and reverse-Helmert contrasts Ϫ Њ 0.001). The thermolability of Tb (DTb/DTa) was 0.00042 C for sequential comparisons of categories with all previous or Њ Ϫ1 p Њ Њ C fromTa 9 to 31 C (MANOVAR linear contrast); it was Њ Њ Ϫ1 p Њ Њ עsubsequent Ta categories. ϩ Њ 0.283 0.067 C C from Ta 31 to 35 C. Ϫ1 ע The t statistic for an a priori contrast was calculated for each The Vo2 of dibblers decreased from2.65 0.12 mL O2 g Ϫ1 ע row of the contrast matrix (C) as Ϫ1 p Њ h at Ta 9C to a minimum of 0.619 0.036 mL O2 g Ϫ1 0.5 T p p Њ n cy¯ h ()atn 8 Ta 31 C (Fig. 1); we consider this minimal t p i , Њ i (cScT0.5) value at 31 C to be BMR. There were no differences in Vo2 ii p p between individuals (F7, 40 0.131 ,P 0.995 ), but there was T p p where n is the number of subjects,ccii is a row and is the a significant effect of Ta (F5, 3 58.2 ,P 0.004 ). The pattern transpose of a row of the contrast matrix,y¯ is a vector consisting of Vo2 with Ta (Fig. 1) suggests that Vo2 decreased linearly with p Њ of the means for each repeated category, and S is the covariance increasing Ta but increased atTa 35 C. Polynomial a priori matrix (which can be obtained from various statistical proce- contrasts confirmed this pattern. Linear (P ! 0.001 ), quadratic dures in many statistics packages, e.g., from principal com- (P p 0.001 ), and cubic (P p 0.029 ) polynomials were signifi- Ϫ p Њ ponent analysis in statistiXL); the test statistic hasn 1 degrees cant whenTa 35 C data were included, but there was only ! p Њ of freedom (Rencher 2002). Contrast tests were accomplished a significant linear pattern (P 0.001 ) whenTa 35 C data in an Excel spreadsheet using a custom-written a priori contrast were omitted (P ≥ 0.475 for quadratic and cubic contrasts), Technical Comment 517

Table 1: Contrast matrices used for a priori comparison tests of dibbler Њ Њ Њ physiological variables at ambient temperatures (Ta’s) of 9.4 , 15.3 , 19.9 , 25.3Њ, 30.8Њ, and 35.3ЊC Њ Ta ( C) Contrast 9.4 15.3 19.9 25.3 30.8 35.3 Simple 1 0 0 0 Ϫ10 010 0Ϫ10 001 0Ϫ10 000 1Ϫ10 000 0Ϫ11 Helmert 1 Ϫ1/5 Ϫ1/5 Ϫ1/5 Ϫ1/5 Ϫ1/5 01Ϫ1/4 Ϫ1/4 Ϫ1/4 Ϫ1/4 001Ϫ1/3 Ϫ1/3 Ϫ1/3 000 1Ϫ1/2 Ϫ1/2 000 0 1Ϫ1 Reverse Helmert Ϫ110 0 00 Ϫ1/2 Ϫ1/2 1 0 0 0 Ϫ1/3 Ϫ1/3 Ϫ1/3 1 0 0 Ϫ1/4 Ϫ1/4 Ϫ1/4 Ϫ1/4 1 0 Ϫ1/5 Ϫ1/5 Ϫ1/5 Ϫ1/5 Ϫ1/5 1 Polynomial: Linear Ϫ13.3 Ϫ7.4 Ϫ2.8 2.6 8.1 12.6 Quadratic 92.4 Ϫ27.0 Ϫ71.9 Ϫ70.5 Ϫ9.1 86.1 Cubic Ϫ379.9 594.5 288.6 Ϫ403.0 Ϫ547.6 447.4 Note. Contrasts: simple compares a specified category with all other categories (specified group is 30.8ЊC), Helmert tests whether a category is different from all subsequent categories pooled together, reverse Helmert tests whether a category is different from all previous categories pooled, and polynomial test is for an ordered pattern such as a linear or quadratic relationship for a variable with categories on a numeric scale.

