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Individual-based mathematical models may be considered a promising tool for studying the patterns of aquatic animals population development under conditions of exposure to various environmental factors including those ones that are difficult to measure directly. To test the hypotheses on the role of chemoreception in vital activity of aquatic invertebrates, we used the previously designed individual-based simulation model of a mass pelagic species, Daphnia longispina, population. The model describes a population as an ordered list of individuals with specific set of traits. For each individual, its energetic traits are calculated, also the probabilities of outcomes from different life situations are assigned or calculated. Included in the model are responses of adult individuals to two types of chemical signals: 1) diurnal vertical migrations from surface to hypolimnion when detecting fish cairomones; 2) active search for mature females by adult males via pheromones, effects of which grow stronger with water temperature raising. By comparison with previous versions of the model, introduction of these responses allowed to reproduce seasonal dynamics of the model population most closely to real dynamics of the prototype population. Consecutive, and then joint switching off of the ability to detect chemical signals made it possible to obtain a quantitative estimate of their role in population dynamics optimization and to determine limiting levels of predators, both vertebrate and invertebrate, pressure on organisms lacking the ability to use chemotaxis. In particular, it was found out that, in the model population, the size of water flea spring generation is determined by the amount of overwintered dormant eggs which increases as a result of active search for mature females due to chemoreception. The size of summer-autumn generation is practically independent of initial numbers and is determined by living conditions during the season, first of all by the factor of consumption by predators. Chemoreception helps adult water fleas in avoiding to be eaten, which turns out to be effective in maintaining high abundance even at considerable pressure by predatory fishes. When a water flea population is deprived of the ability to response to chemical signals (for example, when there is no hypolimnion or shelters among vegetation), predation press increasing above some threshold, which depends on duration of embryonic development, leads to population instability and its decreasing in numbers till the total extinction. The model allowed to obtain a quantitative estimate of the role of chemoreception in forming of water flea population dynamics. In the present version of the model, annual production of the population is shown to raise 1.5 times due to chemoreception. In the absence of chemoreception, water flea population fails to use environmental resources in full measure and come up to production rates observed in nature.

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We propose two different approaches to defining variable units of intrinsic time (physiological time units in a strict sense, or PTU). For continuously growing animals, we suggest the use of specific mass growth rates; and for animals that cease to grow at some point, we recommend specific metabolic rates. Longevity of animals in terms of PTU is equal to the total specific rate (per lifetime) of the respective processes. A method is proposed to describe age-related changes in respect of specific metabolic rates of non-growing constant-mass adult birds. Maximum intrinsic longevity values have been estimated for certain fish species (continuously growing animals), and birds (that cease growth). Estimates of the maximum PTU longevity across both passerine and non-passerine groups differ slightly and are actually estimates of the Rubner constant for birds.

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An assumption was made that age constituent alpha x(beta) of mortality of individuals in a population in Weibull equation mx = m0 + alpha x(beta) (Ricklefs, 2000) reflects change of specific metabolic rate of one individual with age. Based upon that hypothesis a formula was proposed for relationship of specific metabolic rate of an adult individual after cessation of growth, when mass W is attained, and age t: q(t) = q0(1-omega(beta) + 1t(beta)) where q0 = aW(-b) is value q(t) at the moment of growth cessation and omega = alpha(1/(beta + 1)) is "ageing rate", determined and estimated by R. Ricklefs. Maximum longevity of an individual was determined as [equation: see text], where qcrit is specific metabolic rate at the age tmax. Parameter beta and relationships omega(W) and (qcrit/q0)(W) were approximated for birds from data of Ricklefs. Statistical comparison of results of calculations of tmax was carried out on the basis of the above formula and other known formulas for groups of Passeriformes and non-Passeriformes. Rubner constant [equation: see text] was calculated assuming that body mass of an adult individual (W) is attained in the first year of life (tA = 0). Average values of 602.4 +/- 2.5 kcal g(-1) (n = 83) for non-Passeriformes and 963 +/- 6.3 kcal g(-1) (n = 41) for Passeriformes were obtained.

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We provide a definition of the unit internal (physiological) time based on metabolism. If q(t) is specific rate of metabolism, i.e. the amount of energy (oxygen) consumed by unit of active mass per physical time unit, the unit of physiological time tau(t) is defined as physical time, during which unit of active mass consumes one unit of energy: tau(t) = 1/q(t). The dimension of unit physiological time is the same as that of unit physical time and its value depends on q(t). Therefore, the unit physiological time tau(t) is a variable value, while the internal time is unequal relative to the physical time. The more internal time units tau, i.e., elementary acts of energy consumption, fit in the unit physical time t, the longer is the unit physical time for the unit active mass relative to the internal time unit, i.e., the physical time is seemingly slowed down. And, on the contrary, the less elementary acts of energy consumption take place during unit physical time, the shorter seems unit t, i.e. physical time is seemingly accelerated. Unequal course of the internal time is determined by the curve of specific metabolism q(t) during the life under specific conditions and, hence, internal time is individual. It has been questioned that the total (during lifetime) specific metabolism, often called Rubner constant, can serve as specie specific characteristic.

