This paper presents a mathematical unique origin model of humanity. It suggests algorithms for testing different historical scenarios of the human population under the assumption that we all descend from one single couple. For each such scenario, DNA variation is repeatedly simulated from a sample of individuals of today in order to estimate statistics of DNA variation. Comparison of these statistics to real data makes model validation possible. Each simulation repeat is divided into three steps, where first the genealogy of the sampled individuals is simulated backwards in time until the founder generation is reached, then founder DNA is generated and thereafter spread forwards in time to the present, along the lineages of the ancestral tree. The model is applicable to predefined demographic scenarios that may include population expansions and bottlenecks. Colonization/range expansion and geographic migration is achieved by dividing the metapopulation into geographically separated, but more or less connected, subpopulations. Age structure is modeled in terms of overlapping generations, with various mating rules for males and females and reproduction rules of mating couples. On the genetic level, our model incorporates mitochondrial as well as nuclear (autosomal, X and Y chromosomal) DNA, ordinary (reciprocal) recombination events and gene conversion. The source of genetic variation is selectively neutral germline mutations, and for autosomal and X chromosomal DNA, a second source of variation is created diversity. An extension of the model allows for balancing selection. It combines forward and backward simulation of the genealogy. Our paper is a first step towards a future goal to compare a best fitting unique origin model with a common descent model where humans and other species have a shared ancestry.