Calculates Shannon entropy based on square root of phenotype count.
    This might account for relationship between population size and
    evolvability.

def sqrt_shannon_entropy(filename):
    """
    Calculates Shannon entropy based on square root of phenotype count.
    This might account for relationship between population size and
    evolvability.
    """
    data = load_grid_data(filename, "int")
    data = agg_grid(data, mode)
    phenotypes = {}
    for r in data:
        for c in r:
            if c in phenotypes:
                phenotypes[c] += 1
            else:
                phenotypes[c] = 1

    for key in phenotypes.keys():
        phenotypes[key] = sqrt(phenotypes[key])

    return entropy(phenotypes)