# The Novel Concept of “Behavioural Instability” and Its Potential Applications

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{7}

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Developmental Instability

#### 1.2. Phenotypic Variance

_{p}

^{2}) [8,9] or by using fluctuating asymmetry (FA) [1]. In a sexually reproducing population, σ

_{p}

^{2}is given by: σ

_{p}

^{2}= σ

_{g}

^{2}+ V σ

_{e}

^{2}+ σ

_{s}

^{2}, where σ

_{s}

^{2}is the stochastic variance, which is equivalent to DI according to [10]. Therefore, it is only when environmental variability (σ

_{e}

^{2}) and σ

_{g}

^{2}are negligible that σ

_{p}

^{2}can be utilized for the estimation of DI [11]. Hence, the use of σ

_{p}

^{2}as an estimator of DI is restricted to investigation with monoclonal strains or highly inbred strains where the within line genetic variance can be considered equal to 0 (g

_{p}

^{2}= 0). However, even using monoclonal strains the σ

_{p}

^{2}estimates can be affected by σ

_{e}

^{2}[12]. The genetic factors that increase the developmental instability might be high levels of inbreeding [13] and hybridisation [2]. The environmental factors might be unusual temperatures [14] and chemical pollution [15,16,17].

#### 1.3. Fluctuating Asymmetry

_{p}

^{2}[18,19].

#### 1.4. Directional Asymmetry and Antisymmetry

#### 1.5. Behavioural Instability

## 2. Material and Methods

#### 2.1. Behavioural Data

_{g}

^{2}= 0, and, consequently, we expect that σ

_{p}

^{2}= σ

_{e}

^{2}+ DI. Considering that all experiments have been conducted under the same environmental conditions, we further assume that σ

_{e}

^{2}= 0; thus, σ

_{p}

^{2}= DI.

#### 2.2. Phenotypic Variance

_{p}

^{2}. For clarity in the rest of the article, the number of clockwise and counter-clockwise movements will be mentioned as r and l, respectively.

_{p}

^{2}values estimated within a line were compared among lines with an F-test [27].

_{e}

^{2}.

_{e}

^{2}; given the fact that σ

_{p}

^{2}= σ

^{2}

_{(r+l)}= σ

_{r}

^{2}+ σ

_{l}

^{2}+ 2cov

_{(r,l)}and σ

^{2}

_{(r−l)}= σ

_{r}

^{2}+ σ

_{l}

^{2}− 2cov

_{(r,l)}, (σ

_{r}

^{2}and σ

_{l}

^{2}are variances of right and left side) and 2cov

_{(r,l)}is the covariance between the right and the left side) in absence of σ

_{e}

^{2}these two terms should be identical; σ

^{2}

_{(r+l)}= σ

^{2}

_{(r−l)}, if σ

_{e}

^{2}is present, we get: σ

_{r}

^{2}+ σ

_{l}

^{2}+ 2cov

_{(r,l)}= σ

_{r}

^{2}+ σ

_{l}

^{2}− 2cov

_{(r,l)}+ σ

_{e}

^{2}rearranging σ

_{e}

^{2}= 4cov

_{(r,l)}.

_{(r,l)}= r

_{(r,l)}× σ

_{r}× σ

_{l}(where r is the Pearson product moment coefficient of the correlation between r and l values. Hence, if the regression coefficient of r versus l is not significantly different from zero, then σ

_{e}

^{2}≈ 0. Consequently, if σ

_{e}

^{2}≈ 0, we can consider σ

_{p}

^{2}as a reliable estimator of DI. If σ

_{e}

^{2}≠ 0 and the correlation between r and l is positive, the σ

_{p}

^{2}will be overestimated and the FA will be underestimated [9].

#### 2.3. Fluctuating Asymmetry

#### 2.4. Directional Asymmetry and Antisymmetry

#### 2.5. Scaling of Fluctuating Asymmetry with the Mean

## 3. Results

#### 3.1. Phenotypic Variance

_{e}

^{2}, which showed a significant negative relationship in five lines out of 19 lines tested (lines 385; r = −0.81 ***, 392; r = −0.63 **, 491; r = −0.76 ***, 508; r = −0.56 **, 584; r = −0.87 ***, 703; and r = −0.6 ***).

#### 3.2. Fluctuating Asymmetry

_{(r−l)}of the total activity of the 19 lines are listed in Table 4.

