Advantages of the division of labour for the long-term population dynamics of cyanobacteria at different latitudes

Abstract

A fundamental advancement in the evolution of complexity is division of labour. This implies a partition of tasks among cells, either spatially through cellular differentiation, or temporally via a circadian rhythm. Cyanobacteria often employ either spatial differentiation or a circadian rhythm in order to separate the chemically incompatible processes of nitrogen fixation and photosynthesis. We present a theoretical framework to assess the advantages in terms of biomass production and population size for three species types: terminally differentiated (heterocystous), circadian, and an idealized species in which nitrogen and carbon fixation occur without biochemical constraints. On the basis of real solar irradiance data at different latitudes, we simulate population dynamics in isolation and in competition for light over a period of 40 years. Our results show that in isolation and regardless of latitude, the biomass of heterocystous cyanobacteria that optimally invest resources is comparable to that of the idealized unconstrained species. Hence, spatial division of labour overcomes biochemical constraints and enhances biomass production. In the circadian case, the strict temporal task separation modelled here hinders high biomass production in comparison with the heterocystous species. However, circadian species are found to be successful in competition for light whenever their resource investment prevents a waste of fixed nitrogen more effectively than do heterocystous species. In addition, we show the existence of a trade-off between population size and biomass accumulation, whereby each species can optimally invest resources to be proficient in biomass production or population growth, but not necessarily both. Finally, the model produces chaotic dynamics for population size, which is relevant to the study of cyanobacterial blooms.

Figure 1.

A schematic of the model species. (a) Undifferentiated cyanobacteria (both single-celled and filamentous species) fix carbon and nitrogen according to a circadian rhythm. All cells perform photosynthesis during the day and fix nitrogen during the night; hence, the two processes alternate on a day/night rhythm. (b) In terminally differentiated cyanobacteria, vegetative cells perform photosynthesis during the daytime (i.e. when light is available). Heterocyst cells provide an anoxic environment where nitrogen fixation can take place at any time, and hence is limited only by the availability of resources. (c) In the idealized species, nitrogen and carbon fixation can be performed without temporal inhibitory restrictions and are limited only by the availability of substrates. Oscillation amplitude and position of the red and grey lines for carbon and nitrogen fixation are arbitrary and for illustrative purposes only. Green circles, vegetative cell; blue circles, heterocystous cell; red line, carbon fixation; grey line, nitrogen fixation; black line, night; yellow line, day.

Figure 2.

Sample runs of the three modelled species for a number of iterations corresponding to 40 years.

Figure 3.

Box plot of (a) the biomass production and (b) population size computed daily over the last 35 years of a simulated 40 year period at different latitudes and values of cell investment r. Biomass is expressed in fmol µm⁻³. In each box, the central mark is the median, the horizontal edges of the box are the 25th and 75th percentiles and the whiskers extending to the most extreme data points are not considered outliers (outliers not shown). Blue line, unconstrained; red line, heterocystous; black line, circadian.

Figure 4.

(a) A comparison of the box plots corresponding to the (a, r) providing the highest biomass at each latitude for each species. Parameter r represents the resource investment into reproduction, a is the resource investment in nitrogen-fixation. Both r and a are measured in fmol cell⁻¹ h⁻¹ and biomass is expressed in fmol µm⁻³. Data correspond to daily biomass over a 35 year period. (b) Box plot of the number of cells over the last 35 years of a simulated 40 year period obtained with the same (a, r) values as in panel (a). The open circle in each box plot corresponds to the mean values of biomass and number of cells, respectively. Blue, unconstrained; red, heterocystous and black, circadian.

Figure 5.

Best cell investment for each species and latitude. Coloured dots and diamonds indicate that the corresponding grid point is an optimal (a, r) pair that provides the highest biomass and population size, respectively, at a given latitude (table 2).