Project: s41467-024-53065-z | Function: SetFertility (cpp)

system: You are an expert C++ programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow C++ best practices and maintain consistent code style.
Return **only** the complete C++ function code.

user: Complete this C++ function:

**DESCRIPTION:** Implements the gene drive inheritance mechanism for dsx-targeting suppression drives, calculating offspring genotype probabilities based on parental genotypes with homing rate and fitness costs

**KEY TERMS:** {
  "pa.e": "homing rate in females",
  "pa.xi": "somatic Cas9 expression fitness cost",
  "pa.gamma": "rate of r2 allele formation",
  "Fwdwd": "offspring from W/D x W/D cross",
  "f[i][j][k]": "inheritance probability matrix",
  "0:ww,1:wd,2:dd,3:wr,4:rr,5:dr": "genotype indices"
}

**CONTEXT CODE:**
    "0:ww,1:wd,2:dd,3:wr,4:rr,5:dr": "genotype indices"
  }
  We are provided with a description. The code provided includes reading input parameters from files? Perhaps the incomplete function is encompassed in a "Complete this function" directive. The incomplete code has this part:

  "Complete this CPP function: <function code> replacing 'throw std::runtime_error("Not implemented");'"

  The code snippet from the conversation is:

  Complete the function implementation replacing 'throw std::runtime_error("Not implemented");'.

  So what is the function? It is likely the function which computes probabilities? It is not exactly given. We might guess it's something like "SetFertility()" or some other function that calculates genotype inheritance probabilities for dsx-targeting suppression drives. And the missing function is something like "complete function Implementation?"; but we might assume the function is called "SetFertility" (the comment says "/*--------------------------------Set inheritance architecture--------------------------*/". "SetFertility" is called before the simulation runs. "gene drive inheritance mechanism for dsx-targeting suppression drives, calculating offspring genotype probabilities based on parental genotypes with homing rate and fitness cost" - this is calculated using a matrix maybe called "f[i][j][k]" of size? The key terms indices (genotype indices: "0:ww,1:wd,2:dd,3:wr,4:rr,5:dr"). So we shall try to design a function that handles the probabilities. 

  We know the key term Fwdwd refers to "offspring from W/D x W/D cross", which is exactly the cross between a W allele? But likely parent genotypes refer to wild type cross. There is mention "rs or dd? Actually "WD" might be: maybe "W" stands for 'wasp'? Wait, but the text "dsx-targeting suppression drives" implies editing the dsx gene. So "w" could be wild allele, "d" could be drive allele, "r" could be reversion allele? Yes, likely: 
  - "w" allele = wild allele 
  - "d" allele = normal allele that has drive insert (but not dsx-targeting gene drive because it targets dsx)
  - "r" allele = reversion allele formed with recalle of gene drive maybe; or r2 allele. Wait construct: key term: "wd" is genotype index 1, "dd" is genotype index 2, then "wr" is genotype index 3, "rr" is genotype index 4, and "dr" is genotype index 5. So not a standard VCF: 
  Index: 
  0:ww means both copies are wild allele, 
  1:wd means one wild allele and one drive allele from suppression drive? 
  2:dd means two drive alleles? 
  3:wr means one wild allele and one reversion allele? 
  4:rr means two reversion alleles? 
  5:dr means one drive allele and one reversion allele? 
  Fwdwd mentioned is offspring from W/D x W/D cross, meaning females with genotype W/D, so possbily they are heterozygous mothers crossing with wild type or drive allele? But Fwdwd stands for independent genotype "F" stands for female and "wd" stands for genotype? Wait, the code portion "Fwdwd = offspring from W/D x W/D cross" which is already in the snippet. It suggests that in a simulation model of Mosquito suppression, two classes of inheritance probabilities - for a cross of a female with genotype 1 (maybe dsx-targeting gene drive genotype that targets only females? Because the dsx gene is female in Drosophila? Actually "dsx" in mosquitoes? "DSX gene" stands for doublesex gene. But in mosquitoes, the dsx gene is expressed differently in males and females. The text says gate dsx-targeting suppression drives implement gene drive inheritance mechanism. In mosquitoes, female specific drives maybe? "pa.e" refers to "homing rate in females". So the function likely calculates the outcomes of crosses, where the drive allele is transmitted at high rate in females assuming homing occurs in germline editing. In males,Fitness cost due to presence of Cas9 is maybe dsx Cas9? Possibly explanation:
  - In females, the dsx-targeting CRISPR system enhances homing of drive, target dd cross? 
  - Meanwhile, 'pa.xi' is "somatic Cas9 expression fitness cost": so cas9 expression in cells may reduce viability.

  The text "pa.gamma: rate of r2 allele formation" is "r2 allele formation". Perhaps the r2 allele is the spontaneously mutated allele that gives gene drive reversions. We could design a function that takes parent's genotype codes (like indices with 0:ww, 1:wd, 2:dd, 3:wr, 4:rr, 5:dr) probability matrix might be stored in f[i][j][k] whereby i and j are parental genotypes and k is the resulting genotype index. The code snippet does not show this matrix definition, but we want to compute cross probabilities for drive inheritance.

  Also "dsx-targeting suppression drives" means that the drive doesn't self-perpetuate in males maybe because homing event only occurs in female germline. "Fwdwd" is an indicator for certain cross: female with genotype "wd" (i.e., heterozygous for drive allele) crossing with a male presumably. But wait, "x" stands for second parent's genotype: x likely is heterozygous as well? 
  Maybe the function is to calculate "inheritance probability matrix f". The matrix f[i][j][k] seems to be a 3-d array, where i, j, and k are i, j and k indices representing parental genotype codes: i, j (which is parent's genotype? Possibly maternal genotype and paternal genotype) and k indexing the offspring genotype? We see key terms "Fwdwd" (i.e., from cross W/D x W/D) yields a list of probabilities which are then used. Alternatively, it's not detailed.

