Possible Causes of Instability of Reproduction of Heliobiological Results

Zenchenko Tatiana ORCID: 0000-0002-0520-2029 Doctor of Biology Senior Researcher at the Institute of Theoretical and Experimental Biophysics of RAS; Senior Researcher at the Space Research Institute of RAS 142290, Russia, Moscow region, Pushchino, Institutskaya str., 3 zench@mail.ru

Breus Tamara Doctor of Physics and Mathematics Chief Researcher at the Space Research Institute of RAS 142290, Russia, Moscow region, Moscow, ul. Profsoyuznaya, 84/32 breus36@mail.ru

Introduction

Heliobiology is a scientific field that studies the patterns of solar-biospheric connections. From the scattered observations of individual naturalists into a serious science, heliobiology took shape in the 20s of the XX century in the works of the Russian scientist Alexander Leonidovich Chizhevsky, who has since been considered its founder.

The scientist and poet A.L.Chizhevsky reflected the discovery formulated by him in the figurative titles of the books he wrote: "The Earth in the arms of the Sun", "The Cosmic Pulse of Life", "The Earthly Echo of solar Storms". The essence of the discovery was that literally all processes on Earth occurring in wildlife, in the atmosphere, hydrosphere, lithosphere, etc.  they experience the effect of solar activity. Such a conclusion inevitably suggested itself due to the presence of 11-year cycles in these processes, which have long been known in the dynamics of solar activity.

Chizhevsky gives a long list of such processes: "To date, the following physical phenomena on Earth are causally dependent on the degree of intensity of solar activity:

1. The intensity of terrestrial magnetism. Magnetic storms (Lamont. 1850; Sabin, Cautur, Wolf. 1852), as well as the frequency of magnetic storms.

2. The frequency of auroras (Fritz, 1863; Loomis).

3. Frequency of occurrence of cirrus clouds (Klein), their radiation (A. Moiseev).

4. The frequency of the appearance of halos and crowns around the Sun and Moon (Messerschmidt, Moiseev, 1917).

5. The amount of ultraviolet radiation (Dobson, 1924; Pettit).

6. The amount of radioactive emanation in the air (Bongards, 1923).

7. The degree of ionization of the upper atmosphere (Schuster. Pieard, Austin, 1927). Changes in the electrical envelope of the atmosphere, radio reception, audibility, etc.

8. Fluctuations in the intensity of atmospheric electricity (Wislicinus, 1872; Chree, Bauer).

9. Frequency and intensity of thunderstorm activity (Lenger. 1887; Hess, D. Svyatsky, A. Moiseev, 1920).

10. The amount of ozone in the air (Moffat, 1876; Dobson, Harrisson, Lowrens).

11. The amount of cosmic dust in the air (Busch, Arrhenius, Berberich), etc. and the color of the sky (Busch).

12. The amount of thermal radiation (insolation) (Saveliev, 1884, 1905-1920).

13. The temperature of the air at the surface of the Earth and the water of the seas (Gautier. 1844; K?ppen, Fr?hlich, Flammarion, Ricco, Nordmann, Langley, M. Dowall, Meisner Mielke, Terada, etc.).

14. Air pressure (Broun, Archibald, Lockyer, Leist, Walker, Clayton, Fedorov, etc.).

15. Frequency of storms, hurricanes, tornadoes (Meldrun, 1872; Rocy, Reich, Kawazoe-Pampei, Myrbach, m-me Flammarion, Kulmer).

16. The amount of precipitation (Meldrun, Lockyer, Symons, Archibald, Hill, Kassner, Huntington, Moreux, Shostakovich, etc.), the frequency of hail (Fritz) and the number of polar icebergs.

17. The height of the lake level (Moreux, Wallen, Wiese, Svyatsky, Shostakovich and many others)." ^[1].

The second list includes phenomena in the biosphere for which a connection was previously found with the periodic activity of the Sun, as well as electricity and magnetism of the Earth:

"1. The value of the crop of fodder cereals (Sir, W. Herschel, 1801; Clarce, Danson, Fritz, Show, Hunter, Endstrom, Flammarion, M. Semenov, B. Yastremsky).

2. Quantity and quality of the extracted wine (Sartorius, H. Fritz, 1878; Memery, Lackowsky).

3. Growth of wood (thickness of annual rings) (Lem-strom, Helland-Hansen, Nansen, Huntington, Douglass).

4. The flowering time of plants (Marchand, Flammarion, Nansen, Helland-Hansen).

5. The splendor of flowering plants (Belot, 1927).

6. Epiphytes (Chizhevsky, 1927).

7. Reproduction and migration of insects (K?ppen, 1870; Fritz, Hahn, Giard).

8. Reproduction and migration of fish (Nansen. Helland-Hansen, 1909; Shostakovich). The amount of caviar in the liver of some fish.

9. The time of the spring arrival (migration) of birds (Marchand, Flammarion, Moreux, Shostakovich).

10. Reproduction and migration of animals (rodents, fur) (Turkin, 1900; Simrotti. 1907).

11. Duration of stable keeping of cattle (Yastremsky, 1926).

12. Epizootics, the death of cattle (Chizhevsky, 1927).

13. The quality of calcium in the blood (H. et R. Bakwin).

14. The frequency of human lesions by lightning strikes and the frequency of fires from lightning (Bondin, O. Steffens, 1904).

