Directory UMM :Data Elmu:jurnal:A:Agricultural Systems:Vol65.Issue1.Jul2000:
Agricultural Systems 65 (2000) 29±41
www.elsevier.com/locate/agsy
Comparing genetic coecient estimation
methods using the CERES-Maize model
E. RomaÂn-Paoli a,*, S.M. Welch b, R.L. Vanderlip b
a
Agricultural Experiment Station, University of Puerto Rico, Lajas, PR 00667, Puerto Rico
b
Department of Agronomy, Kansas State University, Manhattan, KS 66502, USA
Received 13 July 1999; received in revised form 25 May 2000; accepted 3 June 2000
Abstract
Many crop simulation models use genetic coecients to characterize varieties or hybrids.
Two methods now used with CERES-Maize to obtain genetic coecients are: (1) direct
experimental measurement; and (2) estimation using the Genetic Coecient Calculator
(GENCALC), an iterative computerized procedure. The objective of this research was to
compare an adaptation of the Uniform Covering by Probabilistic Region (UCPR) method
with these two approaches. UCPR delineates a joint con®dence region for the parameters
corresponding to a goodness-of-®t threshold level. The study focuses on two genetic coecients, duration of the juvenile phase (P1) and photoperiod sensitivity (P2), for ®ve maize
hybrids. Field experiments were conducted at Rossville, KS, during 1995 in which genetic
coecients of four of the hybrids were determined. Silking date data for the same hybrids
were obtained from the Kansas Corn Performance Tests for use in estimating coecients with
UCPR and GENCALC. UCPR was better than GENCALC at minimizing squared error but
at the cost of much longer run times. Both estimation procedures underestimated P1 relative
to the ®eld data. This may have resulted from the model's propensity to overestimate leaf
number. An independent set of silking date data for B73Mo17 from the Kansas Corn Performance Tests was used for comparing methods. Simulated silking dates using P1 and P2
values obtained by UCPR and GENCALC accounted for only 26 and 47%, respectively, of
the variability in actual dates. Both underestimated longer durations to silking. Use of published values for P1 and P2 accounted for 45% of variability but underestimated all data (bias
ÿ 9.5 days). # 2000 Published by Elsevier Science Ltd.
Keywords: Parameter; Search; Con®dence region; Corn; Goodness-of-®t
* Corresponding author.
E-mail address: epaoli@cariba.net (E. RomaÂn-Paoli).
0308-521X/00/$ - see front matter # 2000 Published by Elsevier Science Ltd.
PII: S0308-521X(00)00024-X
30
E. RomaÂn-Paoli et al. / Agricultural Systems 65 (2000) 29±41
1. Introduction
With suitable inputs, crop simulation models allow us to extrapolate across different conditions and places (Thornton et al., 1991). Parameters in a simulation
model should have a physical or biological meaning. Those parameters can be
measured in independent experiments or estimated from observed data. The process
of measuring parameters in a real system, however, may be complex or impractical,
which may result in some level of uncertainty concerning accuracy of the estimated
values.
Crop growth simulation models often are complex and nonlinear. Therefore,
the use of traditional statistical methods to estimate parameters may not be
appropriate (Klepper and Rouse, 1991). A new method, Uniform Covering by
Probabilistic Region (UCPR), has been proposed to estimate parameters for nonlinear models from observed data (Klepper and Hendrix, 1994). The advantage of
this technique over the iterative computerized procedure Genetic Coecient Calculator (GENCALC; Hunt et al., 1993) is that it provides both parameter estimates and a joint con®dence region for the parameters. The con®dence region may
have an arbitrary shape; it need not be ellipsoidal, as is common with standard
nonlinear regression methods (e.g. Kmenta, 1971). GENCALC and ®eld estimation
provide only point estimates of each coecient with associated individual con®dence limits.
Many crop growth models use the concept of genetic coecients to characterize
varieties or hybrids (Ritchie et al., 1989). Genetic coecients are sets of parameters
that describe the genotypeenvironment interaction (IBSNAT, 1993). They summarize quantitatively how a particular cultivar responds to environmental factors.
