Modeling the Temperature Response of Nitrification
Author(s): John M. Stark
Source: Biogeochemistry, Vol. 35, No. 3, (Dec., 1996), pp. 433-445
Published by: Springer
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Biogeochemistry35: 433-445, 1996.
@ 1996 KluwerAcademicPublishers. Printed in the Netherlands.
Modelingthe temperatureresponseof nitrification
JOHN M. STARK
Departmentof Biology and the Ecology Center,Utah State University,Logan, UT
84322-5305; Telephone:(801) 797-3518; FAX:(801) 797-1575; Email:[email protected]
Received 17 January1996; accepted 17 June 1996
Key words: ammoniumoxidation, growthrate, maintenanceenergy,modeling, nitrification,
soil nitrate,temperature
Abstract. To model nitrificationrates in soils, it is necessaryto have equationsthat accurately
describethe effect of environmentalvariableson nitrificationrates.A varietyof equationshave
been used previouslyto describethe effect of temperatureon ratesof microbialprocesses. It is
not clear which of these best describesthe influenceof temperatureon nitrificationratesin soil.
I comparedfive equationsfor describingthe effects of temperatureon nitrificationin two soils
with very different temperatureoptima from a California oak woodland-annualgrassland.
The most appropriateequation depended on the range of temperaturesbeing evaluated. A
generalizedPoisson density function best describedtemperatureeffects on nitrificationrates
in both soils over the range of 5 to 50 oC; however, the Arrheniusequationbest described
temperatureeffects over the narrowerrange of soil temperaturesthat normally occurs in
the ecosystem (5 to 28 ?C). Temperatureoptima for nitrificationin most of the soils were
greater than even the highest soil temperaturesrecorded at the sites. A model accounting
for increasedmaintenanceenergy requirementsat higher temperaturesdemonstrateshow net
energy production,ratherthan the gross energy productionfrom nitrification,is maximized
duringadaptationby nitrifierpopulationsto soil temperatures.
Introduction
Simulation models are necessary to predict the effects of elevated temperaturesdue to global warming, and elevated substrateconcentrationsdue to
atmosphericdeposition,on nitrificationrates.This informationwill help evaluatethe potentialfor undesirableprocessessuch as NO3 leachingandtrace-N
gas production;however, to accuratelymodel the dynamics of nitrification
in ecosystems, one must first know the nature of the relationshipbetween
environmentalvariablesand nitrificationrates.
The responseof nitrificationto temperaturehas been studiedin soils from
a varietyof geographicregions (Russel et al. 1925; Sabey et al. 1959; Mahendrappaet al. 1966; Myers 1975; Malhi & McGill 1982), and temperature
optimahave been shown to vary with the environment.In all of these studies,
the temperatureresponsewas describedusing line segmentsto connectpoints
representingrates at different temperatures.The temperatureoptimum was
definedas the incubationtemperaturethatresultedin the highest nitrification
rate. For this method,the precision of the estimate dependson the choice of
434
temperaturesfor incubations.For example, a studythatused incubationtemperaturesdistributedat 5 'C intervals(e.g. 25, 30, 35, and 40 'C) would be
unableto distinguishbetween soils with optimaat 33 and 37 'C. In addition,
becausethe estimatesdependon a single point, a single spuriouslyhigh value
could greatly influencethe estimateof the temperatureoptimum.Statistical
methodsarerarelyused to determineif a rateis significantlyhigherthanrates
at higheror lower temperatures.
A more robustmethodfor estimatingtemperatureoptima involves using
nonlinearregressionto fit an appropriateequationto ratedata,and then identifying the optimum based on values predicted from the equation. In this
method, data points from a range of temperaturesare used to estimate the
temperatureoptimum,ratherthana single datapoint or mean. Because softwarepackagesarenow widely availablethathave the capabilityof performing
nonlinearregression,it is no longer necessary to rely on linear transformations, which may produce inaccurateestimates of coefficients (Robinson
1985).
A varietyof mathematicalequationshave been used to describethe effect
of temperatureon microbialprocesses. The effect of temperaturehas been
describedby the Arrheniusequation(Laudelout1978), a double Arrhenius
equation (Moore 1986), a generalized Poisson density function (Partonet
al. 1987), an exponential function (Innis 1978), and "squareroot" model
(McMeekin et al. 1988). It is not clear which of these models are most
appropriatefor describingnitrificationrates in soils.
