Production and Respiration in Animal Populations
Author(s): W. F. Humphreys
Source: Journal of Animal Ecology, Vol. 48, No. 2 (Jun., 1979), pp. 427-453
Published by: British Ecological Society
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Journalof AnimalEcology(1979),48, 427453
PRODUCTION AND RESPIRATION IN ANIMAL
POPULATIONS
BYW. F. HUMPHREYS
School of BiologicalSciences, Universityof Bath, ClavertonDown, Bath, BA2 7AY,
Avon,England
SUMMARY
(1) Analysis is made of 235 energy budgets from the literatureto determinethe
relationshipbetweenannualproductionandrespirationin naturalpopulationsof animals.
(2) Homoiothermsseparate into four groups; insectivores,birds, small mammal
communitiesand othermammals.
(3) Poikilothermsseparate into three groups; fish and social insects, non-insect
invertebratesand non-socialinsects.
(4) The invertebrategroupsare separableinto trophiccategoriesand herbivoreshave
the lowestproductionefficiency.
(5) Thereis no relationshipbetweenanimalweightand productionefficiency.
(6) Withinthe groupsderived,specieswith differenthabitats(aquaticand terrestrial)
do not have differentproductionefficiencies.
(7)Thereis no firmevidencethatproductionefficiencyis dependentuponthe magnitude
of production.
(8) Distributionof the data indicatesthat there is no quantumjump in production
efficiencybetweenpoikilothermicand homoiothermicanimals.
(9) Regressionequationsare given for each of the derivedgroups relatingannual
productionto respiration(both as logl0 cal m-2 yr' ) in animalpopulations.
INTRODUCTION
Engelmann(1966)suggestedthat therewas a linearrelationshipbetweenannualproduction and respirationper unit area in animal populations.Additionaldata have been
added to the 'Engelmannline' (Golley 1968; Hughes 1970; McNeill & Lawton 1970;
Shorthouse1971; Leveque1973)but the relationshiphas been analysedseriouslyonly
thrice.
McNeill & Lawton(1970)plotted respirationagainstproduction(both as logl0 kcal
m-2 yr'1) and wereable to separateclearlythe homoiothermsfrom the poikilotherms.
Theysuggestedthatwhensufficientdatawereavailablethe poikilothermswouldbe divisible into threegroups;short lived with low cost resting (overwintering)stages, short
stagesand long lived poikilotherms,and thatthe prolived withhighcost overwintering
ductionefficiencywould decreasein the same order.They showedthat the relationship
for the short lived poikilothermshad a slope (b in y = a + bx) differentfrom 1.0
whetherproductionor respirationwas taken as the dependentvariablebut the slope
for the homoiothermdata did not so differ.
Shorthouse(1971)addeda few additionaldatato thoseconsideredaboveandwas able
to derivepredictiveequationswithnarrowerconfidenceintervalsby separatingthepoikilo0021-8790/79/0600-0427$02.00 ?1979 Blackwell ScientificPublications
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428
Productionand
respirationin animalpopulations
thermsby habitat(aquaticv. terrestrial)ratherthan life cycleduration(for his equations
see Humphreys1978:Table 6).
Grodzifiski& Frenchin Grodzin'ski
& Wunder(1975)analysedthe data availablefor
smallmammalsand separatedinsectivoresfrom rodentsby theirdifferentslopeswhich
wererespectivelygreaterand less than unity.
Almost everyenergybudgethas been derivedfrom a uniqueset of assumptionsand
methods,some of whichlead to detectableerrors(e.g. Kozlowski's(1968)reinterpretation of Birch'sreworking(in Allee et al. 1949)of Lindeman's(1942)CedarBog budget)
while others may lead to undefinablebias (see Humphreys1978).It has been claimed
that these differencesin assumptionsand methodsmay introducesufficientnoise into
energybudgetsto preventthe separationof some of the subdivisionsdiscussedabove
and particularlythe separation of animals by trophic level (Humphreys1978) as
suggestedby Kozlovsky (1968). In addition it has been claimed that the resolution
obtainablefrom energybudgetsmay be insufficientto test hypothesesusingenergetics
methodologies(Humphreys1978)as attemptedby Sutherland(1972).
The numberof energybudgetsnow availableshouldpermitthe analysisof someof the
energyrelationsof animalpopulationsmentionedabove.This hasbecomemoreimportant as the originalequationsderivedby McNeill & Lawton(1970)areincreasinglybeing
used to completeenergybudgetsfrom a knowledgeof eitherproductionor respiration
(Phillipson1971;Mason 1971, 1977;Hughes 1972;Olah 1976).
MATERIALSAND METHODS
I follow the terminologyof Petrusewicz& Macfadyen(1970) to describethe energy
budgetswhereP is net production(thatdue to growth,Pg, and reproduction,Pr) and R
is metabolic heat loss; A = P + R = C
-
FU all in caloric units. Energy budgets for
235 naturalpopulationswereextractedfromthe literature(Appendix).With one exception (Llewellyn1975)energybudgetshaveno varianceestimate;differencesin methodologies and assumptionsused by differentworkerssuchas the arbitraryadjustmentof R,
the inclusionor not of Pr in the estimationof P and the effectsof immigrationshould
resultin energybudgetsthat varywidelyaroundthe truevalue (see McNeill & Lawton
1970; Humphreys1978).No objectivemethod is availableto distinguish'good' from
'bad'energybudgetsso I haveappliedno selectionto the data with the followingexceptions. The data for Pogonomyrmex
badius(Golley & Gentry 1964) were excludedas
they are widelybelievedto be aberrant(set Petal 1978).Budgetspartiallyderivedusing
the equationsfrom McNeill & Lawton (1970) were excludedas were those covering
more than one taxonomiccategory(see below). I have not excludedbudgetscovering
only the larvalstagesof insectsas I did elsewhere(Humphreys1978).
