Philippe P
Department of Social and Preventive Medicine, University of Montreal, Canada.
Ann Hum Biol. 1994 Sep-Oct;21(5):423-34. doi: 10.1080/03014469400003442.
Classically, researchers considered monozygotic twinning (MZT) a random phenomenon. This paper tests the hypothesis with the aid of nonlinear dynamics techniques. The latter can tell true randomness from chance-like variation. Chaos, the endpoint of the threshold state of a nonlinear deterministic system, can mimic constrained randomness. From a practical standpoint, recognizing chaos in a time series data set means that the paradigmatic multifactorial model of causation is essentially ruled out. Specifically, time series of MZ, DZ, and single maternities were analysed. First, spectral analysis was used to uncover periodicities embedded in the series. Second, a singular value decomposition was undertaken to reduce noise from the series. Third, phase space attractors were drawn up that describe the 'asymptotic' trajectory of the system at any time. Results suggested that DZ, MZ, and single maternities shared a similar 32-year periodicity. Owing to two interwoven similar periodicities, the single-maternity cycle kinetics proved to be faster than that of DZ's. The MZ series was the only one to display secondary interacting harmonics, thus eliciting a rather unusual trajectory in the bidimensional phase space. The MZ time points were not spread in a haphazard fashion; on the contrary, a fine structure was present that did not reduce to a limit cycle such as the one characterizing the DZ- or the single-maternity trajectory. It was concluded that a complex nonlinear dynamic underlies MZ twinning. Therefore, calling for extrinsic causes to account for what appears to be random variation overtime would be pointless. MZ twinning should rather be traced to a limited number of intrinsic and deterministic interacting system components. The most likely candidates are presented and discussed.
传统上，研究人员认为单卵双生（MZT）是一种随机现象。本文借助非线性动力学技术对这一假设进行了检验。后者能够区分真正的随机性和类似随机的变化。混沌作为非线性确定性系统阈值状态的终点，可以模拟受约束的随机性。从实际角度来看，在时间序列数据集中识别混沌意味着因果关系的典型多因素模型基本上被排除。具体而言，对单卵双生、双卵双生和单胎生育的时间序列进行了分析。首先，使用频谱分析来揭示序列中嵌入的周期性。其次，进行奇异值分解以减少序列中的噪声。第三，绘制相空间吸引子，以描述系统在任何时候的“渐近”轨迹。结果表明，双卵双生、单卵双生和单胎生育具有相似的32年周期性。由于两个相互交织的相似周期性，单胎生育周期动力学被证明比双卵双生的更快。单卵双生序列是唯一显示二次相互作用谐波的序列，从而在二维相空间中引出了一条相当不寻常的轨迹。单卵双生的时间点并非随机分布；相反，存在一种精细结构，它不会简化为极限环，例如双卵双生或单胎生育轨迹所特有的极限环。得出的结论是，单卵双生背后存在复杂的非线性动力学。因此，要求外部原因来解释随着时间推移看似随机的变化是没有意义的。单卵双生应该追溯到有限数量的内在和确定性相互作用的系统组件。文中提出并讨论了最有可能的候选因素。
