Type:	Package
Title:	Estimates Allele Frequency on qPCR DeltaDeltaCq from Bulk Samples
Version:	0.4.0
Maintainer:	Masaaki Sudo <masaaki@sudori.info>
Description:	Interval estimation of the population allele frequency from qPCR analysis based on the restriction enzyme digestion (RED)-DeltaDeltaCq method (Osakabe et al. 2017, <doi:10.1016/j.pestbp.2017.04.003>), as well as general DeltaDeltaCq analysis. Compatible with the Cq measurement of DNA extracted from multiple individuals at once, so called "group-testing", this model assumes that the quantity of DNA extracted from an individual organism follows a gamma distribution. Therefore, the point estimate is robust regarding the uncertainty of the DNA yield.
URL:	https://github.com/sudoms/freqpcr
Depends:	R (≥ 3.6), cubature
Imports:	methods
License:	GPL (≥ 3)
Encoding:	UTF-8
RoxygenNote:	7.1.1
Suggests:	knitr, rmarkdown, remotes
VignetteBuilder:	knitr
NeedsCompilation:	no
Packaged:	2022-01-26 10:57:50 UTC; masaa
Author:	Masaaki Sudo [aut, cre]
Repository:	CRAN
Date/Publication:	2022-01-27 10:30:04 UTC

The freqpcr package

Description

Allele Frequency Estimation on qPCR \Delta\DeltaCq Values from Bulk Samples

Author(s)

Maintainer: Masaaki Sudo masaaki@sudori.info (ORCID)

See Also

Useful links:

• https://github.com/sudoms/freqpcr

Log-likelihood of obtaining Cq values under given parameter set.

Description

The internal function is called from the optimizer, nlm(), running in freqpcr(). It defines the log-likelihood by obtaining the two \DeltaCq values (differences in the four Cq measurements) provided that the allele mixing ratio for each bulk sample is given together with other parameters. This function is vectorized over multiple bulk samples.

Usage

.freqpcr_loglike(
  X,
  N,
  DCW,
  DCD,
  zeroAmount,
  para.fixed = NULL,
  beta = TRUE,
  diploid = FALSE,
  dummyDCW = FALSE
)

Arguments

Value

Scalar of the log likelihood.

Log-likelihood when sample allele ratio is continuous.

Description

Called from freqpcr() instead of .freqpcr_loglike() when the model is ‘continuous’. This function assumes that each sample does not consist of n individual organisms with certain genotypes, but the result of a direct DNA extraction from the sub-population having the allele ratio around p:(1-p). Each sample allele ratio is considered to follow Beta(apk, a(1-p)k), where a and k are the relative DNA content of the sample and the gamma shape parameter, respectively.

Usage

.freqpcr_loglike_cont(
  X,
  A,
  DCW,
  DCD,
  zeroAmount,
  para.fixed = NULL,
  beta = TRUE,
  dummyDCW = FALSE
)

Arguments

Value

Scalar of the log likelihood.

Integration of likelihood function based on the beta assumption.

Description

Internal function to integrate the likelihood getting the \DeltaCq value (the argument del) over the entire range of the allele ratio (0 to 1). Vectorized for multiple bulk samples. Having the same arguments with .integrate_gamma.

Usage

.integrate_beta(
  del,
  SHR,
  SHS,
  zeroAmount,
  targetScale,
  sdMeasure,
  xsm = 2,
  EPCR,
  cubmethod = "hcubature",
  relTol = 0.1,
  absTol = 1e-08,
  maxEval = 10^6
)

Arguments

Value

A numeric vector of marginal likelihoods having the same length as del.

Methods for cubintegrate

The following methods are available for cubintegrate(): cubmethod = c("hcubature", "pcubature", "cuhre", "divonne", "suave", "vegas").
hcubature is considerably fast, but less accurate with larger reltol. cuhre is moderately fast and the most accurate in most relTol range. If you can wait longer, hcubature with relTol = 1e-4 or cuhre with relTol = 1e-1 is recommended. At reltol = 1e-1, hcubature is three times faster than cuhre, but the log-likelihood fluctuate by 0.1 (by 0.001 in cuhre). The speed and accuracy of hcubature at reltol = 1e-5 is comparable with cuhre at reltol = 1e-1.
pcubature and divonne frequently returns NaN and are not recommended.
suave and vegas are Monte Carlo integration and slow. They are certainly accurate even at reltol = 1, but interior to cuhre with same reltol.

