\name{rfitness}
\alias{rfitness}

\title{Generate random fitness.}

\description{ Generate random fitness landscapes under a House of Cards,
Rough Mount Fuji, additive model, and Kauffman's NK model.  }

\usage{

rfitness(g, c = 0.5, sd = 1, mu = 1, reference = "random", scale = NULL,
wt_is_1 = c("subtract", "divide", "force", "no"),
log = FALSE, min_accessible_genotypes = NULL,
accessible_th = 0, truncate_at_0 = TRUE,
K = 1, r = TRUE, model = c("RMF", "NK"))
}

\arguments{

\item{g}{Number of genes.}

\item{c}{The decrease in fitness of a genotype per each unit increase
in Hamming distance from the reference genotype (see \code{reference}).}

\item{sd}{The standard deviation of the random component (a normal
distribution of mean \code{mu} and standard deviation \code{sd}).}

\item{mu}{The mean of the random component (a normal distribution of
mean \code{mu} and standard deviation \code{sd}).}

\item{reference}{The reference genotype: for the deterministic, additive
part, this is the genotype with maximal fitness, and all other
genotypes decrease their fitness by \code{c} for every unit of Hamming
distance from this reference. If "random" a genotype will be randomly
chosen as the reference. If "max" the genotype with all positions
mutated will be chosen as the reference. If you pass a vector (e.g.,
\code{reference = c(1, 0, 1, 0)}) that will be the reference genotype.
If "random2" a genotype will be randomly chosen as the reference. In
contrast to "random", however, not all genotypes have the same
probability of being chosen; here, what is equal is the probability
that the reference genotype has 1, 2, ..., g, mutations (and, once a
number mutations is chosen, all genotypes with that number of
mutations have equal probability of being the reference). }

\item{scale}{Either NULL (nothing is done) or a two-element vector. If a
two-element vector, fitness is re-scaled between \code{scale[1]} (the
minimum) and \code{scale[2]} (the maximum).}

\item{wt_is_1}{If "divide" the fitness of all genotypes is
divided by the fitness of the wildtype (after possibly adding a value
to ensure no negative fitness) so that the wildtype (the genotype with
no mutations) has fitness 1. This is a case of scaling, and it is
applied after \code{scale}, so if you specify both
"wt_is_1 = 'divide'" and use an argument for \code{scale} it is most
likely that the final fitness will not respect the limits in
\code{scale}.

If "subtract" (the default) we shift all the fitness values (subtracting fitness of
the wildtype and adding 1) so that the wildtype ends up with a fitness
of 1. This is also applied after \code{scale}, so if you specify both
"wt_is_1 = 'subtract'" and use an argument for \code{scale} it is most
likely that the final fitness will not respect the limits in
\code{scale} (though the distorsion might be simpler to see as just a
shift up or down).

If "force" we simply set the fitness of the wildtype to 1, without any
divisions. This means that the \code{scale} argument would work (but
it is up to you to make sure that the range of the scale argument
includes 1 or you might not get what you want). Note that using this
option can easily lead to landscapes with no accessible genotypes
(even if you also use \code{scale}).

If "no", the fitness of the wildtype is not modified.  }

\item{log}{If TRUE, log-transform fitness. Actually, there are two
cases: if \code{wt_is_1 = "no"} we simply log the fitness values;
otherwise, we log the fitness values and add a 1, thus shifting all
fitness values, because by decree the fitness (birth rate) of the
wildtype must be 1.}

\item{min_accessible_genotypes}{If not NULL, the minimum number of
accessible genotypes in the fitness landscape. A genotype is
considered accessible if you can reach if from the wildtype by going
through at least one path where all changes in fitness are larger or
equal to \code{accessible_th}. The changes in fitness are considered
at each mutational step, i.e., at each addition of one mutation we
compute the difference between the genotype with \code{k + 1}
mutations minus the ancestor genotype with \code{k} mutations. Thus, a
genotype is considered accessible if there is at least one path where
fitness increases at each mutational step by at least
\code{accessible_th}.

If the condition is not satisfied, we continue generating random
fitness landscapes with the specified parameters until the condition
is satisfied.

