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Developmental stability, the ability of an individual to eliminate environmental disturbances while expressing a heritable phenotypic trait, was compared in two walnut (

Adaptation of organisms to changing environments is becoming a very important issue, especially in the context of climate change. Developmental stability is the ability of an individual to eliminate environmental disturbances while expressing a heritable phenotypic trait. Developmental stability is an important notion for evolutionary and ecological studies, since it provides valuable information on the adaptation of organisms or populations to certain environments. There is evidence that developmental stability has a genetic basis (

The lack of data and models does not allow direct estimations of developmental stability. In practice, the pattern of bilateral variation in a random sample of the population, called fluctuating asymmetry (

There is some underlying additive genetic variance associated with fluctuating asymmetry and relevant QTLs have been identified in poplars (

In this study, we compared the fluctuating asymmetry as an indicator of developmental stability in two adjacent walnut (

The two populations compared in this study are located in the region of Sohos, near Thessaloniki (Greece) in the area of Mt. Vertiskos at an elevation of 650-700 m (40^{o} 49’ N, 23^{o} 22’ E), characterized by sand-clay soils and typical Mediterranean climate. The region is renown for its walnut and features both wild populations and walnut orchards with trees that attain a height of up to 25 m. The average age of the natural population is about 60 years, however older trees can be found. The artificial population comprises of locally selected genotypes of younger age (40 years old on the average). We chose randomly 29 individuals to sample from each population at a minimum distance of 20 m from each other, avoiding sampling filial structures. Isolated trees (no other tree present at a radius of 100 m) were excluded from sampling. Trees exhibiting natural (infection) or anthropogenic (pruning) disturbance were excluded as well. Ten leaves per tree were randomly selected from lower branches at a height of 2 m, being approximately equally distributed on the circumference of the tree canopy. Measurements were taken after careful drainage.

We measured the perimeters of the left (L) and the right (R) side of the leaf in a resolution of 1 mm and used the log-ratio: log(L/R) as Signed Asymmetry (SA) measure per leaf. We were interested to study developmental stability (DS) at the population level, thus fluctuating asymmetry (FA) was estimated using the pooled samples per population. We approached our analysis from a Bayesian perspective. We employed a model to infer SA and Directional Asymmetry (DA -

where _{ip} denotes the _{p} corresponds to the expected value of the observation. Deviation from zero indicates the presence of DA in both populations. Otherwise, in case of DA absence, _{p} should be equal to zero. Parameter ^{2}_{FA(p)} denotes the variance of SA in the population _{p}_{ ~ N(0.10)} and ^{-2}_{FA(p) } ~

We applied Markov Chain Monte Carlo (MCMC) to estimate the probability in eqn. 2 and used the JAGS (_{FA(nat)} / _{FA(art)} to monitor the ratio of developmental stability values in the two populations. In addition to our Bayesian analysis, we tested the hypothesis that the variances between the two populations are equal by performing a F-test with null hypothesis H_{0}: ^{2}_{FA(nat) } = ^{2}_{FA(art)} and alternative H_{1}: ^{2}_{FA(nat) } > ^{2}_{FA(art)} and using the statistic r^{2} = ^{2}_{FA(nat) } /^{2}_{FA(art)}.

Summary statistics and posterior densities are shown in ^{2} = 1.27) resulting to p-value = 0.021 (with the classical statistics interpretation) with confidence intervals CI = (1.047, +inf). We regard this outcome as noteworthy. Our results show that the right side of the leaf is slightly larger than the left side, but still the difference is small and additional experimentation is needed to further elucidate this finding. The natural population can be regarded as presenting reduced levels of developmental stability. It is noted that a significant amount of genetic erosion has been indicated for European

We consider our findings as a potentially early warning indication for problems that may occur in the natural population under scenarios of future environmental uncertainty. Given that expression of both sides of a leaf bilateral trait is due to the same genes, then any asymmetry between the sides can be a consequence of environmental disturbance. Hence, fluctuating asymmetry could be considered as a proxy for environmental or genetic stress (

Two anonymous reviewers are thanked for their constructive comments and suggestions.

^{rd}International Workshop on “Distributed Statistical Computing”.

Traces and posterior densities for the parameters of interest. Plots were produced by concatenating the four MCMC chains.

Summary statistics for the posterior densities of parameters. Column Mean denotes the posterior mean. SD is the standard deviation. The last four columns show quantiles for each variable.

Parameter | Mean | SD | 2.50% | 25.00% | 50.00% | 75.00% | 97.50% |
---|---|---|---|---|---|---|---|

DA (·10^{-3}) | 5.57 | 3.45 | -0.93 | 3.33 | 5.54 | 7.86 | 12.71 |

_{FA} _{(nat)} | 0.088 | 0.004 | 0.082 | 0.086 | 0.088 | 0.090 | 0.096 |

_{FA} _{(art)} | 0.079 | 0.003 | 0.072 | 0.076 | 0.079 | 0.080 | 0.085 |

r | 1.128 | 0.066 | 1.010 | 1.081 | 1.126 | 1.174 | 1.261 |