  The question: "Complete this CPP function" and "replacing throw std::runtime_error()" means that originally a catch-all placeholder provided in some library. We are to complete the implementation.

  Let us assume we have something like:

  For a given cross between maternal genotype i and paternal genotype j, the probability matrix f is computed as follows.

  We have parental indices: 0:ww, 1:wd, 2:dd, 3:wr, 4:rr, 5:dr

  Now, we need to incorporate "pa.e" (homing rate in females); "pa.xi" (fitness cost); "pa.gamma": formation rate conversion of one allele to "r2"? Possibly "r2" allele is a reversed allele that disrupts the drive.

  We can guess the following logic:
  - In a gene drive inheritance model, we have a "drive" allele (say "d") which has a high conversion rate in the germline in heterozygotes, called homing, with rate pa.e. But also there's fitness cost pa.xi affecting somatic cells, so maybe if the offspring are heterozygous or drive carry, they have reduced fitness.

  Look up: "dsx-targeting suppression drives" likely means that the drive is targeted to the doublesex locus so that mostly one sex is the target then? But here, pa.e is exclusively for females? There's the "gene drive inheritance mechanism for dsx-targeting suppression drives", so likely male germlines do not have CRISPR editing and thus they produce wild-type gametes for the allele, meaning the drive allele is maternal in females. But in addition there is r2 allele formation. The parameter "pa.gamma" is the rate of r2 allele formation. 

  Maybe we need to simulate bisexual crosses with maternal drive activity. Perhaps we need to compute 6 probabilities of offspring genotype from each combination:

  Let's assume the following general mechanism: 
  For each maternal genotype:
  - If maternal genotype contains "w" allele exclusively (i.e. 0, and 3/W or possibly 3? because 3 is "wr" which has a wild allele plus a r allele, not drive allele) the drive is not present, so standard Mendelian segregation with no homing transmission. But not exactly if the female is heterozygous drive (wd, dd, dr maybe drive allele)? However, note that the key terms indices: 
  - 1: wd, 2: dd. 
  So drive alleles are "d", while wild alleles are "w". There are also alleles "r". The r allele might be a reversion mutation of the drive allele. 
  Maybe outcomes for cross of two heterozygotes (for maternal and paternal): Some events: 
  1. If there is a drive allele "d", then in female offspring, there might be a homing event converting the homologous chromosome to the drive allele with probability pa.e, unless already mutated to r or something? 
  But wait, no, dsx-targeting gene drives with CRISPR have high conversion rates in germline cells for the drive allele in heterozygotes, resulting in drive allele transmission in all progeny. But previously published models (like those of O. heyduk) assume that in females, the drive allele in the germline is converted to maintain drive frequency. So if a female heterozygote mates, then autosomal drive allele is transmitted with probability close to 1 in female offspring, due to homing.

  But "dsx-targeting suppression drives" might try to suppress a population by gene conversion of wild type to drive allele. Let us assume: In females, if genotype is heterozygous (either 1 for w/d or 5 for d/r, or possibly 2 for dd? But 2: dd is already homozygous drive, so no homing is needed since it's already drive allele). 
  But since "pa.e" is the homing rate in females, that only applies if homologous drive is present. So:
  - For a female heterozygote with genotype X, where one allele is wild and the other drive (or possibly mutations), the drive will be home with probability pa.e, provided that the homing enzyme on the drive allele is not affected by a mutation? 
  But given the code snippet, we see Fwdwd, likely indicates the probability distribution for offspring from a W/D cross. Let's define some probabilities using "pa.e" and maybe a no-homing chance.

  Maybe we should consider if parent is heterozygous with genotype index 1 (w/d). Then in her eggs: With probability pa.e, the homologous wild allele gets converted to drive allele, so all eggs get drive allele, and with probability (1 - pa.e) eggs have standard Mendelian segregation. But standard segregation: if the female is heterozygous, then there is a 50% chance of drive allele and 50% wild allele, correct? So the overall probability of offspring being drive allele is pa.e*1 + (1-pa.e)*0.5 = 0.5 + pa.e*0.5. However, this is not exactly what gene drive typically do; correct gene drive inheritance (for homing in females with a dsx-targeting drive) is nearly deterministic: drive allele is copied into the homolog and the wild allele is diluted out. But for dsx drives, typically, all female offspring inherit the drive allele if homing is effective enough, but here there is possibility of homing cost if no homing occurs, maybe? 
  Maybe then, if a daughter is heterozygote (w/d), then there is a probability (1 - pa.e) that the wild allele segregs and the offspring gets wild allele.

  We then also consider that drive expression in females might cause fitness cost in somatic cells of female germline, which could lower overall viability. This is parameter pa.xi. 
  So for female offspring genotype "W" (wild) and "D" (drive) there would be a difference of fitness cost. But the function "SetFertility" likely sets the fertility probabilities for inheriting genotype? 
  No, it says: "Complete the function implementation replacing throw std::runtime_error("Not implemented");" So we are rewriting a function that implements gene drive inheritance. And then the provided code snippet ends with "Complete this function". 
  Maybe function name is "SetFertility" since it's called right before RunNReps. But then later we see "Fwdwd = offspring from W/D x W/D cross" is defined (maybe a variable in the simulation).