See Also

Other integrators: .integrate_gamma()

Double integration of likelihood over the two DNA quantities obeying the gamma distributions.

Description

Internal function to integrate the likelihood getting \DeltaCq value (the argument del) over the entire range of the DNA quantities of the two alleles, 0 <= x_S < Inf and 0 <= x_R < Inf. Vectorized for multiple bulk samples. It shares the arguments with .integrate_beta.

Usage

.integrate_gamma(
  del,
  SHR,
  SHS,
  zeroAmount,
  targetScale,
  sdMeasure,
  xsm = 2,
  EPCR,
  cubmethod = "hcubature",
  relTol = 0.1,
  absTol = 1e-08,
  maxEval = 10^6
)

Arguments

Value

A numeric vector of marginal likelihoods having the same length as del.

See Also

Other integrators: .integrate_beta()

Log-likelihood of getting Cq values when exact allele mixing ratios are known.

Description

Internal function to return the log-likelihood getting the four Cq measurements under true allele frequency for each bulk sample is known.

Usage

.knownqpcr_loglike(X, A, trueY, Digest, Gene, Cq)

Arguments

Value

A scalar of the log likelihood.

Log-likelihood of getting Cq values when exact allele mixing ratios are known, lacking the quartet structure.

Description

Internal function to return the log-likelihood getting the four Cq measurements under true allele frequency for each bulk sample is known. This is a variant for the 'duo' structure dataset and baseChange is absent. obs.housek0 and obs.target0 are defined for the parity of source code, but they actually accept no data.

Usage

.knownqpcr_loglike_duo(X, A, trueY, Digest, Gene, Cq)

Arguments

Value

A scalar of the log likelihood.

Output object of freqpcr().

Description

Output object of freqpcr().

Slots

report

A matrix of the simultaneous parameter estimation result. The rows represent the parameters P, K, targetScale (\delta_{T}), sdMeasure (\sigma_{c}), and EPCR (\eta).

obj

Returned value of the optimizer function nlm() as a list.

cal.time

Calculation time of nlm(), stored as a proc_time class object.

S4 class storing the dummy Cq data for performance test.

Description

A dummy Cq dataset suitable for a package test, typically obtained as the output of make_dummy().

Slots

N

Sample sizes as a numeric vector. The ntrap and npertrap arguments of make_dummy() are inherited to the length of N and each N[i] element, the number of individuals (both for haploidy and diploidy) contained in the ith bulk sample, respectively.

m

Segregation ratio. As for haploidy, m is a matrix with 2 rows and ntrap columns. m[1, i] and m[2, i] stores the number of R (mutant) or S (wild type) individuals while N[i] = sum(m[, i]) specifies the total in the bulk sample. It has 3 rows and ntrap columns as for diploidy. While m[1, i] stands for the number of RR hogozygote individuals, m[2, i] and m[3, i] stand for the numbers of RS heterozygotes and SS homozygotes, respectively.

xR,xS

Numeric vector of the same length with N. xR[i] stores the amount of the template DNA for R allele contained in the ith bulk sample.

housek0,target0,housek1,target1

Numeric vectors of the same lengths with N. Store the generated Cq values.

DCW

\DeltaCq values measured on the control samples (DNA extract without endonuclease digestion in the RED-\Delta\DeltaCq method, or pure R solution in a general \Delta\DeltaCq method), DCW, is defined as (target0 - housek0).

DCD

\DeltaCq values measured on the test samples (samples after endonuclease digestion in the RED-\Delta\DeltaCq method, or samples with unknown allele mixing ratios in a general \Delta\DeltaCq method), DCD, is defined as (target1 - housek1).

deldel

\Delta\DeltaCq value, defined as (DCD - DCW).

RFreqMeasure

A classical index of the allele frequency calculated for each bulk sample, which is defined as (1.0+EPCR)^(-deldel). Note that the values of EPCR and other parameters, such as P or K, are not recorded in the object to avoid leakage of information.

ObsP

As RFreqMeasure can exceed 1 by definition, ObsP is defined as min(RFreqMeasure, 1).

rand.seed

The seed of the random-number generator (RNG) which was fed to the current R session to generate dummy m, xR and xS data.

Estimate population allele frequency from the set of Cq measurements.

