general_cline_eqn: Calculate allele frequencies for a cline
In tjthurman/BAHZ: Bayesian Analysis of Hybrid Zones

Description Usage Arguments Details Value Examples

A flexible function to evaluate hybrid zone genetic cline equations, with or without introgression tails.

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general_cline_eqn(transectDist, decrease = c(TRUE, FALSE), center, width,
  pmin = 0, pmax = 1, deltaL = NULL, tauL = NULL, deltaR = NULL,
  tauR = NULL)

`transectDist`	The position(s) at which to evaluate the cline equation. Must be a numeric vector.
`decrease`	Is the cline decreasing in frequency? `TRUE` or `FALSE`.
`center`	The location of the cline center, in the same distance units as `transectDist`. Numeric.
`width`	The width of the cline, in the same distance units as `transectDist`. Numeric, must be greater than 0.
`pmin, pmax`	Optional. The minimum and maximum allele frequency values in the tails of the cline. Default values are `0` and `1`, respectively. Must be between 0 and 1 (inclusive). Numeric.
`deltaL, tauL`	Optional delta and tau parameters which describe the left exponential introgression tail. Must supply both to generate a tail. Default is `NULL` (no tails). Numeric. tauL must be between 0 and 1 (inclusive).
`deltaR, tauR`	Optional delta and tau parameters which describe the right exponential introgression tail. Must supply both to generate a tail. Default is `NULL` (no tails). Numeric. tauR must be between 0 and 1 (inclusive).

This function evaluates hybrid zone cline equations of the general form:

p = (e^(4*((x-center))/(width))/((1+ e^(4*((x-center))/(wwidth)))

Where center is the center of the cline, width is the width of the cline, x is the distance along the transect, and p is the expected frequency of the allele.

This function can also include introgression tails by specifying delta and tau paramters. For the left introgression tail, when x ≤ (center - δ):

p = 1/(1 + e^(4(δ)/(w)))*\exp((4τ(x-c+δ)/width)/(1+e^(-4(δ)/(w))))

For the right introgression tail, when x ≥ (center + δ):

p = 1- 1/(1 + e^(4(δ)/(w)))*\exp((-4τ(x-c-δ)/width)/(1+e^(-4(δ)/(w))))

The above equations all describe an increasing cline with minimum and maximum values of 0 and 1. This equation can be rescaled for other minima and maxima:

p' = p_{min} + (p_{max} - p_{min})*p

And for clines which decrease in frequency:

p' = p_{min} + (p_{max} - p_{min})*(1-p)

The function will automatically use the appropriate equation based on arguments supplied by the user.

The result of evaluating a cline equation with the specified parameters at the specified distance(s) (that is, p' in the notation of the equations above). A numeric vector equal in length to the transectDist argument.

## Not run: 
# Calculate the allele frequency at x = 100 for an increasing cline
# with a center at x = 125, a width of 40, and no tails.

general_cline_eqn(transectDist = 100, decrease = F,
                  center = 125, width = 40)

# Calculate the allele frequency at x = 84 and x = 100 for a decreasing cline
# with a center at 76, a width of 22, and a right tail
# with deltaR = 7.5, tauR = 0.45.

general_cline_eqn(transectDist = c(84,100), decrease = TRUE,
                 center = 76, width = 22,
                 deltaR = 7.5, tauR = .45)

## End(Not run)