Estimating the Energy Expenditure of Endotherms at the Species Level

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Canadian Journal of Zoology

Estimating the energy expenditure of endotherms at the species level

Journal: Canadian Journal of Zoology

Manuscript ID cjz-2020-0035

Manuscript Type: Article

Date Submitted by the 17-Feb-2020 Author:

Complete List of Authors: McNab, Brian; University of Florida, Biology

Is your manuscript invited for consideration in a Special Not applicable (regular submission) Issue?: Draft arvicoline rodents, BMR, Anatidae, energy expenditure, endotherms, Keyword: Meliphagidae, Phyllostomidae

Estimating the energy expenditure of endotherms at the species level

Brian K. McNab

B.K. McNab, Department of Biology, University of Florida 32611 Email for correspondence: [email protected] Telephone number: 1-352-392-1178 Fax number: 1-352-392-3704 The author has no conflict of interest

Draft

McNab, B.K.

Estimating the energy expenditure of endotherms at the species level.

Abstract

The ability to account with precision for the quantitative variation in the basal rate of metabolism (BMR) at the species level is explored in four groups of endotherms, arvicoline rodents, ducks, melaphagid honeyeaters, and phyllostomid bats. An effective analysis requires the inclusion of the factors that distinguish species and their responses to the conditions they encounter in the environment. These factors are implemented by changes in body composition and are responsible for the non-conformity of species to a scaling curve. Two concerns may limit an analysis. The factors correlatedDraft with energy expenditure often correlate with each other, which usually prevents them from being included together in an analysis, thereby preventing a complete analysis, implying the presence of factors other than mass. Many of the relevant factors, such as food habits and an island residence, are qualitative, which complicates their inclusion in a quantitative analysis, a difficulty that is solved by ANCOVA. The precision of an analysis, based on an inclusive equation, can be determined by comparing its estimates to measurements of the performance of species. Without this comparison, the effectiveness of an analysis cannot be determined, which then simply becomes a suggestion. A proposed standard for a precise estimate is for it to be within 10% of the measured rate.

Key words: arvicoline rodents, BMR, ducks, energy expenditure, endotherms, meliphagid honeyeaters, phyllostomid bats

1 Estimating the energy expenditure of endotherms at the species level

2 INTRODUCTION

3 The goal of this article is to determine the extent to which the basal rate of

4 metabolism (BMR) of birds and mammals can be estimated with precision. This can

5 be accomplished through an equation that includes the various factors that correlate

6 with basal rate. The reason why BMR is worthy of consideration is that data are

7 available from >1400 species, which gives an enhanced view of biological diversity.

8 And many aspects of species’ performance correlate with BMR, including their

9 thermal biology, environmental tolerance, reproductive output, and field energy

10 expenditure (McNab 2013, 2015).

11 A series of operative factorsDraft determine basal rate, including body mass, body

12 composition, and tissue activity, as reflected in their correlations with food habits,

13 climate, substrate, and an island or continental distribution (Raichlen et al. 2010;

14 McNab, 2015, 2019b). These observations go beyond demonstrating correlations of

15 basal rate with various ecological and behavioral factors. It goes to their

16 implementation and collective action. Correlations are not determinative, they

17 reflect and introduce the action of the mechanisms that determine basal rate

18 (McNab 2019b). The rate of endotherms stands at the interface between energy

19 income and expenditure and therefore accounts for the restriction or expansion of

20 the behavior of endotherms.

21 The consequences of the correlates of basal rate have not been pursued. This

22 article deals with whether the information that we have on the correlatives of basal

23 rate can collectively account for its variance at the species level. Without this

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24 approach we do not know the extent to which we understand how basal rates are

25 determined and we are left with the superficiality of correlations (McNab 2019b).

26 A common approach in the analysis of quantitative physiological data from a

27 variety of species is to examine a scaling relationship. An r2  0.85 mass accounts

28 for at least 85% of the interspecific variance of the basal rate of the species. The

29 problem with this conclusion is that r2 increases with the range in mass, thereby

30 obscuring the appearance of other factors that also may be determinative. If a group

31 of species has no difference in mass, an appreciable variance in expenditures usually

32 remains, which contributes to the residual variation around the scaling curve. This

33 implies that factors other than mass also determine energy expenditure. The

34 adequacy of an analysis can be determinedDraft by its ability to account for the basal

35 rates of species with precision, but it must include the factors responsible for the

36 residual variation. If a multifactorial analysis is effective, the residual variation

37 around a scaling curve would decrease, or even disappear.

38 The attempt to account for the variance in basal rate is complicated. When

39 relatives differ in behavior and/or face different environmental conditions, they

40 often have different expenditures. This has been seen in deer mice (McNab and

41 Morrison 1963; Mueller and Diamond 2001; McNab 2019a), heteromyid rodents

42 (McNab 2012), and larks (Tieleman et al. 2003) with regard to their position along a

43 mesic/xeric gradient. And when unrelated species converge on a behavior, their

44 basal rates are more similar than expected from ancestry, as seen in ant- and

45 termite-eating mammals, including a monotreme, a marsupial, and many unrelated

2 © The Author(s) or their Institution(s) Page 5 of 42 Canadian Journal of Zoology

46 eutherians (McNab 2012). A similar convergence in energy expenditure occurs

47 among arboreal folivores and fossorial rodents (McNab 2012).

48 Another complication is that a factor does not necessarily have a uniform

49 performance. Small frugivores may have high or low mass-independent basal rates,

50 but all frugivores that weigh > 0.5 kg have low rates, a decrease that increases with

51 mass (McNab 2015). We shall see the impact of climate on nectarivory. To what

52 extent can an analysis account for the variance in the basal rate of species? This is a

53 physiological question. It concerns the mechanisms by which performances are

54 implemented, not history. Occurrence is not performance.

55 Energy expenditure has often been demonstrated to correlate with

56 behavioral and ecological factors (McNabDraft and Morrison 1963, McNab 1969, Soriano

57 et al. 2002; McNab 2003b; Tieleman et al. 2003; McNab 2012, 2015). However,

58 these correlations have not been pursued to determine the extent to which they

59 account for the basal rate of individual species.

60 The ability to account for the variation of BMR with precision is addressed

61 here by examining four sets of species with different characteristics. One analysis is

62 of 34 arvicoline rodents, a behaviorally and ecologically uniform group. This

63 subfamily of the Cricetidae includes voles, lemmings, and muskrats. An assembly of

64 27 species of anatids, i.e., ducks and geese, demonstrates the consequences of factor

65 interactions. An analysis of data from 20 meliphagid honeyeaters is examined to see

66 the extent to which their basal rates can be estimated with precision. Finally the

67 basal rate of 30 phyllostomid bats, characterized by their great ecological and

68 behavioral diversity, is reexamined. Phyllostomids have the greatest range in food

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69 habits of all mammalian families. Data from other families with large diversities in

70 factors are not available.

71 Some possible difficulties with estimation must be faced. One is that the

72 mutual correlation of some characters often prevents an analysis from being

73 completed. Many of the correlates are qualitative, which are difficult to include in a

74 quantitative analysis. Furthermore, the identity of relevant factors is not always

75 obvious.

