A coalescent model of a sample of size n is derived from a birth–death process that originates at a random time in the past from a single founder individual. Over time, the descendants of the founder evolve into a population of large (infinite) size from which a sample of size n is taken. The parameters and time of the birth–death process are scaled in N₀, the size of the present-day population, while letting N₀→∞, similarly to how the standard Kingman coalescent process arises from the Wright–Fisher model. The model is named the Limit Birth–Death (LBD) coalescent model. Simulations from the LBD coalescent model with sample size n are computationally slow compared to standard coalescent models. Therefore, we suggest different approximations to the LBD coalescent model assuming the population size is a deterministic function of time rather than a stochastic process. Furthermore, we introduce a hybrid LBD coalescent model, that combines the exactness of the LBD coalescent model model with the speed of the approximations.