Depending on the coecient, estimation involves ®eld or growth chamber studies,
many samples, and/or exposure to dierent photoperiods. CERES-Maize (Jones
and Kiniry, 1986) is a growth and development model of maize (Zea mays L.) which
simulates phenology, growth, and yield using soil, climatic, and management inputs.
New maize hybrids are released each year, thereby increasing the need for new
CERES-Maize genetic coecients. These can be measured by direct experiment
(Jones and Kiniry; Ogoshi et al., 1991) or, after the fact, estimated by GENCALC
from outcome data using the simulation model (Hunt et al.,1993).
Simulation of date of tassel initiation is very important, because that is when the
growing point changes from producing leaves to producing reproductive parts.
Determination of tassel initiation in the ®eld is dicult and requires destructive
sampling. In CERES-Maize, tassel initiation is controlled by two coecients: duration of the juvenile phase (P1) and photoperiod sensitivity (P2). The approximate
end of P1 is assumed to be 4 days before tassel initiation (Jones and Kiniry, 1986).
For hybrids that are photoperiod sensitive, tassel initiation is delayed with photoperiods longer than 12.5 h (Hanks and Ritchie, 1991). P2 is normally determined in
controlled environment studies (Kiniry et al., 1983a, b). The objective of this investigation was to use the CERES-Maize model (Jones and Kiniry, in DSSAT V. 3.0;
Tsuji et al., 1994) to compare UCPR and GENCALC estimates of P1 and P2 with
®eld data.
E. RomaÂn-Paoli et al. / Agricultural Systems 65 (2000) 29±41
31
2. Materials and methods
Genetic coecients for four corn hybrids (GH-2404, GH-2573, NC+ 4616, ICI8599) were estimated using UCPR and GENCALC. A more detailed study of the
two methods was also conducted using the hybrid B73Mo17. Field data for comparison were obtained from plantings described below. Silking date data for the
computer methods were extracted from records of the Kansas Corn Performance
Tests (Roozeboom, 1993). The number of performance test observations varied by
hybrid (Table 1). Performance test data represent a range of photoperiod and management conditions. B73Mo17 was included because (1) a large amount of data is
available, and (2) P1 and P2 estimates have been published (Jones and Kiniry, 1986),
against which our results could be compared.
2.1. Field data
Hybrids GH-2404, GH-2573, NC+ 4616, and ICI-8599 were planted on 10 May
1995, at Rossville, KS. The experimental design was a randomized complete block
with four replications. The soil was a Eudora silt loam (coarse silty, mixed, mesic,
¯uventic Haplustoll). Plant population was 3.4 plants mÿ2; row width was 0.76 m.
Growing conditions were managed to attain optimal conditions. Irrigation was
applied to ensure adequate water. Plant samples were observed periodically under a
stereoscope for tassel initiation (Ritchie et al., 1992). Date of tassel initiation was
also observed for GH-2404 and GH-2573 in 1996 experiments planted on 13 June at
Rossville and 4 June at Powhattan, KS. Temperature data were obtained from
automatic weather stations at each location. Growing degree days (GDD8) were
calculated using the method of Gilmore and Rogers (1958).
The plantings just described did not provide the range of photoperiods necessary
to obtain independent estimates of P1 and P2. We estimated P1 (under the assumption that P2=0) by summing GDD8 from emergence to 4 days before tassel initiation (Jones and Kiniry, 1986). Climate records were used to ®nd all other
combinations of P1 and P2 consistent with the observed tassel initiation.
2.2. UCPR
Plots of multivariate con®dence regions universally delimit them with closed
curves, often ellipses. Ellipses result from simplifying mathematical assumptions
which date from a time when only in®nitesimal computing power was available
(Rao, 1965). It has been shown, however, that regions derived in this fashion can
dramatically misrepresent the probable location of nonlinear model parameters
(Donaldson and Schnabel, 1987). Nevertheless, these methods are still widely
incorporated in statistical software. Nonelliptical curves can be produced to bound
con®dence regions but, as dimensionality increases, the computer power required
becomes prohibitive even by modern standards.