77 METHODS

78 At first, a scaling relationship is described. Then the included species are put into

79 categories with respect to their positionDraft along the scaling curve, i.e., above, below, or

80 in agreement with the curve. This is the basis for judging whether a particular

81 species has a ‘high’ or ‘low’ mass-independent basal rate. Factors that have more

82 than one state may differentially influence energy expenditure, which is what

83 contributes to the diversity of species and the complexity of analysis. Here the goal

84 is to account for the deviation of a species’ basal rate from the scaling curve: why are

85 high species high and low species low? Can residual variation be reduced, or even

86 eliminated, by including influential factors other than mass?

87 The intent of this article is to compare measurements of basal rate with

88 estimates derived from an equation that includes mass and the other factors that

89 correlate with BMR. A difficulty with this approach is that many of the appropriate

90 factors to be included are qualitative, as in food habits, being volant or flightless, and

91 living on islands or continents. How they are to be included in an equation?

4 © The Author(s) or their Institution(s) Page 7 of 42 Canadian Journal of Zoology

92 The quantification of these factors is made by ANCOVA. If two quantitative

93 factors are included in an analysis, here body mass and basal rate of metabolism, an

94 unlimited number of qualitative factors are quantified. Then one of the states in a

95 factor is designated by ANCOVA as a standard (its value equals 1.00) and the other

96 states in that factor are numerically compared to it as decimal fractions. The impact

97 of the states in a factor therefore is differential, not all or none.

98 How close must an estimate be to a measurement for it to be designated an

99 effective estimate? A suggested criterion is that the estimate be within 10% of the

100 measurement, much wider criteria being too inclusive. A complication is that if an

101 estimate is within 10% of a measurement, it can be either above or below the

102 measurement, which represents aDraft < 20% range of estimates around the

103 measurement, but it still is within 10%. Coefficients for each factor in a

104 multifactorial analysis are found in Table (1). All statistical analyses are based on

105 ANCOVA.

106

107 RESULTS

108 Arvicoline rodents

109 Basal rates are available on 34 species of arvicoline rodents (McNab, 2008). Body

110 mass (g) accounts for 95.7% of the interspecific variance in basal rate (F = 143.94, P

111 < 0.0001):

112

0.600 113 BMR (mLO2/h) = 8.67 m . (1)

114

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115 The high r2 results from a 56:1 mass ratio, i.e., the largest species has a mass 56

116 times that of the smallest species. Equation (1) estimates basal rate in 17 species

117 within 10% of the measurements, i.e., 50% of the species.

118 Do other factors influence basal rate? Arvicolines are widely distributed in

119 many environments in the northern hemisphere, the characteristics of which could

120 potentially influence their energy expenditure. Several potential factors were

121 examined, including a polar or temperate climate (F = 1.96, P = 0.171), altitude (F

122 1.36, P = 0.267), and substrate (F = 0.83, P = 0.367), none of which were significant.

123 The only significant factor is distribution along a mesic/xeric environmental

124 gradient (F = 8.41, P = 0.0067). Of six species living in xeric environments, two had

125 standard basal rates and four had Draftlow basal rates (Table 2). Species living in mesic

126 environments had a mean dimensionless coefficient (H) equal to 1.30, whereas it

127 was 1.00 in species living in xeric environments (Table 1A2):

128

0.587 129 BMR (mLO2/h) = 8.36 (H) m . (2).

130

131 This relationship accounts for 95.9% of the interspecific variance in basal rate,

132 essentially the same as equation (1). In spite of adding the statistically significant

133 mesic/xeric factor to the analysis, equation (2) estimated basal rate in only in seven

134 species (21%) within 10%, which is much poorer than in equation (1).

135 The assignment 1.00 in xeric environments and 1.30 in mesic environments

136 was arbitrarily determined by ANCOVA to be compatible with the equation

137 coefficient, 8.36. However, if the coefficient in mesic environments is designated as

6 © The Author(s) or their Institution(s) Page 9 of 42 Canadian Journal of Zoology

138 1.00, that in xeric environments would be 0.77, which maintains the quantitative

139 difference between these two conditions. Then the coefficient for equation (2)

140 would be 10.87, which gives the same estimates for individual basal rates as the

141 original version of equation (2) and the same r2, 0.959. The equation coefficient

142 must be compatible with the coefficients of the factors, which requires it to increase,

143 if the numerical values of the factors decrease because the product of the coefficient

144 and the factors should remain the same:

145

146 In xeric environments: 8.36 x 1.00 = 8.36 = 10.87 x 0.77

147 In mesic environments: 8.36 x 1.30 = 10.87 = 10.87 x 1.00

148 Draft

149 Then 10.87/8.36 = 1.30, which retains the difference between the two

150 environments.

151 The reduction of the number of species that were within 10% of

152 measurements occurred because the coefficient of the equation decreased from 8.67

153 to 8.36, and the power from 0.600 to 0.587, thereby lowering the multifactorial

154 curve (Fig. 1b). This separated equation (2) from 14 species whose basal rates that

155 were within 10% of equation (1). Equation (2) only shared precision at 10% with

156 equation (1) in three species (Table 2).

157 The failure of equation (1) to account for the basal rates of more species is

158 patterned: species estimates are too low in species with high basal rates and too

159 high in species with low rates (Table 2). Some factor(s) may be hidden from the

160 analysis because of a great range in mass.

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161 .

162 Anatids 163 164 Data on BMR are available from 27 species of anatids (McNab 2008). Body mass (g)

165 (F = 175.87, P < 0.0001) accounts for 87.6% of the interspecific variance in their

166 basal rates (Fig. 2a):

167

0.844 168 BMR (mLO2/h) = 2.51 m . (3)

169

170 The mass range is 13:1. Mass alone accounts for the basal rates in seven species

171 (26%) within 10% of the measurements, all of which have basal rates expected from

172 mass (Table 3). The principal difficultyDraft with a mass analysis, as always, is that

173 species differ by more than mass.

174 Additional factors that potentially contribute to the residual variation of

175 basal rate include having a flightless or volant condition (F), a sedentary or

176 migratory activity (A), and a distribution on islands or continents (D). However,

177 these factors are not independent. The two flightless ducks are found on

178 subantarctic islands of New Zealand. Flight and islands correlate (2 = 4.72, P =

179 0.030). Therefore, island/continent (F = 19.54, P = 0.0002) and volant/flightless (F

180 = 0.12, P = 0.727) cannot be combined in an analysis with mass (F = 247.43, P <

181 0.0001). Furthermore, activity correlates with distribution (2 = 26.54, P < 0.0001)

182 in that all island endemics, whether they fly or not, are sedentary and all migratory

183 species are continental. And, obviously, a volant or flightless condition correlates

184 with the activity/sedentary factor (2 = 5.61, P = 0.022).

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185 However, these factors could potentially account for some of the interspecific

186 variance of basal rate when individually combined with mass. Yet, the

187 volant/flightless condition, when combined with mass, is not a significant correlate

188 with BMR (F = 1.00, P = 0.327) because the great variation in the mass-independent

189 basal rates of volant species encompasses those of the flightless ducks.