The objectives of this study were i) to determinethe most appropriate
mathematicalfunctionsfor describingthe effects of temperatureon nitrification rates in soils from a Californiaoak woodland-annualgrasslandand ii)
to determinehow the temperatureoptima of nitrifiercommunitiesrelate to
the distributionof soil temperaturesat this site. Equationswere fit to nitrification rate and temperaturedata determinedin laboratoryassays of soils
collected frombeneathoak canopiesandfrom open grassyinterspaces.Nitrifiercommunitiesin the open grassyareasat this site have temperatureoptima
comparableto nitrifiersfrom tropicalecosystems, whereasthe nitrifiersfrom
beneathoak canopies have temperatureoptima more representativeof nitrifiers from temperateecosystems (Starkand Firestonein press). The nitrifier
communities in the two soil types also differ more than 2-fold in absolute
nitrificationrates.Therefore,the fit of equationsto datafrom these two soils
shouldprovidea good test of the abilityof the equationsto accuratelypredict
the effect of temperatureon nitrificationrates in a varietyof soils.
435
Methodsand materials
The soil samples used to evaluate the effect of temperatureon nitrification
rates were collected from a Californiaoak woodland-annualgrasslandsite
at the SierraFoothill Range Field Station,approximately30 km northeastof
Marysville,CA. The site is at an elevation of 200 m, mean annualprecipitation is 644 mm, and mean annualtemperatureis 16.5 'C. The meanmonthly
minimumof 6.7 'C occurs in Januaryduringthe wet season, while the mean
monthlymaximumof 25.6 'C occursin July duringthe dryseason.The vegetationconsists of scatteredoaks (Quercusdouglassii H.&A. and Q. wislizenii
A.) providingapproximately50% canopy cover and an understoryof annual
grassesandforbs(Bromusspp.,Hordeumhystrix,Avenabarbata,Vulpiaspp.,
and Trifoliumspp.). The soil is an Argonautsilt loam (Mollic Haploxeralf),
with a pH (1:1 soil:water)of 6.4, and total C and N concentrationsof 49 and
3.4 g kg-1, respectively.
Six plots were establishedwithin a 0.5-ha site. Three of the plots were
located beneath the canopies of oak trees, and three plots were located in
open grassy areas between oak trees. Plots of the two cover types were
interspersedover the entire study site. Soil temperaturesbeneath one oak
canopy and in an adjacentinterspacewere monitoredfor 18 monthswith a
21X data-logger(CampbellScientific,Logan, UT). Thermistorswere placed
at the litter - mineral soil interface and at 4-cm and 10-cm soil depths.
Temperaturereadingswere made at 2 min. intervals,and mean values were
recordedevery 2 h.
In March, samples of the 0 to 1 cm and 1 to 9 cm mineral soil layers
were collected from each of the six plots and sieved (<2 mm). The effect
of temperatureon Vmax of nitrifier(ammonium-oxidizer)populationswas
evaluatedusing a nitrificationpotentialassay describedby Hartet al. (1994).
In this assay, soil slurries(10 g dry wt. soil + 100 mL solution) are shaken
for 24 h with a buffersolution containingsufficientNH+ (1 mM) to produce
maximumnitrificationrates (Vmax) and eliminateNO3 assimilation.Nitrate
+ nitriteaccumulationcan then be used as the measureof nitrificationrate.
The weak phosphatebuffer solution used in the slurries was the same as
thatdescribedby Belser & Mays (1980) except thatsodiumchloratewas not
included.This nitrificationpotentialassay was performedat ten temperatures
rangingfrom 5 to 50 oC. Duplicateassays were performedfor each of the 12
soil samples (2 vegetationcover types x 2 soil depths x 3 plots).
Nitrifierpopulationsfrom beneaththe oak canopies were shown to have
lower temperatureoptima (31.8 oC) than populationsfrom open interspaces
(35.9 oC) (StarkandFirestoneinpress). Populationsfromdifferentsoil depths
had similartemperatureoptima;thereforedatafrom the two soil depthswere
combined to obtain a weighted average for the 0 to 9 cm layer, where the
436
thicknessof the soil layer was used for weighting. Separateequationswere
fit to datafor the 0 to 9 cm layer of soils from beneaththe oak canopies and
in open interspaces.
Five differentequationswere fit to the nitrificationrate and temperature
data. The Arrheniusequation (Tinoco et al. 1985) was fit to nitrification
ratesfrom the lowest three incubationtemperatures(5 to 22 oC) to estimate
activationenergy (Ea) (in kJ mole-') and the pre-exponentialfactor (A) (in
mg kg-' d-1):
Vmax = Ae
RT
whereVmax is the rate(mg kg-1 d-1) from the nitrificationpotentialassay,T
is the temperature(oK), and R is the universalgas constant.