Klepper and Hendrix (1994) realized that these problems could be surmounted
by just not assuming that enclosing regions with curves is the only viable way to
E. RomaÂn-Paoli et al. / Agricultural Systems 65 (2000) 29±41
32
Table 1
Corn performance test data used for coecient estimation
Year
Location
1979
1979
1981
1981
1983
1987
1987
1988
1988
1988
1988
1988
1989
1989
1989
1989
1989
1993
1993
1993
1993
1993
1993
1993
1993
1993
1994
1994
1994
1994
1994
1994
1994
1994
1994
1994
1994
1995
1995
1995
1995
1995
1995
1995
1995
1995
1995
Colby
Garden City
Colby
Tribune
St. John
Ottawa
Scandia
Colby
Garden City
Parsons
Scandia
St. John
Garden City
Ottawa
Rossville
Scandia
St. John
Belleville
Garden City
Manhattan
Ottawa
Parsons
Powhattan
Rossville
Scandia
St. John
Bellevilleb
Colbyb
Garden Cityb
Hutchinson
Manhattanb
Ottawab
Parsonsb
Powhattanb
Rossvilleb
Scandiab
St. Johnb
Belleville
Garden City
Hutchinson
Manhattan
Ottawa
Parsons
Powhattan
Rossville
Scandia
St. John
a
b
GH-2404
ICI-8599
NC+4616
GH-2573a
B72Mo17
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Additional data from Rossville and Powhattan in 1996 were used.
Locations used to compare methods of estimating P1 and P2 for B73Mo17.
x
x
x
x
x
x
x
x
x
x
x
E. RomaÂn-Paoli et al. / Agricultural Systems 65 (2000) 29±41
33
display them. Instead of computing the border, they search for the interior. In particular, they plot a cloud of points whose extent well approximates that of the con®dence region. A uniformity principle is used to ensure that no subregions are missed.
Let Gmin symbolize the minimum of a sum of squares goodness-of-®t criterion and
let Gc be the sum of squares along the boundary of an con®dence region. Given
Gmin, Gc can be calculated by:
nF n; K ÿ n;
Gmin ;
Gc 1
Kÿn
where K is the sample size, n is the number of parameters, and F is the corresponding Fisher F-value (Draper and Smith, 1966). Readers should note that Klepper and
Hendrix (1994) omitted the ``1'' in this equation which gives impossible results. Our
interpretation is that this represents a typographical error.
Klepper and Hendrix (1994) used a novel iterative random procedure to seek a
combination of parameter values with a minimal sum of squares (Gmin). Along the
way, combinations were retained if they represented a new minimum or if their
goodness-of-®t was less than the current Gc. These latter combinations delineate the
interior of the con®dence region. If a new minimum is found, Gc is recalculated and
all points are rechecked to see if they are still appropriate to include in a revised
estimate of the region. To characterize a two-parameter con®dence region, a scatter
of 200 parameter combinations is recommended.
We wrote a C-language computer program including the UCPR algorithm. The
program can be summarized as follows:
1. the user enters the desired number of (P1, P2) pairs in the con®dence region
and the F-value and sets the limits on P1 and P2;
2. the computer randomly generates candidate (P1, P2) pairs;
3. the CERES-Maize model is run for each observation (K) and each (P1, P2)
pair (N);
4. each model run produces an output ®le containing predicted and measured
silking dates;
5. the sum of squares for each candidate pair (N) is calculated from K model runs
(one per observation) by summing the square of the dierence between
CERES-Maize predicted and measured silking dates;
6. the best (P1, P2) pair produces the ®rst estimate of Gmin and a corresponding Gc;
7. a new candidate pair is generated at random and its sum of squares computed;
a. if the new point is better than the worst previous point, the new point
replaces it; otherwise the new point is dropped;
b. if the new point's sum of squares is
www.elsevier.com/locate/agsy
Comparing genetic coecient estimation
methods using the CERES-Maize model
E. RomaÂn-Paoli a,*, S.M. Welch b, R.L. Vanderlip b
a
Agricultural Experiment Station, University of Puerto Rico, Lajas, PR 00667, Puerto Rico
b
Department of Agronomy, Kansas State University, Manhattan, KS 66502, USA
Received 13 July 1999; received in revised form 25 May 2000; accepted 3 June 2000
Abstract
Many crop simulation models use genetic coecients to characterize varieties or hybrids.