15. Fluctuations in the weight of infants (Zhukov, 1928)". ^[1].

From the above lists, one can see, firstly, how long and widely naturalists have been interested in the question of the possible influence of the rhythmics of the Sun on terrestrial processes: scientific works from the middle of the XIX century are mentioned in the list. It is also possible to estimate the breadth of coverage of natural phenomena for which such a connection is observed, from auroras and hurricanes, the dynamics of the height of lakes and the arrival of birds to the composition of human blood and the weight of newborn babies.

In these collected and systematized lists of scientific observations known by that time, Chizhevsky also included long-term patterns discovered by himself, in particular, the occurrence of large epidemics. Several examples from his book are shown in Figures 1-3.

Figure 3. - Relationship between diphtheria incidence (thin curve) and solar activity in Denmark. The diphtheria curve is shifted five years to the right. The spontaneous course of the epidemic was stopped by the human mind: the pink sector (since 1894) - the introduction of serotherapy.^[1]

However, a careful analysis of the above figures reveals one feature: the processes under consideration do have a bright 10-11 year periodicity, but their phases differ when compared with the course of solar activity. For example, in Figure 1, there is a coincidence of the moments of extremes in two rows, in Figure 2, to combine the moments of maxima, one curve is shifted relative to the other by 2 years, and in Figure 3, the phase shift is five years, i.e. the processes are almost in the opposite phase.

Chizhevsky describes this phenomenon in this way: "Studying various manifestations of organic life in our other investigations, we had to come to the conclusion that in addition to the dependence of the organic world on periodic fluctuations of solar activity, there are still some interrelationships and known interactions of various regions of the biosphere among themselves, regulated by this solar periodicity. So, for example, fluctuations in yield, seed growth, and wood growth, although they are closely related to the activity of the Sun, but for different localities they reveal various deviations with a shift of the points of maxima and minima in the course of the curve in different directions, and sometimes giving an obvious counter-parallelism. Similar phenomena are observed in the distribution of some epidemics in time and space, which we saw above." ^[1]

Thus, the founder of heliobiology himself wrote at the beginning of the XX century that when studying the relationship of various biospheric indicators with solar activity, we obviously will not be able to transfer conclusions from observations made in one area of the Earth to other regions. At some point, the steadily observed synchronicity suddenly disappeared (Fig. 3), and it was not always possible to find possible reasons for this desynchronization.

Thus, the main problem of the study of solar-biosphere dependencies was discovered and formulated, namely, their insufficient universality and reproducibility from the point of view of classical physics.

There were other serious claims to heliobiological research on the part of classical academic science, which remained relevant throughout the XX century. Firstly, it was not possible to accurately reproduce the observed effects in the laboratory. The problem was that the simulation in the laboratory of the entire complex complex of interrelated space weather factors accompanying, for example, the development of a magnetic storm, was and remains an impossible task to this day. Therefore, the setting of experiments was reduced to studies of the influence of one physical factor from this complex on living objects, namely, a low-intensity alternating magnetic field. These experiments yielded positive results, but with significant caveats: in order to obtain a stable magnetobiological response, either increased (compared to natural) amplitudes of the variable component of the magnetic field were required, or repeated, for several days, periodic exposures of the field, i.e. accumulation of the effect was necessary ^[2-5].

Of course, the attempt to replace a complex interconnected complex of solar-magnetospheric factors, called space weather, with one monochrome signal of a magnetic field of a certain frequency and amplitude was, from the point of view of methodology, very naive. But the lack of successful experiments on stable reproduction in the laboratory of the observed effects of a magnetic storm caused serious skepticism among physicists.

The third claim to heliobiology on the part of official science was that modern physics did not have theoretical models capable of satisfactorily explaining the mechanism of significant influence on living systems of such low-intensity physical factors as variations of the geomagnetic field or cosmic particles.

The existence of these claims to the results and conclusions of heliobiology led to a situation where researchers, unable to directly refute the criticism expressed, were again and again searching for confirmation of the existence of a heliobiological effect. The list of objects for which the effect was detected expanded, the frequency of observations increased - from annual data to monthly, daily and even minute data, the volume of samples and the length of observation series increased. However, the situation did not change fundamentally: firstly, the heliobiological effect was detected in all forms of observation organization, and secondly, it remained insufficiently stable, i.e. it was not always detected.

Such a confrontation lasted for almost a hundred years: on the one hand, there were numerous results of observations by heliobiologists, as well as many years of experience of practicing bioclimatologists and cardiologists who saw and took into account the adverse effects of space weather in their work. On the other hand, there is the skepticism of "academic" scientists, primarily physicists, who repeatedly cited the above arguments against the existence of significant solar-biosphere connections: insufficient reproducibility of the observed effects, the impossibility of their accurate reproduction in laboratories, the absence of theoretical models of the influence of ultra-weak factors.

However, in the last decade, heliobiology has managed to make serious progress in solving two of the aforementioned contradictions: physical theoretical models have appeared describing the possible mechanisms of action of an extremely weak alternating magnetic field, comparable in amplitude to the earth's, on living organisms ^[6,7]. The results of experiments with magnetic storms recorded and reproduced in the laboratory were also published, the exposure of living organisms in which gave steadily reproducible effects ^[8-10]. Thus, it can be concluded that by now it has been shown both theoretically and experimentally that magnetic fields of such low intensity may well have an effect on living systems.

