Researchers at the Complexity Science Hub and Santa Fe Institute have developed a model to calculate how quickly or slowly an organism should ideally learn in its surroundings. An organism's ideal learning rate depends on the pace of environmental change and its life cycle, they say.
Every day, we wake to a world that is different, and we adjust to it. Businesses face new challenges and competitors and adapt or go bust. In biology, this is a question of survival: every organism, from bacteria to blue whales, faces the challenge of adapting to environments that are constantly in flux. Animals must learn where to seek nourishing food, even as those food sources change with the seasons. However, learning takes time and energy – an organism that learns too slowly will lag behind environmental changes, while one that learns too quickly will waste effort trying to track meaningless fluctuations.
The new mathematical model provides a quantitative answer to the question: What is the optimal pace of learning for an organism in a changing world? "The key insight is that the ideal learning rate increases in the same way regardless of the pace of environmental change, whether the organism changes its environment or alters its interaction with it. This suggests a generalizable phenomenon that may underlie learning in a variety of ecosystems," states CSH PostDoc Eddie Lee .
The researchers' model imagines an environment that alternates between different states, such as wet and dry seasons, at a characteristic tempo. The organism senses this environmental state and records a memory of the past states. But older memories decay in importance over time, at a rate that defines the organism's learning timescale.
LEARNING AT THE SQUARE ROOT OF CHANGE
What is the optimal learning timescale to maximize adaptation to the environment? The model predicts a universal law: the learning timescale should scale as the square root of the environmental timescale.
For example, if the environment fluctuates twice as slowly, the organism's learning rate should decrease by a factor of 1.4 (the square root of 2). This square root scaling represents an optimal compromise between learning too quickly and too slowly. Importantly, a square root relation indicates that there are diminishing returns to longer memory.
"The model also simulates organisms that don't just passively learn, but can actively reshape their environment – an ability called niche construction," says Lee, who is an ESPRIT Fellow of the Austrian Science Fund (FWF) at CSH. If an organism has "stabilizing" powers to make its environment more constant, it gains an evolutionary edge. However, this advantage only accrues if the organism can monopolize the benefits of the stable environment. If freeloading competitors also exploit the stabilized niche, the niche construction strategy falls apart. An example: Beavers actively shape their environment by building dams in rivers, creating stable ponds that provide habitats for themselves and other species. This construction offers them a significant evolutionary advantage, as it ensures a consistent food supply and protection from predators. However, this advantage can diminish if other organisms, like muskrats or fish, exploit the resources of the created habitat.
METABOLIC OVERHEAD FOR LARGE ANIMALS
Finally, the researchers assess how learning ability interacts with the metabolic costs of being alive, meaning the energy demands of the body. They predict that for small, short-lived creatures like insects, the costs of learning and memory are paramount. In contrast, for larger, longer-lived animals like mammals, the costs of learning are dwarfed by metabolic overhead.
This predicts that small, short-lived organisms have well-tuned memory for their environments. "In contrast, larger organisms like elephants have longer memories, but exactly how long they retain information may have more to do with non-learning costs or other types of environments such as social groups which impose further cognitive demands,", says Lee. Thus, it might not be totally appropriate to deride the well-tuned, "memory of a flea."
The new model offers a quantitative framework for understanding how organisms balance the competing demands of learning and other survival imperatives in an ever-changing world. The results suggest an optimal pace of adaptation tuned to the speed of environmental change and the lifespan of the organism across the living world–from microbes to humans.
About the study
The study " Constructing stability: optimal learning in noisy ecological niches ," by E.D. Lee, J.C. Flack and D.C. Krakauer was published in Proceedings of the Royal Society B: Biological Sciences (doi: 10.1098/rspb.2024.1606).
About CSH
The Complexity Science Hub (CSH) is Europe's research center for the study of complex systems. We derive meaning from data from a range of disciplines — economics, medicine, ecology, and the social sciences — as a basis for actionable solutions for a better world. Established in 2015, we have grown to over 70 researchers, driven by the increasing demand to gain a genuine understanding of the networks that underlie society, from healthcare to supply chains. Through our complexity science approaches linking physics, mathematics, and computational modeling with data and network science, we develop the capacity to address today's and tomorrow's challenges.