A doubleArrheniusmodel (Moore 1986) was fit to nitrificationratesover
the completerangeof incubationtemperatures:
- Ea,
2
-Eat,
=
Vmax
Ale RT - A2e RT
This equationdescribesthe effects of temperatureon two opposingprocesses.
The first of the two Arrheniusequationspredictsthe increase in rate due to
a reducedenergy barrierfor the reaction at higher temperatures,while the
second predicts the decrease in rate due to enzyme denaturationand other
destructiveprocesses thatoccur at highertemperatures.This equationallows
simultaneousestimationof activationenergies for both processes.
The third model fit to the temperatureand rate data was a generalized
Poisson density functionof the form:
Relative
rate=
(b
)exp
(d)
[1-(b-T)d
where T is the temperature(oC), a is the temperatureoptimum (rel. rate =
1), b is the temperaturemaximum (rel. rate = 0), and c and d are shape
parametersfor portionsof the curve to the right and left of the temperature
optimum.The relative rates from this equationwere multipliedby a scalar
(m) to convert relative rates into absolute rates of Vmax (in mg kg-' d-1).
While this equationhas no theoreticalrelationshipto temperatureresponses,
it has a flexible form andallows estimationof the temperatureoptimumusing
data from the full range of temperatures.The equation has also been used
previouslyto model temperatureresponse(e.g. Partonet al. 1987).
The fourthequationwas an exponentialfunction thathas also been used
to model temperatureresponse (Innis 1978; Wight& Skiles 1987):
Vmax
-
e(a+bT+cT2)
437
where T is the temperature(oC) and a, b, and c are empiricallydetermined
coefficients. This exponentialfunction has an advantagein that initial estimates of the coefficients are easily obtainedby taking the naturallogarithm
of both sides of the equationandusing linearregressionto solve the resulting
polynomialequation.
The fifth equationis an empiricalfunction referredto as a "squareroot"
model (McMeekin et al. 1988) because the square root of the rate is proportionalto temperatureup to the optimum. Above the optimum, the rate
decreasesexponentiallywith temperature:
Vmax= a(T - Tmin)(1- eb(T-Tmax))
where T is the temperature(?C), Tminis the minimumtemperature(Vmax =
0), Tmax is the maximumtemperature(Vmax= 0), and a andb are empirically
determinedcoefficients.McMeekinet al. (1988) used this equationto model
the effect of temperatureon growth rates of heterotrophicmicroorganisms,
and Prosser(1990) recommendedthat it be investigatedfor use in modeling
the temperatureresponseof nitrification.
Rate and temperaturedata were fit to the five models by nonlinearleast
squaresanalysis. Sum of squareserrorswere minimized in successive iterations using a Marquardtalgorithmin a routineprovidedby the KaleidaGraph
softwarepackage (Synergy Software, Reading, PA). Different initial values
were used to verify end-pointstability.The fit of the models were compared
using an F-test describedby Beck & Arnold (1977) and recommendedby
Robinson(1985).
Results and discussion
All five of the equationshad significantfits to nitrificationand temperature
datafrom soils of both vegetativecover types (p < 0.05) (Table 1) (Figures 1
and 2). An F-test showed thatthe Poisson functionhad a significantlybetter
fit to datathanthe exponential,double Arrhenius,or squareroot functions(p
< 0.05). The exponentialequationhad a reasonablefit to rates at moderate
temperatures,but tendedto underestimateratesat the lowest temperatureand
overestimateratesat the highest temperature.
Nonlinearregressionusing the double Arrheniusequationsometimesproduced unstableestimatesof model coefficients,primarilywhen the equation
was fit to data from soils beneath oak canopies. This equation produces a
curve thatis stronglyskewed to the right(Figures 1 and2). The portionof the
curve to the right of the temperatureoptimum is so steep that, as the curve
shifts to the left to fit the low temperaturedata, the residualsum of squares
438
15
- Poisson
---- -exponential
root
square
-...... .
sot%
10 -
-
i).
dbl.Arrhenius
-a-s--- dbl.Arrhen.
5-40C
.....Arrhenius
c
s
S
o
,
f.
