22.02.2011 г.

  На главную раздела "Академик Сапунов В.Б."


Modern ecology has no methods appropriate for general check of biological diversity of the biosphere. The real approach toward resolve of this question is use of insects as numerical well studied and representative group and any representative region of the Earth. This local data may  become base for works toward study of general diversity and pattern of distribution of the species within taxons and ecological niches. The present work consider insects of natural landscape "Veppsky les"(North-West of Russia) as material for modeling of general species diversity. Insect species  may  be  distributed  into  three  groups - dominant, rare and hidden. Quantitative relations between them may be  described by mathematical model. Majority of species are hidden, that is undetectable by methods of field ecology. The number of them may be  between  30  000 000 and 1 billion. During evolution of ecological systems pattern of distribution of insects within three groups may change. Sometimes  extinction of insects is not real but means that population got state of hidden. Decrease of insect population doesn't make any  ecological  niche free. They occupied by  other species of animals. Because of great resistance of ecological systems, artificial  control  of  insects  has  no  sense. The  number of insect species, biological mass of them and distribution within ecological niches are  fundamental  constants of biosphere.

Key words:  biosphere, insects, species diversity


     The important task of global ecology is essay of species  diversity  within taxon, ecological system and biosphere. This task has relation to a big number of international programs of  variability  and diversity safety. Theoretical basis of such a programs is not sufficient firm because the following questions are unclear:
  1.      How much species exists?
  2.      What is biological variability of  main  classes  of  animals  and plants?
  3.      What is tempo of extinction?
  4.      What is  tempo  of new species apporation (and does this process take place)?
I am unable to answer  all this questions within one articles. The aim of the present work  is looking for way toward answering of the questions.

     Modern ecological problems are resolved without fundamental scientific basis. "Red book" is important document suggesting some international programs for diversity conservation. Unfortunately, the importance of such  a document as "Red Book" [1] is limited because of:
 1. There is no criteria for listing of species into Red Book.
 2. The number of species in international Red Book - about 1 000 - is less then general number of known species - about 4 000. The number of all possible species according to different authors is between 8 and 100 millions. In Red book of Latvia 164 species are mentioning as extinct, disappearing, rare between 19 000 species occurring in Latvia [2,3].

     The question on general biological diversity and pattern of species of biosphere is very complicated. The complete design of the question may be gotten in far future. Present task is looking of the first steps for such a design. Such a step may become selection of any taxon and any region of the earth convenient for study of species diversity.

     The aims of present work were:
  1. To consider approach toward estimation of general species variability and looking for basic mathematical models for such a estimation.
  2. To essay number of hidden species within one animal group and one region.
  3. To propose criteria  for  including species into Red Book.
  4. To use insect field population data for considering listed questions. Insects are wied spread populated and well studied class. The big number of species and specimens is prerequisite for successful use of applied mathematics. I used both literature data and data goted in expedition of 1996 - 1997 to "Vepssky les" - natural landscape at Leningrad and Vologda regions. This region is representative for North-West of Russia and partly for Baltia because it is place with extremely low anthropogenic press. The initial state of natural ecological systems is safed there.


     According to theory of Vernadsky [4],
     1. The mass of biosphere is constant. According to modern data [4,5], this wet mass is:
     Mb = 250 000 000 000 tonn [5,6].
     2. Biosphere is organized as ecological pyramid (Fig.1). It describe  relations  between  producents and consuments. Every following flow has mass less 10 - 100 times [5]
     3. The range  distribution of species within orders and classes is asymmetrical [5,7]. That is, majority of  species  belongs  to  some  orders. The distribution of specimens within species is asymmetrical too.

The theoretical figure of such a distribution is demonstrated in fig.2 and accorded to formula:

     f(n) = A + B e-Cn, where A, B, C - constants [7].

     Let minimal number of specimens needed for stable population is Nk. According to population genetics, it may be 150 - 200 [8]. Let Nk' would be minimal number of specimens needful for recurrent detection of species in nature. Species from K' to K would be hidden species. Between hidden and dominant species rare species exist too.

     The species, which population close to extinction (K - the size of population) must be listed in Red Book. The number of organisms per generum is

     N = Mg/mav        (1)

     where Mg  -  biomass  of  generum, m.av - average mass of organism within taxon. General number of specimens according to fig.2

                  Ng =   ∫   f(n) dn                (2)
Let us applied this basis of model to empirical data goted on insects.

          Empirical data

     Precise design of equations listed above is impossible. We are toward approximate design. Let us use examples from literature and own field data. Fig.3 demonstrates range distribution of species within orders by literature data [9 et.al.]. Fig.4 demonstrates own field data on distribution of insects by orders within field catches ( made by author together with pupils during field expedition in "Veppsky les" ). Fig. 5 (own field data)  describe distribution of beetles by species within  family  Carabidae. Fig. 3 - 5 summarize  material without processing and analysis. After mathematical analysis and study of theoretical distribution (fig.2), we may go  toward empirical description of the curve ( analysis by methods  λ 2 and minimal quadrates):

     f(n) = 1 + 138 e-n.