190 An analysis that increases the ability to determine the variance in BMR

191 combines distribution (F = 22.00, P < 0.0001) with body mass (F = 261.15, P <

192 0.0001):

193

0.821 194 BMR (mLO2/h) = 2.70 (D) m . (4)

195 Draft

196 Then, the interspecific r2 equals 0.968. The non-dimensional coefficient for

197 distribution (D) equals 0.76 for species endemic to islands and 1.00 for species

198 resident on continents (Table 1B2). Continental species, therefore, have basal rates

199 that average 1.32 (= 1/0.76) times those of island endemics.

200 All volant ducks endemic to islands have lower basal rates than most

201 northern hemisphere species (pers. obs.). They include two species that reside in

202 Hawaii, one from the Philippines, one from South Georgia Island, and two from

203 Madagascar. Given data from nine New Zealand species (McNab 2003a), 15 island

204 endemics have lower basal rates than is found in the 18 northern hemisphere,

205 continental species (F = 16.90, P = 0.0004).

206 Basal rate in ducks also correlates with activity (F = 14.75, P = 0.0008) when

207 combined with body mass (F = 235.93, P < 0.0001):

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208

0.780 209 BMR (mLO2/h) = 3.64 (A) m , (5)

210

211 where the non-dimensional coefficient for activity (A) equals 1.41 for migratory

212 species and 1.00 for sedentary species (Table 1B3). This relationship accounts for

213 97.0% in interspecific variance of basal rate (Fig. 2b), which is identical to equation

214 (4), reemphasizing the correlation of activity with distribution.

215 The ability of these two analyses, although correlated, make different

216 estimates of basal rate (Table 3). The activity analysis accounts for 11 species

217 (41%) within 10%, seven species with high basal rates, three with basal rates

218 expected from body mass and, oneDraft with a low rate (Table 3). In contrast, the

219 distribution analysis accounts for no species with high rates, five species that have

220 basal rates expected from mass, and four species with low basal rates, a total of nine

221 species (33%). Neither analysis accounts for the basal rate in the majority of

222 species, although both are somewhat more effective than the mass analysis, as is

223 marginally to be seen in a comparison of Figure (2a) with Figure (2b), the marginal

224 compression in the multifactorial analyses occurring in the smallest species.

225 Because island endemics are sedentary and migratory species are

226 continental, this raises the question, which factor, island/continental or

227 sedentary/activity, is operative? Relative to the answer is that some anatids in

228 South America and Africa are sedentary. Do continental, sedentary species have low

229 basal rates like island endemics, or do they have high basal rates like northern

230 hemisphere, continental anatids? Preliminary observations on a sedentary species

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231 from South America, the Brazilian Duck (Amazonetta brasiliensis [Gmelin, 1789]),

232 and one from Africa, the White-backed Duck (Thalassornis leuconotus [Eyton,

233 1838]), have low basal rates (pers. obs.).

234 The factor principally responsible for depressed basal rates in anatids

235 appears to be sedentary habits, both on continents and islands. Anatids in the

236 northern hemisphere seasonally encounter harsh environments at high latitudes in

237 winter, characterized by frozen lakes and rivers. These species must migrate, which

238 requires larger pectoral muscle masses and higher basal rates than found in

239 sedentary species (McNab 2003a, 2019b).

240 The activity analysis at present can only account for the basal rates of 41% of

241 species within 10% of the measurementsDraft (Table 3), some of the failure reflecting

242 factor interactions. However, this analysis accounts for 97.0% of the interspecific

243 variance in basal rate compared to the 87.6% by mass. A high interspecific r2 clearly

244 does not guarantee reliable estimates of the basal rate of species. As inadequate as

245 the multifactorial analyses may be, they are more effective than the mass-based

246 analysis, as long as the mass range is not too great. Other factors that may influence

247 the basal rates of anatids are unknown.

248

249 Melaphagid honeyeaters 250 251 Data are available on 20 species of meliphagids (McNab 2016), mass (g) accounting

252 for 91.5% of the interspecific variance in their basal rates (F = 480.49, P < 0.0001):

253

0.729 254 BMR (mLO2/h) = 5.97 m . (6)

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255

256 The high r2 reflects a 15:1 range in mass (Fig. 3a). Mass accounts for BMR in 11

257 species within 10%, i.e., 55% of the species (Table 4).

258 Basal rate also correlates with climate and altitude. These factors correlate

259 (2 = 19.62, P = 0.0012) with each other in an asymmetrical manner: a restriction to

260 high altitude only occurs in the tropics. Climate C (F = 9.99, P = 0.0061) and altitude

261 A (F = 7.56, P = 0.0143), in combination with mass (F = 140.62, P < 0.0001), account

262 for 98.6% of the interspecific variance in basal rate (Fig. 3b):

263

0.686 264 BMR (mLO2/h) = 6.87 (A · C) m . (7)

265 Draft

266 The coefficients for altitude (A) equal 1.40 in tropical species limited to altitudes <

267 2000m and 1.00 in tropical species found at higher altitudes (Table 1C2,3). The

268 coefficients for climate (C) equal 0.68 for temperate species and 1.00 for lowland,

269 tropical species. Notice the parallel depression of basal rate in temperate species

270 and high altitude, tropical species, both possibly reflecting cooler environments and

271 reduced nectar availability. In fact, the depressions are nearly identical; lowland

272 tropical species have basal rates 1.47 (= 1/0.68) times those of temperate species

273 and 1.40 times those of tropical species at altitudes > 2,000 m.

274 This analysis accounts for the basal rates of 15 species (75%) within 10% of

275 the measured rates (Table 4), a 50% increase over the mass analysis. Both analyses

276 account for all species with basal rates expected from mass and the multifactorial

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277 analysis accounts for most species with a low basal rate. Neither analysis is

278 effective in species with high basal rates (Table 4), which implies the absence of one

279 or more factors in the analysis.

280 Two meliphagids found in temperate environments, the Red Wattlebird

281 (Acanthochaera carnuculata [Shaw, 1790]) from Australia (MacMillen 1985) and the

282 Tui (Prosthemadera novaeseelandiae [Gmelin, 1788]) from New Zealand (McNab

283 2015), are principally found in the lowlands. They have the lowest basal rates

284 among large species (Fig. 3a), which are completely accounted for by equation (7),

285 as it does for the largest species with a high basal rate (Philemon buceroides 286 [Swanson, 1836]) (Fig. 3b). An occurrenceDraft in lowlands is not correlated with a high 287 basal rate in temperate areas, as it is in the tropics, again reflecting the

288 consequences of living in cool environments.

289

290 Phyllostomid bats

291 A reexamination of basal rate in 30 phyllostomid bats demonstrates a potential

292 solution for the analysis of a highly complex factor, food habits (McNab 2003b).

