  We propose a mathematical model for collective sensing in a population
growing in a stochastically varying environment. In the population, individuals
use an information channel for sensing the environment, and two channels for
signal production and comprehension to communicate among themselves. We show
that existence of such system has a positive effect on population growth, hence
can have a positive evolutionary effect. We show that the gain in growth due to
the collective sensing is related to information theoretic entities, which can
be considered as the information content of this system from the environment.
We further show that heterogeneity in communication resulted from network or
spatial structure increases growth. We compute the growth rate of a population
residing on a lattice and show that growth rate near the maximum noise level in
observation or communication, increases exponentially as noise decreases. This
exponential effect makes the emergence of collective observation an easy
outcome in an evolutionary process. Furthermore, we are able to quantify
interesting effects such as accelerated growth, and simplification of decision
making due to information amplification by communication. Finally, we show that
an amount of noise in representation formation has more disadvantageous effect
compared to the same noise in signal production.