Wherenecessarythe followingconversionfactorswereused: 1 g carbon = 10.94kcal.
1 kJ = 0.2388kcal. Maximumlive weight for a specieswas taken from the original
sourcedirectly,readfromfigures,or convertedfromdry weightassuming75%/waterin
the livinganimal(fleshweightonly in molluscs)or from caloricvalueusingcaloricdata
for the appropriategroupcompiledby Cummins& Wuycheck(1971).
The data wereinitiallygroupedinto 'taxonomic'categorieswhichin some caseswere
welldefined(mice,voles, shrews,fish,socialinsects,orthoptera,hemiptera,molluscaand
crustacea)or, wheredatawereinsufficient,into loose taxonomicgroups(othermammals,
other insectsand othernon-insectinvertebrates).
Data for birdswerepooled from both
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W. F. HUMPHREYS
429
single speciesstudiesand communitystudiesand a separatecategoryerectedfor small
mammalcommunitybudgets.
Statisticaltreatment
As discussedby W. Grodzin'ski& N. R. French(personalcommunication)production
cannot occur in the absenceof respirationwhile the converseis not true; theoretically
thereforeproductionshouldbe treatedas the dependentvariable.In practicerespiration
is calculatedfrom the biomassat differenttimes and ideally as an integralso that the
changeof biomassplus a constantis tracked.Changein biomassis an index of production whichmakesrespirationthe dependentvariablein practice.However,as discussed
elsewhere(McNeill & Lawton1970),both R and P are derivedfrom eithernumbersof
individualsor biomass and are thus not strictlyindependent.I see no alternativeto
presentingthe analysestreatingboth P and R as dependentvariables;this has the added
advantageof permittingpredictionof the other parameterfrom either known P or
known R.
Leastsquaresregressionswerecalculatedfor each of the originalfourteentaxonomic
groupstreatingeitherP or R (log1ocal m-2 yr 1)as the dependentvariable.Regressions
werecompared(see below)with each otherand pooled if not significantlydifferentuntil
the minimumnumberof separategroupswas found. Withinsome of the pooled groups
the data wereanalysedin an attemptto separatefurthertaxonomiccategories(Diptera
from otherinsects,ants fromtermitesand gastropodfrompelecypodmolluscs),trophic
categories(herbivoresfrom carnivoresfrom detritivores),life cycle duration (short
lived, < 2 years,from long lived, > 2 years),and habitat(aquaticfrom terrestrial).
Least squaresregressionswere calculatedfor each group consideredand the lines
comparedusingthe analysisof varianceprocedureof Davies & Goldsmith(1972:Table
7.7). Analyseswereconductedto test fourrelationshipswithinandbetweenthe regression
lines of the form log y = a + b log x. Firstlywhetherx and y werecorrelatedand the
slope(b) of the equationdifferedfromzero.Analysiscontinuedto test whetherthe two (or
more) regressionlines had a similarslope (P > 0.05); if the slopes were statistically
similarthe lines weretestedfor commonintercept(a). If the interceptswere similarthe
lines were pooled otherwisethey were treatedas separategroups. In this mannerall
groupsweretestedagainstall adjacentgroupsbeforepooling.Finallythe individuallines
or the commonslopefor severalpooledgroupsweretestedfor a slopeof 100. Wherethe
slope is 1.00,thereis no relationshipbetweenthe magnitudeof annualR (or P) per unit
area and the productionefficiencyP/(P + R) = P/A.
The estimatesfor P and R containunspecifiedmeasurementerroras well as natural
variability.The groupsof data are typicallynon-normaland open ended.In a lengthy
discussionof varioustypes of linearregressionRicker(1973)recommendsthe use of the
geometricmean estimateof the functionalregressionof y on x (the GM regression),
especiallyif it is desirableto avoid decisionsabout the relativeaccuracyof measuringx
andy. Thisformof regressiongivesthe best estimateof the slopefor predictivepurposes
and Ricker recommendsthe use of ordinarysymmetricalconfidencelimits. For this
reasonI presentfor the derivedgroupsthe functional(GM) regressionsand the more
familiarleastsquarespredictiveequations.Whereit is necessaryto obtainGM regressions
for the common slope of severalgroupsit has been approximatedfrom the weighted
meancorrelationcoefficientfor the groups.
Unless specifiedthe equations given are standardpredictiveregressions.Anyone
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430
Productionandrespirationin animalpopulations
interestedin the slope of the relationshipsfor specificgroupscan calculatethe slope(v)
for the GM regressionfrom the appropriatepredictiveequationsas: v = b/r (Ricker
1973).
The indexP/A was also analysedfromthe individualstudieswithoutconsiderationof
the magnitudeof P or R. Data wereanalysedfor homogeneityof variancesby Bartlett's
test (Sokal & Rohlf 1969).Analysisof variancewas conductedand the meanstested by
the Student-Newman-Keuls
a posterioritest for unequalsamplesizes (Sokal & Rohlf
1969).