Њ p indicating that Vo2 decreased linearly with Ta to 31 C; it did 0.993), but there was a significant effect of Ta (,F5, 3 154 p Њ p ! not increase significantly atTa 35 C (simple contrast P P 0.001). As for Cwet, there were highly significant linear, qua- p Њ ! 0.128). The linear relationship (excluding Ta 35 C) was dratic, and cubic effects (P 0.003 ) for all Ta’s but no linear, p Ϫ 1 ≤ Њ VO2a3.44 0.095T , which extrapolates to a predicted Tb of quadratic, or cubic effects (P 0.186 ) for Ta 31 C. This pat- Њ 36.2 C. The pattern in Vco2 was similar to that of Vo2 and is tern was supported by the reverse Helmert contrast being sig- Њ p therefore not analyzed or presented separately. The RER was nificant only for Cdry at 35 C compared to lower Ta (P p p independent of individual (F7, 40 1.34 ,P 0.258 ) and Ta 0.002) and significance for all Helmert contrasts of Cdry for all ! Њ ! ע p p (F5, 3 5.88 ,P 0.088 ), at 0.72 0.015 (mean for all 6 Ta’s). Ta’s (P 0.003 ) at 35 C compared to lower Ta’s (P 0.003 ). Ϫ1 ע p Њ Dibblers’ Cwet varied little from Ta 9C( 1.93 0.083 Jg Individual dibblers did not differ with respect to EWL Ϫ1 Ϫ1 Њ Ϫ1 p p ע Ϫ1 Њ Ϫ1 Њ h C )to25C(1.77 0.085 Jg h C ), then increased (F7, 40 1.63 ,P 0.155 ) and there was no overall Ta effect by Ϫ1 Ϫ1 Њ Ϫ1 p p ע Њ slightly at 31 C(2.27 0.15 Jg h C ) and substantially MANOVAR (F5, 3 4.07 ,P 0.139 ). However, examination of Ϫ1 Ϫ1 Њ Ϫ1 ע Њ at 35 Cto6.51 0.70 Jg h C (Fig. 1). There was no the pattern of EWL with Ta suggests that EWL decreased from p p p Њ Њ difference in Cwet between individuals (F7, 40 0.099 , P Ta 9 to 31 C, then increased to the highest value of Ϫ1 Ϫ1 Њ ע p 0.998), but there was a significant effect of Ta (,F5, 3 130 1.65 0.12 mg H2Og h at 35 C (Fig. 2). A priori contrasts P p 0.001). There were highly significant linear, quadratic, and indicated a significant linear (P p 0.043 ), quadratic (P p ! p p cubic patterns (P 0.001 ) for all Ta’s but no linear (P 0.001) and cubic (P 0.003 ) effect over all Ta’s but only a p p p p Њ 0.200), quadratic (P 0.060 ), or cubic effects (P 0.140 ) for significant linear effect (P 0.016 ) if Ta 35 C was excluded. ≤ Њ Њ Ta 31 C. This pattern was supported by reverse Helmert con- This suggests a negative linear effect of Ta on EWL from 9 C Ϫ1 Ϫ1 ע Ϫ1 Ϫ1 Њ ע ! Њ trasts being significant for Cwet only at 35 C(P 0.001 )and (mgg1.10 0.10h )to31C ( 0.86 0.065 mg g h ) Њ p p Њ 31 C (P 0.037 ) compared to lower Ta’s, and significant Hel- and a marked increase in EWL at Ta 35 C. The linear re- ! p Њ p Ϫ mert contrasts for all Ta’s (P 0.0012 ). Cdry was constant from lationship (excluding Taa35C) was EWL 1.31 0.017T . p Њ ע Ϫ1 Ϫ1 Њ Ϫ1 Њ ע p Њ Ta 9C( 1.84 0.081 Jg h C )to31C( 1.89 EWL was also significantly higher at Ta 35 C than all lower Ϫ1 Ϫ1 Њ Ϫ1 ! 0.135 Jg h C ) and then increased substantially at Ta’s (simple and reverse Helmert contrasts,P 0.001 ) and EWL Ϫ1 Ϫ1 Њ Ϫ1 Њ Њ Њ Њ ע p Њ Ta 35Cto 4.74 0.56 Jg h C (Fig. 1). There was no at 20 ,25 and 31 C was lower than at 35 C by Helmert con- p p ! difference in Cdry between individuals (F7, 40 0.148 , P trasts (P 0.037 ). 518 P. C. Withers and C. E. Cooper

Ϫ1 ≤ Њ ≤ Њ 2.09 mL min ) for both Taa31 C and T 35 C but no sig- 1 ≤ Њ nificant quadratic or cubic contrasts (P 0.071 ). For Ta 31 C, p Ϫ VI 196 5.49 Ta. VI was not significantly different between 31Њ and 35ЊC (simple contrastP p 0.227 ). There were no sig- 1 nificant polynomial contrasts for Eo2 (P 0.350 ) and no de- p Њ crease in Eo2 at Ta 35 C compared to the lower Ta’s (reverse ע p HelmertP 0.440 ); mean Eo2 was 19.3% 0.5% over all Ta’s.

