Distributions of reproductive and somatic cell numbers in diverse Volvox (Chlorophyta) species

Abstract

Background: Volvox (Chlorophyta) asexual colonies consist of two kinds of cells: a large number of small somatic cells and a few large reproductive cells. The numbers of reproductive and somatic cells correspond directly to the major components of fitness - fecundity and viability, respectively. Volvox species display diverse patterns of development that give rise to the two cell types.

Questions: For Volvox species under fixed conditions, do species differ with respect to the distribution of somatic and reproductive cell numbers in a population of asexual clones? Specifically, do they differ with respect to the dispersion of the distribution, i.e. with respect to their intrinsic variability? If so, are these differences related to major among-species developmental differences?

Data description: For each of five Volvox species, we estimate the number of somatic and reproductive cells for 40 colonies and the number of reproductive cells for an additional 200 colonies. We sampled all colonies from growing, low-density, asexual populations under standard conditions.

Search method: We compare the distribution of reproductive cell numbers to a Poisson distribution. We also compare the overall dispersion of reproductive cell number among species by calculating the coefficient of variation (CV). We compare the bivariate (reproductive and somatic cell) dataset to simulated datasets produced from a simple model of cell-type specification with intrinsic variability and colony size variation. This allows us to roughly estimate the level of intrinsic variability that is most consistent with our observed bivariate data (given an unknown level of size variation).

Conclusions: The overall variability (CV) in reproductive cell number is high in Volvox compared with more complex organisms. Volvox species show differences in reproductive cell number CV that were not clearly related to development, as currently understood. If we used the bivariate data and tried to account for the effects of colony size variation, we found that the species that have fast embryonic divisions and asymmetric divisions have substantially higher intrinsic variability than the species that have slow divisions and no asymmetric divisions. Under our culture conditions, the Poisson distribution is a good description of intrinsic variability in reproductive cell number for some but not all Volvox species.

Keywords: Volvox; cellular differentiation; development; eco-devo; evolution; multicellularity; reproductive allocation; robustness.

Fig. 1

Histograms showing the count of colonies that have a particular number of gonidia (n = 200 colonies per species). Grey bars are the observed data; white bars are the expectations based on the Poisson distribution. Maximum likelihood was used to estimate λ for each species and a chi-squared goodness-of-fit test was implemented using the vcd package in R. V. africanus: λ = 5.696, P = 0.258; V. carteri f. weismannia: λ = 5.77, P = 1.3 × 10⁻¹¹; V. tertius: λ = 7.17, P = 1.9 × 10⁻¹²; V. aureus: λ = 9.345, P = 2.4 × 10⁻²³; V. rousseletii: λ = 5.77, P = 0.605.

Fig. 2

Estimates of the coefficient of variation (CV) of gonidial cells per colony for each species. Black circles show the CV (sample standard deviation divided by sample mean). Error bars show ± 2 standard errors. Standard error of the CV was estimated by jackknifing (using R). Because the distributions of gonidial cells were generally not normally distributed (Fig. 1), we also calculated a robust version of the CV for comparison. White circles show a robust version of the CV, the F-pseudosigma (Hoaglin et al., 1983, p. 40) divided by the median.

Fig. 3

Relationship between log-transformed gonidial cell number and somatic cell number for five species of Volvox. Each point is one colony (n = 40) and the ellipse is a 95% confidence ellipse. The R², radii of the ellipse semi-axes, and slope of a standardized major axis best-fit line are also given.

Fig. 4

The similarity of the simulated and observed data is shown according to two metrics: radii of 95% confidence ellipses (left column) and slope of SMA line (right column). Each data point represents the mean of 50 simulations with a particular combination of parameter values. The CV_A values used are: 0.10, 0.19, 0.28, 0.37, 0.46, 0.54, 0.63, 0.72, 0.81, and 0.90. The CV_M values are indicated in the figure legend. The S.D._A value that was used for the simulation is the CV_A times the species-specific Ā (Table 4) and likewise for S.D._M. For the similarity of the radii of the 95% confidence ellipses (left column), we fit a polynomial curve (order 3) to the pooled data to get a rough estimate of the value of CV_A for which the difference between the data and simulations was the lowest. This value of CV_A is: V. africanus, 0.26; V. carteri f. weismannia, 0.32; V. tertius, 0.11; V. aureus, 0.31; V. rousseletii, 0.29.

Fig. 4

The similarity of the simulated and observed data is shown according to two metrics: radii of 95% confidence ellipses (left column) and slope of SMA line (right column). Each data point represents the mean of 50 simulations with a particular combination of parameter values. The CV_A values used are: 0.10, 0.19, 0.28, 0.37, 0.46, 0.54, 0.63, 0.72, 0.81, and 0.90. The CV_M values are indicated in the figure legend. The S.D._A value that was used for the simulation is the CV_A times the species-specific Ā (Table 4) and likewise for S.D._M. For the similarity of the radii of the 95% confidence ellipses (left column), we fit a polynomial curve (order 3) to the pooled data to get a rough estimate of the value of CV_A for which the difference between the data and simulations was the lowest. This value of CV_A is: V. africanus, 0.26; V. carteri f. weismannia, 0.32; V. tertius, 0.11; V. aureus, 0.31; V. rousseletii, 0.29.