RESULTS
Variance
Regressionsfor the originalfourteentaxonomicgroupshave significantheterogeneity
in the residualvariances(P < 0.005). This heterogeneityremainsafter exclusion of
severalof the more extremevariancesand cannotbe removedby transformationof the
data. I follow McNeill & Lawton (1970) in the belief that the empiricalrelationship
betweenP and R is of sufficientinterestto use standardregressiontechniquesin its
analysis.My use of analysisof varianceis to obtain objectivesubdivisionsof the data
available:while I retainthe usual criterionof significanceat the 5%.probabilitylevel,
any tests givingprobabilitiesclose to the 5%?level may be viewedwith caution.While
moderateheterogeneityof variancesis not seriousfor overalltests of significance,single
degreeof freedomcomparisonsmay be seriouslyin error(Sokal & Rohlf 1969).
Productionas the dependentvariable
Regressionstatisticsfor the originalfourteen'taxonomic'categoriesare presentedin
Table 1. All the relationshipsare significant(P < 0-003)and none of the slopes differ
significantlyfrom the others; these lines have a common slope of 0.961 (?0.021 S.E.)
which does not differfrom a slope of 1.0 (ts233= 1.857, 0.1 > P > 0.05). Sequential
comparisonof the interceptspermittedpooling of severalgroups leaving 7 separate
regressionlines(Table2); summaryanalysesof variancefor some of the moreinteresting
comparisonsare givenin Table3. Withinthe pooledgroupsnone of the regressionlines
differsfrom any other with whichit has been pooled and the pooled groupsare clearly
separatedwithone exception;the interceptsfor the insectivorelinediffersfromthatof the
birds(P = 0.0001)but the smallmammalcommunityline does not differfromthose for
the birdsor the insectivores.Poolingthe insectivoredatawiththosefor the smallmammal
communitiesresultsin a regressionnot significantlydifferentfrom that for the birds
(Table3). Hencethese threelines are kept separate(Fig. 1).
The common slope of the GM regressionfor the seven derivedgroups(v = 1.026)
does not differfrom 1.0. Re-analysisfor commonslope, havingexcludedall budgetsfor
more than one species, gives a common slope not differentfrom 1.0 (v = 1.000;
Table2). Analysisfor commonslopebetweengroupsfor the homoiothermsandpoikilothermsseparatelyshowsneitherdiffersfrom unity (v = 1.085and 0.984 respectively).
Furthertaxonomiccategoriescould not be separatedfrom the seven derivedgroups
(Table 3). None of the following could be separated;rodents from non-insectivore
mammals,dipterafrom any non-socialinsect group,ants from termitesnor gastropod
frompelecypodmollusca.Howeversplittingthe non-socialinvertebrates
into arthropods
and non-arthropodsgave significantseparationbut with generallywider confidence
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TABLE
1. Regression statistics relating annual production (log10 P cal m-2 yr-') to respiration (lo
Community studies for birds and small mammals are includ
Group
Correlation
Regression equation coefficient N
Mean
R
Mean
P
P = 0-608R - 0-684
6
3-151
1. Insectivores
0.958
1-052
P = 0-854R - 0-946
0-920
22
1-524
2-893
2. Mice
20
3.801
2-233
P = 1-078R - 1-866
0.923
3. Voles
P = 0-911R - 1-190
14
3.724
2.202
0*963
4. Other mammals
P = 1-139R - 2-399
0.840
8
1.997
3.859
5. Small mammal communities
P = 0.734R - 0-830
0.929
9
2.105
4.000
6. Birds
0.965
P = 0.834R - 0-249
9
4-337
3-370
7. Fish
P = 1.002R - 1-048
0.858
13
3.241
2.198
8. Social insects
0.919
P = 0.859R + 0.337
22
3.286
3.432
9. Orthoptera
P = 1-015R - 0.188
0.967
14
2-980
2.838
10. Hemiptera
P = 0-961R - 0.006
0.977
25
3.827
3.673
11. All other insects
P = 1-033R - 0-717
0.860
45
4-832
4.272
12. Mollusca
P = 0-946R - 0-231
0.959
9
4.608
4.130
13. Crustacea
P = 1.018R - 0.483
0.911
19
3.703
3-286
14. All other non-insect invertebrates
Non-insect invertebrates:
P = 0-979R - 0-407
0.902
11
3-323
2-847
15. Carnivores
0-907
22
4-298
P = 1-069R - 0-601
4-583
16. Detritivores
16
4.617
3-982
17. Herbivores
P = 0-971R - 0-500
0*943
Arthropods:
P = 0-970R - 0-060
0.971
62
3.480
3.316
18. Short lived (<2 yrs)
P = 1.206R - 0-224
0.889
12
3-120
3.539
19. Long lived (>2 yrs)
Common slope (? standarderror): Groups 1-14 b = 0-961 ? 0.021 N = 235 tsj.o = 1.857 NS v = 1.0
15-17 b = 1-013 ? 0-057 N = 49 tsj.0 = 0.228 NS
18-19 b = 0-987 ? 0-035 N = 74 ts1.o = 0*371NS
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TABLE2. Seven different predictive regression equations relating annual respiration (loglo R ca
