Final answer:
Evolutionary psychology best explains the higher susceptibility of females to experience anxiety related to the safety of themselves and their children, due to evolved behaviors stemming from the need to ensure offspring survival.
Step-by-step explanation:
The theory that BEST explains why females may be more susceptible to anxiety due to vigilance in keeping themselves and their offspring safe is a) Evolutionary psychology.
Evolutionary psychology is the field that posits certain behaviors and psychological traits arise from the evolutionary pressures that shaped our ancestors' survival and reproductive success. It studies how natural selection has influenced our psychological dispositions and behaviors, including the protective behaviors that would contribute to an individual's anxiety in situations perceived as threatening. With the high investment in raising offspring, it is theorized that females are evolutionarily programmed to be more vigilant and cautious to safeguard their offspring, as this would have increased the chances of their children's survival and thus, the passage of their genes to the next generation.
This heightened vigilance and responsibility for dependents could contribute to a greater propensity for anxiety-related responses when safety is perceived to be at risk. While both men and women possess these protective instincts, the theory suggests that females, due to their biological and social roles in child-rearing, might experience these responses more intensely. In essence, evolutionary psychology provides a biological and historical foundation for understanding gender differences in anxiety related to safety and child protection.