Abstract
Understanding the balance between robustness and evolvability is crucial in evolutionary dynamics. This study aims to determine how varying mutation rates and valley depths affect this interplay during adaptation. Using a two-peak fitness landscape model requiring populations to cross a fitness valley to reach a higher peak, we investigate how mutation rates and valley depths influence both evolvability-the capacity to generate beneficial mutations-and mutational robustness, which stabilizes populations at the highest peak. Our experiments reveal that at low mutation rates, populations struggle to cross fitness valleys, reducing the occurrence of pioneers. As mutation rates increase, valley crossing becomes more frequent, but organisms forming a majority at the highest peak are less common and tend to arise at intermediate mutation rates. Although pioneers reach the highest peak, they are often replaced by more mutationally robust organisms that later form a majority. This suggests that while evolvability aids in valley crossing, long-term stability at the highest peak requires greater mutational robustness. Our findings highlight that adaptations in epistasis and pleiotropy facilitate the trade-off between evolvability and robustness, providing insights into how organisms navigate complex fitness landscapes. These results can also inform the design of genetic algorithms that balance evolvability with robustness to optimize outcomes.