in animal populations. The GM regression which better estimates the slope is given b
the predictive regressions
m-2 yr')
Group
Insectivores
Birds
Small mammalcommunities
All other mammals
Fish and social insects
Non-insect invertebrates
Non-social insects
Mean
R
Mean
Standa
P
intercept
Regression equation
N
P = 0-608R - 0-864
P = 0-636R - 0.952
P = 0-734R - 0.830
P-0790R - 1.055
P = 1*139R - 2.399
P = 1356R - 3-236
P = 0-885R - 1.084
P = 0-938R - 1.259
P = 0-912R - 0-749
P = 1.042R - 1.234
P = 0-974R - 0.394
P = 1-068R - 0-820
P = 0-969R - 0.037
P = 10OR -0.144
6
As in
9
As in
8
As in
56
3.447
1.967
0.289
22
3.742
2.646
0.470
73
4.511
3-998
0.397
61
3.456
3-312
0.288
Common slope for above groups: b = 0-942 ? 0.0209 N = 234 ts.o
Common slope for non-community studies*: b = 0.952 + 0.0208 N
=
=
2-758 P < 0.01
210 ts1.0 = 2.28
* Excludes birds, small mammal communities and other budgets pooled for more than on
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TABLE 3. Synopses of analyses of variance testing for common slopes and intercepts for s
annual respiration (log1o R cal m-2 yrT-) to production (log10 P cal m2 yr-) i
Group
Homoiotherms v. poikilotherms
Insectivoresv. birds
Insectivoresv. small mammal communities
Birds v. non-insectivoremammals
Rodents v. other non-insectivoremammals
Fish v. social insects
Diptera v. Orthopterav. Hemiptera v. all
other non-social insects
Non-social arthropods v. non-arthropod
Test for parallel lines
F
P
d.f.
1.5
0.215
1,232
0*8
0.397
1,11
0.131
1,10
2-7
0-4
0.546
1,64
0.288
1.2
1,55
0-4
0.560
1,17
1.1
0.361
3,54
Test for common
F
d.f.
427.7
1,233
32.1
1,12
2.7
1,11
12.1
1,65
0.01
1,56
1,18
0-3
0.1
3,57
0.01
1,131
0.908
10-7
1,132
0.0
1,131
0.946
23.5
1,132
0.2
0.2
2,43
2,56
0.799
0.823
3-5
2-4
2,45
2,58
0-04
3.2
0.2
1,18
1,70
1,58
0.842
0.079
0.660
1-3
6.1
0.1
1,19
1,71
1,59
0
0
0.6
1,58
1,44
1,130
0.984
0.982
0.461
0.01
0.7
2-4
1,59
1,45
1,131
invertebrates
Non-social insects v. non-insect invertebrates
Herbivoresv. carnivoresv. detritivores:
non-insect invertebrates
non-social insects
Short v. long lived:
non-insect invertebrates
non-social insects
Insect larvae v. all stages
Aquatic v. terrestrial:
non-social insects
non-insect invertebrates
all invertebrates
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Productionandrespirationin animalpopulations
434
0
6
6 -
7
V
0
X_
+Ov/
~~~~~~v
00
~~
4
~~~~~~~~~~~0
N
0
0
4
C
o-E24-
51y
u
X
A
10
+
4
10
V/
x
2
o
?~
(Am
L
40
*
xu
*
EU
U
2
0
40
~
~~~
Respiration(logl0 cal m-2y'1)
FIG.1. The relationshipbetweenrespirationand production (both as log10cal m-2 yr'1)
in naturalpopulations of animals.The regressionlines, not adjustedfor common slope, of
the seven derivedgroups (Table 2) are shown. The points for Perognathuspenicillatis and
P. baileyi(Appendix)are not plotted. The lines are numbered1 = insectivores,2 = small
mammal communities, 3 = birds,4 = other mammals, 5 = fish and social insects, 6 =
non-insectinvertebratesand 7 non-social insects. The symbols denote: O insectivores,
I small mammal communities, * other mammals, * birds, + fish, x social insects, 0
molluscs, 0 Crustacea,j other non-insect invertebrates,A Orthoptera,* Hemiptera,
V other non-social insects.
intervals than the separation into non-social insects and non-insect invertebrates (95%/
confidence intervals of P at R = 1 and R = 6 respectively: non-social insects, + 0-596
and ? 0.597; non-insect invertebrates, +0.871 and + 0.806; arthropods, ? 0.694 and
+ 0.693; non-arthropodinvertebrates,+1.073 and + 0.861). The former division is
thereforeretained.
Habitat
andboth groupspooledcould
Data for the non-socialinsects,non-insectinvertebrates
not be separatedaccordingto habitattype (aquaticv. terrestrial)and all gavecommon
lines (Table3).
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W. F. HUMPHRES
435
Life stage
Studiesconductedon the larvalstagesonly of the non-socialinsectswouldbe expected
to have higherP/A than those studiescoveringall life stages.Separationof the data by
these criteriaresultedin commonregressionlines (Table3).
Durationof life cycle
Insufficientdataarepresentto separatethe non-socialinsectsinto long and short lived
species.No separationwas possible (commonintercept;P = 0.273) betweenthe long
lived (> 2 y) and short lived (< 2 y) invertebrates(excludingsocial insects).However,
arthropodsare divisibleinto shortand long lived speciesgivingparallel(P = 0.079)but
separate(P = 0.016)lines (Table3).