At the same time, the fact of instability of heliobiological effects has traditionally been considered by researchers as a consequence of the imperfection of the experimental base and methods of analysis: errors in the collection of medical data, suboptimal choice of space weather parameters characterizing its biotropicity, inefficiency of the selected mathematical methods of analysis.

For example, there is a very large number of studies in the literature devoted to the effect of "Ambulance", when during magnetic storms there was an increase in the number of hospital visits for acute cardiovascular complications and even an increase in cases of sudden death. But when comparing the specific characteristics of the effect ? what is its amplitude, on what day from the beginning of the storm there is a maximum increase in morbidity ? there were significant discrepancies between the results of different authors. Among the possible reasons for such discrepancies, it was discussed, for example, an incorrect diagnosis or inaccuracy of the date of the onset of the disease: for example, whether a heart attack diagnosed by an ambulance doctor was confirmed already in the hospital; whether it occurred on the day of the Ambulance call or in the preceding days. Gradually, these shortcomings, which actually existed, were eliminated, appropriate clarifications were added to the data collection methodology, but the multidirectional effect of this did not disappear.

Another illustrative example of an attempt to reduce the instability of heliobiological results by improving methodological aspects relates to clinical studies of the dynamics of blood pressure (BP) in patients with diseases of the cardiovascular system. The doctors who conducted the research paid great attention to ensuring that the groups of patients were homogeneous by gender, age, anamnesis, and the duration of the disease, since these traditional medical criteria for selecting patients are considered fundamentally important for the reliability of the result. However, in the case of heliobiological studies, this did not help much: even if the criteria for selecting groups of patients were met, the same type of studies conducted at different times or in different places very often showed differences in results. For example, the effect of an increase in blood pressure was observed only in some (variable in magnitude) part of the experimental group, or the moment of the onset of the reaction maximum differed in shift time from the beginning of the magnetic storm. Sometimes even different reaction signs were observed: in one study the values grew, and in another they did not.

For example, in two homogeneous groups of healthy volunteers (86 people in Bulgaria ^[11] and 51 people in Mexico ^[12]), possible changes in blood pressure indicators during periods of strong magnetic storms were investigated. According to the authors' conclusions, in the first case, the rise in the average group blood pressure level was quite long and was observed from -1 to 2 days relative to the day of the storm, and in the second, the greatest increase in systolic blood pressure was observed two days before and one day after this storm.

Significant differences in conclusions about the specific characteristics of the effect are observed in the study of the reaction of heart rate in response to space weather phenomena ^[13-15].

In order to somehow explain such a difference in results, usually at the end of each specific article, the authors suggested that there were some other factors that they had not taken into account that distinguished their study from others and led to variability of the heliobiological effect they observed.

          Finally, the third characteristic example of attempts to overcome instability concerns methodological approaches to data analysis. For a long time, there have been cases in the literature of incorrect use of traditional statistical and spectral methods, which caused mathematicians to justly criticize and doubt the results obtained. The most common mistake was calculating the correlation coefficient for time series that did not meet the necessary criteria for data stationarity, i.e. containing low-frequency trends or periodic fluctuations, without first eliminating them. Over time, such errors in the application of traditional methods gradually disappeared, and new analysis algorithms developed specifically for heliobiological problems appeared, but all these improvements did not solve the problem of instability of the results.

Thus, despite a significant improvement in the methodology for collecting experimental data, a cardinal increase in the volume of experimental samples and a variety of types of observations, the development of new mathematical algorithms for analysis, it was not possible to get seriously closer to solving the causes of the instability of the effect.

In fact, the main reason for the variability of the heliobiological effect was formulated by Chizhevsky: "The complexity of the analysis of epidemiological phenomena lies in the complexity of the analysis of a common, unified system of the biosphere, the vital activity and interrelation of various functions of which are presented to us in even more vague contours." ^{[1, p. 233]}.

In other words, since the XVII century, the basic approach of physics to the study of nature is based on the technique of constructing idealized working models of the studied law or process: a scientist needs to include significant, in his opinion, elements of the system in the model at the initial stage of his research and exclude insignificant ones. And this technique applies not only to theoretical constructions, but also to experiments.

The system of solar-geospheric-biospheric connections turned out to be too complex for the traditional methodological approaches of natural science of the XX century, and attempts to build a working model within this framework led to the fact that critical factors or connections did not fall into the number of its significant elements.

Several such factors have been discovered purely empirically in the last three decades during the development of heliobiological science. Including with the active participation of our group, several aspects specific to heliobiological studies were identified and confirmed:

1) The individual nature of the reaction: the analysis of individual data gives much more self-consistent and logical results than the traditionally accepted medium-group approach in medicine. The group averaging operation largely hides the heliobiological effect.

2) The necessity of simultaneous consideration of the effects of factors of terrestrial and space weather: these two classes of factors affect the same body systems, and their combination can both enhance and weaken the heliometeotropic effect.

3) Taking into account the time factor, i.e. the phases of rhythmic heliophysical processes, and at any time scale: the 11-year solar cycle, the average level of geomagnetic activity during the observation period, on the intra?day scale - the ratio of the phases of the magnetic storm and the daily geomagnetic variation.

