Female fertilization: effects of sex-specific density and sex ratio determined experimentally for Colorado potato beetles and Drosophila fruit flies

Abstract

If males and females affect reproduction differentially, understanding and predicting sexual reproduction requires specification of response surfaces, that is, two-dimensional functions that relate reproduction to the (numeric) densities of both sexes. Aiming at rigorous measurement of female per capita fertilization response surfaces, we conducted a multifactorial experiment and reanalyzed an extensive data set. In our experiment, we varied the density of male and female Leptinotarsa decemlineata (Colorado potato beetles) by placing different numbers of the two sexes on enclosed Solanum tuberosum (potato plants) to determine the proportion of females fertilized after 3 or 22 hours. In the reanalysis, we investigated how the short-term fertilization probability of three Drosophila strains (melanogaster ebony, m. sepia, and simulans) depended on adult sex ratio (proportion of males) and total density. The fertilization probability of female Leptinotarsa decemlineata increased logistically with male density, but not with female density. These effects were robust to trial duration. The fertilization probability of female Drosophila increased logistically with both sex ratio and total density. Treatment effects interacted in m. sepia, and simulans. These findings highlight the importance of well-designed, multifactorial experiments and strengthen previous experimental evidence for the relevance of sex-specific densities to understanding and prediction of female fertilization probability.

Figure 1. Schematic depiction of the design of the experimental run in which trial duration was ‘long’.

Depicted is how, approximating a Graeco-Latin Square, each of the 36 unique combinations of the six levels of male density ‘M’ and female density ‘F’ were laid out over the six levels of the block factors experimental day and cage. The 36 trials of the experimental run in which trial duration was ‘short’ were laid out over the same cages but six other experimental days (days 2, 4, 6, 8, 10 and 12) in a similar manner, although their exact distribution was different.

Figure 2. Schematic depiction of the experimental design used in Wallace .

Depicted is the minimum number of trials performed for each of the combinations of six levels of the number of females ‘F’ and seven levels of the number of males ‘M’.

Figure 3. Schematic depiction of the experimental design used in Wallace .

Depicted is, for each of the three Drosophila strains, the minimum number of trials performed per combination of the whole plot factors number of cages ‘nC’ and trial duration ‘TD’. For each combination of these two factors (each cell), the same combinations of the subplot factors number of males and number of females as in Wallace (; see Fig. 2) were examined.

Figure 4. Proportion of female Leptinotarsa decemlineata fertilized at different combinations of male density and female density.

Open and filled symbols depict single observations from short (3 h) trials and long (22 h) trials, respectively. Symbol size indicates the proportion of females fertilized, with the smallest and largest symbols corresponding to none and all of the females being fertilized, respectively. Long Tick marks indicate treatment levels. For representational purposes, results of short trials and long trials have been slightly shifted diagonally. Note that in two trials (short M₄,F₂ and long M₃₂,F₄), treatment levels were not as intended; dissection proved one supposed male to be a female (see Appendix S3).

Figure 5. Fertilization probability in relation to male density (panel A) and female density (panel B).

Presented are the back-transformed values of the ln-transformed odds (i.e. logits) of fertilization of a female Leptinotarsa decemlineata. To avoid taking the natural logarithm of 0, the smallest proportion of fertilized or unfertilized females observed (i.e. 0.03) was added and subtracted to observations of 0 and 1, respectively. Open and filled symbols depict single observations from short trials and long trials, respectively, after variation accounted for by model terms other than the ones depicted in the panel at issue has been taken out. Superimposed are the back-transformed fitted linear regression lines based only on the model terms depicted in the panel at issue (thick lines), with dotted lines and solid lines presenting predictions for short trials and long trials, respectively. The back-transformed approximate 95% confidence intervals (Collett §3.15) of the fitted models are indicated by thin lines. Long tick marks indicate treatment levels and response values. Bracketed information in the axis labels concerns the dimension of the variable at issue (‘−’ indicating dimensionless). For representational purposes, results of short trials and long trials, as well as results overlapping within trial duration, have been slightly shifted horizontally. Note that despite distortion, not all observations are visible at the lower densities. Also note the log-scale of the x-axis.

Figure 6. The proportion of female Drosophila fertilized at different combinations of sex ratio and total density.

Data is from the experiment presented in Wallace . Composition is as in Fig. 4.

Figure 7. Fertilization probability in relation to sex ratio (panel A) and total density (panel B).

Data concerns female Drosophila and is from the experiment presented in Wallace . Presented are back-transformed values. Superimposed are the back-transformed fitted linear regression lines (continuous lines) and 95% confidence intervals (dotted lines) calculated at specific levels of total density ‘T’ or sex ratio ‘S’. Grey lines show residuals associated with the depicted regression lines (for representational purposes, corresponding observations have been slightly shifted horizontally in panel A). Long tick marks indicate treatment levels and response values. Note the log-scale of the x-axis in panel B.

Figure 8. Interaction effects on the ln-transformed odds (i.e. logits) of fertilization of female Drosophila.

Depicted are the parameter estimates of the joint effect size of the total number of flies (N) and sex ratio (S); data is from the twelve experiments presented in Wallace . Symbols indicate trial duration (30 min: open symbols, 60 min: filled symbols), and the number of mating chambers in the experiment (1: circles, 2: triangles). Solid and dotted error bars indicate the standard error and the 95% confidence intervals of these parameter estimates, respectively. Positive joint effect sizes can be interpreted as indicating that the positive effect of the total number of flies was more pronounced when sex ratio was higher (more male-biased), and vice versa.