10
0-
0
10
20
40
30
50
Temperature
(?C)
Figure 1. Fit of models to temperatureresponsedatafor nitrificationratesin soils frombeneath
oak canopies.Datapointsanderrorbarsrepresentmeansandstandarderrors(n = 3) for samples
collected from the 0 to 9 cm soil layer of threeplots in March.
rapidlyapproachesinfinity.Therefore,the rates at high temperaturestend to
have a stronginfluenceon the model coefficients.When the high temperature
data (>41 OC) were excluded, the double Arrheniusequation had a much
439
66Poisson
,------exponential
...... squareroot
.
---- -dbl Arrhen.
5-40
..... Arrhenius
0 )
42?
-
2
-q
Temperature
0
10
20
(C)
30
40
50
Temperature
(0C)
Figure 2. Fit of models to temperatureresponse data for nitrificationrates in soils from open
Datapointsanderrorbarsrepresent
meansandstandard
errors(n = 3) for
grassyinterspaces.
samples collected from the 0 to 9 cm soil layer of three plots in March.
betterfit to the remainingdata. The R2 values for this limited data set were
0.949 and 0.953 for fits to rates from canopy and open sites, respectively,
comparedto R2 values of 0.856 and 0.927 for the fit of the originalequation
to datafor temperatures<41 'C.
Table1. Coefficientsfor various temperatureresponse functions fit to nitrificationrates in soils collected
interspacesin a Californiaoak woodland-annualgrassland.
Poisson function
Arrheniusequation
Open
Double Arrh
Canopy
Canopy
-3.09
0.277
-0.00415
A=4.69 x 10'0 5.12 x 109
52.5
Ea = 54.9
Al = 2.34 x
Ea = 52.9
A2 = 6.49 x
Ea2 = 55.6
0.918
0.875
0.927
0.835
0.861
0.78
0.87
0.97
1.05
1.26
Exponentialfunction
Open
Canopy
Canopy
Open
a = 32.6
b = 59.8
c = 20.1
d = 0.326
m =12.9
35.6
61.4
97.7
0.0625
4.64
a=-1.55
b = 0.269
c = -0.00442
R2 =0.976
0.949
predictedrelativerate':
1.00
1.00
1 Rates predictedby the equationsfor temperaturesthatnormallyoccur in the 0 to 1 cm soil layers beneat
(shown in Figure 3). All values are expressed relative to the rates predictedby the Poisson function.
441
The square root function had a reasonable fit at moderateto high temperatures,but a poor fit at low temperatures(Figures 1 and 2). This was
because the curve to the left of the temperatureoptimumtended to be concave downward,whereasthe ratedatashowed a concave upwardrelationship
with temperature.
When only the three lowest temperatures(<22 'C) were considered,the
simple Arrheniusequationhada significantlybetterfitthanany otherequation
(p < 0.05). This equationhad a reasonablefit to data from temperaturesas
high as 28 'C; however, at temperaturesnear the optimum or higher the
equationhad a poor fit.
Formanymodelingapplications,it maynot be necessaryto use anequation
that predicts the response at temperatureshigher than the optimum. This
is because temperatureoptima may be higher than the temperaturesthat
normallyoccur in the environment.In almost all cases, nitrifierpopulations
in the soils of the oak woodland-annualgrasslandhad temperatureoptima
thatwere higherthaneven the most extreme soil temperatures(Figure3).
While the Poisson equationhadthe best fit over the entirerangeof temperaturesassayed, the Arrheniusequationhad an excellent fit over much of the
temperaturerange thatnormallyoccurs in this soil, and temperatureswhere
the Arrheniusequationhad a poor fit (>28 'C) occurredat a relatively low
frequency (Figure 3). The five equations were used to predict nitrification
rates, given the frequencydistributionof temperaturesin the 0 to 1 cm soil
layers. Ratespredictedby the Arrheniusequationwere within 5%of the rates
predictedby the Poisson equation(Table 1), while rates predictedusing the
other equationswere 8 to 26%higheror lower thanthe Poisson equation.