Description

The function estimates the population allele frequency using the dataset of Cq values measured over length(N) bulk samples, each of which has a sample size of N[i] as the number of individuals included. N[i] can be 1, meaning that every individual is analyzed separately. For the ith sample, the four Cq values were measured as housek0[i], target0[i], housek1[i], and target1[i]. The function can estimate up to five parameters simultaneously when the Cq sets are available for more than two (bulk) samples: P, K, targetScale, sdMeasure, and EPCR.
Since v0.3.2, user can also use an experimental ‘continuous model’ by specifying A instead of N. That is, each sample DNA is directly extracted from the environment and the sample allele ratio y follows y ~ Beta(apk, a(1-p)k) instead of y ~ Beta(mk, (n-m)k), m ~ Binomial(n, p), where p and k are the population allele frequency and the gamma shape parameter of the individual DNA yield, respectively. Each element of A, a is a scaling factor of relative DNA contents between the samples. The continuous model is likely when each sample directly comes from the environment e.g., water sampling in an eDNA analysis or cell culture in a petri dish.
Since v0.4.0, freqpcr() also works without specifying housek0 and target0 i.e., it can estimate population allele frequency from \DeltaCq values instead of \Delta\DeltaCq. In this setting, the sizes of targetScale and sdMeasure should be fixed in addition to EPCR and zeroAmount.

Usage

freqpcr(
  N,
  A,
  housek0,
  target0,
  housek1,
  target1,
  P = NULL,
  K = NULL,
  targetScale = NULL,
  sdMeasure = NULL,
  EPCR = 0.99,
  XInit0 = c(P = NULL, K = NULL, targetScale = NULL, sdMeasure = NULL, EPCR = NULL),
  zeroAmount = NULL,
  beta = TRUE,
  diploid = FALSE,
  pvalue = 0.05,
  gradtol = 1e-04,
  steptol = 1e-09,
  iterlim = 100,
  maxtime = 600,
  print.level = 1,
  ...
)

Arguments

Value

Object of the S4 class CqFreq. The slot report is a matrix and each row contains the estimated parameter value with 100*(1-pvalue)% confidence interval. The following parameters are returned:

1. P, the population allele frequency from which the test samples are derived.

2. K, the gamma shape parameter of the individual DNA yield.

3. targetScale (\delta_{T}), the relative template DNA amount of the target to the houskeeping loci.

4. EPCR (\eta), the amplification efficiency per PCR cycle.

5. sdMeasure or "Cq measurement error" (\sigma_{c}).

Choise of the parameters to be estimated

Estimation is conducted only for parameters where the values are not specified or specified explicitly as NULL. If one feeds a value e.g. K=1 or sdMeasure=0.24, it is then treated as fixed parameter. Notwithstanding, EPCR is estimated only when EPCR = NULL is specified explicitly.
You must verify the size of EPCR and zeroAmount beforehand because they are not estimable from the experiments with unknown allele ratios. Although targetScale and sdMeasure are estimable within freqpcr(), it is better to feed the known values, especially when you have only a few bulk samples (length(N) <= 3). Fixing targetScale and sdMeasure is also strongly recommended when housek0 and target0 are absent (\DeltaCq method). The functions knownqpcr() or knownqpcr_unpaired(), depending on your data format, provide the procedure to estimate the sizes of the experimental parameters using the DNA solutions of known allele mixing ratios.
For the unknown parameters, XInit0 optionally specifies initial values for the optimization using nlm() though the use of internal default is strongly recommended. The specification as a fixed parameter has higher priority than the specification in XInit0. Every user-specified parameter values, fixed or unknown, must be given in linear scale (e.g. between 0 and 1 for the allele frequency); they are transformed internally to log or logit.

See Also

Other estimation procedures: knownqpcr_unpaired(), knownqpcr(), sim_dummy()

Examples

# Dummy Cq dataset with six bulk samples, each of which comprises of eight haploids.
EPCR <- 0.95; zeroAmount <- 0.0016; # True values for the two must be known.
P <- 0.75
dmy_cq <- make_dummy(   rand.seed=1, P=P, K=2, ntrap=6, npertrap=8,
                        scaleDNA=1e-07, targetScale=1.5, baseChange=0.3,
                        EPCR=EPCR, zeroAmount=zeroAmount,
                        sdMeasure=0.3, diploid=FALSE   )
print(dmy_cq)

# Estimation with freqpcr, where P, K, targetScale, and baseChange are marked unknown.
result <- freqpcr( N=dmy_cq@N, housek0=dmy_cq@housek0, target0=dmy_cq@target0,
                   housek1=dmy_cq@housek1, target1=dmy_cq@target1,
                   EPCR=EPCR, zeroAmount=zeroAmount, beta=TRUE, print.level=0 )
print(result)