Discussion

This study of the thermal, metabolic, hygric, and ventilatory physiology of the dibbler follows a repeated-measures experi- mental design that is common in physiological (and many other) studies, that is, the measurement of a parameter (e.g., metabolic rate) repeated for the same individuals over a range

of ordered categorical experimental conditions (e.g., Ta). We demonstrate here the power of a priori contrasts in a multi- variate repeated-measures analysis in the absence of post hoc tests, by examining specific hypotheses for thermal patterns in the first physiological data available for dibblers. This approach enables us to describe the presence as well as statistically con-

firming the pattern of physiological responses with Ta for this endangered dasyurid marsupial. MANOVAR consistently found significant effects for those physiological variables that we anticipated would be influenced

by Ta, that is, Tb,Vo2, Cwet, Cdry, RWE, fR, VT, and VI. An overall

Ta effect was insignificant for EWL and Eo2, but a Ta effect is

Figure 1. Body temperature, metabolic rate, and wet (black symbols) and dry (white symbols) thermal conductance of dibblers (Parantech- inus apicalis) at a range of ambient temperatures. Solid lines indicate patterns supported by a priori contrast analysis (see text). Values are . standard error;N p 8 ע mean

p RWE (Fig. 2) decreased significantly with Ta (,F5, 3 34.2 ע p Њ ע p P 0.008), from 1.45 0.13 at Ta 9Cto 0.26 0.04 at Њ p 35 C but did not differ between individuals (F7, 40 0.501 , p ! P 0.828). The pattern was highly linear for all Ta’s (P 0.001) but not quadratic or cubic (P 1 0.085 ); RWE p Ϫ p Њ 1.92 0.052Ta, and PRWE 20.3 C.

There was a significant effect of Ta on fR, VT,, and VI (Fig. ≥ ≤ p p 3;F5, 310.5 ,P 0.041 ), but not on Eo2 (F 5, 3 0.552, P 0.738), with no differences between individual dibblers for any ≤ ≥ respiratory variable (F7, 40 1.70 ,P 0.138 ). Contrasts indicated linear (P ! 0.001 ) and quadratic (P p 0.023 ) components for the effect of all Ta’s on fR but only a linear component when p Њ p Ϫ ! TaR35 C was excluded (f 105 2.59 Ta;);P 0.001 fR in- creased significantly from 31Њ to 35ЊC (simple contrast P p -Figure 2. Evaporative water loss and relative water economy (meta ע p Њ 0.018). VT decreased linearly from Ta 9.4C( 2.10 0.259 -p Ϫ bolic water production/evaporative water loss) of dibblers (Parantech ע p Њ mL) to TaT35C ( 1.01 0.55 mL); V 2.46 0.044 Ta p inus apicalis) at a range of ambient temperatures. Solid lines indicate (P 0.003 ) for all Ta’s, with no significant quadratic effect patterns supported by a priori contrast analysis (see text). The dashed p ! standard ע P 0.790 ). For VI there was a significant (P 0.001 ) linear line indicates relative water economy p 1. Values are mean) . error;N p 8 ע mL minϪ1)to31ЊC( 27.7 25.5 ע decline from 9ЊC (166.4 Technical Comment 519

even if the overall MANOVAR test is not significant. They are also useful for examining specific hypotheses in non-repeated- measures ANOVA and univariate repeated-measures ANOVA models.

For Tb, the overall significant MANOVAR was supported by various significant a priori contrasts (polynomial, Helmert, re-

verse Helmert) that reflected a pattern of constant Tb from p Њ Њ Ta 10 to 31 C and then an increase in Tb above thermo- p Њ neutrality (Ta 35 C). This pattern of Tb consistency at lower

Ta and then hyperthermia at high Ta is expected for a euthermic (e.g., McNab 1980; Withers 1992) and is consistent with that observed for other species of dasyurid marsupial (e.g., Robinson and Morrison 1957; Nicol and Maskrey 1980; Daw- son and Dawson 1982; Geiser 1986; Schmidt et al. 2009; Cooper and Withers 2010). Many smaller dasyurid species are relatively

thermolabile at low Ta (Morton and Lee 1978; Dawson and Wolfers 1978; Withers and Cooper 2009a, 2009b; Warnecke et

al. 2010), but dibblers maintained a constant Tb below ther- moneutrality and showed no tendency for torpor during experiments.

For Vo2, the overall significant MANOVAR resulted from a

slightly different pattern to Tb, of a linear decrease in Vo2 with p Њ increasing Ta and then an increase atTa 35 C; there were

significant differences between the thermoneutral Ta and all

other Ta’s, and there was a significant quadratic relationship ! Њ for Vo2 at all Ta’s but only a linear relationship forTa 35 C. This is the expected pattern from the Scholander-Irving model for an (e.g., McNab 1980; Withers 1992), reflecting the increased metabolic heat production required for ther-

moregulation of a constant Tb at low Ta, and it is typical of normothermic dasyurid marsupials (e.g., Nicol and Maskrey 1980; Geiser 1986; MacMillen and Dawson 1986; Schmidt et al. 2009; Withers and Cooper 2009a, 2009b; Cooper and With-