293 Body mass (g) accounts (F = 103.94, P < 0.0001) for 86.3% of the interspecific

294 variance in BMR (Table 5):

295

0.671 296 BMR (mLO2/h) = 4.13 m . (8)

297

298 Body mass estimated the BMR of nine species within 10% of the measurements, i.e.,

299 30% of the species (Table 6). This analysis accounts for only three of the 24 species

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300 with high and low basal rates, but all six with mass-expected basal rates. The

301 inability of mass to account for the basal rates of more species, in spite of its

302 appreciable range (11:1), reflects the absence of three factors that correlate with

303 BMR (Fig. 4a).

304 They are food habits (F = 29.31, P < 0.0001), a maximal altitudinal

305 distribution (F = 16.01, P < 0.0010), and an island or continental distribution (F =

306 134.79, P < 0.0001). These factors, in combination with mass (F = 1091.21, P <

307 0.0001), account for 99.4% of the interspecific variance in basal rate. However, this

308 analysis cannot incorporate the 10 designated food habits, in spite of their collective

309 significance. None of the individual foods has a unique correlation with a basal rate,

310 as is demonstrated by shared leastDraft square mean basal rates (Table 5). If a food (e.g.,

311 nectar) shares a basal rate with a second food (e.g., insects), neither can be included

312 as an independent correlate, but together can be considered one food (nectar and

313 insects), as long as it is independent of other combinations. Therefore, foods were

314 combined to determine whether BMR has significant, non-overlapping correlations

315 with combined food categories. The boundaries for these combinations are best

316 indicated by gaps in the sequence of least square mean basal rates (Table 5). They

317 must be combined in sequence, or their means become scrambled.

318 Food habits are grouped into combinations consisting of two, four, five, and

319 six foods. Each of the divisions of basal rate within a combination is statistically

320 independent, if represented by a different letter, which obviously is not the case

321 with the 10 food categories (Table 5). The two-food analysis combines nectar &

322 insects through vertebrates in one combination and Clusiaceae through bird &

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323 mammal blood in the other. Then BMR correlates with F (food, F = 68.89, P =

324 0.0003), A (altitude, F = 19.10, P = 0.0002), D (island/continent distribution, F =

325 50.41, P = < 0.0001), and mass (F = 595.85, P < 0.0001), r2 equaling 97.8%. This

326 equation and its coefficients are found in Table (1D2). This analysis estimates the

327 basal rate in only one species within 10% (Table 6), far below the mass analysis, in

328 spite of having a much larger interspecific r2.

329 In a four-category food division (Table 5), F (F = 65.64, P < 0.0001), A (F =

330 25.91, P < 0.0001), D (F = 135.95, P < 0.0001), and mass (F = 1200.36, P < 0.0001),

331 has an r2 equaling 98.9%. The equation and its coefficients for the categories are

332 summarized in Table (1D3). This analysis estimates rates of four species within

333 10%, 13% of the species (Table 6),Draft again poorer than the mass analysis.

334 Another complication potentially exists with these analyses. Their

335 effectiveness depends on the distribution of foods among the divisions. For

336 example, two analyses have foods divided into five categories (Table 5). They differ

337 by the inclusion of an intermediate food, fruits of Clusiaceae into different

338 subdivisions.

339 When Clusiaceae is placed in level (C) (analysis 5a, Table 5), this analysis is

340 described by:

341

0.755 342 BMR (mLO2/h) = 2.63 (F · A · D) m , (9)

343

344 the factors are F (F = 56.17, P < 0.0001), A (F = 16.99, P = 0.0005), D (F = 138.41, P <

345 0.0001), and mass (F = 1388.61, P < 0.0001). The coefficients for these factors are in

15 © The Author(s) or their Institution(s) Canadian Journal of Zoology Page 18 of 42

346 Table (1D4). The estimates from this analysis account for 23 species within 10% of

347 the measurements (Table 6), 77% of the species. This analysis accounts for 99.0%

348 of the interspecific variance in basal rates, which is only 0.1% greater than in the

349 four-food category analysis, although it estimates 5.8 times as many species within

350 10% of measurements (Table 6). Equation (9) accounts for the basal rates in 18 of

351 the 24 species having high and low basal rates (Table 6).

352 When Clusiaceae is placed into level (D) (analysis 5b, Table 5):

353

0.725 354 BMR (mLO2/h) = 2.90 (F · A · D) m . (10)

355

356 The factors are F (F = 58.82, P < 0.0001),Draft A (F = 18.20, P = 0.0004), D (F = 148.12, P <

357 0.0001), and mass (F = 1407.48, P < 0.0001); r2 equals 99.2%. The coefficients are

358 in Table (1D5). This analysis estimates basal rate in 24 species within 10% (Table

359 6), i.e., 80% of the species. The increase from 23 to 24 species occurs by shifting

360 Clusiaceae from level (C) in analysis 5a to (D) in analysis 5b (Fig. 4b).

361 Illustrative of the effectiveness of equation (10), it accounts for four species

362 (13%) within 1% of the measurements, seven (23%) within 2%, and 10 (37%)

363 within 5%. This analysis accounts for BMR in 19 of the 24 species with high and low

364 BMRs within 10% of the measurements (Table 6).

365 The division of foods into six food categories (Table 5) accounts for no

366 species with a basal rate within 10% of measurements. Six and 10 food categories

367 are too narrow, whereas two and four food categories are too broad. The near

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368 equality of the results of two five-category analyses indicates that this is the

369 appropriate size of the categories for these data.

370 The separate impacts on BMR by body mass, food habits, altitude, and

371 presence on islands or continents (as represented by equation [8]; r2 = 0.863), is

372 shown in the mass analysis (Fig. 4a). The combination of factors in equation (10)

373 found in Figure (4b), reflects the 5b food analysis and r2 = 0.992, which essentially

374 eliminates residual variation.

375 Five categories of food give the maximum ability to account for the variation

376 in the basal rate of these bats. Of the six species with their BMRs not included

377 within the 10% range of measurements by equation (10), two missed being

378 included by one percent, and four Draftby four to six percent (Table 6). If a 11% criterion

379 for accuracy were accepted, 26 (87%) of the 30 phyllostomids would be included

380 with only four not included.

381

382 DISCUSSION

383 Nine conclusions can be derived from these analyses.

384 1)Body mass is the single most important factor determining basal rate as

385 long as it shows a variation. 386 387 2) The persistent preoccupation with whether the power of the metabolism/mass

2 388 curve is /3 or ¾ is artificial and at best only applies to a mass analysis. But a mass

389 analysis ignores the other factors that influence basal rates, which, when included,

390 modify the power because many of these factors correlate with mass. For example,

391 the power of the metabolism/mass curve varies with food habits because the mass-

17 © The Author(s) or their Institution(s) Canadian Journal of Zoology Page 20 of 42

392 independent basal rate correlates with food habits. In the four analyses in this

393 article, three show a decrease in the power when various factors are added to the

394 analysis. And in the phyllostomids the power goes from ca., 0.67 to 0.75 upon

395 adding food, altitude, and islands, which may interact in a complex manner.

396 Multifactorial analyses are more representative of the behavior of species than is a

397 strict mass analysis.

398 3) The ability of a multifactorial analysis to diminish the residual variation in the

399 basal of species depends on the ability to identify the factors that are effective. Body

400 mass does not diminish the presence of other factors, but may hide their presence,

401 as the range in mass increases. This might have been the difficulty in the analysis of

402 arvicolids and to some extent in ducks.Draft

403 4) An effective analysis at the species level requires the inclusion of the

404 characteristics that distinguish species and their response to the conditions

405 encountered in the environment. The two five-category analyses were effective

406 accounting for the variation in the basal rates of the phyllostomids because all

407 factors influencing their basal rates were apparently identified. One of the analyses

408 accounted for 80% of the basal rates within 10% of the measured rates and 87%

409 within 11% of the measurements, whereas the mass-based analysis only accounted

410 for 30% of the species within 10%. The melaphagid analysis improved with the

411 inclusion of climate and altitude. Many of these correlations are the byproducts of

412 modifying the proportion of body mass that is muscle (Raichlen et al. 2010; McNab

413 2019b).