Let's look at them in more detail.

New methodological approaches

1. The individual nature of the reaction

For a long time in science, including in heliobiology, the method of averaging a certain parameter over a sample of the studied objects was used to identify systematic changes and to level out noise effects. It was within the framework of this approach that the above-mentioned experiments were carried out to study the blood pressure response of healthy people to magnetic storms.

However, about 30 years ago, the thesis was put forward and substantiated that "heliometeotropic reactions in different people can be different" ^[16]. Up to this point, traditionally, "by default", it was assumed that people (or animals) of the same sex, age and medical status should show a similar reaction to the action of the same external factor, and in particular, elements of space or terrestrial weather. This basic assumption allowed the researchers to combine the subjects into groups and determine the parameters of the average group reaction. However, the results described by V.N. Shepovalnikov and S.I. Soroko clearly showed the ineffectiveness of such an approach in heliobiology. "The actual spectrum of meteotropic reactions of individuals turns out to be much wider than the "average" reactions derived from the addition of indicators of different people. At the same time, at the expense of the majority, the idea of different forms of connection of physiological parameters with meteorological elements in the minority completely disappears, and, on the other hand, the minority data do not fit into the general system, they distort the majority data" ^{[16, p. 142]}.

This discovery made it possible to explain why attempts to identify medium-group reactions to space weather factors in some cases yielded statistically significant results, while in others they showed no reaction.

Figure 4 shows the results of the analysis of the individual reaction of 86 young (18-20 years old) healthy women to the effect of geomagnetic activity. Each participant's blood pressure, systolic (SAD) and diastolic (DAD), as well as heart rate (HR) were measured daily for 100 days. Those who had a statistically significant correlation coefficient between the daily values of the blood pressure level and the Kr indicator of the level of geomagnetic activity were considered magnetically sensitive; 25% of them turned out to be in this group. The parameter "reaction amplitudes" was also calculated for them ? the relative range of blood pressure and heart rate values observed at high and low values of the geomagnetic activity level. In Figure 4, the values of individual changes in blood pressure and heart rate are given in fractions of the maximum observed spread of values for this subject.

Figure 4. - Distribution of response amplitudes of systolic and diastolic blood pressure and heart rate indicators to an increase in the level of geomagnetic activity for magnetically sensitive volunteers (observation data provided by P.E. Grigoriev).

It can be seen from the histograms of Figure 4 that, firstly, the relative magnitude of the change in BP, potentially caused by a change in the level of geomagnetic activity, is 20-40% of the maximum observed range of this parameter. For heart rate, these changes are 20-30%. Secondly, the relative number of people whose blood pressure and heart rate increases when the level of geomagnetic activity changes, and in whom this level decreases, turns out to be almost the same. It is obvious that the mathematical operation of searching for the averaged effect for this rather large group would give zero effect.

In another case, a study very similar in design ^[17] showed that a significant reaction of blood pressure indicators to changes in geomagnetic activity is observed in 53% of the subjects, i.e. the percentage of magnetically sensitive people in this group is about twice as large as in the study in Figure 4. But most importantly, in the case of ^[17], all it has the same sign for all participants, i.e., with an increase in the level of geomagnetic activity, the blood pressure level increases for all subjects. If we apply the classical group averaging method to the results of this experiment, we will get a statistically significant effect of an increase in the average group blood pressure level on the day of a magnetic storm.

From the examples given, it follows that in heliobiology, wherever the volumes of the obtained data arrays allow, an individual approach is preferred, followed by combining the same type of reactions into groups and calculating the relative proportion of each type. In this case, the "average group" reaction automatically follows, as a sum, from the set of individual ones, but at the same time information about the "internal structure" of the set is preserved, and not only about the resulting sum. The main disadvantage of the individual approach is its significantly higher labor costs than in the case of the average group, however, it would be incorrect to say that the first is somewhat less accurate than the second.

2. The complex influence of terrestrial and cosmic weather

The second important methodological point, which has not been taken into account in heliobiological studies for a long time, is the complex effect of factors of terrestrial and space weather on humans.

Historically, heliobiology and biometeorology (or, another name, "climatophysiology") have been moving almost independently of each other for a long time. Biometeorologists studied the effect of heat and cold waves, cyclones, and baric minima on patients' bodies, and only ultraviolet light was considered from cosmic factors ^[18]. Heliobiologists, starting with Chizhevsky, have been looking for the effects of solar flares, magnetic storms, strong proton events, Schumann resonances, etc., which is described in detail in the review ^[19]. And only since the beginning of the 80s. many factors of terrestrial and space weather began to be gradually combined within the framework of some studies, the term "heliometeotropic effect" appeared^[20]. However, such a union was performed mechanically, by simply combining two parameter lists. In addition, there are still studies that consider the possible influence of only heliogeophysical factors.

At the same time, the problem of taking into account the possible simultaneous influence of terrestrial and space weather on biosystems contains two important aspects.

The first is the connection between the dynamics of heliofactors and meteorological factors. Chizhevsky, having discovered the phenomenon of synchronization of solar and terrestrial processes, formulated this problem in this way: "Does space weather directly affect living organisms (for example, through variations of the geomagnetic field, flows of secondary energy particles from galactic or solar cosmic rays, etc.) or do atmospheric factors serve as an intermediate link in this chain?" ^[1].

