In a genetic adaptation model, a beneficial trait increases survival by 12% per generation. Starting with 500 organisms carrying the trait, how many carry it after 8 generations, assuming no loss?
["Genetic Adaptation Explained: How a 12% Survival Boost Enhances Trait Spread Over Generations", "In the dynamic process of evolution, genetic adaptations that improve survival can significantly influence population growth. A compelling example involves a beneficial trait that boosts survival by 12% per generation. This increase means individuals with the trait are more likely to survive and reproduce, enabling the trait to spread exponentially over time.", "### Understanding Population Growth with Genetic Advantage", "When a genetic trait enhances survival, the population carrying that trait grows faster than those without it. In this scenario, each generation sees a 12% survival advantage—equivalent to a multiplicative growth factor of 1.12. Unlike simple linear increase, this 12% boost compounds continuously across generations, leading to substantial accumulation.", "### Starting Population: 500 Organisms", "We begin with 500 individuals carrying the beneficial trait. Since no losses occur, only survival and reproduction drive the increase. Each generation, the number of organisms with the trait multiplies by 1.12.", "### Calculating Total After 8 Generations", "To find how many carry the trait after 8 generations, apply exponential growth:\n[ N = N_0 \ imes (growth\ factor)^{generations} ]\n[ N = 500 \ imes (1.12)^8 ]", "Using calculations:\n( (1.12)^8 \approx 2.476 )", "So:\n[ N = 500 \ imes 2.476 = 1,238 ]", "### Conclusion", "After 8 generations, approximately 1,238 organisms carry the advantageous trait, demonstrating how a modest 12% survival increase per generation can drive significant population expansion over time. This model highlights the powerful role of genetic adaptation in evolutionary biology and underscores the importance of compounding benefits in natural selection processes.", "Keywords: genetic adaptation, evolutionary growth, 12% survival increase, population genetics, exponential trait spread, natural selection, population increase per generation, adaptive advantage."]