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An individual-oriented model of the population of Daphnia longispina, an abundant zooplankton species in lakes and temporary water bodies of the Palaearctic temperate zone, is described. The concept of the model is based on the growth and reproduction potential of an individual and its ability to switch from parthenogenesis to gamogenesis, which is determined by the life conditions of three successive generations. The model was used for testing hypotheses on the role of maternal effect in the population dynamics of Daphnia. Several important conclusions are made, including the verification of the importance of this phenomenon for the seasonal adaptations in crustaceans. The possibility of maternal effect accumulation in a series of successive generations probably increases the tolerance of populations to annual oscillations of environmental factors. The model affirms the role of the maternal effect, along with the interpopulational polimorphism, as a mechanism providing for the stability of biological systems at the species (population) level.

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Seasonal energy flows were calculated, based on a simulation balance model, from unique data collected during three vegatation seasons, 1986-1988, in the ecosystem of the Lake Bolshoy Okunyonok, Leningrad province. The model is based on principles developed by G.G. Winberg's school of production hydrobiology and was described in detail in an earlier work (Kazantseva, 2003). Analysis and comparison of the results showed that certain regularities of energy transformation processes in any lake ecosystem are apparent in spite of natural differences determined by differences in the environment properties and the levels of development of the ecosystem components. For instance, the extreme importance of the bacteriadetritus element in the food chains of water-body was confirmed. Broad spectrum of food and considerable changes in food composition during a vegetation season were clearly shown for most hydrobionts. The degree of consumption was estimated for the production of the organisms at each trophic level. It was shown that all the consumers eat away ca. 50-60 per cent of the production of the forage phytoplankton, 90 per cent of the production of non-predatory benthos, and 20-50 per cent of the production of the other trophic groups during a season. The proposed coefficient of energy transformation, CET(s, k) = Ps(k)/Pk, where Ps(k) in the production of the consumer s created by consuming the source k, and Pk is the production of the source itself, proved to be more stable than the generally accepted coefficient q = Ps/Ps -1.

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A definition is proposed for biological ("internal") time tau(t) for a growing organism whose weight variation obeys the law w(t): tau(t) = 1/c(w) (t) = w(t)/w'(t), where t is physical ("external") time, w'(t) is weight increase rate, and c(w) (t) = w'(t)/w(t) is specific growth rate. Properties of functions tau(t) and w(tau) were studied for those cases when growth curves w(t) were described by Bertalanffy's or logistic equations.

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We consider an ideal population with a stable age composition changing according Lotka equation. Additional assumptions are made concerning the constancy of population size, independence of specific mortality rate on age, and linear dependence of female fecundity on its weight. A relationship has been obtained [formula: see text] where N0 is initial numbers of a generation, N[alpha, omega] is total numbers of the mature part of the population, w[alpha, omega] is a mean weight of a mature individual, s is sex ratio, c is specific fecundity (per unit of weight) and l0 is the probability of larval surviving. The growth of an individual is described by the Bertalanffy function. Methods of calculation of life history parameters are discussed. A method is proposed to calculate the age of maturity (alpha) and at the end (omega) of the reproduction period as first and second inflection points of the growth rate curve. Based upon data on development of 27 populations of several species of fishes of inland waters of Russia the following relationship have been obtained: [formula: see text] for populations with [formula: see text] < or = 100 g, [formula: see text] for populations with [formula: see text] > 100 g, and [formula: see text] for all populations.

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A model of energy budget of Lake Bolshoi Okunenok ecosystem was based on the data received during field studies from May through November 1986. The model takes into account 36 components including dissolved organic matter, bacteria, phytoplankton, zooplankton, meiobenthos, macrobenthos, fish, suspended and sediment detritus. The growing season has been divided into 16 intervals according to the number of observations. The balance equation for each live component describes the change in its biomass for a time interval between two successive sampling dates. The change is considered as a balance of energy input with assimilation or feeding, and energy loss due to respiration, excretion, predation, natural mortality, fishery catchment or and emergence of imago insects. For non-live components we estimate an increase and a decrease in their mass due to the activity of living organisms, as well as organic matter exchange between water and sediments. Seasonal value of balance elements for each component are equal to sums of appropriate interval value. Comparison of energy flows through different links of a trophic web has shown that the role of a bacterial-detrial link was extremely important in Lake Bolshoi Okunenok for the growth season of 1986. Detritus constituted 58% of seasonal diet of non-predatory zooplankton, 39% of diet of predatory zooplankton, 50% of diet of planktivorous fish (fry of whitefish) and 92% of diet of benthivorous fish (fry of carp). The contribution of bacteria to the total seasonal decomposition amounted to 46%. Approximately 57% of the forage phytoplankton production, 86% of non-predatory benthos production, and 23-38% of the other trophic groups production were consumed by all grazers. "Coefficient of energy transformation" is proposed. It is calculated as: CET(s, k) = Ps(k)/Pk, where Ps(k) is production of consumers "s", built due to consumption of source "k"; Pk is production of source "k" itself. In Lake Bolshoi Okunenok only 14% of energy built by phytoplankton were accumulated in organic matter of zooplankton due to direct consumption.

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