414 5) A discernable pattern in the physiological consequences of the food categories

415 is present in the phyllostomids: fruit and/or nectar are in the four categories with

416 the greatest energy equivalencies (Table 5), followed by a vertebrate diet. All other

417 categories, Clusiaceae, bird blood, omnivory, insects, and bird/mammal blood, have

418 lower energy equivalencies.

419 High-energy equivalencies with fruit and nectar diets in the tropics may

420 reflect their abundance and reliability. However, this pattern appears to be limited

421 to small species, given that these foods are predominately sugar and water, protein

422 often supplemented by the consumption of insects. Mass-independent basal rates

423 are increasingly depressed with an increase in mass, as in large frugivorous

424 carnivores (McNab 1995), culminatingDraft in the very low basal rate in the binturong

425 (Arctictis binturong [Raffles, 1821]). In contrast, large carnivorous carnivores have

426 high mass-independent basal rates, reflecting a high protein diet, as well as being a

427 reliable food resource.

428 6) The ability to account for the variation in basal rate may depend on the

429 allocation of complicated factors into subgroups, as was seen in phyllostomids with

430 regard to food habits. The similarity of two five-food category analyses indicates

431 that they were appropriates division of food habits. Any division of food into

432 smaller or larger categories greatly decreased the ability to account for the basal

433 rate of many species. The inability of an analysis to account for all the variation in

434 the BMR of species may reflect the presence of character interactions, as seen in the

435 anatids, and ignorance of appropriate factors.

436 7) The performance of characters is not fixed, as demonstrated by climate and

437 altitude on nectivory in meliphagids. The energy expenditure of phyllostomids

438 reflects their location at altitudes and on islands or continents. And the position of

439 some mammals and birds along a mesic/xeric gradient influences their

440 expenditures. Any attempt to analyze the energy expenditures of birds and

441 mammals under the assumption that the performance of characters is fixed is

442 unacceptable. Again, the occurrence of characters does not define their

443 performance.

444 8) A high r2 in interspecific analyses does not imply an ability to account for the

445 basal rate of species, was also the seen by Konarzewski and Książek (2013).

446 Because the interspecific r2 approachesDraft 1.00 asymptotically, it is increasingly

447 insensitive to the addition of factors that augment the analysis of the energy

448 expenditure of species. Illustrative of the inability of a high interspecific r2 to

449 account for the variance of BMR at the species level with precision, the six analyses

450 of phyllostomid energetics that included food habits accounted for 0 to 24 species

451 within 10% of measurements, even though all mass-independent analyses had r2 >

452 0.978 (Table 5).

453 9) Finally, the persistent search for general principles at the species level requires

454 the inclusion of species-specific character states because they distinguish species.

455 The most effective way to determine the validity of a proposed analysis is to

456 compare its estimates to measurements of the function. In the absence of a

457 comparison, the precision of hypotheses is incapable of being evaluated and at best

458 are suggestions, most of which will ultimately fall by the wayside, only to be

459 replaced by another unsubstantiated suggestion with a similar fate.

460

461 Acknowledgments

462 I thank Doug Glazier, Harvey Lillywhite, and Frank Nordlie, for perceptive,

463 constructive discussions and suggestions on a draft of this manuscript. The design,

464 analysis, and writing of this article was accomplished by B.K.M. Most of the data

465 were obtained from the literature, except for some preliminary data that were

466 contributed by the author.

467 Competing Interests

468 The author declares no competingDraft or financial interests.

469 Author contributions

470 The entire project was conceived and accomplished by B.K.M.

471 Funding

472 The funding was by B.K.M.

473 References

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Table 1. The impact of factors on the basal metabolic rates (BMR) of species.

BMR Least square means Coefficients* A. Arvicoline rodents 1. Mass — — 0.600 2 BMR (mL O2/h) = 8.67m , r = 0.957 2. Habitat (H) i. Mesic 86 1.30 ii. Xeric 66 1.00 0.597 2 BMR (mL O2/h) = 8.36 (H) m , r = 0.959 B. Anatids 1. Mass — — 0.844 2 BMR (mL O2/h) = 2.51m , r = 0.876 2. Distribution (D) i. Continents 668 1.00 ii. Islands Draft 502 0.75 0.821 2 BMR (mL O2/h) = 2.99 (D) m , r = 0.968 Activity (A) i. Migratory 708 1.39 ii. Sedentary 511 1.00 0.780 2 BMR (mL O2/h) = 3.64 (A) m , r = 0.970 C. Meliphagids 1. Mass — — 0.729 2 BMR (mL O2/h) = 5.97m , r = 0.915 2. Climate (C) i. Temperature 60.5 0.68 ii. Tropical 89.1 1.00 3. Altitude (A) i. <2000 m 86.9 1.40 ii. >2000 m 62.1 1.00 0.686 2 BMR (mL O2/h) = 6.87 (A·C) m , r = 0.986

D. Phyllostomid bats 1. Mass — — 0.671 2 BMR (mL O2/h) = 4.13m , r = 0.863 2. Two food categories Food (F) i. Nectar–insects, Piper, fruit–nectar, fig, vertebrates 32.7 1.00 ii. Guttiferae, bird blood, omnivorous, insects, bird–mammal blood 23.1 0.71 Altitude (A) i. ≥2000 m 32.4 1.38 ii. <2000 m 23.4 1.00 Distribution (D) i. Continents 35.9 1.70 ii. Islands 21.1 1.00 0.755 2 BMR (mL O2/h) = 2.63 (F·A·D) m , r = 0.990 3. Four food categories Food (F) i. Nectar–insects, Piper, fruit–nectar Draft 33.3 1.74 ii. Fig, vertebrates 28.9 1.51 iii. Guttiferae, omnivorous, bird blood 23.2 1.21 iv. Insects, bird–mammal blood 19.1 1.00 Altitude (A) i. ≥2000 m 30.3 1.31 ii. <2000 m 23.2 1.00 Distribution (D) i. Continents 34.4 1.81 ii. Islands 19.0 1.00 0.725 2 BMR (mL O2/h) = 2.90 (F·A·D) m , r = 0.992

4. Five food categories Food (F) i. Nectar–insects 36.3 1.00 ii. Piper, fruit–nectar 32.4 0.89 iii. Fig, vertebrates, Guttiferae 28.5 0.79 iv. Omnivorous, bird blood 22.8 0.59 v. Insects, bird–mammal blood 18.8 0.52 Altitude (A) i. ≥2000 m 30.1 1.24 ii. <2000 m 24.3 1.00 Distribution (D) i. Continents 36.1 1.78 ii. Islands 20.2 1.00 0.725 2 BMR (mL O2/h) = 2.90 (F·A·D) m , r = 0.992 5. Alternate five food categories Food (F) i. Nectar–insects Draft 37.0 1.00 ii. Piper, fruit–nectar 32.8 0.89 iii. Fig, vertebrates 28.0 0.76 iv. Guttiferae, omnivorous, bird blood 22.0 0.59 v. Insects, bird–mammal blood 18.8 0.51 Altitude (A) i. ≥2000 m 29.9 1.24 ii. <2000 m 24.2 1.00 Distribution (D) i. Continents 35.8 1.77 ii. Islands 20.2 1.00 0.755 2 BMR (mL O2/h) = 2.63 (F·A·D) m , r = 0.990

*Coefficients are the least square means of BMR divided by the least mean square to which they must be compared, as designated by ANCOVA.

