Fig 1.
Evolution of germ and soma in colonies with identical cells: A convex trade-off, a resource constraint and different ‘importances’ of viability and fecundity (Case 1).
Here we assume that we have three groups of cells within the colony such that all cells from each group have the same level of fecundity and the same level of viability (i.e., we have three ‘aggregate’ cells in the colony). Optimal strategies of the colony are colored in red. The level of specialization in soma and germ depends on the relative ‘importance’ of fecundity to viability. In both panels, k1 = k2 = 1, α = 1, C = 4 and φ = (b-1)2. In panel (a), β = 0.5. In panel (b), β = 2.
Fig 2.
Evolution of germ and soma in colonies with identical cells: A convex trade-off, a resource constraint and different ‘importances’ of viability and fecundity (Case 2).
Here we assume that we have three groups of cells within the colony such that all cells from each group have the same level of fecundity and the same level of viability (i.e., we have three ‘aggregate’ cells in the colony). Optimal strategies of the colony are colored in red. The level of specialization in soma and germ within the set A depends on the relative ‘importance’ of fecundity to viability. In both panels, k1 = k2 = 1, α = 1, C = 2.85 and φ = (b-1)2. In panel (a), β = 0.5. In panel (b), β = 2.
Fig 3.
Evolution of germ and soma in colonies with identical cells: A convex trade-off, a resource constraint and different ‘importances’ of viability and fecundity (Case 3).
Here we assume that we have three groups of cells within the colony such that all cells from each group have the same level of fecundity and the same level of viability (i.e., we have three ‘aggregate’ cells in the colony). Optimal strategies of the colony are colored in red. The evolution of structural complexity in unspecialized large-sized colonies can lead to the emergence of soma specialization (panel (a)) as well as to unspecialized optimal states in the case of environmental quality degradation (panel (b)). In both panels, k1 = k2 = 1, α = 1 and φ = (b-1)2. In panel (a), β = 4 and C = 2.85. In panel (b), β = 4 and C = 2.5.
Fig 4.
Evolution of germ and soma in colonies with identical cells: A linear trade-off, a resource constraint and different ‘importances’ of viability and fecundity.
Here we assume that we have three groups of cells within the colony such that all cells from each group have the same level of fecundity and the same level of viability (i.e., we have three ‘aggregate’ cells in the colony). In panel (a), Case 1 is illustrated. In panel (b), Case 3 is illustrated. With a linear trade-off there is no Case 2 in the model (i.e., it means that the set of parameters that lead to Case 2 in the space of all possible parameters is a set of measure zero). Optimal strategies of the colony are colored in red. With a linear trade-off, identical colony behaves as a single cell. In all panels, α = 1, β = 2, k1 = 1, C = 4 and φ = 1-b. In panel (a), k2 = 1. In panel (b), k2 = 2.
Fig 5.
Evolution of germ and soma in colonies with identical cells: A concave trade-off, a resource constraint and different ‘importances’ of viability and fecundity (Case 1).
Here we assume that we have three groups of cells within the colony such that all cells from each group have the same level of fecundity and the same level of viability (i.e., we have three ‘aggregate’ cells in the colony). Optimal strategies of the colony are colored in red. In both panels, the colonies have a unique optimal strategy and the specialization does not occur. The contribution of the colony to the fitness components depends on the relative importance of fecundity to viability. In both panels, α = 1, φ = 1-b2, C = 8, k1 = 2 and k2 = 1. In panel (a), β = 0.5. In panel (b), β = 2.
Fig 6.
Evolution of germ and soma in colonies with identical cells: A concave trade-off, a resource constraint and different ‘importances’ of viability and fecundity (Case 2).
Here we assume that we have three groups of cells within the colony such that all cells from each group have the same level of fecundity and the same level of viability (i.e., we have three ‘aggregate’ cells in the colony). Optimal strategies of the colony are colored in red. In panel (a) the optimal solutions represent a connected set (set A) of unspecialized states that provides opportunities for adaptation for the colony at hand. In panel (b), the set A is a three-point set. The trade-off between the production difficulties and the fitness benefits of one fitness component (panel (b)) is one of the main reasons for the emergence of specialization in small-sized colonies. In both panels, α = 1, φ = 1-b2, k1 = 2 and k2 = 1. In panel (a), β = 0.5 and C = 5.5, In panel (b), β = 0.25 and C = 5.
Fig 7.
Evolution of germ and soma in colonies with identical cells: A concave trade-off, a resource constraint and different ‘importances’ of viability and fecundity (Case 3).
Here we assume that we have three groups of cells within the colony such that all cells from each group have the same level of fecundity and the same level of viability (i.e., we have three ‘aggregate’ cells in the colony). Optimal strategies of the colony are colored in red. Unspecialized states (panel (a)) can be optimal as well as strategies with some level of specialization (panel (b)). Significant resource constraint (panel (b)) is one of the main reasons for the emergence of specialization in small-sized colonies. In both panels, α = 1, φ = 1-b2 and k2 = 1. In panel (a), β = 2, C = 5 and k1 = 2. In panel (b), β = 1, C = 3.12 and k1 = 1.
Fig 8.
Evolution of germ and soma in colonies with: Positional effects, different curvatures of trade-off functions and different ‘importances’ of viability and fecundity (Case 1).
Here we assume that we have three groups of cells within the colony such that all cells from each group have the same level of fecundity and the same level of viability (i.e., we have three ‘aggregate’ cells in the colony). The following 3-D panels are shown. In all panels, α = 1. In panels (a), (c) and (e), β = 2. In panels (b), (d) and (f), β = 0.5. In panels (a) and (b), φ1 = (b1-2)2, φ2 = (b2-2)2 and φ3 = (b3/√3 - √3)2. In panels (c) and (d), φ1 = 4-b1, φ2 = 4-b2 and φ3 = 2-b3/3. In panels (e) and (f), φ1 = 4-b12, φ2 = 2-b22/8 and φ3 = 3-b32/3. Optimal strategies of the colony are colored in red.