Modelling developmental instability as the joint action of noise and stability: a Bayesian approach - PubMed (original) (raw)

Modelling developmental instability as the joint action of noise and stability: a Bayesian approach

Stefan Van Dongen et al. BMC Evol Biol. 2002.

Abstract

Background: Fluctuating asymmetry is assumed to measure individual and population level developmental stability. The latter may in turn show an association with stress, which can be observed through asymmetry-stress correlations. However, the recent literature does not support an ubiquitous relationship. Very little is known why some studies show relatively strong associations while others completely fail to find such a correlation. We propose a new Bayesian statistical framework to examine these associations

Results: We are considering developmental stability - i.e. the individual buffering capacity - as the biologically relevant trait and show that (i) little variation in developmental stability can explain observed variation in fluctuating asymmetry when the distribution of developmental stability is highly skewed, and (ii) that a previously developed tool (i.e. the hypothetical repeatability of fluctuating asymmetry) contains only limited information about variation in developmental stability, which stands in sharp contrast to the earlier established close association between the repeatability and developmental instability.

Conclusion: We provide tools to generate valuable information about the distribution of between-individual variation in developmental stability. A simple linear transformation of a previous model lead to completely different conclusions. Thus, theoretical modelling of asymmetry and stability appears to be very sensitive to the scale of inference. More research is urgently needed to get better insights in the developmental mechanisms of noise and stability. In spite of the fact that the model is likely to represent an oversimplification of reality, the accumulation of new insights could be incorporated in the Bayesian statistical approach to obtain more reliable estimation.

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Figures

Figure 1

Figure 1

Overview of distributions of DS that were used to simulate datasets The bottom three rows of distributions are skewed to the left. The same right-skewed distributions (obtained by interchanging β1 and β2) are also used (Table 1)

Figure 2

Figure 2

Relationship between the coefficient of variation (CV) of both DS and instability and the hypothetical repeatability (R) Mean values and their standard deviation were obtained for a range of distributions of variation in DS. Details are provided in Figure 1 and Table 1. The theoretical upper limit of R equals 0.637 and is indicated by a horizontal line

Figure 3

Figure 3

Posterior distributions of DS Posterior distributions indicated by the black bars were obtained for datasets with three different sample sizes (left: N = 500; middle: N = 1000; right: N = 5000) and six different underlying shapes generated from different beta-distributions (row 1: β1 = 2, β2 = 5; row 2: β1 = 1, β2 = 0.5; row 3: β1 = 1, β2 = 0.1; row 4: β1 = 0.1, β2 = 1; row 5: β1 = 0.5, β2 = 1; row 6: β1 = 0.1, β2 = 0.1; indicated by the gray lines)

Figure 4

Figure 4

Expected (black) and observed (gray) distribution of between-individual variation in DS (top graph) and population level developmental noise (bottom graph)

Figure 5

Figure 5

Between-individual variation in DS as estimated for six empirical datasets

Figure 6

Figure 6

Association between the hypothetical repeatability and the coefficient of variation in DS for six empirical datasets

References

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    1. Bjorksten TA, Fowler K, Pomiankowski A. What does sexual trait FA tell us about stress? TREE. 2000;15:163–166. doi: 10.1016/S0169-5347(99)01788-7. - DOI - PubMed
    1. Van Dongen S, Lens L, Molenberghs G. Recent developments and shortcomings in the analysis of individual asymmetry: Can Bayesian statistics help us? In: M Polak, editor. Developmental instability: causes and consequences. Oxford University Press, Oxford; 2002.

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