Two methods now used with CERES-Maize to obtain genetic coecients are: (1) direct
experimental measurement; and (2) estimation using the Genetic Coecient Calculator
(GENCALC), an iterative computerized procedure. The objective of this research was to
compare an adaptation of the Uniform Covering by Probabilistic Region (UCPR) method
with these two approaches. UCPR delineates a joint con®dence region for the parameters
corresponding to a goodness-of-®t threshold level. The study focuses on two genetic coecients, duration of the juvenile phase (P1) and photoperiod sensitivity (P2), for ®ve maize
hybrids. Field experiments were conducted at Rossville, KS, during 1995 in which genetic
coecients of four of the hybrids were determined. Silking date data for the same hybrids
were obtained from the Kansas Corn Performance Tests for use in estimating coecients with
UCPR and GENCALC. UCPR was better than GENCALC at minimizing squared error but
at the cost of much longer run times. Both estimation procedures underestimated P1 relative
to the ®eld data. This may have resulted from the model's propensity to overestimate leaf
number. An independent set of silking date data for B73Mo17 from the Kansas Corn Performance Tests was used for comparing methods. Simulated silking dates using P1 and P2
values obtained by UCPR and GENCALC accounted for only 26 and 47%, respectively, of
the variability in actual dates. Both underestimated longer durations to silking. Use of published values for P1 and P2 accounted for 45% of variability but underestimated all data (bias
ÿ 9.5 days). # 2000 Published by Elsevier Science Ltd.
Keywords: Parameter; Search; Con®dence region; Corn; Goodness-of-®t
* Corresponding author.
E-mail address: epaoli@cariba.net (E. RomaÂn-Paoli).
0308-521X/00/$ - see front matter # 2000 Published by Elsevier Science Ltd.
PII: S0308-521X(00)00024-X
30
E. RomaÂn-Paoli et al. / Agricultural Systems 65 (2000) 29±41
1. Introduction
With suitable inputs, crop simulation models allow us to extrapolate across different conditions and places (Thornton et al., 1991). Parameters in a simulation
model should have a physical or biological meaning. Those parameters can be
measured in independent experiments or estimated from observed data. The process
of measuring parameters in a real system, however, may be complex or impractical,
which may result in some level of uncertainty concerning accuracy of the estimated
values.
Crop growth simulation models often are complex and nonlinear. Therefore,
the use of traditional statistical methods to estimate parameters may not be
appropriate (Klepper and Rouse, 1991). A new method, Uniform Covering by
Probabilistic Region (UCPR), has been proposed to estimate parameters for nonlinear models from observed data (Klepper and Hendrix, 1994). The advantage of
this technique over the iterative computerized procedure Genetic Coecient Calculator (GENCALC; Hunt et al., 1993) is that it provides both parameter estimates and a joint con®dence region for the parameters. The con®dence region may
have an arbitrary shape; it need not be ellipsoidal, as is common with standard
nonlinear regression methods (e.g. Kmenta, 1971). GENCALC and ®eld estimation
provide only point estimates of each coecient with associated individual con®dence limits.
Many crop growth models use the concept of genetic coecients to characterize
varieties or hybrids (Ritchie et al., 1989). Genetic coecients are sets of parameters
that describe the genotypeenvironment interaction (IBSNAT, 1993). They summarize quantitatively how a particular cultivar responds to environmental factors.