The observationthat the temperatureoptima for nitrificationare higher
than the maximum soil temperaturesis somewhat surprising,considering
that nitrificationrates would be maximized if the temperatureoptima correspondedto the mean soil temperatureduringthe active period. A lack of
overlapbetweentemperatureoptimaandsoil temperaturesmay occurbecause
the energeticcost of operatingnear the temperatureoptimumis greaterthan
the benefitproducedfrom higherrates. Temperaturesabove the temperature
optimadepressratesby enzyme denaturationand otherdestructiveprocesses
(VanDemark& Batzing 1987). Replacementof these denaturedenzyme systems increasesmaintenanceenergyrequirements.At some pointthe increased
energy productionfrom higher nitrificationrates will be offset by increased
maintenanceenergyrequirements.In fact, it is not high ratesof gross energy
productionthat should be selected for duringadaptationto temperature,but
high rates of net energy production(gross energy productionminus maintenanceenergyrequirement),since net energyproductionrepresentsthe amount
of energy that is availablefor growthand reproduction.Figure 4 shows how
442
open
0-1 cm
a)
open
0
1-9 cm
a
C)
0
0-
a>
a)
E
4J
0C:
C3
canopy
0-1 cm
E0
E
E
a)
cr
canopy
1-9 cm
0
r
10
Soil
20
30
40
50
temperature (oC)
Figure 3. Relative frequencyhistogramsof soil temperatures(2-h means) occurringbetween
Januaryand May, and temperatureresponsecurves for nitrifierpopulationsin the 0 to 1 and 1
to 9 cm soil layers beneathoak canopies and in open grassy interspaces.
443
maintenance
energy
requirement
a) 0.8 -
I
s
ToptforNH4oxid.
I
gross energy
production
I
> 0.6
+a
'
(D 0.4 0.2-
energy available
forgrowth
\
forgrowth
10
20
30
40
Temperature(oC)
Figure 4. Theoreticaleffect of temperatureon maintenanceenergy requirementsand gross
energy producedfrom nitrification.The differencebetween these two curves (indicatedby the
vertical lines and plotted as the dotted curve) representsthe amount of energy available for
growth.The effect of temperatureon nitrificationrateswas modeled by the Poisson equation
using the coefficients determinedfor populationsfrom the 0 to 1 cm soil layer beneathoak
canopies. The effect of temperatureon the maintenanceenergy requirementwas modeled by
the Arrheniusequation.Coefficientsfor the Arrheniusequation(A = 1.3 x 1017mg kg-' d-1,
Ea = 98.7 kJ mole-1) were obtainedusing an optimizationprocedureto maximize the energy
availablefor growthat the temperaturesoccurringin this soil (see Figure 3). In this scenario,
the temperatureoptimumfor nitrificationis 30 C, but the temperatureoptimumfor growth is
20 OC.
differences in the temperatureresponses of nitrificationrates and maintenance energy requirementscould result in maximal growth rates at the soil
temperaturesthatcommonlyoccur.
The nitrifierpopulationfrom the surfaceof open interspaceswas the only
populationthat had temperatureoptima below the maximum soil temperatures encountered(Figure3). This may be because the evolutionarylimit of
temperaturetolerance has alreadybeen reached by the enzymes involved.
The temperatureoptimumof this population(35.9 ?C) is near the maximum
values reportedin the literatureeven for tropicalsoils (35 to 37 ?C) (Myers
1975), while the temperatureoptimumof populationsbeneathoak canopies
(31.8 ?C) is in the middleof the rangeof reportedvalues (20 to 37 ?C) (Malhi
444
& McGill 1982; Haynes 1986). If the maximum temperatureoptimum for
nitrificationis 35 to 37 'C, then soil temperaturesin warmerclimates may
frequentlyexceed the temperatureoptimum.In these cases, the Poisson function would provide more accurateestimates of nitrificationrates than the
simple Arrheniusequation.
Of the models describingtemperatureresponse, the generalizedPoisson
function fit nitrificationrates best over the full range of temperatures(5 to
50 ?C); however, it may not be necessary to model temperatureeffects over
a range this wide. At this site, soil temperaturesfall within a range that can
be adequatelymodeled using the simple Arrheniusfunction (5 to 28 'C).
In fact, for the range of soil temperaturesencounteredat the study site, the
Arrheniusequationmore closely predictednitrificationrates in soil slurries
thandid the Poisson function.However,if one wishes to model growthrates,
nitrificationrates in warmerclimates, or the effects of more drasticchanges
in environmentalconditions such as those that might result from climate
change or habitatdestruction(e.g. eliminationof the oak canopy) where soil
temperaturesreach or exceed temperatureoptima,the Poisson functionmay
providemore reliablepredictionsof temperatureresponses.
Acknowledgments
The authorthanks A. Rudaz for technical assistance and J.M. Norton and
M.K. Firestonefor helpful discussions. This work was supportedby a grant
from USDA-CSRS (No. 92-34214-7326).
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