Simple (functions designated by no number) for the standard model
only is explored in the vignette Simple Normal Data
Example.
Advanced (functions designated by the number 2) for the standard
model with the options of including additional random effects for one
position (e.g. tank) and/or one block effect (e.g. several blocks of 2
\(\times\) 2 factorial matings) is
explored in the vignette Advanced Normal Data
Example.
Non-normal error structures (e.g. binary, proportion, and/or count
data types) are explored in another three vignettes: (1) Simple
Non-normal Data Example, (2) Advanced Non-normal Data Example, and (3)
Expert Non-normal Data Example.
Observed variance components
Model random effects are dam, sire, dam by sire, and any additional
fixed and/or random effects. Extracts the dam, sire, dam, dam by sire,
and residual variance components. Extracts any additional fixed effect
and/or random effect variance components. The fixed effect variance
component is as a single group using the method described by Nakagawa
and Schielzeth (2013). Calculates the total variance component.
Calculates the additive genetic, non-additive genetic, and maternal
variance components.
Assuming the effects of epistasis are of negligible importance, the
additive genetic variance (VA) component is calculated as
four times the sire (VS), the non-additive genetic variance
(VN) component as four times the dam by sire interaction
(VD\(\times\)S), and the
maternal variance component (VM) as the dam (VD) –
sire (VS) (Lynch and Walsh 1998, p. 603). When there is
epistasis, those variance components will be overestimated and this may
explain why the percentage of phenotypic variance explained by the
components can add up to more than 100% in certain cases.
Significance values for the random effects are determined using
likelihood ratio tests (Bolker et al. 2009).
Significance values for any fixed effects are determined using
likelihood ratio tests (LRT) and a parametric bootstrap method (Bolker
et al. 2009) from the mixed function of the
afex package. LRT is not generally recommended for fixed
effects as there are issues calculating the denominator degrees of
freedom.
remain is the remaining formula using lme4
package format.
iter is the number of iterations for computing the
parametric bootstrap significance value for any fixed effects, typically
1,000. For the example, 100 iterations was used.
Nakagawa S, Schielzeth H. 2013. A general and simple method for
obtaining R2 from generalized linear mixed-effects models. Methods in
Ecology and Evolution 4(2): 133-142. DOI:
10.1111/j.2041-210x.2012.00261.x
Lynch M, Walsh B. 1998. Genetics and Analysis of Quantitative Traits.
Sinauer Associates, Massachusetts.
Bolker BM, Brooks ME, Clark CJ, Geange SW, Poulsen JR, Stevens MHH,
White J-SS. 2009. Generalized linear mixed models: a practical guide for
ecology and evolution. Trends in Ecology and Evolution 24(3): 127-135.
DOI: 10.1016/j.tree.2008.10.008
#>length_mod3<- observLmer3(observ=chinook_length,dam="dam",sire="sire",response="length",
#>remain="egg_size + (1|tray)",iter=1000) #full
length_mod3<- observLmer3(observ=chinook_length,dam="dam",sire="sire",response="length",
remain="egg_size + (1|tray)",iter=100)
#> [1] "2024-02-04 15:49:06 PST"
#> Time difference of 11.26486 secs
length_mod3
#> $fixed
#> effect variance percent Chi.sq p.value
#> 1 egg_size NA NA 3.273533 0.07920792
#> 2 Fix_Tot 0.05967965 5.660793 NA NA
#>
#> $LRT.fixed
#> term d.AIC d.BIC Chi.sq p.value
#> 1 egg_size 1.273533 -3.824843 3.273533 0.07040586
#>
#> $random
#> effect effect2 variance percent
#> 1 dam:sire (Intercept) 1.788054e-01 1.696022e+01
#> 2 tray (Intercept) 1.197791e-01 1.136141e+01
#> 3 sire (Intercept) 2.251875e-09 2.135970e-07
#> 4 dam (Intercept) 1.461075e-01 1.385873e+01
#>
#> $LRT.random
#> term d.AIC d.BIC Chi.sq p.value
#> 1 (1 | dam) 14.15463 9.056258 16.15463 5.837558e-05
#> 2 (1 | sire) -2.00000 -7.098376 0.00000 1.000000e+00
#> 3 (1 | dam:sire) 141.43393 136.335557 143.43393 4.724486e-33
#> 4 (1 | tray) 122.90989 117.811511 124.90989 5.325918e-29
#>
#> $other
#> component variance percent
#> 1 Residual 0.5498915 52.15885
#> 2 Total 1.0542631 100.00000
#>
#> $calculation
#> component variance percent
#> 1 additive 9.007498e-09 8.543881e-07
#> 2 nonadd 7.152215e-01 6.784089e+01
#> 3 maternal 1.461075e-01 1.385873e+01
Produces a list object containing up to six data frames. Fixed,
random, other, and calculation data frames contain the raw variance
components and the variance components as a percentage of the total
variance component. The fixed data frame also contains the parametric
bootstrap Chi-square and p-value for any fixed effects. LRT.random and
LRT.fixed data frames contain the difference in AIC and BIC, and
likelihood ratio test Chi-square and p-value for random and any fixed
effects, respectively.
