Every point in the simplex represents a population state . The left down corner is , which has only groups with co-operators; the right down corner is , which has only groups with co-operators; the top corner is , which has only groups with co-operator. The grey lines represent different population structures, all with constant relatedness. Any given grey line gives a population state for every overall frequency of co-operators. Dynamics make populations move along the line that represents the population structure it faces. All grey lines go through the left down corner, where , and the right down corner, where . The straight line on the bottom reflects a totally assorted population that has no mixed groups. The higher up, the more mixed groups there are, and the less assortment there is. The highest up grey line represents a well-mixed population. No violations of Hamilton’s rule in equilibrium with synergies. In panel A, , , and . The regions where cooperation is selected for (green), and where inclusive fitness is positive (blue) are not the same, but selection always takes populations out of the parts where they disagree. Violations with anti-synergies. In panel B , , and . Here populations can settle at mixed equilibria, while inclusive fitness is not . Violations at and are also possible for more extreme choices of .