On large time scales comparable to the length of solar cycles, such a relationship has been shown repeatedly ^[1,21-23].

A recent study ^[24] examines in detail the possible connection of abnormal heat waves on the American continent in 1910, 2012 and 2015 with special cosmic plasma structures generated by the Sun that cause very strong magnetic storms. Therefore, we can say that on the daily scale of consideration, extreme space weather phenomena can be the cause of extreme atmospheric events. At the same time, at the current level of representations, daily non-extreme variations of geomagnetic and meteorological parameters can be considered as independent of each other. However, it cannot be excluded that the dynamics of daily values of meteorological and geophysical parameters will be statistically dependent on the observation interval for purely random or unknown reasons ^[16]. In this case, such a relationship must be taken into account and excluded algorithmically when analyzing the results ^[25,26].

On the other hand, both of these classes of external factors affect the same systems in the human body, despite the fact that the primary targets of exposure and physical mechanisms are certainly different. However, as a result, the body simultaneously forms a reaction to both classes of factors, depending on its internal state and on the degree of intensity of external influence ^[27,28]. In other words, the human body reacts to a magnetic storm in winter and to a magnetic storm in summer, being at different levels of stress caused by the level of air temperature, the duration of daylight hours, low seasonal levels of important hormones, etc.

Thus, any, even the simplest working model of heliobiological connections should include not only space weather factors and parameters of the biological system, but also, without fail, the main meteorological factors. The exclusion of the last component practically guarantees significant errors in the conclusions.

3. The phase factor of heliogeophysical rhythmics

In heliobiological studies, many authors have drawn attention to the fact that in the phase of ascent and in the phase of decline of the solar activity cycle, heliobiological effects look different ^{[13, 29-32]}: for example, in the ascent phase there is a direct statistically significant relationship between the biological indicator and the parameters of solar activity, and in other phases the effect is either not observed, or even has the opposite sign. Unfortunately, the combination of works that report such phenomena does not allow synthesizing their results, since they are performed for different physiological parameters and under different experimental schemes. At the same time, the scale of the main cycle of solar activity is too large for the observations to be repeated and verified under similar conditions 11 years later, or rather, 22 years later, since the full solar cycle is exactly 22 years. During this time, the condition of the subjects and the weather conditions change greatly. And the characteristics of different cycles are very different. Therefore, each such study remains unique and, in a methodological sense, unconfirmed. But it is important to note here that the idea of the importance of taking into account the phase of the solar cycle has been present in heliobiology for a long time.

In the last two decades, results have been obtained confirming this idea on smaller time scales. It turned out that the percentage of magnetically sensitive people in the population strongly depends on the average level of geomagnetic activity during the observation period ^[33]. If we compare the results of the analysis of three groups of volunteers, from Sofia (77 people) ^[34], Syktyvkar (27 people) ^[17] and Simferopol (63 people), it turns out that the percentage of cases of magnetosensitivity for those measured during the maximum of geomagnetic activity was 52% for Sofia and 48% for Syktyvkar, during The minimum is 24% for Simferopol (Fig. 5).

However, these groups differ from each other not only by the percentage of magnetically sensitive people, but also by reaction signs: the distribution for Simferopol is shown in Figure 4, and for the Sofia and Syktyvkar groups, without exception, all the correlations found had a positive sign, i.e. the blood pressure index increased with an increase in the level of geomagnetic activity.

Figure 6 shows the distribution by reaction start time for these three groups. In Sofia and Syktyvkar, the vast majority of reaction cases developed directly on the day of the beginning of the geomagnetic disturbance, and in the case of Simferopol, no reliable maximum is observed.

From the above example of three groups, it can be seen that the introduction of the parameter of average geomagnetic activity during the measurement period allows us to explain the differences that are observed in the Simferopol group in relation to the other two. Taking into account this factor also made it possible to explain why, in some cases, the effect is not observed in the study of the average group blood pressure index.

The third example of the importance of taking into account the phase of the geomagnetic activity cycle already relates to the intra-day scale, and allows us to explain why the effectiveness of magnetic storms repeatedly observed in different studies may differ significantly. In ^[9], the effect of a previously recorded three?component geomagnetic storm signal on the morphological parameters of marine animals and fish was studied in two experimental settings: the first - under conditions of synchronization of the main phase of the simulated magnetic storm with the phase of the daily geomagnetic variation, the second - under conditions of desynchronization, when the shift between phases was 12 hours. It was found that the result of the experiment strongly depends on the magnitude of the phase shift: under desynchronization conditions, the effect was observed on both samples of objects, both for roach and pond fish, and in a situation of synchronicity, changes in biochemical parameters were insignificant and statistically unreliable.

A result similar in meaning, when the amplitude of the observed effect depended on the ratio of the phases of an artificial magnetic storm and the daily geomagnetic variation, was observed in ^[10].

According to ^[35], the results of these two studies (both on hydrobionts and on humans) experimentally confirm the hypothesis that geomagnetic storms are perceived by the body as a violation of regular fluctuations in the diurnal variation of the geomagnetic field, i.e. regular changes in geomagnetic and solar factors serve as a time sensor for living organisms, different from the change of day and night. Such a hypothesis was expressed many times several decades before ^{[35, 36 and references therein]}, but in these studies it was confirmed experimentally for the first time.