Depending on the coecient, estimation involves ®eld or growth chamber studies,
many samples, and/or exposure to dierent photoperiods. CERES-Maize (Jones
and Kiniry, 1986) is a growth and development model of maize (Zea mays L.) which
simulates phenology, growth, and yield using soil, climatic, and management inputs.
New maize hybrids are released each year, thereby increasing the need for new
CERES-Maize genetic coecients. These can be measured by direct experiment
(Jones and Kiniry; Ogoshi et al., 1991) or, after the fact, estimated by GENCALC
from outcome data using the simulation model (Hunt et al.,1993).
Simulation of date of tassel initiation is very important, because that is when the
growing point changes from producing leaves to producing reproductive parts.
Determination of tassel initiation in the ®eld is dicult and requires destructive
sampling. In CERES-Maize, tassel initiation is controlled by two coecients: duration of the juvenile phase (P1) and photoperiod sensitivity (P2). The approximate
end of P1 is assumed to be 4 days before tassel initiation (Jones and Kiniry, 1986).
For hybrids that are photoperiod sensitive, tassel initiation is delayed with photoperiods longer than 12.5 h (Hanks and Ritchie, 1991). P2 is normally determined in
controlled environment studies (Kiniry et al., 1983a, b). The objective of this investigation was to use the CERES-Maize model (Jones and Kiniry, in DSSAT V. 3.0;
Tsuji et al., 1994) to compare UCPR and GENCALC estimates of P1 and P2 with
®eld data.
E. RomaÂn-Paoli et al. / Agricultural Systems 65 (2000) 29±41
31
2. Materials and methods
Genetic coecients for four corn hybrids (GH-2404, GH-2573, NC+ 4616, ICI8599) were estimated using UCPR and GENCALC. A more detailed study of the
two methods was also conducted using the hybrid B73Mo17. Field data for comparison were obtained from plantings described below. Silking date data for the
computer methods were extracted from records of the Kansas Corn Performance
Tests (Roozeboom, 1993). The number of performance test observations varied by
hybrid (Table 1). Performance test data represent a range of photoperiod and management conditions. B73Mo17 was included because (1) a large amount of data is
available, and (2) P1 and P2 estimates have been published (Jones and Kiniry, 1986),
against which our results could be compared.
2.1. Field data
Hybrids GH-2404, GH-2573, NC+ 4616, and ICI-8599 were planted on 10 May
1995, at Rossville, KS. The experimental design was a randomized complete block
with four replications. The soil was a Eudora silt loam (coarse silty, mixed, mesic,
¯uventic Haplustoll). Plant population was 3.4 plants mÿ2; row width was 0.76 m.
Growing conditions were managed to attain optimal conditions. Irrigation was
applied to ensure adequate water. Plant samples were observed periodically under a
stereoscope for tassel initiation (Ritchie et al., 1992). Date of tassel initiation was
also observed for GH-2404 and GH-2573 in 1996 experiments planted on 13 June at
Rossville and 4 June at Powhattan, KS. Temperature data were obtained from
automatic weather stations at each location. Growing degree days (GDD8) were
calculated using the method of Gilmore and Rogers (1958).
The plantings just described did not provide the range of photoperiods necessary
to obtain independent estimates of P1 and P2. We estimated P1 (under the assumption that P2=0) by summing GDD8 from emergence to 4 days before tassel initiation (Jones and Kiniry, 1986). Climate records were used to ®nd all other
combinations of P1 and P2 consistent with the observed tassel initiation.
2.2. UCPR
Plots of multivariate con®dence regions universally delimit them with closed
curves, often ellipses. Ellipses result from simplifying mathematical assumptions
which date from a time when only in®nitesimal computing power was available
(Rao, 1965). It has been shown, however, that regions derived in this fashion can
dramatically misrepresent the probable location of nonlinear model parameters
(Donaldson and Schnabel, 1987). Nevertheless, these methods are still widely
incorporated in statistical software. Nonelliptical curves can be produced to bound
con®dence regions but, as dimensionality increases, the computer power required
becomes prohibitive even by modern standards.
