The highest number of a species that can be captured without disrupting future productivity is the maximum sustained .

The term you're referring to is "Maximum Sustainable Yield" (MSY). It is a key concept in the fields of ecology and fishery management. MSY represents the largest yield (or catch) that can be taken from a specific fish stock or population over an indefinite period under constant environmental conditions, without leading to population decline. This concept is crucial for ensuring that the harvesting of natural resources is conducted sustainably, allowing the population to regenerate and maintain its reproductive capacity.

In practice, determining the MSY involves understanding the dynamics of the species' population growth, reproduction rates, and interactions with other species, as well as the impacts of human activities. Effective management strategies often employ MSY calculations to set quotas, seasons, and other regulatory measures that help balance human needs with ecological sustainability.