Trophictype
The non-insectinvertebratescould be separatedinto three trophic types; when the
interceptswere calculatedfrom the common slope for the three groups(b = 1.013 +
0.0572) the efficiencyP/A is greatestfor detritivores(a = -0.346), intermediatefor
carnivores (a = -0.521) and least for herbivores (a = -0-696). The non-social insects
had commonslopeswith a marginallevel of probabilityfor the intercepts(P = 0.102);
againherbivoreshad the lowestefficiencyP/A but carnivoreswereintermediate.
Respirationas the dependentvariable
Regressionstatisticsfor the originalfourteentaxonomicgroupsarepresentedin Table
4. All the relationshipsare significant(P < 0-003)but the slopesare not common(P =
0.012).Removalof the datafor insectivoresandmolluscsyieldsparallellines(P = 0-130)
with a commonslope of v = 0.997 + 0.019whichdoes not differfrom 1.0.
Analysisof the linesas beforeyieldsthe samesevengroups(Table5) previouslyderived
but with non-parallellines (P = 0.044). Exclusionof the insectivoredata yieldsparallel
lines (P = 0.061) with a common slope (v = 1-012)not differentfrom unity. Further
analysisconfirmsthe taxonomicdivisionspreviouslyfound as well as those for life cycle
duration,habitatand trophictype. Non-insectinvertebratesagain separateinto carnivores, detritivoresand herbivoreswith P/A decreasingin that order.Trophicseparation
TABLE4. Regressionstatisticsrelatingannualrespiration(logio R cal m2 yr-1)
to production(logio P cal m-2 yr 1) in animalpopulations.Communitystudies
for birdsand small mammalsare included
of
Standarderror
Significance
slopefrom1.0
Regressionequation N intercept slope
Group
6
0.201
0.225
R = 1.510P+ 1.563
NS
1. Insectivores
0.348
0.088
NS
R = 0-992P+ 1.392 24
2. Mice
0-193 0.076
<0-02
R = 0-789P+ 2.039 21
3. Voles
NS
0083
R = 1-018P+ 1*483 14 0.332
4. Othermammals
NS
8
0.275
0.163
R = 0.619P+ 2.623
5. Smallmammal
communities
0.156
0.177
9
NS
R = 1-178P+ 1.521
6. Birds
NS
0.114
0.227
R = 1-117P+ 0*574 9
7. Fish
NS
0.189
R = 0.694P+ 1.816 13 0.534
8. Socialinsects
NS
0*246 0.092
R = 0.982P+ 0.203 23
9. Orthoptera
0.070
NS
R = 0*922P+ 0*365 14 0.405
10. Hemiptera
NS
0.046
0.263
R = 0.993P+ 0.179 24
11. All otherinsects
<0.001
0-326 0.065
R = 0.716P+ 1.775 45
12. Mollusca
9
0.259
0.110
NS
R = 0-969P+ 0.607
13. Crustacea
0.086
<0.05
R = 0 812P+ 1.041 19 0.414
14. Othernon-insect
invertebrates
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Productionandrespirationin animalpopulations
436
TABLE 5. Predictive regression equations relating annual production (log1o P cal
m2 yr'1) to respiration (logloRcalMr2yr-')
in animal populations. GM
regressions, which better estimate the slope, are given below each predictive
equation; statistics relate to the latter
Group
1. Insectivores
Significanceof
slope from 1.0
N
R = 1.510P + 1.572
6
0.200
0.2251
NS
R = 1.176P + 1-524
9
0.156
0.1766
NS
8
0.275
0.1635
NS
56
0.308
0.0465
NS
22
0.450
0.1015
NS
73
0.369
0.0446 0.01 > P > 0.001
61
0.287
0.0322
R = 1.576P + 1.493
2. Birds
standarderror
intercept slope
Regression equation
R = 1.266P + 1.335
3. Small mammal
communities
4. All other mammals
R = 0.619P + 2.623
R = 0-737P + 2.387
R = 1-007P + 1.466
R = 1.067P + 1.349
5. Fish and social insects
6. Non-insect invertebrates
R = 0-839P + 1.504
R = 0-959P + 1.187
R = 0.856P + 1.088
R = 0-937P + 0-767
R = 0-963P + 0.271
7. Non-social insects
NS
R = 0.994P + 0-169
Common slope for groups 2-7: b = 0.923 ? 0.018, v = 1.007
Common slope for groups 4-7: b = 0.932 ? 0.018, v = 0.999
TABLE 6. Regression equations relating annual population respiration (log1o R
calm-2yr-1) to production (logloPcalMr2yr'1)
for all significant groups
calculated from the common slopes for P (b = 0.942 ? 0.021) and R (b =
0.923 ? 0.018) as dependent variables. The intercepts for a slope of 1.0 are given
in parentheses. Slopes (v) for GM regressions, approximated from weighted mean
correlation coefficient, are 1*013R and 0.992P
Group
Regression equations
Insectivores
P = 0.942R
-
1.917 (-2.151)
R = 0.923P + 2.180 (2.099)
Birds
P =
P=
P =
P =
-
1.664
1.639
1.281
0.863
R =
R =
R =
R =
Small mammal communities
Other mammals
Fish and social insects
Non-insect invertebrates
Non-social insects
Non-insect invertebrates:
Herbivores
Carnivores
Detritivores
0.942R
0.942R
0-942R
0.942R
-
(-1.895)
(-1.864)
(- 1.480)
(-1.078)
0.923P
0.923P
0.923P
0.923P
+
+
+
+
2.057
2.016
1.632
1-282
(1.895)
(1.864)
(1.480)
(1.078)
P = 0.942R - 0.252 (-0.513)
P = 0.942R + 0.056 (-0.435)
R = 0.923P + 0.821 (0.513)
R = 0.923P + 0.399 (0.144)
P = 0.942R - 0*366(-0.635)
P = 0.942R - 0.283 (-0.476)
P = 0.942R - 0.019 (-0.285)
R = 0*923P + 0.941 (0.635)
R = 0923P + 0.695 (0.476)
R = 0.923P + 0.626 (0.285)
of the non-social insects is again marginal (P = 0.058) with the same rank order of
efficiencyfound previouslywhen the interceptwas calculatedfrom the common slope
for the threegroups.