Table 2. Measured and estimated basal metabolic rates (BMR) of 34 arvicoline rodents.

Estimated BMR (mL O2/h) Measured BMR † ‡ † (mL O2/h) Mass* M/E Multifactorial M/E BMR higher than expected from mass (9 species) Western red-back vole, Myodes californicus (Merriam, 1980) 61.5 49.6 1.23 59.9 1.03§ Western heather vole, Phenacomys intermedius Merriam, 1889 67.5 54.6 1.24 65.8 1.03§ Wood lemming, Myopus schisticolor (Lilljeborg, 1844) 95.5 61.8 1.54 75.2 1.27 Northern red-backed vole, Myodes rutilus (Pallas, 1779) 77.5 64.0 1.21 76.8 1.01§ Tundra vole, Microtus oeconomus (Pallas, 1776) 101.0 73.7 1.37 88.2 1.15 Snow vole, Chionomys nivalis (Martins, 1842) 118.0 76.3 1.55 91.2 1.29 Silver Mountain vole, Alticola argentatus (Severtzov, 1879) 127.5 93.8 1.36 111.6 1.14 Water vole, Microtus richardsoni (DeKay, 1842) 173.5 120.2 1.44 142.3 1.22 Muskrat, Ondatra zibethicus (Linnaeus, 1766) 645.5 548.5 1.18 628.5 1.03§

BMR equal to expected from mass (15 species) Draft European pine vole, Microtus subterraneus (Sely-Longchamps, 1836) 49.5 48.8 1.01§ 58.9 0.84 Pine vole, Microtus pinetorum (Le Conte, 1830) 56.0 58.1 0.96§ 69.9 0.80 Common vole, Microtus arvalis (Pallas, 1779) 60.5 58.4 1.04§ 70.2 0.86 Bank vole, Myodes glareolus (Schreber, 1780) 57.5 59.2 0.97§ 71.2 0.81 Grey red-backed vole, Myodes rufocanus (Sundevall, 1846) 59.5 62.6 0.95§ 75.2 0.79 Field vole, Microtus agrestis (Linnaeus, 1761) 64.0 64.0 1.00§ 76.8 0.83 Sonoma tree vole, Arborimus pomo Johnson and George, 1991 59.0 65.1 1.07§ 66.3 0.89 Long-tailed vole, Microtus longicaudus (Merriam, 1888) 62.5 67.0 0.93§ 61.8 1.01§ Meadow vole, Microtus pennsylvanicus (Ord, 1815) 75.5 78.0 0.97§ 93.2 0.81 Brandt’s vole, Lasiopodomys brandtii (Radde, 1861) 77.5 79.7 0.97§ 73.2 1.06§ Günther’s vole, Microtus guentheri (Danford and Alston, 1880) 80.5 83.7 0.96§ 99.9 0.81 Montane vole, Microtus montanus (Peale, 1848) 90.0 92.0 0.98§ 109.5 0.82 Townsend’s vole, Microtus townsendi (Bachman, 1839) 90.5 93.0 0.97§ 110.8 0.82 Northern collared lemming, Dicrostonyx groenlandicus (Traill, 1823) 105.5 103.4 1.02§ 122.9 0.86 Taiga vole, Microtus xanthognathus (Leach, 1815) 99.0 109.5 0.90§ 129.9 0.76

BMR lower than expected from mass (10 species) Southern red-backed vole, Myodes gapperi (Vigors, 1830) 44.5 56.6 0.79 68.1 0.65 Mexican vole, Microtus mexicanus (Saussure, 1861) 47.0 65.1 0.72 60.1 0.78 © The Author(s) or their Institution(s) Canadian Journal of Zoology Page 30 of 42

Sagebrush vole, Lemmiscus curtatus (Cope, 1868) 50.5 67.1 0.75 61.9 0.82 California vole, Microtus californicus (Peale, 1848)) 68.5 76.9 0.89 100.2 0.68 Cabrera’s vole, Microtus cabrerae Thomas, 1906 49.0 82.8 0.59 76.0 0.64 Nearctic brown lemming, Lemmus trimucronatus (Richardson, 1825) 70.5 84.0 0.84 100.2 0.70 Prairie vole, Microtus ochrogaster (Wagner, 1842) 83.0 87.8 0.95§ 80.5 1.03§ Beach vole, Microtus breweri (Baird, 1857) 74.0 94.0 0.79 111.9 0.66 Eurasian water vole, Arvicola amphibius (Linnaeus, 1758) 113.5 135.3 0.84 159.8 0.71 Round-tailed muskrat, Neofiber alleni True, 1884 217.5 242.7 0.90§ 283.1 0.71

Σ(≤10%) 17 7

Note: The sum (Σ) is the number of species having an estimated BMR that is ≤10% of the value expected from the analysis.

*BMR estimated from eq. 1. †M/E = measured BMR/estimated BMR. ‡BMR estimated from eq. 2. §Estimated BMR ≤ 10% of the measured BMR. Draft

Table 3. Measured and estimated basal metabolic rates (BMR) of 27 anatids.

Estimated BMR (mL O2/h) Measured BMR † ‡ † § † (mL O2/h) Mass* M/E Island M/E Activity M/E BMR higher than expected from mass (8 species) Garganey, Anas querquedula Linnaeus, 1758 400 300 1.33 283 1.41 426 0.94‖ Ferruginous Duck, Aythya nyroca (Guldenstadt, 1770) 586 427 1.37 400 1.47 592 0.99‖ Northern Shoveler, Anas clypeata Linnaeus, 1758 695 519 1.34 483 1.44 708 0.98‖ Northern Pintail, Anas acuta Linnaeus, 1758 782 648 1.24 599 1.30 870 0.90‖ Gadwall, Anas strepera Linnaeus, 1758 1112 701 1.59 647 1.72 935 1.19 Common Pochard, Aythya ferina (Linnaeus, 1758) 1042 720 1.46 644 1.57 958 1.09‖ Red-crested Pochard, Netta rufina (Pallas, 1773) 1272 1022 1.24 934 1.36 1325 1.03‖ Mallard, Anas platyrhynchos Linnaeus, 1758 1358 1022 1.24 933 1.46 1325 1.03‖