For us, in this study, an important role is played by the fact that both within the daily scale, and at the daily sampling rate of data, and when compared with the phase of the 11-year cycle of solar activity, the results obtained largely depend on the position of the moment of observations relative to the phase of the basic heliogeophysical rhythm.

The above examples show that the inclusion in the analysis of additional parameters (individual reaction status, meteorological factors and the phase of the geomagnetic or solar cycle), largely clarifies some situations of the disappearance of the effect or the change of its sign. Other cases of non-reproducibility, not given here, also received their consistent explanation, taking into account the three parameters considered. At the same time, it can be reasonably assumed that the described examples are only some part of the solution to the problem of instability of heliobiological results.

4. Hypothesis

The main condition of the concept of "reproducibility" applied in traditional physics to a scientific result is that when reproducing "other things being equal", it must be repeated by any other researcher. And here, when analyzing the heliobiological results, the question of the accuracy of the implementation of the principle of "other equal conditions" becomes a matter of doubt and discussion.

The above examples confirm the assumption that the practically irremediable instability of the heliobiological effect is primarily due not to methodological errors of experimenters, but to deeper methodological problems of "non-inclusion" of critical factors in the working model of the system.

The difficulty lies in the fact that these factors, which are included in the form of key parameters in the system of solar-biosphere connections, firstly, are not fully known until now, and secondly, the dependence of the effect on each of them is characterized by variability, and according to a law unknown in advance. 

In order to somehow approach the solution of the formulated problem, it is necessary first to systematize the already known heliobiological effects. This task in itself is very voluminous and multifactorial, since, as mentioned above, such effects are observed at all levels of the organization of biosystems, from cells to human populations.

For a relatively small area of heliobiological results, namely for the class of effects of the influence of cosmic factors on human health and well-being, such systematization was performed according to three pre-selected criteria ^[33]:

1) time scale of data sampling (minutes, hours, days, years);

2) the level of organization of the biological system under study (cell, individual organ, body system, individual, group of individuals, population);

3) the degree of response of the biosystem (norm, adaptation, disease (or failure of adaptation), death (destruction of the biosystem).

As a result of the systematization carried out, it became clear that if we consider the three selected criteria as axes in a certain three-dimensional space, then the studies of the heliobiological effect existing in the literature are not chaotically located in it: they densely fill a certain area elongated along the angle bisector. Thus, in practice, all the parameters selected for systematization are closely related: the larger the time scale under consideration, the higher the level of organization of the biological system for which these effects are observed, and the stronger the degree of its response.

Thus, with the use of annual sampling of data, there are studies of exclusively population data sets on morbidity and mortality, i.e. the two strongest degrees of the system's response.

For this scale, the indices of the number of sunspots are most convenient as space weather parameters, since they reflect the most general parameter - the global variability of the main rhythm sensor, which has a main period of 22 years, or two 11-year solar cycles.  The dynamics of all other solar activity indices correlate with them so closely that it is impossible to distinguish their contribution to biological rhythmics, and any detail on physical processes at this level of data sampling is technically unattainable.

At the same time, with the current development of databases and meta-research methods at this level of sampling, it is possible to study the manifestation of solar rhythmics in the dynamics of homogeneous processes at different points of the Earth and in different cycles of solar activity.

The daily scale of data sampling for many years remains the most convenient for studying the phenomenology of the heliobiological effect for both sick and healthy people. At this level, the literature reveals the widest variation in the level of organization of the studied biosystems, from small populations (groups of individuals, for example, patients of individual hospitals) to body systems such as nervous, cardiovascular, and endocrine. Also, at this level of sampling, the degree of the observed response of the system is the widest, from a reversible shift in the average value of physiological indicators (adaptation) to the destruction of the system (death of the organism).

The intraday scale of data sampling, i.e. hourly and minute, is the newest and most promising, since it gives hope for the experimental identification of specific stages of the formation of a physiological reaction. At this scale, the response of individual organs or body systems is studied, this scale allows you to track in real time the changes occurring in the biochemical processes of hormone synthesis, in blood aggregation, in the electrochemical processes of the propagation of excitation through neurons and cardiomyocytes, etc.

At this scale, it is no longer possible to study the irreversible responses of a living system, but it is convenient to observe a reversible reaction ("norm" and "adaptation"), i.e. the two weakest of the listed degrees of reaction of biosystems are observed. What is also extremely important, at this level, the effect manifests itself in the form of adjusting the frequency of the biological rhythm to the geophysical rhythm, often without shifting the average value: the rhythms of the heart and brain of healthy people in a calm mode of functioning are synchronized with variations of the geomagnetic field, which, apparently, is a necessary element of the existence of living organisms.

Also, this scale allows us to study borderline regimes and possible disruptions of functioning, which lead to arrhythmias, fibrillations, rises in blood pressure, vascular spasms, and which manifest themselves on larger time scales in the form of sharp deterioration of well-being and an increase in the mortality rate.

As logical consequences of the results of the systematization carried out, two more important methodological points can be formulated, which are currently practically not taken into account in the performed heliobiological studies:

1) To study the reaction of each biosystem, there is an optimal frequency window for sampling data, outside of it, the reaction of this system turns out to be either smoothed almost to the stage of no effect, or unstable.