Regressionequationsfor the derivedgroupsarepresentedin Table6 for both P and R
as the dependentvariable;interceptsaregivenfor a slopeof 1.0as wellas thosecalculated
from the commonslope.
Productionefficiencyand the magnitudeof P or R
We are concerned here with the slope of the regression lines; as both variables are
taken as logarithms (simple allometry relationship) then a slope of unity shows that the
magnitudeof P or R has no effect on productionefficiency(P/(P + R) = P/A). By
attemptingto groupthe data I am looking for law-likerelationshipsbetweenP and R
where both are subject to error and have random variability (functional relationships
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W. F. HUMPHREYS
437
sensuSprent1969).No independentestimateof the varianceof P and R is availablein
energybudgetsso no maximumlikelihoodestimateof the slopeis possible(Sprent1969).
However,the rangeof the slopefor R can be calculated;it lies betweenthe slopesfor R
as the independentvariableand as the dependentvariable(in the latter case derived
from reciprocalslope P). The rangefor slope P can be derivedin a similarmanner.
Takingthe specificcase of the common slopes in Table 6 the slope rangesbetween
0.942R-1.083R(i.e. 1/0.923)or 0.923P-1.062P(i.e. 1/0-942)with mean slopes of 1.013
and 0.993 respectively.In generalbecausethe slopesare less than 1-0whetherR or P is
treatedas the dependentvariablethe rangeof slope in each case includes1.0.
Themost appropriateestimateof the slopefor dataof this typeis v of the GM regression. In each case v is close to 1.0; while exactconfidenceintervalsare unavailablefor v
calculatedfrom the commonslope, they would have to departwidelyfrom those for b
in the predictiveequationsto show significantdepartureof the slopesfrom unity.
In neitherof the above treatmentsis there any evidencethat the slope departsfrom
unity; the magnitudeof P or R has no effecton productionefficiency.
Productionefficiencyand weight
Regressionof maximumlive weight(logl0, g) of the animalsagainsttheirproduction
efficiencygave the followinglevels of significance(N): insectivores,P = 0.144(6);other
mammals, P = 0.462(52); fish, P = 0.290(7); non-social insects, P = 0-118(52); non-
P = 0.490(31).No significantrelationshipexistsbetweenthese two
insectinvertebrates,
variables.
Productionefficiency
The meanproductionefficiency(P/A) is shownfor variousgroupsin Table7 irrespective of the absolutemagnitudeof P and R. The seven derivedgroupshave significant
heterogeneityas do the trophicgroupswithinthe non-insectinvertebrates.
Therankorder
of productionefficiencybetweenthe trophicclassesfor the non-insectinvertebratesand
the non-socialinsects is the same as in the previousanalyses.However,the between
trophicclassvariancesarehomogeneousfor the non-socialinsectsandthe herbivoresare
clearlyseparatedfrom the carnivores(SNK: P < 0.05) but not from the detritivores;
herbivoreshave the lowest productionefficiency.
DISCUSSION
This analysisconsiderablyextendspreviousanalysesof the relationshipbetweenannual
populationproductionand respirationin animalpopulations(McNeill& Lawton1970;
Shorthouse1971;Grodzin'ski
& Frenchin Grodzin'ski& Wunder1975).Homoiotherms
separatefrom poikilotherms(McNeill & Lawton 1970)but clearseparationis possible
withinthese two groups.
