The relationship between dispersal and differentiation of the European freshwater mussel Unio pictorum (Linnaeus, 1758) was studied with molecular genetic methods. Forty‐two populations from France, Italy and central Europe were analysed. Genetic relationships were assessed from the geographical distribution of allele frequencies at 17 enzyme loci. Neighbouring groups of populations show small to moderate mean genetic distances (0.020 < Dmean < 0.263). With a few exceptions the genetic affinities of the populations are the closest within the same drainage basin. In central Europe and Northern Italy genetic differences between drainage systems are relatively large. Populations from north‐eastern Italy are genetically similar to Danubian populations. Mussels from the islands of Corsica and Sardinia are more closely related to populations from the Italian peninsula than to French populations from the Rhône drainage system. Genetic relationships within U. pictorum from central Europe reflect palaeogeographical relationships between river systems during the Pliocene and Pleistocene. Literature data on two North American unionid species and one European fish species show the same relationship between genetic diversity and the history of drainage systems, although the correlations are less strong. In France and Italy this correspondence is much less evident. Population dynamic processes and human activities leading to populational bottlenecks might have obscured it.

No abstract

Abstract

Analysis of heart rate variability (HRV) often requires a continuous representation of the inherently discrete heart rate measurement. In combination with a suitable cardiac pacemaker model, e.g. the integral pulse frequency modulator (IPFM) , the cardiac event series can be considered as an irregular sampling of a continuous input to the pacemaker model, met). Continuous representation of heart rate can thus be achieved by a reconstruction of the input function met) from the cardiac event series. Two such representations of the heart rate, the instantaneous heart rate (IHR) and the low pass filtered event series (LPFES), have previously been assumed to be consistent with the IPFM model. Simulations show, however, that the LPFES actually is not consistent with the model. The IHR representation, although consistent with the model, suffers from discontinuities which are both unphysiological and inadequate for subsequent signal processing. A solution to the problem has been developed by introducing M(t), the continuous integral of met). The samples of M(t) are specified by the cardiac event series and continuous representation of M(t) is achieved by cubic spline interpolation. The input to the cardiac pacemaker model met), or in other words, the representation of the heart rate is given by the derivative of M(t). IntroductionVariations of heart rate, as a normal physiological phenomenon, reflect the activities of the cardiac control system. Various components of the heart rate variability (HRV) can be identified by spectral analysis. They are related to different cardiac control activities such as blood pressure, thermal regulation and respiration [5]. Sympathetic and parasympathetic origins have been identified for specific spectral components [1]. Thus, analysis of HRV can provide information on autonomic functions, especially the parasympathetic control of the heart [4]. However, because the measured heart rate is inherently a discrete signal, which is not defined between heart beats, study of HRV, especially by digital signal processing, often requires representation of the signal by a substitute continuous function of time in order to obtain regularly sampled data. Finding an adequate continuous function is possible only when enough knowledge and a model of the mechanism of the cardiac pacemaker is available.

We investigate the implications that a sum rule for the average velocity of a geological fault has on the distribution of earthquake sizes. Under general conditions the exponent B of the Gutenberg-Richter law for the distribution of small seismic moments is shown to obey 8 & 1. This result does not rely on any particular earthquake model and should be equally applicable to the case of friction between two sliding blocks as well as to computer simulations of earthquake dynamics. For the distribution of large earthquakes we specifically consider three diA'erent possible models: (a) A single power law exists over the entire range of magnitudes; then B= l. (b) The large events do not fall in the scaling region; in this case we are able to derive a relationship between the exponents relating their frequency and seismic moment to the total size of the system. (c) The large earthquakes also show scaling behavior but with a diAerent exponent B'; then the sum rule implies that B'& l. PACS number(s): 91.30.8i, 46.30.Jv, 05.70.Jk Along a single geological fault there will be earthquakes of many different sizes. The seismic moment m is commonly used as a measure of the size of an earthquake [1]. It is defined here as the amplitude of the motion integrated over the active region m =J xds',where x is the relative displacement of the two sides of the fault and s is the area of the active region of the fault during an earthquake. The rate of occurrence (number of events per unit time) p of an earthquake of seismic moment m is observed to obey the empirical Gutenberg-Richter law [2] p(m) =Amwhere A and 8 are constants [3]. For small to-intermediate magnitudes all available data [4] indicate that the distribution of B values for many different regions around the world is highly concentrated around I, except for volcanic regions, where 8 values between 1 and 2 are common [5]. Also microearthquakes are found to obey Eq.(2) with 8= I [6]. The relation (2) has been used to characterize both the seismicity of a single fault as well as the seismicity in a broad region that includes many faults.A variety of earthquake models have been introduced. The so-called spring-block models [7] and their cellularautomata counterparts [8,9] have recently attracted some attention in the physics community.To a large extent their success has been judged by whether or not they reproduce the Gutenberg-Richter law with the value 8 = l. An essential ingredient of all these models is that the two sides of the "fault" are forced to move at a constant average velocity with respect to one another to mimic the driving mechanism of plate tectonics. The existence of these different models indicates that it is possible to start with quite different assumptions and still produce a power law for the distribution of earthquake sizes. What remains to be understood is why the real earthquake data taken from many different faults as well as the data from computer models which have very different starting assumptions give approximately the same exponent. %'e will argue b...