Fried index — fried

Index of the mating competitiveness of sterile males relative to wild males.

Usage

fried_index(
  sterile_wild_mr,
  natural_fertility,
  sit_fertility,
  residual_fertility
)

Arguments

sterile_wild_mr: Non-negative number. Ratio of sterile to wild males in the target population.
natural_fertility: Number between 0 and 1. Proportion of fertile eggs in a natural (wild) population.
sit_fertility: Number between 0 and 1. Proportion of fertile eggs in the target population.
residual_fertility: Number between 0 and 1. Proportion of fertile eggs in a completely sterile population. Also called residual fertility.

Value

Non-negative number.

Details

The competitiveness $\gamma$ of the sterile male individuals is defined as their relative capacity to mate with a wild female, compared to a wild male.

Thus, in a homogeneously mixed population with $M_s$ sterile males and $M_w$ wild males, the probability that a mating occurs with a sterile individual is $$ p_s = \frac{\gamma M_s}{M_w + \gamma M_s} = \frac{\gamma R_{sw}}{1 + \gamma R_{sw}}, $$ where $R_{sw} = M_s/M_w$ is the sterile-wild male ratio. At a given sterile-wild male ratio $R_{sw} = M_s/M_w$ we observe a fertility rate $H_s$ in the field.

Assuming a residual fertility rate $H_{rs}$ for sterile males and a natural fertility rate $H_w$ for wild males, the observed fertility rate $H_s$ in the field is: $$ H_s = p_s H_{rs} + (1-p_s)H_w = \frac{\gamma R_{sw}}{1 + \gamma R_{sw}} H_{rs} + \frac{1}{1 + \gamma R_{sw}} H_w. $$

Examples

fried_index(
  sterile_wild_mr = 0.3,
  natural_fertility = .9,
  sit_fertility = .71,
  residual_fertility = .05
)
#> [1] 0.959596