Allelic richness (number of alleles) is a measure of genetic diversity indicative of a population's long-term potential for adaptability and persistence. It is used less commonly than heterozygosity as a genetic diversity measure, partially because it is more mathematically difficult to take into account the stochastic process of genetic drift for allelic richness. This paper presents a stochastic model for the allelic richness of a newly founded population experiencing genetic drift and gene flow. The model follows the dynamics of alleles lost during the founder event and simulates the effect of gene flow on maintenance and recovery of allelic richness. The probability of an allele's presence in the population was identified as the relevant statistical property for a meaningful interpretation of allelic richness. A method is discussed that combines the probability of allele presence with a population's allele frequency spectrum to provide predictions for allele recovery. The model's analysis provides insights into the dynamics of allelic richness following a founder event, taking into account gene flow and the allele frequency spectrum. Furthermore, the model indicates that the "One Migrant per Generation" rule, a commonly used conservation guideline related to heterozygosity, may be inadequate for addressing preservation of diversity at the allelic level. This highlights the importance of distinguishing between heterozygosity and allelic richness as measures of genetic diversity, since focusing merely on the preservation of heterozygosity might not be enough to adequately preserve allelic richness, which is crucial for species persistence and evolution.