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For introductory information about Genetix, please go back and read the About Genetix page.
Genetix performs the assignment test as follows. (1) It removes the test individual’s genotype from the population it was sampled in and estimates allele frequencies in that population at each locus (pil, pjl … for alleles i, j, … at locus l). (2) It determines the genotype’s expected frequency in that population at each locus (pil2 for homozygotes, 2pilpjl for heterozygotes). (3) It multiplies across loci and log-transforms the product, producing the "assignment index" for the test genotype in the population it was found in. (4) It performs the same calculations to estimate the genotype’s frequency in the second population (its assignment index in that population). (5) Finally, it assigns the genotype to the population in which it has the highest expected frequency.
In estimating allele frequencies, a problem arises when the test genotype contains an apparently unique allele: because the test genotype is not included when calculating population allele frequencies, the expected frequency of that allele in all the putative source populations is zero. Various "zero-avoidance" procedures have been suggested (Waser and Strobeck 1998, Davies et al. 1999). Genetix uses the following approach: we add 1/a copies of every allele observed in either of the putative source populations into both populations. We then calculate the expected frequency of an allele as p = (f + 1/a)/(n + 1), where f is the number of copies of that allele observed in the population, n is the number of gene copies for that locus in the population, and a is the total number of alleles at that locus observed in either population.
A website that allows you to perform the assignment test and calculate related statistics with data of your own is at: www.biology.ualberta.ca/jbrzusto/Doh.html
Genetix is written in PowerBasic and is a DOS-based program. It will run under DOS, Windows 95,98, and ME. Compatibility under NT has not been tested.
To run Genetix after downloading it:
1. Demographic variables
2. Genetic variables
3. Aspects of sampling and display
1. Demographic variables:
The assignment test is appropriate only when populations are discrete. Normally, Genetix simulates two populations, 1 and 2, that exchange dispersers; outputs are genotype lists and/or assignment indices for 1 and 2’s members. However, Genetix can also simulate either a single population (in which case genotypes can be output, but assignment indices cannot be calculated). Perhaps of more general interest, Genetix can simulate 4, 8, 12 or 16 populations that exchange members randomly (the "island" model). In these cases, complete lists of genotypes are available but Genetix assumes that the investigator is only sampling populations 1 and 2 and calculates only the proportions of animals misassigned between these two populations.
Population size may be fixed at 12, 24, 50, or 100. Whatever the value of N, the first _ of the individuals are females, the second _ males. Population sizes >100 cannot be accommodated with this version of Genetix due to array size limitations. During the simulation, population sizes can drop slightly below N if more individuals emigrate from the population than immigrate into it, but they cannot exceed N.
During the "dispersal" step of the simulation, each individual emigrates from each population with a probability m. Possible m values are 0, 0.0025, 0.005, 0.01, … 0.32 per generation, or all of these in sequence (in this case, the program runs a series of simulations replicates, starting with m = 0 and ending with m = 0.32). After all emigration has occurred, each disperser is allowed to immigrate into the other population. Immigrants move preferentially into slots left empty by emigrants, but if more immigrants exist than slots, each extra immigrant replaces a random, same-sexed resident. As a result, m is the probability per generation that an animal not only emigrates, but also successfully immigrates into another population. In effect, we are assuming that there is a strict upper limit to population size; when the number of emigrants from the two populations is not identical, the population with the larger number of emigrants is slightly reduced in size, but the population with more immigrants cannot grow larger than N.
The dispersal step is applied only to "new" individuals, that is, if annual adult mortality is set < 1.0, surviving adults do not disperse again. Therefore, the simulation deals only with natal dispersal and m is a per-generation dispersal probability. In this implementation of Genetix, dispersal is reciprocal, that is, there is no source-sink structure to the populations.
If desired, This value can be set instead of m. Changing the value of Nm changes the value of m appropriately, and vice versa.
The default is sex-unbiased dispersal (50%) but the proportion of dispersers that are male can also be set to 60%, 70%, … 100% (only males disperse). When only males disperse, the probability of dispersal per male is 2m, that per female is 0; in other words, the proportion of animals dispersing remains constant.
The default is nonoverlapping generations, semelparity, adult mortality rate = 1.0.
Mating follows dispersal; when reproduction is semelparous, mating is repeated until the number of offspring equals N, at which point all adults die and are replaced by offspring. To simulate overlapping generations, we allow each adult to die with a probability d (where d = 0.25, 0.50, or 0.75), then choose randomly among the offspring to bring the population size back up to N.