2) Different degrees of reaction of the biological system have different forms. In some cases, it manifests itself as a shift in the average value of the indicator, and in others, within the physiological norm, the value of the indicator is as an adjustment of the rhythm frequency.

5. Optimal data sampling rate

So, to study the patterns of occurrence of epidemics, only the annual scale of data sampling is possible. This is due to the fact that the process of epidemic development itself takes quite a long time, and a large region is needed to collect data - a country, region, or at least a city. The necessary condition is imposed on the length of the time series of data, it must be at least two solar cycles, i.e. more than 22 years. The positive point is that at this scale, one can reasonably neglect the possible contribution of weather factors that are averaged within the annual interval, which facilitates analysis. However, it is impossible to distinguish which of the factors of solar activity has a direct impact on a biological object on an annual scale.

But already when analyzing the features of the dynamics of the increase in mortality, for example, from cardiovascular diseases, both the annual scale of the analysis and the daily scale are possible, but the tasks that can be solved on these scales will be different. The advantages and limitations of the annual scale are described above. On a daily scale, the possible contribution of weather factors is at least comparable to the cosmic one, and it cannot be neglected. The resolution of this scale makes it possible to distinguish the possible contribution of solar flares, proton events or magnetic storms, but not the phases of a magnetic storm.

At the same time, it is almost impossible to study the features of medical statistics of any disease at the intra-day level, since it will be impossible to separate the potential effects of space weather from the contribution of social factors, such as the rhythm of the working day, endogenous biological rhythms, etc.

It is also important to note that the daily level allows the use of both local geomagnetic activity and planetary indices as space weather parameters, while differences in conclusions when using them will be insignificant. But already the intra-day level requires only local geomagnetic data as close as possible to the place of observation.

A very popular physiological indicator, for which the dependence on space weather factors, namely the blood pressure level, is most consistently detected, is studied in various works at a monthly, weekly, daily or even hourly data sampling rate. In fact, of these, only the daily scale is informative, since, as was shown ^{[16, 37]}, the reaction of blood pressure indicators to a magnetic storm lasts only a day or two, and with large intervals between measurements, the effect is very easy to miss, or it will be noisy.

But, probably, to the greatest extent, the factor of importance of choosing the optimal frequency of data collection relates to such physiological indicators as heart rate, heart rate variability (HRV) parameters and brain activity parameters.

In widespread approaches to analyzing the reaction of these parameters to space weather factors, HRV indicators are measured once a day (i.e. with a daily sampling rate of data) for five minutes, and then the obtained indicators are compared with the daily values of the GMA level.

At the same time, the results of continuous monitoring of these indicators in a person in a calm immobile state show that their variability, even under such conditions, is too great (Fig. 7) for the result obtained from a five-minute fragment of the recording to be considered as a characteristic of the body during these days: measurements carried out on the same subject for half an hour later, they can give a radically different result even in the absence of any events.

Figure 7. - Top - time series of minute-by-minute heart rate values for two healthy middle-aged volunteers recorded in the supine position at rest (awake mode). Below - time series of values of the Stress Index (Stress Index), calculated from successive five-minute segments of the corresponding series of heart rate.

During the first of these experiments, heart rate indicators vary from 52 to 61 beats/min, which is approximately 16% of the average observed heart rate (56 beats/min). At the same time, the scale of changes in the stress index, one of the most popular HRV parameters, ranges from 54 to 360, i.e., depending on the choice of a five-minute time interval, the same volunteer at rest can have six times different stress levels. In the second experiment, the heart rate values are: average 64.7 beats/min, minimum 60, maximum 72 beats/min; voltage index values average 305, maximum 450, minimum 150.

From the examples given, it can be seen that for the daily sampling scale, the heart rate indicators have too rapid variability, which leads to the instability of the effects obtained for this object of study mentioned at the beginning of the article. A similar, and even stronger, conclusion can be drawn regarding the studied parameters of brain activity, for example, the amplitude of the rhythm in a certain frequency range.

At the same time, the intraday (in this case, minute) scale of data sampling allows us to obtain important information about the sensitivity of the cardiovascular system to variations in the magnetic field vector ^[38]. But in this case, the reaction to the geomagnetic agent manifests itself not as a shift of the average value, but as an adjustment of the frequency of the biological rhythm to the geophysical one.

Thus, we can talk about the importance of choosing the optimal frequency response window for each biological system (population, organism as a whole, a separate body system, a separate organ). In the case when the search for the answer of a certain system is carried out by the researcher outside of this window or on its border, i.e. the sampling frequency of the data is too high or too low, the effect itself is noisy, and the deviations of the physiological indicator from the average value obtained in the analysis are largely random, and, as a consequence, unstable and multidirectional.

6. Possible forms of manifestation of the effect

The second important consequence of the systematization of heliobiological results is that in some studies, the search for a biosystem response is carried out in a form uncharacteristic for this system and this time scale. For example, the biological effect of factors such as electromagnetic oscillations at the frequencies of Schumann resonances or geomagnetic pulsations was repeatedly recorded in the form of a shift in the frequency of biological processes, which was not always accompanied by a shift in the average value of the physiological indicator. Attempts to detect the effect of these factors precisely by shifting the average value can also lead to instability of the detected effect.

