# How to define "Quasifixation" in continuous approximation of finite population?

Background

Many models including the famous very first models derived by Sir Ronald Fisher in his early career, assume infinite population size. In an infinite population, an allele can rise in frequency (if its fitness is greater than the fitness of its counterpart(s)). This increase follows a logistic curve that never exactly reach a frequency of 1. Therefore, the term fixation does not apply to these model and in consequence the concept of quasifixation has been created.

Question

An allele is considered to be quasifixed if it reaches a frequency that is very close to 1. But how close? The decision is obviously arbitrary but when using a continuous approximation model in a finite population the question is necessarily raised and a decision needs to be made. How close should the frequency of an allele be to 1 so that it is considered to be quasifxed? The answer is probably a function of the population size $N$. What threshold do authors usually use in the theoretical population genetics literature? It would also be nice to have the definition of the author who first coined this term.

Garrish and Lensky (1998) considered reaching fixation when $p > \dfrac{N-1}{N}$, where $p$ is the allele frequency and $N$ the population size.
As I haven't found any guideline, I just went with chosing a threshold at $p = 1-\frac{1}{4N}$ for a diploid population. Allele $A$ is therefore considered quasifixed if its frequency $p$ is greater than $1-\frac{1}{4N}$ i.e. the number of occurrences (count) or the other allele is lower than $\frac{1}{2}$.