Homoiothermsseparate into three (insectivores,birds and other mammals)and
possiblyfour (smallmammalcommunities)groups.Grodzifisky& Frenchin Grodzinski
& Wunder(1975),takingP as the dependentvariable,showedthat the slopesfor insectivores and rodents were different.I was unable to separaterodents from other noninsectivoremammals;when the lattertwo groupswere pooled the slope did not differ
wheny = P but did so differwheny = R. Althoughinsectivoreswere includedin the
small mammalcommunitybudgets,in only 2 (Hansson 1971) of the 8 budgetswere
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Productionandrespirationin animalpopulations
438
7. Mean production efficiency (P/A) ranked in order of increasing
efficiency. Statistics were calculated using arcsine Vx transformation and have
been reconverted for this table. Vertical lines next to the trophic types include
statistically common groups using Student-Newman-Keuls 'a posteriori test for
unequal sample sizes
TABLE
Group
P/A %
0.86
1.29
1.51
Standard
error
N
Coefficientof
variation
1. Insectivores
0.109
6
35.6
9
0.030
15.3
2. Birds
0.126
8
3. Small mammal
28.8
communities
3.14
0-278
56
4. Other mammals
29.6
9-77
0.890
5. Fish and social insects
22
29.7
6. Non-insect invertebrates 25.0
3-671
73
36.8
7. Non-social insects
40.7
2-036
61
20.7
Non-insect invertebrates:
j 20.8
1-38
15
8. Herbivores
24.9
5.09
9. Carnivores
11
41.2
l 27-6
4.82
1 36.2
10. Detritivores
23
34.3
Non-social insects:
11. Herbivores
1-93
49
| 38.8
20*7
12. Detritivores
1.64
6
| 47.0
17.0
I 55*6
13. Carnivores
0*64
5
9.5
Groups 1-7: Homogeneity x2 = 127.48 P < 0.005; ANOVA, F = 97.83,
P < 0-001. Groups 8-10; Homogeneity x2 6*315,0.05 > P > 0.025;
ANOVA, F = 3.541, 0.05 > P > 0-025. Groups 11-13: Homogeneity x2 =
1.608; 0-5 > P > 0.1; ANOVA, F = 4.230, 0-025 > P > 0.01. Groups 1, 3
and 4: HomogeneityX2 = 1.212, 0-9 > P > 0-5. Group 1 = 3, 1 # 4, 3 # 4
(SNK P < 0-05).
sufficient insectivores present to affect markedly the community P/A ratio. Comparison
of the methodologies used to derive community and single species budgets is beyond the
scope of this paper but separation of community from single species budgets in mammals
does raise questions as to the validity of the bird line which is based mainly (7 of 9
budgets) on community studies.
Poikilotherms separation clearly into three groups (fish and social insects, non-insect
invertebrates and non-social insects). The latter two groups could also be separated into
arthropod and non-arthropod species but the resulting regressions had wider confidence
intervals so I have retained the former division.
The arthropods but not the invertebrates (both excluding social insects) could be
separated into long and short lived species and the latter had the lower production
efficiencies. This separation is mainly due to the long lived arthropods belonging to the
non-insect invertebrate group which have already been separated from the non-social
insects. However, many of the former group are molluscs which probably have long life
cycles but have been excluded from the analysis as insufficient information is available
in the sources. The separation of the non-insect invertebratesfrom the non-social insects
may be due to the difference in average life cycle within the groups; but this is probably
not the case as two other groups (crustacea and general invertebrates), despite both
containing mainly short lived species, are not separable from the molluscs. While
accepting McNeill & Lawton's (1970) arguments concerning the effects of longevity and
cost of overwintering stages on production efficiency it would appear that the resolution
of the budgets is insufficient to distinguish the effects. The separation of insects from
other invetrebrates appears to be real and not a function of trophic type, longevity or
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439
W. F. HUMPHRBYS
habitat.Insectsare not the 'particularlypoor converters'suggestedby Calow(1977),at
least in naturalpopulations.
Shorthouse(1971)separatedaquaticfrom terrestrialpoikilotherms;I was unableto
separateany of the invertebrategroupings(excludingsocialinsects)accordingto habitat.
This again indicatesthe low resolutionof energybudgetsas terrestrialinsects(mainly
orthopteraand hemiptera)tend to have low cost resting stages (eggs) while aquatic
stages(larvae).In thistheycontrastwiththe
speciestendtowardshighcost overwintering
non-insectinvertebrateswhich mostlyfall into one groupwith high cost overwintering
stages(mollusca,crustaceaand arachnids)and are longerlived.
I presentthe groupsonly as the best availabledivisionfor predictivepurposes;when
moredata are availablesome of my groupingsmay be shownto resultfromthe distribution of datapresentlyavailableand it may be possibleto moreclearlydescribethe effects
of habitat,longevity,trophictype and taxa on the relationshipbetweenP and R.
WitheitherP or R as the dependentvariablethe non-insectinvertebratesseparateinto
trophic categories(detritivores,herbivoresand carnivores:for y = P, P = 0.038; for
y = R, P = 0.022)withthe maincontributionto the separationbeingbetweenherbivores
and detritivores(P = 0.006). The same comparisonfor the non-social insects gave
marginal significance in each case (for y = P, P = 0.102; for y = R, P = 0.058). When
the interceptswerecalculatedfor the commonslopewithineachanalysisherbivoreshad,
in eachcase,the lowestproductionefficiency(P/A) andcarnivoresthe greatestin threeof
four analyses.Whentrophiccomparisonsweremadedirectlyfrom P/A withoutregard
to the magnitudeof P or R (Table7) rathersimilarresultswere obtained;howeverthe
analysiswas strengthenedfor the non-socialinsects which gave significantseparation
while having homogeneousvariancesbetween trophic groups. These results do not
supportthe contentionthat detritivoreshavelow P/A becauseof theirpoor qualityfood
(Macfadyen1967),that P/A is inverselyrelatedto trophiclevel (Kozlowski1968)or that
high conversionefficiencyis associatedwith herbivory(Calow 1977).
Whileit has been possibleto separateobjectivelya numberof groupswith differing
productionefficienciesthere is no longer the clear separationof homoiothermsand
poikilothermdata (Fig. 1) seen in McNeill & Lawton(1970: Fig. 1). The production
efficienciesof animalpopulationsform a continuumand there has been no quantum
jump betweenpoikilothermsandhomoiothermsin the evolutionof productionefficiency.
