  Many systems in biology and beyond employ collaborative, collective
communication strategies for improved efficiency and adaptive benefit. One such
paradigm of particular interest is the community estimation of a dynamic
signal, when, for example, an epithelial tissue of cells must decide whether to
react to a given dynamic external concentration of stress signaling molecules.
At the level of dynamic cellular communication, however, it remains unknown
what effect, if any, arises from communication beyond the mean field level.
What are the limits and benefits to communication across a network of neighbor
interactions? What is the role of Poissonian vs. super Poissonian dynamics in
such a setting? How does the particular topology of connections impact the
collective estimation and that of the individual participating cells? In this
letter we construct a robust and general framework of signal estimation over
continuous time Markov chains in order to address and answer these questions.
Our results show that in the case of Possonian estimators, the communication
solely enhances convergence speed of the Mean Squared Error (MSE) of the
estimators to their steady-state values while leaving these values unchanged.
However, in the super-Poissonian regime, MSE of estimators significantly
decreases by increasing the number of neighbors. Surprisingly, in this case,
the clustering coefficient of an estimator does not enhance its MSE while
reducing total MSE of the population.