Klepper and Hendrix (1994) realized that these problems could be surmounted
by just not assuming that enclosing regions with curves is the only viable way to
E. RomaÂn-Paoli et al. / Agricultural Systems 65 (2000) 29±41
32
Table 1
Corn performance test data used for coecient estimation
Year
Location
1979
1979
1981
1981
1983
1987
1987
1988
1988
1988
1988
1988
1989
1989
1989
1989
1989
1993
1993
1993
1993
1993
1993
1993
1993
1993
1994
1994
1994
1994
1994
1994
1994
1994
1994
1994
1994
1995
1995
1995
1995
1995
1995
1995
1995
1995
1995
Colby
Garden City
Colby
Tribune
St. John
Ottawa
Scandia
Colby
Garden City
Parsons
Scandia
St. John
Garden City
Ottawa
Rossville
Scandia
St. John
Belleville
Garden City
Manhattan
Ottawa
Parsons
Powhattan
Rossville
Scandia
St. John
Bellevilleb
Colbyb
Garden Cityb
Hutchinson
Manhattanb
Ottawab
Parsonsb
Powhattanb
Rossvilleb
Scandiab
St. Johnb
Belleville
Garden City
Hutchinson
Manhattan
Ottawa
Parsons
Powhattan
Rossville
Scandia
St. John
a
b
GH-2404
ICI-8599
NC+4616
GH-2573a
B72Mo17
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
Additional data from Rossville and Powhattan in 1996 were used.
Locations used to compare methods of estimating P1 and P2 for B73Mo17.
x
x
x
x
x
x
x
x
x
x
x
E. RomaÂn-Paoli et al. / Agricultural Systems 65 (2000) 29±41
33
display them. Instead of computing the border, they search for the interior. In particular, they plot a cloud of points whose extent well approximates that of the con®dence region. A uniformity principle is used to ensure that no subregions are missed.
Let Gmin symbolize the minimum of a sum of squares goodness-of-®t criterion and
let Gc be the sum of squares along the boundary of an con®dence region. Given
Gmin, Gc can be calculated by:
nF n; K ÿ n;
Gmin ;
Gc 1
Kÿn
where K is the sample size, n is the number of parameters, and F is the corresponding Fisher F-value (Draper and Smith, 1966). Readers should note that Klepper and
Hendrix (1994) omitted the ``1'' in this equation which gives impossible results. Our
interpretation is that this represents a typographical error.
Klepper and Hendrix (1994) used a novel iterative random procedure to seek a
combination of parameter values with a minimal sum of squares (Gmin). Along the
way, combinations were retained if they represented a new minimum or if their
goodness-of-®t was less than the current Gc. These latter combinations delineate the
interior of the con®dence region. If a new minimum is found, Gc is recalculated and
all points are rechecked to see if they are still appropriate to include in a revised
estimate of the region. To characterize a two-parameter con®dence region, a scatter
of 200 parameter combinations is recommended.
We wrote a C-language computer program including the UCPR algorithm. The
program can be summarized as follows:
1. the user enters the desired number of (P1, P2) pairs in the con®dence region
and the F-value and sets the limits on P1 and P2;
2. the computer randomly generates candidate (P1, P2) pairs;
3. the CERES-Maize model is run for each observation (K) and each (P1, P2)
pair (N);
4. each model run produces an output ®le containing predicted and measured
silking dates;
5. the sum of squares for each candidate pair (N) is calculated from K model runs
(one per observation) by summing the square of the dierence between
CERES-Maize predicted and measured silking dates;
6. the best (P1, P2) pair produces the ®rst estimate of Gmin and a corresponding Gc;
7. a new candidate pair is generated at random and its sum of squares computed;
a. if the new point is better than the worst previous point, the new point
replaces it; otherwise the new point is dropped;
b. if the new point's sum of squares is