BMR equal to expected from mass (9 species) Eurasian Teal, Anas crecca Linnaeus, 1758 Draft299 265 1.13 251 1.19 381 0.79 Brown Teal, Anas aucklandica (G.R. Gray, 1844) 338 372 0.91‖ 265 1.27 369 0.92‖ Grey Teal, Anas gracilis Buller, 1869 305 389 0.78 277 1.10‖ 543 0.56 Wood Duck, Aix sponsa (Linnaeus, 1758) 403 433 0.93‖ 406 0.99‖ 600 0.67 New Zealand Scaup, Aythya novaeseelandiae (Gmelin, 1789) 419 466 0.90‖ 331 1.27 455 0.92‖ Lesser Scaup, Aythya affinis (Eyton, 1838) 514 525 0.98‖ 489 1.05‖ 716 0.72 Tufted Duck, Aythya fuligula (Linnaeus, 1758) 484 535 0.91‖ 497 0.97‖ 728 0.66 Ring-necked Duck, Aythya collaris (Donovan, 1809) 590 619 0.95‖ 573 1.03‖ 833 0.71 Mute Swan, Cygnus olor (Gmelin, 1789) 5428 5098 1.06‖ 4456 1.22 5851 0.93‖

BMR lower than expected from mass (10 species) Campbell Teal, Anas nesiotis (J.H. Fleming, 1935) 296 370 0.80 264 1.12 367 0.81 Hooded Merganser, Lophodytes cucullatus (Linnaeus, 1758) 351 405 0.87 379 0.92‖ 563 0.62 Chestnut Teal, Anas castanea (Eyton, 1838) 343 462 0.74 328 1.05‖ 451 0.76 Australasian Shoveler, Anas rhynchotis Latham, 1802 399 482 0.83 342 1.17 470 0.85 Brown Teal, Anas chlorotis G.R. Gray, 1845 416 499 0.83 353 1.18 485 0.86 Eurasian Wigeon, Anas penelope Linnaeus, 1758 562 507 0.86 472 1.19 693 0.81 Blue Duck, Hymenolaimus malacorhynchos (Gmelin, 1789) 564 645 0.87 453 1.24 614 0.92‖ Paradise Shelduck, Tadorna variegata (Gmelin, 1789) 600 992 0.60 689 0.87 914 0.66 Common Eider, Somateria mollissima (Linnaeus, 1758) 1110 1311 0.85 1189 0.93‖ 1667 0.66 © The Author(s) or their Institution(s) Canadian Journal of Zoology Page 32 of 42

Greyling Goose, Anser anser (Linnaeus, 1758) 1944 2310 0.84 2064 0.94‖ 2816 0.69

Σ(≤10%) 7 9 11

Note: The sum (Σ) is the number of species having an estimated BMR that is ≤10% of the value expected from the analysis.

*BMR estimated from eq. 3. †M/E = measured BMR/estimated BMR. ‡BMR estimated from eq. 4. §BMR estimated from eq. 5. ‖Estimated BMR ≤ 10% of the measured BMR.

Draft

Table 4. Measured and estimated basal metabolic rates (BMR) of 20 meliphagid honeyeaters.

Estimated BMR (mL O2/h) Measured † ‡ † BMR (mL O2/h) Mass* M/E Multifactorial M/E BMR higher than expected from mass (5 species) Brown Honeyeater, Lichmera indistincta (Vigors and Horsfield, 1827) 38 32 1.19 32 1.19 White-eared Honeyeater, Lichenostomus leucotis (Latham, 1802) 59 54 1.09§ 52 1.13 Smoky Honeyeater, Melipotes fumigatus A.B. Meyer, 1886 126 114 1.11 111 1.14 Yellow-brown Honeyeater, Melidectes rufocrissalis (Reichenow, 1915) 145 124 1.17 119 1.22 Helmeted Friarbird, Philemon buceroides (Swainson, 1838) 294 220 1.34 286 1.03§

BMR equal to expected from mass (8 species) Eastern Spinebill, Acanthorhynchus tenuirostris (Latham, 1802) 30 31 0.97§ 31 0.97§ White-naped Honeyeater, Melithreptus lunatus (Vieillot, 1802) 40 39 1.03§ 38 1.05§ Fuscous Honeyeater, Lichenostomus fuscus (Gould, 1837) 43 41 1.05§ 40 1.08§ Yellow-faced Honeyeater, Lichenostomus chrysops (Latham, 1802)Draft48 45 1.07§ 44 1.09§ Tawny-crowned Honeyeater, Gliciphila melanops (Latham, 1801) 53 51 1.04§ 49 1.08§ Rufous-backed Honeyeater, Ptiloprora guisei (De Vis, 1894) 51 53 0.96§ 54 0.94§ Grey-streaked Honeyeater, Ptiloprora perstriata (De Vis, 1898) 62 62 1.00§ 62 1.00§ Belford’s Honeyeater, Melidectes belfordi (De Vis, 1890) 133 128 1.04§ 123 1.08§

BMR lower than expected from mass (7 species) White-cheeked Honeyeater, Phylidonyris niger (Bechstein, 1811) 40 46 0.84 44 0.91§ New Holland Honeyeater, Phylidonyris novaehollandiae (Latham, 1790) 43 47 0.91§ 46 0.94§ Sooty Honeyeater, Melidectes fuscus (De Vis, 1897) 54 67 0.81 67 0.81 Noisy Miner, Manorina melanocephala (Latham, 1802) 104 118 0.88 109 0.95§ Little Wattlebird, Anthochaera chrysoptera (Latham, 1802) 115 128 0.90§ 117 0.98§ Red Wattlebird, Anthochaera carunculata (Shaw, 1790) 173 197 0.88 175 0.99§ Tui, Prosthemadera novaeseelandiae (Gmelin, 1788) 199 224 0.89 198 1.01§

Σ(≤10%) 11 15

Note: The sum (Σ) is the number of species having an estimated BMR that is ≤10% of the value expected from the analysis.

†M/E = measured BMR/estimated BMR. ‡BMR estimated from eq. 9. §Estimated BMR ≤ 10% of the measured BMR.

Draft

Table 5. Basal metabolic rates (BMR) of phyllostomid bats in relation to food categories.

Number of food categories Least square mean BMR Alternate Food habit categories (mL O2/h) Ten One Two Four Five five Six Nectar–insects 37.2 A A A A Piper 33.8 AB A B B B Fruit–nectar 32.0 B A B Fig 28.5 C C C Vertebrates 27.9 C B C C A Clusiaceae 25.2 CD D Bird blood* 23.7 D D D C D Omnivorous 21.7 DE B E Insects 19.5 EF F D E E Bird–mammal blood* 18.6 F F r2 0.994 0.863 0.978Draft0.989 0.990 0.992 0.923 Σ(≤10%) 0 9 1 4 23 24 0

Note: If the food habit has a different letter, then the food habit has a BMR that is statistically different (ANCOVA) from a BMR of another food habit. If, however, they share a letter, then these food habits have BMRs that are not statistically different. Food habits can be combined into groups that are separated by horizontal lines in the same column. Food habits within a combination are statistically indistinguishable, but they differ from those in another combination in the same column. Statistically different combinations in a column have a different letter. For example, there are two (A and B) distinct combinations in the two food column and four (A, B, C, D) distinct combinations in the four food column. To add these combined food habits to the analysis, they must be statistically different from other combinations as seen in the other columns (i.e., fruit = nectar, therefore, they are combined as fruit–nectar). The sum (Σ) is the number of species having an estimated BMR that is ≤10% of the value expected from the analysis.

*One vampire (hairy-legged vampire bat, Diphylla ecaudata Spix, 1823) appears to feed only on bird blood, whereas the other two vampires (vampire bat, Desmodus rotundus (E. Geoffroy, 1810); white-winged vampire bat, Diaemus youngi (Jentink, 1893)) feed on blood of birds and mammals and this difference correlates with a different BMR (McNab 2003b).

