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.
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