Figure 1.
(A) Cells have one of two phenotypes, photosynthetic or nitrogen fixing
. Every cell carries 4 traits
but only two traits influence a cell's behavior (shown in color).
determine the behavior of photosynthetic cells and
determine the behavior of nitrogen fixing cells. The case of two interacting cells is shown: photosynthetic cell 1 and nitrogen fixing cell 2. Cell 1 produces sugar through photosynthesis, keeping the fraction
of the product for its own growth and division, the remainder,
, is given to cell 2. Cell 2 uses part of the sugar received to fix nitrogen, keeping the fraction
for its division and gives back
to cell 1. After a cell division, one of the daughter cells has a probability of differentiating according to the parent cell's differentiation rate and phenotype
or
. After a cell division, another cell is chosen at random for death regardless of its fitness. Two different filament topologies were investigated. (B) Connected topology, all cells remain connected after a cell death. (C) Broken chain topology, cell death results in the separation of its neighbours. (D) Effects of interaction range were investigated by increasing the number of connections between the cells and their nearest neighbours.
Figure 2.
Possible developmental strategies.
Developmental strategies classified based on the trait averages (,
,
,
). The arrows that point from one cell type to itself represent investment in growth and division (
or
) while the arrows between cell types represent differentiation (
or
). Six possible developmental strategies exist: I. terminal differentiation with photosynthetic germline and non-dividing nitrogen fixing soma (violet), II. terminal differentiation with photosynthetic germline and dividing nitrogen fixing soma (blue), III. Reversible differentiation (green), IV. symbiosis (yellow), V. terminal differentiation with nitrogen fixing germline and dividing photosynthetic soma (orange), and VI. terminal differentiation with nitrogen fixing germline and non-dividing photosynthetic soma (red). The sign (+) indicates that the trait value is greater than zero. The asterisk (*) indicates that the trait may have any value. For the purposes of classification, we considered trait values bellow the threshold of 0.05 to be effectively 0. On the right, the different developmental strategies are shown to represent observed developmental strategies in cyanobacteria. I. terminal differentiation is seen in heterocystous cyanobacteria in Nostoc and Anabaena, III. reversible differentiation is observed in the cyanobacterium Trichodesmium, and symbiosis is observed between diverse plants and the cyanobacterium Nostoc.
Figure 3.
Examples of the evolution of the population trait averages.
Evolution of trait averages (,
,
,
) of 400 cells over 5000 generations under different conditions of relative division rate
, filament topology, and differentiation costs
. (A,B) simulations of the broken chain topology differing only in the relative division rates
and
, respectively. (B,D) simulations of the connected topology differing only in the differentiation cost
and
, respectively. All simulations shown here have interaction range set to
.
Figure 4.
Frequency of evolved developmental strategies.
The solid lines show the frequency of evolution of each strategy for varying relative division rates (50 simulations per
value). Data points and error bars show the average and 95% confidence interval for simulations using random initial conditions. Confidence intervals were calculated using the bootstrap method on 500 simulations per
value. Each strategy is represented by a different colour according to Fig. 2. Two different cases are shown: (A,B) broken chain topology with no differentiation costs
, (C,D) connected topology with differentiation costs
. Each case is shown for two different interaction ranges
corresponding to the panels on the left, and right, respectively. Each simulation was performed with 400 cells over 10 000 generations. Relative division rates (x-axis) are in logscale.
Figure 5.
All possible developmental strategies evolve under some sets of conditions.
The panels show the most frequently evolved developmental strategies depending on the cell interaction range and the relative division rate of photosynthetic cells
. (A,C) show the results simulated in the broken chain topology with no differentiation costs
and with differentiation costs
, respectively. (B,D) show the results in the connected topology with the same two differentiation costs. Simulations were repeated 50 times for each parameter combination, and the population size was 400. The color represents the strategy found to evolve most frequently, with color codes as in Fig. 2. Relative division rates (y-axis) are in logscale.