Note
Default is Restricted maximum likelihood (REML) as
ml = F. Option for maximum likelihood (ML) is
ml = T.
Maximum likelihood (ML) estimates the parameters that maximize the
likelihood of the observed data and has the advantage of using all the
data and accounting for non-independence (Lynch and Walsh 1998, p. 779;
Bolker et al. 2009). On the other hand, ML has the disadvantage of
assuming that all fixed effects are known without error, producing a
downward bias in the estimation of the residual variance component. This
bias can be large if there are lots of fixed effects, especially if
sample sizes are small. Restricted maximum likelihood (REML) has the
advantage of not assuming the fixed effects are known and averages over
the uncertainty, so there can be less bias in the estimation of the
residual variance component. However, REML only maximizes a portion of
the likelihood to estimate the effect parameters, but is the preferred
method for analyzing large data sets with complex structure.
Statistical Power analysis
Power values are calculated by stochastically simulating data for a
number of iterations and then calculating the proportion of P-values
less than \(\alpha\) (e.g. 0.05) for
each component (Bolker 2008). Simulated data are specified by inputs for
variance component values and the sample sizes.
Bolker BM. 2008. Ecological Models and Data in R. Princeton
University Press, Princeton.
Defaults are alpha = 0.05 for 5%,
nsim = 100 for 100 simulations, and ml = F for
REML. Other default is ftest = "LR" for likelihood ratio
test for fixed effects; option of “PB” for parametric bootstrap for
which the number of iterations need to be specified,
e.g. iter=1000.
var_rand is a vector of dam, sire, dam by sire,
residual, and remaining random variance components, i.e. c(dam,sire,dam
\(\times\)
sire,residual,rand1,rand2,etc.).
n_rand is a vector of dam, sire, family (i.e. dam \(\times\) sire), and remaining random sample
sizes, i.e. c(dam,sire,family,rand1,rand2,etc.).
design is a data frame of the experimental design, using
only integers. First three columns must contain and be named “dam”,
“sire”, “family”. Remaining columns are the random effects followed by
the fixed effects. Continuous fixed effects are a column containing the
values 1:nrow(design).
remain is the remaining formula using lme4
package format. Must be random effects followed by fixed effects. No
interactions or random slopes; formulate as intercepts in design.
var_fix is a vector of known fixed variance components,
i.e. c(fix1,fix2,etc.). Continuous fixed random values are sorted to
match column values.
n_fix is a vector of known fixed sample sizes,
i.e. c(fix1,fix2,etc.). Continuous fixed effects must have a sample size
of 1.
For this example, the random effect variance components of
observLmer3 above are used (i.e. dam= 0.1461, sire= 0, dam
\(\times\) sire= 0.1788, residual=
0.5499, tray= 0.1198) and the sample size of the Chinook salmon data set
(i.e. dam= 11, sire= 11, family= 121 (11 \(\times\) 11), tray= 11). The actual design
was composed of 16 trays with 55–80 offspring each. However,
powerLmer3 uses an equal number of offspring per position,
so the number of trays was decreased from 16 to 11. The fixed effect
variance component (egg_size) is 0.0597 and sample size is 11 as the
mean egg size per dam was used for each offspring. If egg size was more
of a continuous effect, i.e. differed among the offspring within dam,
then the sample size would be 1 for the simulation.
The Chinook salmon data set is reworked to contain only integers for
design.
Full analysis is 100 simulations. Example has 25 simulations.