ers 2010; Warnecke et al. 2010). The predicted Tb from the Њ relationship of Vo2 with Ta below thermoneutrality of 36.2 C Њ was very similar to the measured Tb (36.3 C), confirming the near conformity of dibblers to the Scholander-Irving model. Similar use of a priori contrasts demonstrated the constancy

of Cwet and Cdry at low Ta but elevated values at high Ta. This pattern is typical for endotherms in general (e.g., McNab 1980; Figure 3. Ventilatory variables; respiratory frequency, tidal volume, Withers 1992) and for other dasyurid marsupials in particular minute volume, and oxygen extraction for dibblers (Parantechinus api- (Schmidt et al. 2009; Withers and Cooper 2009a, 2009b; Cooper calis) at various ambient temperatures. Solid lines indicate patterns and Withers 2010; Warnecke et al. 2010). ע supported by a priori contrast analysis (see text). Values are mean Ventilatory parameters of dibblers accommodated changing standard error;N p 8 . O2 demand with Ta. The pattern of change in VI with Ta mir-

rored that of Vo2 and was mediated by a decrease in fR with p Њ not necessarily anticipated for these variables (e.g., Hinds and increasing Ta and then an increase atTa 35 C (like Vo2)and

MacMillen 1986; Cooper and Withers 2002, 2004; Larcombe a linear decrease in VT. Such fR and VT changes are typical of

2002; Withers and Cooper 2009a, 2009b). For any Ta effects, similar-sized marsupials. Smaller species generally increase only it was of interest to establish what that pattern was and/or for fR and larger species only VT to increase VI at low Ta (Hallam which categories of the repeated factor there were significant and Dawson 1993; Chappell and Dawson 1994; Schmidt et al. differences. Although an absence of post hoc tests makes this 2009; Withers and Cooper 2009b; Cooper and Withers 2010; difficult for MANOVAR, a priori contrasts provided a mech- Warnecke et al. 2010). anism by which we could statistically describe the observed Even for EWL and Eo2, for which the overall MANOVAR patterns of response to Ta. A priori contrasts can also be val- was insignificant, it was useful to examine specific a priori uable in examining specific hypotheses (e.g., a linear effect) patterns. EWL of dibblers would be expected to increase at Ta 520 P. C. Withers and C. E. Cooper above thermoneutrality as a thermoregulatory response when Literature Cited heat challenged (e.g., MacMillen and Dawson 1986; Schmidt et al. 2009; Withers and Cooper 2009a, 2009b; Cooper and Beaupre S.J. and F. Zaidan. 2001. Scaling of CO2 production Withers 2010). We confirmed this response using polynomial in the timber rattlesnake (Crotalus horridus), with comments p Њ contrasts including and excludingTa 35 C and simple and on cost of growth in neonates and comparative patterns. reverse Helmert contrasts. The effect of lower Ta on EWL varies Physiol Biochem Zool 74:757–768. amongst dasyurids, from none to negative to positive (Hinds Berg A.M. and A.A. Biewener. 2008. Kinematics and power and MacMillen 1986; MacMillen and Dawson 1986; Cooper et requirements of ascending and descending flight in the pi- al. 2005; Schmidt et al. 2009; Withers and Cooper 2009a, 2009b; geon (Columba livia). J Exp Biol 211:1120–1130. Cooper and Withers 2010; Warnecke et al. 2010). Differences Bock R.D. 1975. Multivariate Statistical Methods in Behavioral in patterns of change in the respiratory component of total Research. McGraw-Hill, New York.

EWL at low Ta presumably contribute to this variation between Chappell M.A. and T.J. Dawson. 1994. Ventilatory accommo- ≤ Њ species. We found a significant negative effect ofTa 31 C for dation of changing oxygen consumption in dasyurid mar- dibblers by linear contrast, and Helmert contrasts reinforced supials. Physiol Zool 67:418–437. this interpretation. The negative EWL-Ta relationship for dib- Cohen B.H. 2008. Explaining Psychological Statistics. Wiley, blers suggests that they have a relatively high respiratory EWL, Hoboken, NJ. presumably reflecting a comparatively poor nasal countercur- Cooper C.E., F. Geiser, and B. McAllan. 2005. Effect of torpor rent exchange system. Contrasts demonstrated the expected on the water economy of an arid-zone dasyurid, the stripe- linear decrease in RWE with increasing Ta, and the PRWE of faced (Sminthopsis macroura). J Comp Physiol B 20.3ЊC was consistent with that for other dasyurids (Schmidt 175:323–328. et al. 2009; Withers and Cooper 2009a, 2009b; Cooper and Cooper C.E. and P.C. Withers. 2002. Metabolic physiology of Withers 2010; Warnecke et al. 2010). the (Myrmecobius fasciatus). J Comp Physiol B 172:

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