# Estimation with freqpcr, assuming diploidy.
result <- freqpcr( N=dmy_cq@N, housek0=dmy_cq@housek0, target0=dmy_cq@target0,
                   housek1=dmy_cq@housek1, target1=dmy_cq@target1,
                   EPCR=EPCR, zeroAmount=zeroAmount, beta=TRUE, diploid=TRUE )

# Estimation where you have knowledge on the size of K.
result <- freqpcr( N=dmy_cq@N, housek0=dmy_cq@housek0, target0=dmy_cq@target0,
                   housek1=dmy_cq@housek1, target1=dmy_cq@target1,
                   K=2,
                   EPCR=EPCR, zeroAmount=zeroAmount, beta=TRUE, print.level=2 )
# (>= v0.3.2)
# Provided the model is continuous (specify A instead of N).
result <- freqpcr( A=dmy_cq@N, housek0=dmy_cq@housek0, target0=dmy_cq@target0,
                   housek1=dmy_cq@housek1, target1=dmy_cq@target1,
                   K=2, EPCR=EPCR, zeroAmount=zeroAmount, beta=TRUE, print.level=1 )
# (>= v0.4.0)
# If the dataset lacks control samples (housek0 and target0 are absent).
# Fixing the sizes of targetScale and sdMeasure is strongly recommended.
result <- freqpcr( N=dmy_cq@N, housek1=dmy_cq@housek1, target1=dmy_cq@target1,
                   K=2, EPCR=EPCR, zeroAmount=zeroAmount,
                   targetScale=1.5, sdMeasure=0.3, beta=TRUE, print.level=1 )

Estimate auxiliary parameters using samples with known allele ratios.

Description

The function to estimate the auxiliary experimental parameters using DNA solutions, provided the dataset contains samples with multiple allele mixing ratios and the exact mixing ratio are known for each sample. This function is used when all replicates in the dataset comprise the complete observations on the 2 \times 2 combinations of the qPCR conditions in a RED-\Delta\DeltaCq analysis: (loci for target or housekeeping genes) and (the target gene is undigested or digested with endonuclease). The quartet of the four Cq data, housek0, target0 (these two are undigested samples amplified with housekeeping and target genes, respectively), housek1, and target1 (digested samples) should be prepared as four numeric vectors having the same length.
One more variable, trueY is needed to run the estimation process; it a numeric vector having the same length with the four Cq data. It holds the exact allele-mixing ratio for each quartet (also see the code example). Optionally, you can adjust the relative DNA concentration between the replicates with a parameter vector A.
Since version 0.3.2, the knownqpcr() function can also deal with general \Delta\DeltaCq analyses. In such cases, samples with any mixing ratios are generally marked as ‘digested samples’ i.e., either of housek1 or target1, depending on the loci to be amplified. The arguments of the corresponding undigested samples, housek0 and target0, must not be specified by the user. Then, the parameter baseChange (\delta_{B}: the change rate of DNA contents before/after the endonuclease digestion) is not included in the estimation result.

Usage

knownqpcr(
  housek0,
  target0,
  housek1,
  target1,
  trueY,
  A = rep(1, length(trueY)),
  XInit = c(meanDNA = -10, targetScale = 0, baseChange = 0, sdMeasure = 1, zeroAmount =
    -5, EPCR = 0),
  method = "BFGS",
  pvalue = 0.05,
  trace = 0,
  report = 10,
  verbose = FALSE
)

Arguments

Value

A table containing the estimated values for the following parameters:

1. meanDNA is the template DNA concentration (of housekeeping gene, per unit volume of sample solution) compared to the threshold line of PCR.

2. targetScale (\delta_{T}) is the relative template DNA amount of the target to the houskeeping loci.

3. baseChange (\delta_{B}) is the change rate in the DNA amount after endonuclease digestion in RED-\Delta\DeltaCq method. In general \Delta\DeltaCq analyses (neither housek0 nor target0 is input), this parameter is not returned. In both cases, baseChange is not required to run freqpcr().

4. sdMeasure (\sigma_{c}) is the measurement error (standard deviation) at each Cq value.

5. zeroAmount (z) is the ratio of non-target allele amplified in qPCR (see the argument list of freqpcr()).