#Reworking the Chinook salmon data set to contain only integers for `design`
#dam ID, sire ID, family ID
desn0<- data.frame(dam=rep(1:11,each=11),sire=rep(1:11,11),family=1:(11*11))
#replicate for offspring sample size (10)
desn<- do.call("rbind", replicate(10,desn0,simplify=F)); rm(desn0)
desn$tray<- rep(1:11,each=nrow(desn)/11) #equal number of offspring per tray
desn$tray<- sample(desn$tray,nrow(desn)) #shuffle tray numbers
desn$egg_size<- desn$dam #egg size is related to dam
head(desn)
#> dam sire family tray egg_size
#> 1 1 1 1 8 1
#> 2 1 2 2 3 1
#> 3 1 3 3 7 1
#> 4 1 4 4 3 1
#> 5 1 5 5 7 1
#> 6 1 6 6 1 1
#>powerLmer3(var_rand=c(0.1461,0,0.1788,0.5499,0.1198),n_rand=c(11,11,121,11),var_fix=0.0597,
#>n_fix=11,design=desn,remain="(1|tray) + egg_size") #full with LR
#full with PB and 1000 iterations
#>powerLmer3(var_rand=c(0.1461,0,0.1788,0.5499,0.1198),n_rand=c(11,11,121,11),var_fix=0.0597,
#>n_fix=11,design=desn,remain="(1|tray) + egg_size",ftest="PB",iter=1000)
powerLmer3(var_rand=c(0.1461,0,0.1788,0.5499,0.1198),n_rand=c(11,11,121,11),var_fix=0.0597,
n_fix=11,design=desn,remain="(1|tray) + egg_size",nsim=25) #25 simulations with LR
#> [1] "2024-02-04 15:49:18 PST"
#> [1] "Starting simulation: 1"
#> [1] "Starting simulation: 2"
#> [1] "Starting simulation: 3"
#> [1] "Starting simulation: 4"
#> [1] "Starting simulation: 5"
#> [1] "Starting simulation: 6"
#> [1] "Starting simulation: 7"
#> [1] "Starting simulation: 8"
#> [1] "Starting simulation: 9"
#> [1] "Starting simulation: 10"
#> [1] "Starting simulation: 11"
#> [1] "Starting simulation: 12"
#> [1] "Starting simulation: 13"
#> [1] "Starting simulation: 14"
#> [1] "Starting simulation: 15"
#> [1] "Starting simulation: 16"
#> [1] "Starting simulation: 17"
#> [1] "Starting simulation: 18"
#> [1] "Starting simulation: 19"
#> [1] "Starting simulation: 20"
#> [1] "Starting simulation: 21"
#> [1] "Starting simulation: 22"
#> [1] "Starting simulation: 23"
#> [1] "Starting simulation: 24"
#> [1] "Starting simulation: 25"
#> Time difference of 12.43282 secs
#> $group
#> group var_in var_out
#> 1 fix_eff 0.0597 0.0222310889901148
#>
#> $fixed
#> term n power
#> 1 egg_size 11 0.08
#>
#> $random
#> term n var_in var_out power
#> 1 dam 11 0.1461 0.224844825853844 1
#> 2 sire 11 0 0.0060524340096173 0
#> 3 dam.sire 121 0.1788 0.173533124995259 1
#> 4 tray 11 0.1198 0.136720128827227 1
#> 5 residual <NA> 0.5499 0.535497995336952 <NA>
There is sufficient power (\(\ge\)
0.8) for dam and dam by sire variance components, whereas there is
insufficient power (< 0.8) for the sire variance component. Albeit,
the sire component is near zero, so the low power may be an artifact.
There was also sufficient power for tray and egg size variance
components.In the cases of insufficient power, the sample size of dam,
sire, and/or offspring per family can be increased until there is
sufficient power.
Taking the reverse approach (can the sample size of dam, sire or
offspring per family be reduced while maintaining sufficient power?)
using the same variance components and offspring per family sample size,
dam and sire sample sizes could be reduced from 11 to 7. The tray sample
size was reduced accordingly to have an equal number of offspring per
tray, i.e. 7 dams \(\times\) 7 sires
\(\times\) 10 offspring = 490, which
can divided equally by 10 trays. The egg size sample size was only
reduced accordingly to match the change in dam sample size.