The default is "random". During the "mating" step, Genetix draws one male and one female randomly from the population, and an offspring is formed by combining, locus by locus, one of the male’s two gene copies at that locus with one of the female’s. Loci are thus assumed to assort independently, and unless otherwise noted, mating is random with the constraint that sexes are separate. Mating is repeated (with replacement of both sexes) until the number of offspring equals N, at which point adult mortality takes place. Alternatives to random mating are strict monogamy (each male mates with one and only one female, and vice versa, during a breeding season; each couple has the same probability of producing offspring) and extreme polygyny (one, randomly-chosen male in each population fathers all young during a breeding season; mothers are drawn randomly, with replacement, from the pool of all females until all young are produced).
2. Genetic variables
The number of loci whose genotypes are tracked by Genetix, can be set at 8, 12, 16 or 20.
The number of possible allelic states that a locus can assume is normally set at 12 but can be set at 25 or 50 (appropriate numbers for microsatellites), or to 2. Note that the actual number of alleles found in any particular population at any one time is often far below k.
During the "mutation" step of the simulation, each gene copy at each locus mutates with a probability m. The default mutation rate is 0.001; an appropriate rate for microsatellites (Weber and Wong 1993); lower (0.0001, 0.0005) and higher (0.005, 0.01) rates are possible.
In the default setting, mutation occurs according to a stepwise model; as is approximately the case for microsatellites, mutation consists of a gain or a loss of one tandem repeat unit. There are upper and lower limits on allele size; the first allelic state can mutate only by gaining a repeat unit (with a probability of _ m) and the kth allelic state can mutate only by losing one (Weber and Wong 1993, Nauta and Weissing 1996, Gaggiotti et al. 1999).
Alternately, under "k-allele" mutation, a mutation causes the number of tandem repeats to change randomly to one of the k possible allelic states, each represented with a probability of 1/k.
3. Aspects of sampling and display
At the beginning of a simulation, Genetix draws alleles randomly from a uniform distribution for all individuals (thus all alleles are approximately equiprobable, and all populations are genetically similar). Genetix can then simulates some number of generations, each consisting sequentially of mutation, dispersal, mating and death. During this period, many of the initial alleles are lost due to drift, and drift and mutation can equilibrate. Following the dispersal step in the last simulated generation, Genetix records individual genotypes and/or performs assignment tests. The default is 1000 generations. Genotypes (or assignment indices) can also be output after 1, 100, 500,or 5000 generations, but with fewer generations populations will not have reached equilibrium.
This sets the number of replicates run before output files are created and can be set at 1, 10, 100, or 500.
When producing genotype lists or running assignment tests, Genetix can randomly sample a proportion s of the adults living in the population during the final generation of the simulation. The default s = 100%, but decreasing s to 12%, 25%, or 50% mimics the situation faced by investigators who cannot sample their populations exhaustively.
Several diagnostics can be displayed as the simulation runs as a function of time (=number of generations): actual dispersal rate (animals per generation); actual mutation rate (mutations/locus/generation); observed heterozygosity; or observed number of alleles. All of these are calculated (arbitrarily) for population 1 only, and the latter three are calculated for locus 1 in population 1 only.
If this option is set to "AI", Genetix will display only the generation and replicate number as the simulation runs but will display a plot of each genotype’s assignment indices in populations 1 vs. 2 at the end of each simulation replicate. This display usually gives a reasonably intuitive picture of the degree of differentiation of genotypes in the two simulated populations. However, note that the scaling of this graph is set to be appropriate for "average" population sizes and numbers of loci. Because the absolute values of the assignment indices will depend on the population size and the numbers of loci used, this display may not be useful when running simulations with very large or small values of these parameters.
Using option "G", Genetix produces lists of genotypes, each individual tagged with its sex and its "status" (resident, immigrant, offspring of immigrant, etc.), in the ASCII format used by program GENPOP (Raymond and Rousset 1995). With option "AI", Genetix produces lists of individuals with their status and assignment indices, again in ASCII format. The first lines of the genotype or assignment index files summarize the parameter values used in the simulation, and should be deleted if the file is to be imported into another program for statistical analysis. The output "PMA" creates a file containing only simulation parameter values and the summary statistic "proportion of animals misassigned" for the two (or the first two of the N) simulated populations. As is described in more detail in Waser et al.(in press), PMA can be used as a reasonable index of interpopulation dispersal rate under many circumstances.
The default is the directory that Genetix is run in. If another directory is desired, enter the name of the directory using DOS conventions (for example \directory\subdirectory\)