#### 3.3. Directional Asymmetry and Antisymmetry

## 4. Discussion

#### 4.1. Behavioural Data

_{p}

^{2}and FA are utilized for estimating DI for behavioural data. We have chosen completely inbred lines because σ

_{p}

^{2}can be used as an estimator of DI if the influence of σ

_{e}

^{2}is minimal or equal to zero. However, the FA indices can be considered reliable estimators of DI even if σ

_{g}

^{2}≠ 0, which is the most common situation when dealing with sexually reproducing organisms. We have converted locomotor behaviour into a deviation from an expected value of 0; however, there are many other possible conversions of behavioural data, as, for example, the number of times in a given interval of time or the time spent holding the head on the right or on the left compared to the body of the axis of a bilateral animal. Another possibility is to estimate the number of times in a given interval of time or the time spent by a grazer in holding the head down and graze compared to when the grazer holds the head up. The concept of behavioural instability can also be applied to the behaviour of animals, which can be tracked with GPS or with a radar system counting the number of times that the individual is turning to the right or to the left in different environmental conditions.

#### 4.2. Phenotypic Variance

_{e}

^{2}is expected to be negligible. However, we have shown that the σ

_{e}

^{2}is not negligible, as in five (lines 385, 392, 491, 508, 584 and 703) of the investigated lines, significant negative correlations between clockwise (CW) and counter-clockwise (CCW) movements were found producing a bias of both the medians of the total activity but also on the σ

_{p}

^{2}and FA estimates.

_{p}

^{2}as shown in Table 3 and Figure 1. The heterogeneity of the 95% confidence intervals indicate large differences of σ

_{p}

^{2}, and several of these differences were also found between lines in which σ

_{e}

^{2}was negligible. Hence, we can consider these differences as differences in the degree of DI, and the lines in which the presence of σ

_{e}

^{2}will produce biased estimates of σ

_{p}

^{2}will be overestimated in the case of positive covariance between the CW and CCW or underestimated in the case of negative correlation between the CW and CCW (which is our case).

_{e}

^{2}should, in fact, reduce the kurtosis making the distributions platykurtic, and the fact that we have not been able to detect significant deviations from normality does not mean that a deviation will be found if we have increased the number of replicates per line. However, the fact that we were able to detect the presence of σ

_{e}

^{2}by testing the correlations between the CW and CCW is clearly showing that the correlational analysis is more sensible even with small sample size (see [12], for details of the method).

#### 4.3. Fluctuating Asymmetry

_{p}

^{2}(Table 3) of the total activity are also not always concordant with the results found in Table 5 and Table 6. The medians of the total activity are not an estimator of DI, but σ

_{p}

^{2}should hypothetically find the same differences found by the FA estimators especially in the absence of a scaling effect. The reasons for the discrepancy could be due to the sampling error of the variance [29].

#### 4.4. Directional Asymmetry and Antisymmetry

#### 4.5. Scaling of Fluctuating Asymmetry with the Mean

#### 4.6. Perspectives

_{p}

^{2}as an indicator of behavioural instability if we follow the correct procedures described in this paper. The concept of behavioural instability could have several possible applications as a biomonitoring tool if we expect that changes in environmental conditions can produce changes in the behavioural traits. For example, behavioural traits have been used in toxicological studies as a sensitive indicator of stress using traits such as swimming activity, locomotor activity or flight [30,31,32,33]. Behavioural instability provides another way of analysing data compared to traditional measures such as total distance traveled, activity per hour or swimming distance. Likewise, behavioural traits have been used in evolutionary studies to evaluate plasticity and genotypic difference or in psychological studies [34]. Similarly, several genome-wide association studies (GWAS) studies are trying to associate genetic variation with variation in behavioral traits [35]. These studies will clearly be beneficial if it is possible to associate the concept of behavioural instability with genetic variation. In addition, the procedure described in this paper could also be useful for excluding samples where σ

_{e}

^{2}is present, as it will bias the GWA analysis due to the fact that σ

_{e}

^{2}will, most of the time, increase the sizes of the traits and therefore invalidate the analysis.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Overall mean of the number of clockwise and counter-clockwise movements and 95% confidence interval of the total activity of the 19 lines.

**Table 1.**Pairwise tests for differences between the medians of the total activity between the 19 lines. All of the p-values have been corrected for multiple comparisons, following Bonferroni [19], and only significant p-values are reported.

