Reward-rate maximization is a prominent normative principle in behavioral ecology, neuroscience, economics, and AI. Here, we identify, compare, and analyze equations to maximize reward rate when assessing whether to initiate a pursuit. In deriving expressions for the value of a pursuit, we show that time’s cost consists of both apportionment and opportunity cost. Reformulating value as a discounting function, we show precisely how a reward-rate-optimal agent’s discounting function (1) combines hyperbolic and linear components reflecting apportionment and opportunity costs, and (2) is dependent not only on the considered pursuit’s properties but also on time spent and rewards obtained outside the pursuit. This analysis reveals how purported signs of suboptimal behavior (hyperbolic discounting, and the Delay, Magnitude, and Sign effects) are in fact consistent with reward-rate maximization. To better account for observed decision-making errors in humans and animals, we then analyze the impact of misestimating reward-rate-maximizing parameters and find that suboptimal decisions likely stem from errors in assessing time’s apportionment—specifically, underweighting time spent outside versus inside a pursuit—which we term the ‘Malapportionment Hypothesis’. This understanding of the true pattern of temporal decision-making errors is essential to deducing the learning algorithms and representational architectures actually used by humans and animals.

The basic excitatory neurons of the cerebral cortex, the pyramidal cells, are the most important signal integrators for the local circuit. They have quite characteristic morphological and electrophysiological properties that are known to be largely constant with age in the young and adult cortex. However, the brain undergoes several dynamic changes throughout life, such as in the phases of early development and cognitive decline in the aging brain. We set out to search for intrinsic cellular changes in supragranular pyramidal cells across a broad age range: from birth to 85 y of age and we found differences in several biophysical properties between defined age groups. During the first year of life, subthreshold and suprathreshold electrophysiological properties changed in a way that shows that pyramidal cells become less excitable with maturation, but also become temporarily more precise. According to our findings, the morphological features of the three-dimensional reconstructions from different life stages showed consistent morphological properties and systematic dendritic spine analysis of an infantile and an old pyramidal cell showed clear significant differences in the distribution of spine shapes. Overall, the changes that occur during development and aging may have lasting effects on the properties of pyramidal cells in the cerebral cortex. Understanding these changes is important to unravel the complex mechanisms underlying brain development, cognition, and age-related neurodegenerative diseases.