6. EPCR (\eta) is the amplification efficiency per PCR cycle.

See Also

Other estimation procedures: freqpcr(), knownqpcr_unpaired(), sim_dummy()

Examples

# A dummy Cq dataset: four mixing ratios with four replicates.
# K:2, scaleDNA:1e-11, targetScale:1.5, baseChange:0.3, zeroAmount:1e-3,
# sdMeasure:0.3, and EPCR:0.95. Assuming a RED-DeltaDeltaCq analyses.
trueY <- c(rep(0.1, 4), rep(0.25, 4), rep(0.5, 4), rep(1, 4))
housek0 <- c( 19.39, 19.78, 19.28, 19.58,  18.95, 19.91, 19.66, 19.96,
              20.05, 19.86, 19.55, 19.61,  19.86, 19.27, 19.59, 20.21 )
target0 <- c( 19.16, 19.08, 19.28, 19.03,  19.17, 19.67, 18.68, 19.52,
              18.92, 18.79, 18.8, 19.28,   19.57, 19.21, 19.05, 19.15 )
housek1 <- c( 21.61, 21.78, 21.25, 21.07,  22.04, 21.45, 20.72, 21.6,
              21.51, 21.27, 21.08, 21.7,   21.44, 21.46, 21.5, 21.8 )
target1 <- c( 24.3, 24.22, 24.13, 24.13,   22.74, 23.14, 23.02, 23.14,
              21.65, 22.62, 22.28, 21.65,  20.83, 20.82, 20.76, 21.3 )
d.cmp <- data.frame(A=rep(1, 16), trueY, housek0, target0, housek1, target1)
print(d.cmp)

# In RED-DeltaDeltaCq analyses, four observations stem from one sample solution.
# Each argument must be specified with its name (name=source).
knownqpcr(  housek0=d.cmp$housek0, target0=d.cmp$target0,
            housek1=d.cmp$housek1, target1=d.cmp$target1,
            trueY=d.cmp$trueY, A=d.cmp$A, verbose=FALSE  )

# In general DeltaDeltaCq analyses, the experimental design will not include
# dedicated control samples. The function then runs without 'housek0' and 'target0'.
knownqpcr(  housek1=d.cmp$housek1, target1=d.cmp$target1,
            trueY=d.cmp$trueY, A=d.cmp$A, verbose=TRUE  )

Estimate auxiliary parameters when the sample pairs are incomplete.

Description

A variant of knownqpcr() that accepts the Cq values concatenated into a vector (the argument Cq) accompanied with the experimental conditions (the arguments Digest and Gene). Their exact allele mixing ratios are known as trueY.

Usage

knownqpcr_unpaired(
  Digest,
  Gene,
  trueY,
  Cq,
  A = rep(1, length(Cq)),
  XInit = c(meanDNA = -10, targetScale = 0, baseChange = 0, sdMeasure = 1, zeroAmount =
    -5, EPCR = 0),
  method = "BFGS",
  pvalue = 0.05,
  trace = 0,
  report = 10,
  verbose = FALSE
)

Arguments

Value

A table containing the estimated parameter values. The format is same as knownqpcr().

See Also

Other estimation procedures: freqpcr(), knownqpcr(), sim_dummy()

Examples

# A dummy Cq dataset: four mixing ratios with four replicates.
# K:2, scaleDNA:1e-11, targetScale:1.5, baseChange:0.3, zeroAmount:1e-3,
# sdMeasure:0.3, and EPCR:0.95. Assuming a RED-DeltaDeltaCq analyses.
trueY <- c(rep(0.1, 4), rep(0.25, 4), rep(0.5, 4), rep(1, 4))
housek0 <- c( 19.39, 19.78, 19.28, 19.58,  18.95, 19.91, 19.66, 19.96,
              20.05, 19.86, 19.55, 19.61,  19.86, 19.27, 19.59, 20.21 )
target0 <- c( 19.16, 19.08, 19.28, 19.03,  19.17, 19.67, 18.68, 19.52,
              18.92, 18.79, 18.8, 19.28,   19.57, 19.21, 19.05, 19.15 )
housek1 <- c( 21.61, 21.78, 21.25, 21.07,  22.04, 21.45, 20.72, 21.6,
              21.51, 21.27, 21.08, 21.7,   21.44, 21.46, 21.5, 21.8 )
target1 <- c( 24.3, 24.22, 24.13, 24.13,   22.74, 23.14, 23.02, 23.14,
              21.65, 22.62, 22.28, 21.65,  20.83, 20.82, 20.76, 21.3 )