Any departureof the slopeof the regressionequationsfromunitywouldimplythatthe
magnitudeof P or R affectsthe productionefficiency;if this werethe case some cogent
theory would be neededto accountfor the effect. The common slope for the original
fourteentaxonomicgroups (y = P) does not differfrom unity nor does that for the
twelveparallellineswheny = R. In contrastto McNeilland Lawton(1970)who found
the slopefor the shortlivedpoikilothermsbut not the homoiothermshada slopediffering
from 1.0,I findthe reverseto be the case. Usingthe moreappropriateGM regressionsit
is clearthat the slopes do not differfrom unity; when many speciesare consideredthe
magnitudeof P or R does not influenceproductionefficiency.Intraspecificeffectsare
consideredlater.
McNeill & Lawton(1970)suggestedtwo reasonsfor the departureof theirregression
fromunityfor shortlivedpoikilotherms;animalsfor somereasonlimitedto low productivity may compensateby having maximumproductionefficiency,or the slope may
reflectthe distributionwithintheiranalysisof datafromspeciesof differinglongevityand
overwinteringcosts. SeveralfactorsmayinfluenceP/A: the energeticcost of competition
may increaseat high intraspecificproductivitylevelswherespeciesnumbersare reduced
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440
Productionandrespirationin animalpopulations
and competitiontends to be intraspecificand should be most intense;converselyP/A
may be reducedin rare species (low density and low productivity)by the energetic
requirementsof findingresources.Suchhypothesisare relativeto the speciesconcerned.
If productivityinfluencesP/A then differentspecies should be affectedover different
rangesof P or'Rdependingon theirnormalvaluesfor populationdensityor productivity.
The sumeffectson the regressionlineswouldnot be expectedto causethe slopeto depart
from unity.
The sizeclassstructureof a populationhasan identifiableeffecton P/A; younganimals
tend to havegreaterP/A than old ones (Calow1977)so that growingpopulationswith a
high proportionof youngindividualshave greaterP/A than stableor decliningpopulations. While this should not cause a departureof the regressionfrom unity, at least
within one metabolicclass of animals,it may explainthe separationof the non-social
insectsfromthe non-insectinvertebrates.
Theformertend to haveindividualsdeveloping
rapidlyfrom eggs within one or two seasonsand short reproductivelife which should
give high P/A; most non-insectinvertebratesdo not have this phenologyand would
have lowerP/A.
The firmestevidenceI have showsthat the slopes of the regressionequationsdo not
depart from unity; until a body of theory is developedand firm empiricalevidence
obtainedto suggestotherwise,I recommendthe use of a slopeof 1.0for all the predictive
equationsin Table6.
It has beensuggestedthat P/A is greaterin highdensitypopulations(highproduction)
(Bobek 1969;W. Grodzin'sky& N. R. Frenchpersonalcommunication).Examination
of the trendin the relationshipbetweenP/A andP in speciesfor whichthereareavailable
more than two energybudgetsdoes not supportthis contention.Five of sevenhomoiothermicspeciesshow no trend in the relationshipwhile six of eleven poikilothermic
specieshave a directrelationshipand threehave no trendin the relationship.
None of the five taxa consideredshoweda significantrelationshipbetweenadult live
weightand productionefficiency.The increasedefficiencyof resourceutilizationsuggested (Cody 1966)for more K-selectedand hence larger(Southwood1976)speciesis
not achievedthrough changes in productionefficiency(or P/C; unpublished)within
the groupsI considered.In additionthe field data do not supportFenchel's(1974)view
that R/A is directlyrelatedto body size.
Despite the largerdata base used here the confidenceintervalswithinany regression
line do not improveon those of McNeill & Lawton(1970)and in some cases they are
wider.Neverthelessthe predictivepower of the regressionsis improvedby therebeing
morespecificmetabolicgroupsfromwhichto choose.Whilethe failureto improveon the
confidenceintervalspartlyreflectsmy lackof dataselectiontheyarea realmeasureof the
innatevariabilityof energybudgetsand of the varianceintroducedby differingmethodologiesandassumptions.Methodologicaldifferencesmaygiveat leasta twofoldvariation
in the estimateof R (Humphreys1978);this would give 1.59-1.77and 1.764184 fold
variation in P/A for non-social insects and non-insect invertebratesat production
efficienciesin Table 7. This variationcompareswith 2.7 and 3.2 fold variationin P/A
within the 95%/confidenceintervalsin Table 6 for non-socialinsects and non-insect
invertebratesrespectively.These methodologicaldifferencespreventany true measure
of withingroupplasticityof P/A in animalpopulations.The contentionthat the noise
introducedinto energybudgetsby methodologicaldifferencesmay preventseparation
of manygroups(Humphreys1978)is clearlyincorrect.However,the resolutionis low and
some subdivisionsthat would be expectedcannotbe found.
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W. F. HUMPHREYS
441
ACKNOWLEDGMENTS
I am gratefulfor the considerableassistancegiven me by the Bath UniversityLibrary
staffin obtaininga largeamountof loan material.A. J. Collinsand P. K. Nandi of the
Departmentof Mathematicsdiscussedwith me variousstatisticalproceduresbut I am
responsiblefor the use made of them. D. Clark obtainedfor me various computer
andN. R. Frenchkindlysentme an unpublishedmanuscript.
softwareandW. Grodzin'ski
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