Line | 383 | 385 | 386 | 392 | 426 | 443 | 461 | 491 | 357 | 492 | 508 | 509 | 531 | 563 | 584 | 589 | 358 | 703 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

385 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

386 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

392 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

426 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

443 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

461 | 0.000 | 0.000 | - | 0.000 | 0.000 | 0.000 | - | - | - | - | - | - | - | - | - | - | - | - |

491 | - | - | - | - | - | - | 0.000 | - | - | - | - | - | - | - | - | - | - | - |

357 | 0.000 | 0.000 | - | 0.001 | 0.001 | 0.000 | - | 0.000 | - | - | - | - | - | - | - | - | - | - |

492 | 0.008 | - | - | - | - | 0.006 | - | - | - | - | - | - | - | - | - | - | - | - |

508 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

509 | 0.008 | - | - | - | 0.013 | 0.010 | - | - | - | - | - | - | - | - | - | - | - | - |

531 | 0.013 | - | - | - | - | 0.008 | 0.007 | - | - | - | - | - | - | - | - | - | - | - |

563 | 0.006 | - | - | - | - | 0.000 | 0.027 | - | - | - | - | - | - | - | - | - | - | - |

584 | - | - | - | - | - | - | 0.000 | - | 0.000 | 0.000 | - | 0.001 | 0.000 | 0.000 | - | - | - | - |

589 | 0.012 | - | - | - | - | 0.021 | - | - | - | - | - | - | - | - | 0.001 | - | - | - |

358 | 0.014 | - | - | - | - | 0.010 | 0.013 | - | 0.047 | - | - | - | - | - | 0.001 | - | - | - |

703 | 0.000 | 0.000 | 0.011 | 0.000 | 0.000 | 0.000 | - | 0.000 | - | 0.001 | - | - | 0.000 | 0.000 | 0.000 | 0.003 | 0.000 | - |

716 | 0.016 | - | - | - | - | - | 0.038 | - | - | - | - | - | - | - | 0.002 | - | - | 0.001 |

**Table 2.**Means of the total activity of the 19 lines. The variance, the median, the skewness and kurtosis are listed and a Shapiro–Wilk’s test for deviation from normal distribution has been tested within every line. Significant deviations from normality are highlighted in bold. However, none of the deviations were significant after Bonferroni correction (K = 19) [19].

Line | 383 | 385 | 386 | 392 | 426 | 443 | 461 | 491 | 357 | 492 | 508 | 509 | 531 | 563 | 584 | 589 | 358 | 703 | 716 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Mean | 53.40 | 51.60 | 40.62 | 45.10 | 52.43 | 51.78 | 27.43 | 47.77 | 29.23 | 38.65 | 38.82 | 31.77 | 40.57 | 39.60 | 54.02 | 38.42 | 40.47 | 23.58 | 40.25 |

Variance | 214.30 | 244.42 | 299.96 | 101.24 | 317.32 | 71.84 | 162.46 | 127.17 | 149.56 | 139.80 | 334.39 | 383.65 | 113.53 | 70.39 | 80.56 | 194.05 | 91.32 | 93.19 | 151.75 |

Median | 54.50 | 48.75 | 42.75 | 46.50 | 57.25 | 52.25 | 29.00 | 51.50 | 29.00 | 40.50 | 42.75 | 32.00 | 41.00 | 39.50 | 56.25 | 42.50 | 41.50 | 22.25 | 43.50 |

Skewness | −0.95 | −0.21 | −0.67 | −0.79 | −0.87 | 0.36 | −0.49 | −1.05 | −0.04 | −0.47 | −0.05 | −0.20 | −1.57 | 0.22 | −0.81 | −1.11 | −0.62 | 0.19 | −0.92 |

Kurtosis | 0.76 | −0.61 | −0.33 | −0.16 | 0.02 | −0.08 | −0.47 | 0.26 | −0.72 | 0.11 | −1.28 | −1.25 | 4.83 | 0.07 | 0.10 | 0.90 | −0.08 | −0.25 | 0.03 |

Shapiro–W | 0.92 | 0.97 | 0.94 | 0.93 | 0.92 | 0.97 | 0.95 | 0.89 | 0.98 | 0.98 | 0.94 | 0.92 | 0.88 | 0.97 | 0.93 | 0.90 | 0.95 | 0.98 | 0.90 |

P (normal) | 0.02 | n.s. | n.s. | 0.05 | 0.02 | n.s. | n.s. | 0.00 | n.s. | n.s. | n.s. | 0.04 | 0.00 | n.s. | n.s. | 0.01 | n.s. | n.s. | 0.01 |

**Table 3.**F-tests of the log-transformed variances of the total activity; the log-variances have been sorted in descending order. The tests have been corrected for multiple comparisons (Bonferroni correction; K = 171) [19], and only significant p-values are reported.

