More Is Faster: Why Population Size Matters in Biological Search

Many biological scenarios have multiple cooperating searchers, and the timing of the initial first contact between any one of those searchers and its target is critically important. However, we are unaware of biological models that predict how long it takes for the first of many searchers to discover a target. We present a novel mathematical model that predicts initial first contact times between searchers and targets distributed at random in a volume. We compare this model with the extreme first passage time approach in physics that assumes an infinite number of searchers all initially positioned at the same location. We explore how the number of searchers, the distribution of searchers and targets, and the initial distances between searchers and targets affect initial first contact times. Given a constant density of uniformly distributed searchers and targets, the initial first contact time decreases linearly with both search volume and the number of searchers. However, given only a single target and searchers placed at the same starting location, the relationship between the initial first contact time and the number of searchers shifts from a linear decrease to a logarithmic decrease as the number of searchers grows very large. More generally, we show that initial first contact times can be dramatically faster than the average first contact times and that the initial first contact times decrease with the number of searchers, while the average search times are independent of the number of searchers. We suggest that this is an underappreciated phenomenon in biology and other collective search problems.