MGDrivE-Cube.RdTo model an arbitrary number of genotypes efficiently in the same mathematical framework, we use a 3-dimensional array structure (cube) where each axis represents the following information:
x: female adult mate genotype
y: male adult mate genotype
z: proportion of the offspring that inherits a given genotype (layer)
The cube structure gives us the flexibility to apply tensor operations to the elements within our equations, so that we can calculate the stratified population dynamics rapidly; and within a readable, flexible computational framework. This becomes apparent when we define the equation we use for the computation of eggs laid at any given point in time:
$$\overline{O(T_x)} = \sum_{j=1}^{n} \Bigg( \bigg( (\beta*\overline{s} * \overline{ \overline{Af_{[t-T_x]}}}) * \overline{\overline{\overline{Ih}}} \bigg) * \Lambda \Bigg)^{\top}_{ij}$$
In this equation, the matrix containing the number of mated adult females (\(\overline{\overline{Af}}\)) is multiplied element-wise with each one of the layers containing the eggs genotypes proportions expected from this cross (\(\overline{\overline{\overline{Ih}}}\)). The resulting matrix is then multiplied by a binary 'viability mask' (\(\Lambda\)) that filters out female-parent to offspring genetic combinations that are not viable due to biological impediments (such as cytoplasmic incompatibility). The summation of the transposed resulting matrix returns us the total fraction of eggs resulting from all the male to female genotype crosses (\(\overline{O(T_x)}\)).
Note: For inheritance operations to be consistent within the framework the summation of each element in the z-axis (this is, the proportions of each one of the offspring's genotypes) must be equal to one.
An inheritance cube in an array object that specifies inheritance probabilities (offspring genotype probability) stratified by male and female parent genotypes. MGDrivE provides the following cubes to model different gene drive systems:
cubeOneLocusTA: 1 Locus Maternal-Toxin/Zygotic-Antidote System
cubeTwoLocusTA: 2 Locus Maternal-Toxin/Zygotic-Antidote System
cubeClvR: 1 Locus Cleave and Rescue (ClvR)
cubeClvR2: 2 Locus Cleave and Rescue (ClvR)
cubeHoming1RA: Homing Drive with 1 Resistance Allele
cubeHomingDrive: CRISPR (Clustered Regularly Interspaced Short Palindromic Repeats) with 2 Resistance Allele
cubeECHACR: ERACR-CHACR
cubeECHACRX: ECHACR, X-Linked
cubeKillerRescue: Killer-Rescue System
cubeMEDEA: MEDEA (Maternal Effect Dominant Embryonic Arrest)
cubeReciprocalTranslocations: Reciprocal Translocation
cubeRIDL: RIDL (Release of Insects with Dominant Lethality)
cubeMendelian: Mendelian
cubeSplitDrive: Split CRISPR drive
cubeTGD: trans-complementing Gene Drive
cubeTGDX: trans-complementing Gene Drive, X-Linked
cubeWolbachia: Wolbachia
We provide one auxiliary function to operate on cube objects.
cube2csv: Export slices of a cube to .csv format