     Let us assay mass of all living insects using literature data [3-6]. The wet mass of animals is 20 000 000 000 ( wet mass is more stable that mass with water). According to own field  data, average wet mass of cached insect is 0.0004 g ( m a v). Distribution of insects on mass is asymmetrical too. That is, majority of  insects have low weight, a little number of them are hard. Insects occupy ecological niches of predators, super-predators, parasites and super- parasites. They must be less general mass of animals three orders times. Mg of insects must be 20 000 000 tonn. It is accorded
                      5 *10 16   

specimens (see (1)).
     Using (1) , (2) and fig.2 we will have:

                ∫   (1 + 138e-n) dn - Kn = 5*10
     Correct design of such a equation has no sense. The approximate design is: the most populated species may have 10 000 000 organisms, the general number of species, including  hidden, may be between 100 millions - 1 billion. Majority of species are hidden. They may be described in future. The relation between hidden and dominant species may change after change of environment. The decrease of population of dominant species may become free ecological niche . The number of hidden species is so high, that natural selection may select between them species accorded to new ecological state of environment. That means that despite of change of populations of any species, the general pattern of species distribution within niches is solid and stable. This fact support suggestion by Vernadsky [ 4 ] of resistant stability of biosphere and safety of its main characters such as species diversity and niche distribution and biological mass.

     The problem of biological diversity consists of two subproblems: the check of present diversity and check  of the dynamic of diversity. Both problems have no quantitative designs. Both the tempo of extinction and tempo of new species apporation are obscure. The only attempt to check the process of apporation of a new insect species during time available for analysis was gotten by Shaposhnikov [10 ,11 ]. He demonstrated that apporation of a new species in Hemiptera is recurrent in a big scale. Unfortunately this data deals only with one group of insect. Hence, complete description  of a new species may prolong unlimited time. Majority of species are candidate to Red Book, having population close to K'. At the same time we may list into Red Book species close to K. But this species undetectable. There are no significant data on real extinction of insect during historical  (not geological) time. Hence, Red Book has sense only for big vertebrates and not for insects. Actual task  of close future is suggestion of correct methods for getting of criteria for listing of species in Red book.

     Concluding, I may summarize that species variability and diversity and resistance of biosphere is extremely high. Limits for this means may be checked approximately using undirect methods and mathematical models.


  1. Red book, every edition. Including:
    Latvijas Sarkana Gramata (1998). Institute of Biology, University of Latvia. Riga. 388 p.
  2. Cкворцов А.К. 1996. Разнообразие живого мира и его сохранение.\\ Природа, №6, с.95 - 105. Skvortsov A.K. 1996. Variability of the living world and it's safety//Priroda (Nature), No.6, pp.95-105 (Russ.).
  3. May R.1986.How many species are there // Nature, v. 234, p. 514.
  4. Вернадский В.И.1975. Размышления натуралиста. Москва, Наука, 175 с. Vernadsky V.I.1975.Thinking of naturalist. Moscow, Nauka (Science). 175 pp. (Russ).
  5. Камшилов М.М. 1979. Эволюция биосферы. М.,Наука, 275 с. Kamshilov M.M.1979. Evolution of biosphere. Moscow, Nauka (Science), 257 pp. (Russ).
  6. Базилевич Н.И., Родин Л.Е., Розов Н.Н. 1971. Сколько весит живое вещество планеты? \\ Природа , №1, с.43 - 53. Basilevich N.I., Rodin L.E., Rosov N.N.1971. How mach  living material of the planet weights? // Priroda (Nature), No1, pp. 46-53 (Russ.).
  7. Михайловский Г.Е.1988. Описание о оценка состояний планктонных сообществ. Москва, Наука, 314 с.Mikhailovsky G.E. 1988. Description and check of plankton societies. Moscow, Nauka (Science), 214 pp. (Russ.).
  8. Sapunov V.B.1991.The role of stress in processes of  adaptation and evolution. In. Ivanovich  I., Jankovich-Hladny, M. (eds.) Hormones and metabolism in insect stress, CRC Press, Boca Raton, pp.149-164.
  9. Догель В.А. 1981. Зоология беспозвоночных. Москва, Высшая школа, 600 с. Dogel V.A.1981. Invertebrate zoology. Moscow, Highest school, 600 pp. (Russ.).
  10. Shaposhnikov G. Ch. 1981. Population and species in Aphids and their need for universal species concepts. Agricultural Canada, Montreal, 62 pp.
  11. Шапошников Г.Х. (1983). Биологические предпосылки защиты растений от тлей и задачи афидологов. В кн. Систематика и экология тлей - вредителей растений, Рига, Зинатне, с. 4 - 11.

 Fig.1.Distribution of species in relation to number of speciements. Fig.2.Ecological piramid
  Fig.3. Distribution of insect generum by species number -
check basing on literature data

1 - Coleoptera, 2 - Hymenoptera, 3 - Lepidoptera,4 - Diptera, 5 - Homoptera,
6 - Orthoptera, 7 - Odonatae, 8 - Hemiptera, 9 - Blattoidea, 10 - Trichoptera,
11 - Isoptera, 12 - Ephemeroptera, 13 - Aphaniptera, 14 - Thysanura, 15 - Anoplura
(Orders 8 - 15 has less 10 000 species)
 Fig.4.Percents of different orders insects in field catchings -
own data.

     1 - Heteroptera, 2 - Diptera, 3 - Homoptera,
4 - Coleoptera, 5 - Hymenoptera, 6 - Orthoptera,
7 - Lepidoptera

 Fig.5. Distribution of ground-beetles by species within field
     1 - Broscus cephalotes, 2 - Cicindella hybrida, 3 - Amara plebeja,
4 - Carabus glabratus, 5 - C. granulatus, 6 - Cyhrus carabiodes,
7 - Pterostichus nuger


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