(Why check against NULL and not against zero? Because this allows you
to count accessible genotypes even if you do not want to ensure a
minimum number of accessible genotypes.)
}

\item{accessible_th}{The threshold for the minimal change in fitness at
each mutation step (i.e., between successive genotypes) that allows a
genotype to be regarded as accessible. This only applies if
\code{min_accessible_genotypes} is larger than 0.  So if you want to
allow small decreases in fitness in successive steps, use a small
negative value for \code{accessible_th}.  }

\item{truncate_at_0}{If TRUE (the default) any fitness <= 0 is
substituted by a small positive constant (a random uniform number
between 1e-10 and 1e-9). Why? Because MAGELLAN and some plotting
routines can have trouble (specially if you log) with values <=0. Or
we might have trouble if we want to log the fitness. This is done
after possibly taking logs. Noise is added to prevent creating several
identical minimal fitness values.}

\item{K}{K for NK model; K is the number of loci with which each locus
interacts, and the larger the K the larger the ruggedness of the
landscape.}

\item{r}{For the NK model, whether interacting loci are chosen at random
(\code{r = TRUE}) or are neighbors (\code{r = FALSE}).}

\item{model}{One of "RMF" (default), for Rough Mount Fuji, or "NK", for
Kauffman's NK model.}
}

\details{

When using \code{model = "RMF"}, the model used here follows
the Rough Mount Fuji model in Szendro et al., 2013 or Franke et al.,
2011. Fitness is given as

\deqn{f(i) = -c d(i, reference) + x_i}

where \eqn{d(i, j)} is the Hamming distance between genotypes \eqn{i}
and \eqn{j} (the number of positions that differ) and \eqn{x_i} is a
random variable (in this case, a normal deviate of mean \code{mu}
and standard deviation \code{sd}).

Setting \eqn{c = 0} we obtain a House of Cards model. Setting \eqn{sd
= 0} fitness is given by the distance from the reference and if the
reference is the genotype with all positions mutated, then we have a
fully additive model (fitness increases linearly with the number of
positions mutated).

For OncoSimulR, we often want the wildtype to have a mean of
1. Reasonable settings are \code{mu = 1} and \code{wt_is_1 =
'subtract'} so that we simulate from a distribution centered in 1, and
we make sure afterwards (via a simple shift) that the wildtype is
actuall 1. The \code{sd} controls the standard deviation, with the
usual working and meaning as in a normal distribution, unless \code{c}
is different from zero. In this case, with \code{c} large, the range
of the data can be large, specially if \code{g} (the number of genes)
is large.

When using \code{model = "NK"}, the model used is Kauffman's NK model
(see details in Ferretti et al., or Brouillet et al., below), as
implemented in MAGELLAN
(\url{http://wwwabi.snv.jussieu.fr/public/Magellan/}). This fitness
landscape is generated by directly calling the \code{fl_generate}
function of MAGELLAN. Fitness is drawn from a uniform (0, 1)
distribution.

}

\value{

An matrix with \code{g + 1} columns. Each column corresponds to a
gene, except the last one that corresponds to fitness. 1/0 in a gene
column denotes gene mutated/not-mutated. (For ease of use in other
functions, this matrix has class  "genotype_fitness_matrix".)

If you have specified \code{min_accessible_genotypes > 0}, the return
object has added attributes \code{accessible_genotypes} and
\code{accessible_th} that show the number of accessible
genotypes under the specified  threshold.
}

\note{MAGELLAN uses its own random number generating functions; using
\code{set.seed} does not allow to obtain the same fitness landscape
repeatedly.}

\references{

Szendro I.~G. et al. (2013). Quantitative analyses of empirical
fitness landscapes. \emph{Journal of Statistical Mehcanics: Theory and
Experiment\/}, \bold{01}, P01005.

Franke, J. et al. (2011). Evolutionary accessibility of mutational
pathways. \emph{PLoS Computational Biology\/}, \bold{7}(8), 1--9.

Brouillet, S. et al. (2015). MAGELLAN: a tool to explore small fitness
landscapes. \emph{bioRxiv},
\bold{31583}. \url{http://doi.org/10.1101/031583}

Ferretti, L., Schmiegelt, B., Weinreich, D., Yamauchi, A., Kobayashi,
Y., Tajima, F., & Achaz, G. (2016). Measuring epistasis in fitness
landscapes: The correlation of fitness effects of mutations. \emph{Journal of
Theoretical Biology\/}, \bold{396}, 132--143. \url{https://doi.org/10.1016/j.jtbi.2016.01.037}

MAGELLAN web site: \url{http://wwwabi.snv.jussieu.fr/public/Magellan/}

}

\author{ Ramon Diaz-Uriarte for the RMF and general wrapping
code. S. Brouillet, G. Achaz, S. Matuszewski, H. Annoni, and L. Ferreti
for the MAGELLAN code.

}

\seealso{

}
\examples{

## Random fitness for four genes-genotypes,
## plotting and simulating an oncogenetic trajectory

r1 <- rfitness(4)
plot(r1)
oncoSimulIndiv(allFitnessEffects(genotFitness = r1))

## NK model
rnk <- rfitness(5, K = 3, model = "NK")
plot(rnk)
oncoSimulIndiv(allFitnessEffects(genotFitness = rnk))
}

\keyword{ datagen }