On the basis of 100
000 optimal sets of pairwise comparisons, we determined that egg size is significantly associated with parental care in frogs (for 100
000 sets of pairs, the range of p
to 0.0012). Hence, in all cases the results were highly significant. A representative maximal pairing set showed 47 pairs, of which 34 showed a positive relationship, 11 showed a negative relationship, and two were neutral (p
). Hence parental care is strongly associated with increased egg size, as a number of researchers have argued on the basis of non-phylogenetically controlled analyses.
The results from the maximum likelihood analysis using Discrete also supported the inference of correlated evolution between the evolution of parental care and egg size in a phylogenetically controlled framework. The final log-likelihood under the maximum likelihood model of independent evolution was −361.19, whereas that under the model of dependent evolution was −333.23. This yields a log-likelihood ratio of 27.97, which is a highly significant difference under a χ2 distribution with four degrees of freedom (p<0.0001).
The reconstruction of the ancestral state of parental care across our phylogenetic tree indicated that no parental care is the most likely state. Under maximum likelihood reconstruction, the probability that absence of parental care is ancestral was 0.92 (log-likelihood=−166.25). Reconstruction using parsimony also returns no parental care as the ancestral state. The reconstruction of the ancestral state of egg size (large versus small) was equivocal. Under maximum likelihood, the probability of small egg size was 0.33, and of large egg size was 0.67 (log-likelihood=213.15). Under parsimony, the most likely ancestral state was equivocal. Hence the ancestral state of egg size was uncertain. For our purposes, the assumption that small egg size is primitive is the most favourable for Shine's (1978)
original hypothesis, which proposed that the evolution of parental care in species with small eggs led to the evolution of larger eggs. Hence we will use that assumption as a starting point in our discussion of the order of the evolution of parental care and egg size.
shows the pattern of evolutionary transitions, with rates for each type of transition. We first tested to see if all the transitions toward the state with both parental care and large egg size from no parental care and small egg size were significantly different than 0. This is accomplished by setting the particular rate parameter (e.g. q12, for the transition rate from no parental care and small eggs to parental care and small eggs) to 0, then comparing the log-likelihood of the appropriate maximum likelihood model to the log-likelihood of the unrestricted model (again using a LRT). Each of these rates was significantly different than 0 under the LRT. The log-likelihoods and LRT results for each specific rate parameter (rates in parentheses) were as follows: q12 (0.03): −333.53 (p<0.05), q24 (0.23): −338.96 (p<0.05), q13 (0.1): −352.05 (p<0.01), q34 (0.14): −339.17 (p<0.05).
Figure 1 Path diagram illustrating transitions between different states of parental care and egg size calculated with Discrete. Simultaneous transitions between both parental care and egg size are not calculated. Parameters q12, etc. give transition rates between (more ...)
For the purpose of distinguishing between the order of transitions proposed as common by Shine (1978)
versus Nussbaum (1985
), we can compare the transition rates from no parental care, small eggs to parental care, small eggs, and from there to parental care, large eggs (the pathway proposed as prevalent by Shine 1978
) to the alternative of no parental care, small eggs to no parental care, large eggs, and from there to parental care and large eggs (the pathway proposed as prevalent by Nussbaum 1985
The rate of the transition from no parental care, small eggs to parental care, small eggs (q12) is very low. Although this rate is significantly different than zero (see above), it is also significantly lower than the rate from no parental care, small eggs to no parental care, large eggs (log-likelihood=−335.63, LRT=4.8, p<0.05), and significantly lower than the rate from no parental care, large eggs to parental care, large eggs (log-likelihood=−335.61, LRT=4.76, d.f. =1, p<0.05). The rate from parental care, small eggs to parental care, large eggs is quite high (0.23), but is not significantly different from the rate from no parental care, small eggs to no parental care, large eggs (log-likelihood=−334.69, LRT=2.92, d.f.=1, p>0.05).
Overall, our results indicate that, even making the assumption (favourable to Shine's (1978)
hypothesis) that small egg size is the ancestral state, the most common evolutionary trajectory is from small to large egg size in the absence of parental care, followed by the evolution of parental care, as suggested by Nussbaum (1985
). The high transition rate from parental care, small eggs to parental care, large eggs supports Shine's (1978)
contention that the presence of parental care will tend to select for large egg size, but the argument that this will be the most common pathway to the evolution of large egg size is not supported in this study. Our results do not negate the possibility that either of the two other hypotheses mentioned above (coevolution and a third factor affecting both egg size and parental care) affect the evolution of egg size, but they would be expected to contribute noise to the system in terms of the order of the evolution of parental care and large egg size, and hence should not bias the results in favour of either Shine or Nussbaum's hypotheses.
Finally, it should be noted that our analysis focuses on the evolution of egg size and assumes that egg size is the major target of selection (either via an interaction with parental care or with other aspects of the environment), with clutch size evolving in response to egg size as the result of an inherent tradeoff between these two traits. This is consistent with the focus of the hypotheses we have addressed in this paper (e.g. Shine 1978
; Nussbaum 1985
). However, it is possible that selection could act directly on clutch size (with egg size evolving in response). Although we do not address that issue in this paper, the potential importance of this possibility is highlighted in a recent comparative analysis of the evolution of egg and clutch size in cichlid fish (Kolm et al. in press