#dam ID, sire ID, family ID
desn0_2<- data.frame(dam=rep(1:7,each=7),sire=rep(1:7,7),family=1:(7*7))
#replicate for offspring sample size (10)
desn_2<- do.call("rbind", replicate(10,desn0_2,simplify=F)); rm(desn0)
desn_2$tray<- rep(1:10,each=nrow(desn_2)/10) #equal number of offspring per tray
desn_2$tray<- sample(desn_2$tray,nrow(desn_2)) #shuffle tray numbers
desn_2$egg_size<- desn_2$dam #egg size is related to dam
#>powerLmer3(var_rand=c(0.1461,0,0.1788,0.5499,0.1198),n_rand=c(7,7,49,10),var_fix=0.0597,
#>n_fix=7,design=desn_2,remain="(1|tray) + egg_size") #full with LR
#full with PB and 1000 iterations
#>powerLmer3(var_rand=c(0.1461,0,0.1788,0.5499,0.1198),n_rand=c(7,7,49,10),var_fix=0.0597,
#>n_fix=7,design=desn_2,remain="(1|tray) + egg_size",ftest="PB",iter=1000)
powerLmer3(var_rand=c(0.1461,0,0.1788,0.5499,0.1198),n_rand=c(7,7,49,10),var_fix=0.0597,
n_fix=7,design=desn_2,remain="(1|tray) + egg_size",nsim=25) #25 simulations with LR
#> [1] "2024-02-04 15:49:30 PST"
#> [1] "Starting simulation: 1"
#> [1] "Starting simulation: 2"
#> [1] "Starting simulation: 3"
#> [1] "Starting simulation: 4"
#> [1] "Starting simulation: 5"
#> [1] "Starting simulation: 6"
#> [1] "Starting simulation: 7"
#> [1] "Starting simulation: 8"
#> [1] "Starting simulation: 9"
#> [1] "Starting simulation: 10"
#> [1] "Starting simulation: 11"
#> [1] "Starting simulation: 12"
#> [1] "Starting simulation: 13"
#> [1] "Starting simulation: 14"
#> [1] "Starting simulation: 15"
#> [1] "Starting simulation: 16"
#> [1] "Starting simulation: 17"
#> [1] "Starting simulation: 18"
#> [1] "Starting simulation: 19"
#> [1] "Starting simulation: 20"
#> [1] "Starting simulation: 21"
#> [1] "Starting simulation: 22"
#> [1] "Starting simulation: 23"
#> [1] "Starting simulation: 24"
#> [1] "Starting simulation: 25"
#> Time difference of 7.957783 secs
#> $group
#> group var_in var_out
#> 1 fix_eff 0.0597 0.0415828511017653
#>
#> $fixed
#> term n power
#> 1 egg_size 7 0.16
#>
#> $random
#> term n var_in var_out power
#> 1 dam 7 0.1461 0.168882750794075 0.8
#> 2 sire 7 0 0.00548358319542521 0
#> 3 dam.sire 49 0.1788 0.174208501240021 1
#> 4 tray 10 0.1198 0.117153234207914 1
#> 5 residual <NA> 0.5499 0.545370141358096 <NA>
Bootstrap confidence intervals
Confidence intervals for the additive genetic, non-additive genetic,
and maternal variance components can be produced using the bootstrap-t
resampling method described by Efron and Tibshirani (1993, p. 160‒162).
Observations are resampled with replacement until the original sample
size is reproduced. The resampled data are then used in the model and
the additive genetic, non-additive genetic, and maternal variance
components are extracted. The process is repeated for a number of
iterations, typically 1,000 times, to produce a distribution for each
component. The confidence interval lower and upper limits and median are
extracted from the distribution.
Efron B, Tibshirani R. 1993. An Introduction to the Bootstrap.
Chapman and Hall, New York.
Resample observations
The resampRepli function is used to bootstrap resample
observations grouped by replicate ID within family ID for a specified
number of iterations to create the resampled data set. A similar
resampFamily function is able to resample observations
grouped by family ID only.
copy is a vector of column numbers (to copy the
contents). Does not need to contain the family and/or replicate
columns.
Full analysis is 1000 iterations. Example has 5 iterations.