# Incomplete observation dataset, prepared as the "long" format.
# If the undegested (Digest == 0) samples were only analyzed when trueY == 1.
d.long.all <- data.frame(
    trueY=rep(trueY, 4), Digest=c(rep(0, 16 + 16), rep(1, 16 + 16)),
    Gene=c(rep(0, 16), rep(1, 16), rep(0, 16), rep(1, 16)),
    A=rep(1, 16*4), Cq=c(housek0, target0, housek1, target1)  )
d.long <- d.long.all[d.long.all$Digest == 1 | d.long.all$trueY == 1, ]
print(d.long)

knownqpcr_unpaired( Digest=d.long$Digest, Gene=d.long$Gene,
                    trueY=d.long$trueY, Cq=d.long$Cq, A=d.long$A )

# In general DeltaDeltaCq analyses, the experimental design will not include
# dedicated control samples (Digest == 0).
d.long <- d.long.all[d.long.all$Digest == 1, ]
knownqpcr_unpaired( Digest=d.long$Digest, Gene=d.long$Gene,
                    trueY=d.long$trueY, Cq=d.long$Cq, A=d.long$A )

Generate dummy DNA dataset ready for allele-frequency estimation.

Description

The function generates a dummy dataset of typical RED-\Delta\DeltaCq analysis. You can directly feed the output of this function to the first argument of sim_dummy().

Usage

make_dummy(
  rand.seed,
  P,
  K,
  ntrap,
  npertrap,
  scaleDNA = (1/K) * 1e-06,
  targetScale,
  baseChange,
  EPCR,
  zeroAmount,
  sdMeasure,
  diploid = FALSE
)

Arguments

Value

Object of the S4 class CqList, storing the dummy experiment data of Cq-based qPCR analysis. Note that a CqList object in no way contains original information on P, K, targetScale, sdMeasure, and EPCR.

Examples

P <- 0.25
# Just a test: segregation ratios for six bulk samples, 1000 individuals for each.
rmultinom(n=6, size=1000, prob=c(P, 1-P)) # haploidy
rmultinom(6, size=1000, prob=c(P^2, 2*P*(1-P), (1-P)^2)) # diploidy

# Dummy Cq dataset with six bulk samples, each of which comprises eight haploids.
dmy_cq <- make_dummy( rand.seed=1, P=0.15, K=2, ntrap=6, npertrap=8,
                      scaleDNA=1e-07, targetScale=1.5, baseChange=0.3, EPCR=0.95,
                      zeroAmount=1e-3, sdMeasure=0.3, diploid=FALSE )
print(dmy_cq)

Simulate freqpcr estimation based on user-generated dummy data.

Description

Wrapper of freqpcr() suitable for the performance test using a randomly-generated data object.

Usage

sim_dummy(
  CqList,
  EPCR,
  zeroAmount,
  P = NULL,
  K = NULL,
  targetScale = NULL,
  sdMeasure = NULL,
  beta,
  diploid,
  maxtime,
  print.level,
  aux = NULL,
  verbose = TRUE,
  ...
)

Arguments

Value

Object of the S4 class CqFreq, which is same as freqpcr().

See Also

Other estimation procedures: freqpcr(), knownqpcr_unpaired(), knownqpcr()

Examples

# Prepare the parameter values.
K <- 2 # You already know the size of K in this case.
EPCR <- 0.97 # The sizes of EPCR and zeroAmount must always be supplied.
zeroAmount <- 1.6e-03
is.diploid <- FALSE

# First, make a dummy Cq dataset with six bulk DNA samples,
# each of which comprises of eight haploid individuals.
dmy_cq <- make_dummy( rand.seed=1, P=0.75, K=K, ntrap=6, npertrap=8, scaleDNA=1e-07,
                      targetScale=1.5, baseChange=0.3, EPCR=EPCR,
                      zeroAmount=zeroAmount, sdMeasure=0.3, diploid=is.diploid )

# Estimate the population allele frequency on the dummy dataset, presupposing K = 2.
sim_dummy(  CqList=dmy_cq, EPCR=EPCR, zeroAmount=zeroAmount,
            K=K,
            beta=TRUE, diploid=is.diploid, maxtime=60, print.level=2, aux="test" )

# If the maximum calculation time was too short to converge, nlm() returns error.
# Then sim_dummy() returns a matrix filled with zeros.
sim_dummy(  CqList=dmy_cq, EPCR=EPCR, zeroAmount=zeroAmount,
            beta=TRUE, diploid=is.diploid, maxtime=0.01, print.level=2 )