Lines | 509 | 461 | 386 | 589 | 531 | 508 | 357 | 703 | 426 | 716 | 492 | 383 | 385 | 491 | 358 | 392 | 563 | 584 | 443 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Log-Variances | 0.240 | 0.110 | 0.097 | 0.086 | 0.065 | 0.064 | 0.056 | 0.050 | 0.042 | 0.031 | 0.029 | 0.024 | 0.023 | 0.016 | 0014 | 0.012 | 0.009 | 0.006 | 0.005 | |

509 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | |

461 | * | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | |

386 | * | n.s. | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | |

589 | * | n.s. | n.s. | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | ||

531 | * | n.s. | n.s. | n.s. | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | |

508 | * | n.s. | n.s. | n.s. | n.s. | - | - | - | - | - | - | - | - | - | - | - | - | - | - | |

357 | * | n.s. | n.s. | n.s. | n.s. | n.s. | - | - | - | - | - | - | - | - | - | - | - | - | - | |

703 | * | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | - | - | - | - | - | - | - | - | - | - | - | - | |

426 | * | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | - | - | - | - | - | - | - | - | - | - | - | |

716 | * | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | - | - | - | - | - | - | - | - | - | - | |

492 | * | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | - | - | - | - | - | - | - | - | - | |

383 | * | * | * | * | * | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | - | - | - | - | - | - | - | - | |

385 | * | * | * | * | * | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | - | - | - | - | - | - | - | |

491 | * | * | * | * | * | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | - | - | - | - | - | - | |

358 | * | * | * | * | * | * | * | * | * | n.s. | n.s. | n.s. | n.s. | n.s. | - | - | - | - | - | |

392 | * | * | * | * | * | * | * | * | * | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | - | - | - | - | |

563 | * | * | * | * | * | * | * | * | * | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | - | - | - | |

584 | * | * | * | * | * | * | * | * | * | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | - | - | |

443 | * | * | * | * | * | * | * | * | * | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | - |

**Table 4.**Signed fluctuating asymmetry mean

_{(r−l)}of the total activity of the 19 lines. The variance, the median, the skewness and kurtosis are listed and a Shapiro–Wilk’s test for deviation from normal distribution has been tested within every line. Significant deviations from normality are highlighted in bold. However, none of the deviations were significant after Bonferroni correction (K = 19) [19].

Line | 383 | 385 | 386 | 392 | 426 | 443 | 461 | 491 | 357 | 492 | 508 | 509 | 531 | 563 | 584 | 589 | 358 | 703 | 716 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Mean | 9.60 | −15.60 | 1.03 | 2.21 | 7.47 | 15.37 | 5.27 | 9.47 | 3.20 | 10.97 | 2.37 | −5.07 | −4.87 | 1.20 | 2.37 | 3.03 | 7.97 | −1.17 | 0.97 |

Variance | 8139.1 | 2183.4 | 2877.1 | 1838.0 | 1721.2 | 1863.7 | 1441.2 | 3583.8 | 602.2 | 1051.0 | 4758.1 | 1819.4 | 606.1 | 571.3 | 4992.0 | 2060.4 | 870.0 | 1424.5 | 1234.9 |

Median | 29.00 | −25.50 | 1.00 | 4.00 | 5.50 | 10.00 | 9.00 | 17.50 | 3.00 | 7.00 | −0.50 | −2.50 | −5.00 | −5.00 | 9.50 | 8.00 | 7.00 | 1.00 | 7.00 |

Skewness | −0.29 | 0.01 | −0.36 | 0.07 | −0.20 | 0.28 | −0.31 | 0.04 | 0.70 | −0.02 | −0.12 | −0.25 | −0.20 | 0.74 | −0.14 | −0.12 | 0.12 | −0.29 | −0.51 |

Kurtosis | −1.25 | 1.08 | 0.35 | −0.52 | −0.76 | 0.01 | −0.68 | −0.81 | 1.51 | 1.06 | −0.61 | 1.44 | 0.72 | 0.61 | −0.75 | −0.48 | −0.36 | −0.47 | 0.35 |

Shapiro–W | 0.92 | 0.94 | 0.98 | 0.97 | 0.97 | 0.97 | 0.96 | 0.94 | 0.95 | 0.98 | 0.97 | 0.89 | 0.97 | 0.93 | 0.97 | 0.98 | 0.98 | 0.98 | 0.97 |

P (normal) | 0.03 | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | n.s. | 0.01 | n.s. | 0.05 | n.s. | n.s. | n.s. | n.s. | n.s. |

**Table 5.**Pairwise tests for differences between the medians of the total activity mean absolute FA; |FA|= ∑ |r − l|/N. (FA1 index) between the 19 lines. All the p-values have been corrected for multiple comparisons, following Bonferroni [19], and only significant p-values are reported.