#>resampRepli(dat=chinook_length,copy=c(3:8),family="family",replicate="repli",iter=1000) #full
#>resampFamily(dat=chinook_length,copy=c(3:8),family="family",iter=1000) #family only
resampRepli(dat=chinook_length,copy=c(3:8),family="family",replicate="repli",iter=5) #5 iterations
Because of the large file sizes that can be produced, the resampling
of each replicate Y per family X is saved separately as a common
separated (X_Y_resampR.csv) file in the working directory. These files
are merged to create the final resampled data set (resamp_datR.csv).
If using resampFamily, the file names are X_resampF.csv
per family and resamp_datF.csv for the final resampled data set.
Iteration variance components
The equivalent to observLmer3 is available for the final
bootstrap resampled data set, i.e. resampLmer3.
Default is ml = F for REML. The starting model number
start = and ending model number end = need to
be specified.
remain is the remaining formula using lme4
package format with # sign, e.g. fixed# + (1|random#).
Full analysis is 1000 iterations. Example has 5 iterations.
#>length_datR<- read.csv("resamp_datR.csv") #1000 iterations
#>length_rcomp3<- resampLmer3(resamp=length_datR,dam="dam",sire="sire",response="length",
#>remain="egg_size# + (1|tray#)",start=1,end=1000) #full
data(chinook_resampL) #5 iterations
head(chinook_resampL)
#> dam1 sire1 tray1 cell1 length1 egg_size1 dam2 sire2 tray2 cell2 length2
#> 1 d1 s1 t7 1A 23.1 7.27 d1 s1 t7 1A 23.1
#> 2 d1 s1 t7 1A 22.7 7.27 d1 s1 t7 1A 22.7
#> 3 d1 s1 t7 1A 22.9 7.27 d1 s1 t7 1A 22.9
#> 4 d1 s1 t7 1A 23.1 7.27 d1 s1 t7 1A 22.7
#> 5 d1 s1 t7 1A 23.1 7.27 d1 s1 t7 1A 22.9
#> 6 d1 s1 t8 1A 22.4 7.27 d1 s1 t8 1A 22.3
#> egg_size2 dam3 sire3 tray3 cell3 length3 egg_size3 dam4 sire4 tray4 cell4
#> 1 7.27 d1 s1 t7 1A 23.8 7.27 d1 s1 t7 1A
#> 2 7.27 d1 s1 t7 1A 23.8 7.27 d1 s1 t7 1A
#> 3 7.27 d1 s1 t7 1A 23.8 7.27 d1 s1 t7 1A
#> 4 7.27 d1 s1 t7 1A 23.8 7.27 d1 s1 t7 1A
#> 5 7.27 d1 s1 t7 1A 23.8 7.27 d1 s1 t7 1A
#> 6 7.27 d1 s1 t8 1A 22.4 7.27 d1 s1 t8 1A
#> length4 egg_size4 dam5 sire5 tray5 cell5 length5 egg_size5
#> 1 22.6 7.27 d1 s1 t7 1A 22.9 7.27
#> 2 23.8 7.27 d1 s1 t7 1A 22.6 7.27
#> 3 23.1 7.27 d1 s1 t7 1A 22.6 7.27
#> 4 22.9 7.27 d1 s1 t7 1A 22.9 7.27
#> 5 23.8 7.27 d1 s1 t7 1A 22.7 7.27
#> 6 22.0 7.27 d1 s1 t8 1A 22.4 7.27
length_rcomp3<- resampLmer3(resamp=chinook_resampL,dam="dam",sire="sire",response="length",
remain="egg_size# + (1|tray#)",start=1,end=5)
#> [1] "2024-02-04 15:49:38 PST"
#> [1] "Working on model: 1"
#> [1] "Working on model: 2"
#> [1] "Working on model: 3"
#> [1] "Working on model: 4"
#> [1] "Working on model: 5"
#> Time difference of 0.4564121 secs
length_rcomp3[1:5,]
#> dam:sire tray sire dam Residual Fixed Total
#> 1 0.2138559 0.1160011 0.000000e+00 0.1340714 0.4995956 0.06131461 1.0248386
#> 2 0.2402589 0.1242010 6.029765e-09 0.1376951 0.5203867 0.06188805 1.0844298
#> 3 0.2194606 0.1161735 4.287067e-08 0.1357622 0.4844443 0.04275863 0.9985993
#> 4 0.1960044 0.1330174 1.204095e-03 0.1341200 0.4919724 0.05875469 1.0150730
#> 5 0.2247567 0.1466172 0.000000e+00 0.1305175 0.4787519 0.08000904 1.0606523
#> additive nonadd maternal
#> 1 0.000000e+00 0.8554237 0.1340714
#> 2 2.411906e-08 0.9610355 0.1376951
#> 3 1.714827e-07 0.8778425 0.1357622
#> 4 4.816382e-03 0.7840176 0.1329159
#> 5 0.000000e+00 0.8990270 0.1305175
The function provides a data frame with columns containing the raw
variance components for dam, sire, dam by sire, residual, total,
additive genetic, non-additive genetic, and maternal. Also columns
containing the raw variance components for any additional fixed and/or
random effects. The number of rows in the data frame matches the number
of iterations in the resampled data set and each row represents a model
number.
