Population Recovery with Limited Founder Pairs: A Mathematical Analysis

Embarking on a mission to repopulate Earth with just 50 men and 50 women involves a myriad of logistical and genetic challenges. However, by carefully planning and ensuring genetic diversity, a feasible scenario can be envisioned. This article explores the feasibility of repopulating Earth under this scenario, analyzing the population growth and genetic diversity challenges.

Genetic Diversity and Record Keeping

The primary requirement would be maintaining meticulous records to ensure accurate genetic lineage tracking. Encouraging women to have children with different men from the pool of 50 founders helps create a diverse genetic base, thereby reducing the risk of inbreeding and ensuring offspring are not accidentally marrying their half-siblings. This approach is vital in maintaining genetic health and overall population diversity.

Mathematical Population Growth Analysis

If each woman in the initial 50 had 10 children, the population growth would occur at a rapid rate. This can be modeled mathematically to understand the scale of the population increase with each generation.

First Generation

The initial population is 50 individuals.

Second Generation

Each person in the first generation has 10 children, leading to a second generation population of 250 individuals (25 couples, 10 children each).

Subsequent Generations

The population increases fivefold with each generation, following the formula: PopulationG 50 * 5^G.

By the 10th generation, the world population reaches over 488,281,250 individuals. By the 12th generation, the population exceeds 1,220,703,125 individuals, which is more than 8 times the Earth's current population. A reasonable estimate, taking 30 years per generation, suggests that it would take about 360 years to reach the 10th generation, given the rapid growth rate.

Assumptions and Realistic Population Growth

However, in a more realistic scenario, where 4 children out of 10 survive, the population doubles every generation. To reach a target population of 5 billion, the 25 initial breeding pairs would need to increase by 100 million times. Assuming a population doubling every 25 years, it would take about 26 generations to achieve this, or approximately 650 years.

Historical Examples of Rapid Population Recovery

Historically, endangered species have recovered from extremely low population counts with just a handful of founding breeding pairs. These include the Northern Elephant seal, which fell to 30 and now numbers in the hundreds of thousands, and the European Bison, which recovered from a population of just 12 individuals.

The success in these instances can be attributed to careful breeding programs and maintaining genetic diversity. With 25 founding breeding pairs, the genetic diversity is maintained as each first-generation child has 96 different options to marry, ensuring further generations are less likely to experience inbreeding. By the third generation, the risk of inbreeding is significantly reduced.

Genetic Health and Inbreeding

Studies show that offspring from parents with known relatedness (like third cousins) are generally healthier than those with no known common ancestors. In the scenario described, the initial 50 pairs would produce a few 'misfits' as the population grows, but overall, the initial genetic pool ensures minimal inbreeding risk.

Population Growth Over Centuries

If the 50 individuals are well-selected, they could each have 10 children, resulting in a population of 300 in 20 years. Assuming the population growth rate similar to that of the Amish, where the population doubles every 20 years, the population could grow significantly over time:

After 100 years, the population would be about 150,000. After 200 years, the population could reach 150,000,000, 1024 times the initial population.

This analysis suggests that within 6 centuries, with continuous fertile reproduction and a focus on maintaining genetic diversity, the population could indeed surpass the current global population, given the rapid growth rates observed in similar breeding scenarios.

Conclusion

While the initial challenge of repopulating Earth with just 50 men and women is daunting, the rapid population growth and genetic diversity can be managed with careful planning and record-keeping. Historical examples of rapid population recovery and studies on genetic health in related populations provide a promising outlook for such a mission to succeed.