As an example, we can cite the work ^[35], in which the effect of a previously recorded three-component signal of a magnetic storm on the morphological parameters of fish and marine life was studied. In one of the studies, two frequency ranges were filtered out of the recorded broadband storm signal: a low–frequency signal (frequency range up to 0.001 Hz) and a range of 0.001-5 Hz. In the experiment, it was found that the initial broadband signal from the geomagnetic storm and its lowest frequency component affected the same biological parameters: the gravitropic response of flax, lipid peroxidation in D. magna juveniles, superoxide dismutase activity in D. magna juveniles, calpain activity in the brain of crucian carp and proteolytic activity of digestive enzymes of crucian carp. Moreover, the effect of this low-frequency component of the geomagnetic field in the frequency range up to 0.001 Hz was as strong or even stronger than the effects of the original broadband signal of the geomagnetic storm.

At the same time, the impact of individual frequency components of geomagnetic storm signals in the frequency range of 0.001–5 Hz led to a decrease in only one measurable bioparameter - the proteolytic activity of digestive enzymes of crucian carp ^[8].

Thus, the lowest frequency component of the geomagnetic storm signal influenced both irreversible changes in biological objects, for example, changes in the number of vertebrae or fin rays, and reversible ones, such as the biochemical activity of a number of enzymes. The signal in the frequency range 0.001–5 Hz also affected, but only reversible reactions, in this case, the activity of food enzymes.

From these results, the authors conclude that the biological effect is exerted by the low-frequency component of the variations of the geomagnetic vector, which in nature is described by the Dst variation indicator, and not by the geomagnetic variations of the millihertz range. However, an objection can be raised here, or rather, a clarification. In the light of the observed heliobiological effects described above, it is reasonable to assume that geomagnetic variations in the 0.001–5 Hz range can have an effect close to the synchronization effect, and without a significant shift in the average value that could be recorded in the experiment.

Thus, we can agree with the conclusions of the authors of these studies that the extremely low-frequency component of the geomagnetic storm signal can lead to biological responses with a shift in the mean value. However, in our opinion, it is impossible to draw an unambiguous conclusion from the results obtained that geomagnetic variations of the millihertz range do not have any biological effect, since in this design of the experiment the effect could simply manifest itself in a different way.

The validity of such a clarification is confirmed, for example, by the results of the work ^[39,40]. In the first of them, a reversible change in heart rate parameters was observed when a person was exposed to a magnetic field with parameters commensurate with PC1 geomagnetic pulsations. In the second work, the influence of an alternating magnetic field in the frequency range of the first mode of Schumann resonances (7.8 Hz, 90 Nt) on electrochemical processes in rat cardiomyocyte cell cultures was studied. The influence of the field was reversible, regardless of the magnitude of the field in the range from 20 Pt to 100 NT and from an external permanent magnetic field.

Conclusion

For many decades in heliobiology, the main efforts have been focused on proving the very fact of the existence of solar-biospheric connections. At the same time, the authors left the task of finding the causes of the instability of the effect, which manifested itself in the form of differences in the characteristics of the results obtained, for the future, explaining it by the presence of a number of uncontrolled (and even not really known) additional external factors affecting the degree and nature of the heliobiological effect.

Earlier, we assumed that the instability of the heliobiological effect is primarily due to methodological reasons: existing methodological approaches, traditional for physics and biology, are poorly suited for studying the system of solar-biospheric connections due to the complexity of the system under study.

Over the past decade, several aspects specific to heliobiological research have been identified, confirmed and included in the scientific worldview:

1) The individual nature of the reaction: the analysis of individual data gives much more self-consistent and logical results than the traditionally accepted medium-group approach in medicine. The group averaging operation largely hides the heliobiological effect.

2) The necessity of simultaneous consideration of the effects of terrestrial and space weather factors: these two classes of factors affect the same body systems, and their combination can both enhance and weaken the meteotropic effect.

3) Taking into account the time factor, i.e. the phases of rhythmic heliophysical processes, and at any time scale: the 11-year solar cycle, the average GMA level during the observation period, on the intra?day scale - the ratio of the phases of the magnetic storm and the daily geomagnetic variation.

Two more methodological principles can be added to the already listed ones:

1) The existence of an optimal frequency window for studying the reaction of a certain biosystem. So, to study the patterns of occurrence of epidemics, the annual data sampling scale is most convenient, for the reaction of blood pressure indicators ? daily, for the reaction of heart rate and electrical activity of the brain ? minute (or even more frequent). For a daily scale, heart rate indicators have too rapid variability, which leads to the instability of the effects obtained mentioned above. Therefore, in the case when a researcher chooses a non-optimal data sampling scale to study the effect, the result obtained is either completely smoothed (there is no effect), or too variable, i.e. unstable.

2) The existence of different types of biological system response at different time scales. The biological effect of electromagnetic oscillations at the frequencies of Schumann resonances or geomagnetic pulsations was repeatedly recorded in the form of a shift in the frequency of rhythmic biological processes, which was not accompanied by a shift in the mean value of the AF. Attempts to detect the effect of these factors precisely by shifting the average value can also lead to instability of the detected effect.

Thus, methodological principles, both those already included in heliobiological studies in the last 10 years, and new ones obtained on the basis of the systematization of heliobiological effects, can significantly reduce the percentage of unexplained non-reproducible results.