Plotting confidence intervals
The barMANA and boxMANA functions are
simple plotting functions for the confidence intervals or all values,
respectively, from the bootstrap and jackknife approaches. Default is to
display the percentage values as type = perc. Raw values
can be displayed as type = raw.
Within the functions, there are simple plot modifications available.
For the y-axis, min and max values can be species as ymin
and ymax, as well as the increment as yunit.
Also, magnification of the axis unit as cex_yaxis and label
as cex_ylab. The position of the legend can be specified as
leg. Default is “topright”.
Bar plot
The barMANA function produces bar graphs with the
bootstrap-t median (ciMANA3) or jackknife pseudo-value mean
(ciJack3) as the top of the shaded bar and error bars
covering the range of the confidence interval for each of the additive
genetic, non-additive genetic, and maternal values of a phenotypic
trait.
The length of the error bar can be specified in inches as
bar_len.
length_ci<- ciJack3(comp=chinook_jackL,remain=c("tray","Residual"),full=c(0,0.7192,0.2030,1.0404,
0.1077,0.5499))
oldpar<- par(mfrow=c(2,1))
barMANA(ci_dat=length_ci) #basic, top
barMANA(ci_dat=length_ci,bar_len=0.3,yunit=20,ymax=100,cex_ylab=1.3) #modified, bottom
Different traits can also be combined on the same bar plot using
trait specified in ciMANA3 or
ciJack3. The information is combined into a list object.
For the example, the jackknife CI is duplicated to simulate ‘different
traits’.
length_ci1<- ciJack3(comp=chinook_jackL,remain=c("tray","Residual"),full=c(0,0.7192,0.2030,1.0404,
0.1077,0.5499),trait="length_1")
length_ci2<- ciJack3(comp=chinook_jackL,remain=c("tray","Residual"),full=c(0,0.7192,0.2030,1.0404,
0.1077,0.5499),trait="length_2")
comb_bar<- list(raw=rbind(length_ci1$raw,length_ci2$raw),
percentage=rbind(length_ci1$percentage,length_ci2$percentage))
barMANA(ci_dat=comb_bar,bar_len=0.3,yunit=20,ymax=100,cex_ylab=1.3)
The legend is slightly off in the presented html version but is fine
with the R plotting device.
Box plot
The boxMANA function produces box plots using all values
for the bootstrap-t resampling data set (resampLmer3) or
jackknife resampling data set (JackLmer3).
oldpar<- par(mfrow=c(2,1))
boxMANA(comp=chinook_bootL) #from resampLmer3, basic, top
boxMANA(comp=chinook_bootL,yunit=20,ymax=100,cex_ylab=1.3,leg="topleft") #modified, bottom
Different traits can also be combined on the same box plot by adding
a “trait” column to the resampling data set. For the example, the
bootstrap-t data frame is duplicated to simulate ‘different traits’.
chinook_bootL1<- chinook_bootL; chinook_bootL2<- chinook_bootL #from resampLmer3
chinook_bootL1$trait<- "length_1"; chinook_bootL2$trait<- "length_2"
comb_boot<- rbind(chinook_bootL1,chinook_bootL2)
comb_boot$trait<- as.factor(comb_boot$trait)
boxMANA(comb_boot,yunit=20,ymax=100,cex_ylab=1.3,leg="topleft")
The recommended follow-up vignette is the Simple Non-Normal
Data Example, covering the standard model only for non-normal
error structures (e.g. binary, proportion, and/or count data types).
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.