Lines | 383 | 385 | 386 | 392 | 426 | 443 | 461 | 491 | 357 | 492 | 508 | 509 | 531 | 563 | 584 | 589 | 358 | 703 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

385 | 0.00 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

386 | - | 0.02 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

392 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

426 | - | 0.01 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

443 | - | 0.00 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

461 | - | 0.01 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

491 | - | 0.00 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

357 | 0.03 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

492 | - | 0.00 | 0.04 | - | - | - | - | - | 0.00 | - | - | - | - | - | - | - | - | - |

508 | - | 0.00 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

509 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

531 | - | 0.00 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

563 | - | 0.00 | - | - | - | - | - | - | 0.01 | - | - | - | - | - | - | - | - | - |

584 | - | 0.00 | 0.05 | - | - | - | - | - | 0.00 | - | - | 0.02 | - | - | - | - | - | - |

589 | - | - | - | - | - | - | - | - | - | - | - | - | - | 0.04 | 0.02 | - | - | - |

358 | - | 0.01 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

703 | - | 0.00 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

716 | - | 0.00 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

**Table 6.**Pairwise tests for differences between the medians of the total activity’s scaled FA index; |r − l|/(0.5r + 0.5l) (FA3 index) between the 19 lines. All the p-values have been corrected for multiple comparisons, following Bonferroni [19], and only significant p-values are reported.

Lines | 383 | 385 | 386 | 392 | 426 | 443 | 461 | 491 | 357 | 492 | 508 | 509 | 531 | 563 | 584 | 589 | 358 | 703 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

385 | 0.00 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

386 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

392 | 0.00 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

426 | 0.00 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

443 | 0.00 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

461 | - | - | - | - | 0.04 | 0.05 | - | - | - | - | - | - | - | - | - | - | - | - |

491 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

357 | 0.00 | - | - | - | - | - | 0.02 | - | - | - | - | - | - | - | - | - | - | - |

492 | 0.00 | - | - | - | - | - | 0.03 | - | - | - | - | - | - | - | - | - | - | - |

508 | - | - | - | - | - | 0.04 | - | - | - | 0.05 | - | - | - | - | - | - | - | - |

509 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

531 | 0.00 | - | - | - | - | - | 0.00 | 0.02 | - | - | 0.00 | - | - | - | - | - | - | - |

563 | 0.00 | - | - | - | - | - | 0.00 | 0.01 | - | - | 0.00 | - | - | - | - | - | - | - |

584 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

589 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

358 | 0.00 | - | - | - | - | - | 0.02 | - | - | - | 0.03 | - | - | - | - | - | - | - |

703 | - | - | - | - | 0.03 | - | - | - | 0.01 | 0.03 | - | - | 0.00 | 0.00 | - | - | 0.03 | - |

716 | 0.00 | - | - | - | - | - | 0.03 | - | - | - | - | - | - | - | - | - | - | 0.03 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Pertoldi, C.; Bahrndorff, S.; Kurbalija Novicic, Z.; Duun Rohde, P.
The Novel Concept of “Behavioural Instability” and Its Potential Applications. *Symmetry* **2016**, *8*, 135.
https://doi.org/10.3390/sym8110135

**AMA Style**

Pertoldi C, Bahrndorff S, Kurbalija Novicic Z, Duun Rohde P.
The Novel Concept of “Behavioural Instability” and Its Potential Applications. *Symmetry*. 2016; 8(11):135.
https://doi.org/10.3390/sym8110135

**Chicago/Turabian Style**

Pertoldi, Cino, Simon Bahrndorff, Zorana Kurbalija Novicic, and Palle Duun Rohde.
2016. "The Novel Concept of “Behavioural Instability” and Its Potential Applications" *Symmetry* 8, no. 11: 135.
https://doi.org/10.3390/sym8110135