Table 6. Measured and estimated basal metabolic rates (BMR) of 30 phyllostomid bats.

Estimated BMR (mL O2/h) Measured Alternate BMR Five food five food † ‡ † § † (mL O2/h) Mass* M/E categories M/E categories M/E BMR higher than expected from mass (13 species) Pallas’s long-tongued bat, Glossophaga soricina (Pallas, 1766) 21.4 17.8 1.20 22.2 0.96‖ 21.4 1.00‖ Tailed tailless bat, Anoura caudifer (E. Geoffroy, 1818) 28.1 21.0 1.34 29.9 0.94‖ 29.0 0.97‖ Broad-toothed tailless bat, Anoura latidens Handley, 1984 (high altitude)¶ 36.6 23.7 1.54 42.2 0.87 41.2 0.89 Miller’s long-tongued bat, Glossophaga longirostris Miller, 1898 26.5 23.7 1.12 30.3 0.87 29.6 0.90‖ Seba’s short-tailed bat, Carollia perspicillata (Linnaeus, 1758) 29.4 25.3 1.16 32.6 0.90‖ 31.8 0.92‖ Hairy yellow-shouldered bat, Sturnira erythromos (Tschudi, 1844) (high altitude)¶ 39.9 26.4 1.51 42.3 0.94‖ 41.5 0.96‖ Brown fruit-eating bat, Artibeus concolor Peters, 1865 32.9 30.5 1.08‖ 35.1 0.97‖ 33.6 0.98‖ Tilda yellow-shouldered bat, Sturnira tildae de la Torre, 1959 39.9 31.3 1.27 41.0 0.97‖ 40.5 0.99‖ Little yellow-shouldered bat, Sturnira lilium (E. Geoffroy, 1810) 39.2 32.8 1.20 43.1 0.91‖ 42.6 0.92‖ Southern long-nosed bat, Leptonycteris curasoae Miller, 1900 39.3 33.9 1.16 44.6 0.88 44.2 0.89 Fringed fruit-eating bat, Artibeus fimbriatus Gray, 1838 Draft77.9 67.2 1.16 79.9 0.97‖ 87.7 0.99‖ Great fruit-eating bat, Artibeus lituratus (Olfers, 1818) 86.4 71.2 1.23 85.1 1.02‖ 87.7 0.99‖ Big-eared woolly bat, Chrotopterus auritus (Peters, 1856) 101.9 88.4 1.15 107.4 0.95‖ 111.1 0.92‖

BMR equal to expected from mass (6 species) Little yellow-eared bat, Vampyressa pusilla (Wagner, 1843) 18.6 17.8 1.04‖ 19.0 0.98‖ 18.3 1.02‖ Godman’s long-tailed bat, Choeroniscus godmani (Thomas, 1903) 19.9 19.5 1.02‖ 24.6 0.81 23.7 0.84 Tent-making bat, Uroderma bilobatum Peters, 1866 26.6 26.8 0.99‖ 29.5 0.90‖ 29.0 0.92‖ Brazilian big-eyed bat, Chiroderma doriae Thomas, 1891 31.1 30.7 1.01‖ 34.3 0.91‖ 33.8 0.92‖ Greater round-eared bat, Tonatia bidens (Spix, 1823) 39.2 38.1 1.03‖ 433 0.91‖ 43.1 0.91‖ Jamaican fruit-eating bat, Artibeus jamaicensis Leach, 1821 56.5 53.3 1.06‖ 62.2 0.91‖ 62.9 0.90‖

BMR lower than expected from mass (11 species) Leach’s single leaf bat, Monophyllus redmani Leach, 1821 (island)¶ 11.1 17.6 0.63 12.4 0.90‖ 12.0 0.93‖ Dwarf little fruit bat, Rhinophylla pumilio Peters, 1865 (Clusiaceae food)¶ 16.2 18.7 0.87 20.1 0.81 19.4 0.84 California leaf-nosed bat, Macrotus californicus Baird, 1858 14.6 21.5 0.68 15.7 0.93‖ 15.2 0.96‖ Brown flower bat, Erophylla bombifrons (Miller, 1899) (island)¶ 17.7 26.7 0.66 19.4 0.91‖ 19.1 0.93‖ White-lined broad-nosed bat, Platyrrhinus lineatus (E. Geoffroy, 1810) 30.9 33.2 0.93‖ 37.3 0.83 36.9 0.90‖ White-winged vampire bat, Diaemus youngi (bird–mammal blood)¶ 34.0 36.6 0.93‖ 35.8 0.95‖ 36.0 0.94‖ Hairy-legged vampire bat, Diphylla ecaudata (bird blood)¶ 33.9 38.5 0.88 32.8 1.03‖ 35.4 0.98‖ Vampire bat, Desmodus rotundus (bird–mammal blood)¶ 26.8 39.9 0.67 30.5 0.88 31.4 0.85 Pale spear-nosed bat, Phyllostomus discolor Wagner, 1843 34.5 43.6 0.79 37.5 0.92‖ 39.6 0.87 © The Author(s) or their Institution(s) Page 37 of 42 Canadian Journal of Zoology

Lesser spear-nosed bat, Phyllostomus elongatus (E. Geoffroy, 1810) 38.8 45.4 0.85 39.2 0.99‖ 41.4 0.94‖ Greater spear-nosed bat, Phyllostomus hastatus (Pallas, 1767) 70.7 80.1 0.87 73.2 0.97‖ 78.8 0.93‖

Σ(≤10%) 7 9 11

Note: The sum (Σ) is the number of individuals having estimated BMRs that are ≤10% of the value expected from a particular model.

*BMR estimated from eq. 8. †M/E = measured BMR/estimated BMR. ‡BMR estimated from eq. 9. §BMR estimated from eq. 10. ‖Estimated BMR ≤ 10% of the measured BMR ¶Distinctive characteristic. Draft

Figure legends

Fig. 1. a) BMR (mLO1/h) in 34 arvicoline rodents as a function of the mass-estimated BMR from equation (1). b) BMR as a function of multifactorial estimated of BMR derived from equation (2).

Fig. 2. a) BMR (mLO2/h) in 27 anatids having a sedentary or migratory habit and a distribution on island or continents as a function of mass-estimated BMR derived from equation (3). b)

BMR as a function of multifactorial estimates of BMR derived from equation (5).

Fig. 3. a) BMR (mLO2/h) in 20 meliphagidDraft honeyeaters in various climates and altitudes as a function of mass-estimated BMR derived from equation (6). b) BMR as a function of multifactorial estimate of BMR derived from equation (7). Acanthochaera carnuculata (A.c.),

Prosthemadura novaeseelandiae (P.n.), and Philemon buceroides (P.b.) are indicated.

Fig. 4. a) BMR (mLO2/h) in 30 phyllostomid bats with a variety of food habits, at high and low altitudes, and a distribution on islands and continents as a function of mass-estimated BMR derived from equation (8). b) BMR as a function of multifactorial estimated of BMR derived from equation (10).

Draft

Fig. 1

Draft

Fig. 2

Draft

P.b.

P.n.

A.c.

Fig. 3

Draft

Fig. 4