The population is determined by the ratio of fertility and mortality, then its growth is affected by all factors that can affect at least one of these processes, shifting the balance between them in one direction or another. In the case of an excess of births over deaths, the population usually grows (if migration is excluded).
Remark 1
As a rule, with an increase in population density, the growth rate gradually decreases to zero, or fluctuates from positive to negative. negative side under the influence of the dynamics of environmental environmental factors. With the predominance of mortality over fertility, population sizes decrease.
Stopping factors
Stopping the growth of the population and its stabilization at a certain level of density can occur under the influence of various factors. Weight they are interconnected by the mechanism of negative feedback. For example, a shortage of any resource (for example, food) increases intraspecific competition, which reduces the population and leads to the establishment of a new balance of resource availability.
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The total resistance of the environment is determined by the totality of limiting factors that prevent the population from realizing its maximum reproductive potential. This includes both external factors (resource availability, biotic relationships, abiotic factors) and intrapopulation regulatory mechanisms. Some of these factors act independently of population density, while others depend on it, and their impact may increase in proportion to the increase in density, or at a faster pace.
Experimental studies of population growth
Under natural conditions, it is extremely difficult to study the interaction of factors determining population growth, since we are usually dealing with factors that have long existed on the planet. certain territory populations, the density of which was formed in given environmental conditions, and the environment itself experienced the impact of these populations for many generations.
Remark 2
Very promising in this regard are laboratory populations, as well as the study of the facts of acclimatization and, especially, reacclimatization of organisms. In the latter case, we have a unique opportunity to follow the growth of the population in its natural environment (but not transformed by this population due to the long absence of organisms of the species under study in the given territory) actually "from scratch".
All such observations show a general pattern. At the very initial stage, when a population is formed from several individuals that have fallen into a new place, reproduction is slow. Many individuals do not take part in reproduction, having lost the rest for some reason, or having not found a place for themselves in the existing social structure.
After the formation of a sex-age and socio-ethological structure normal for a population, its reproduction intensifies. At this stage, the number of individuals is still insignificant, their density is low, and intraspecific competition is practically absent, and natural enemies often have not had time to master a new type of food. Therefore, individuals show a high reproductive potential, close to the theoretically possible, and there is an explosive growth of the population.
Further events depend on the presence of internal mechanisms of population regulation in the species. If they are present, then with an increase in density, they begin to actively influence the population, reducing its reproduction due to territoriality, tension in hierarchical relations, stress reactions, etc. if this does not happen, then as the population approaches the limit of the biological capacity of the environment, its growth not only does not slow down, but may even accelerate. This is due to an increase in fertility with an increase in mortality.
Although this mechanism works for a short time, the population density may still have time to rise well above the permissible limits. This causes a catastrophic decline in numbers, usually by two orders of magnitude or more.
After that, the environment is partially restored, a new increase in numbers begins, and the situation repeats itself. However, the new capacity of the environment usually turns out to be lower, and both growth and subsequent decline become less catastrophic. Gradually, over several similar cycles, the population adapts to the environment, its ecological niche begins to more closely correspond to local conditions, and the density specializes at a certain level.
Factors limiting population growth
Despite the fact that the potential for population growth in all species of organisms is very high, under natural conditions, growth as such usually does not occur, at least for a long time. The number of populations is either fairly stable, or it is characterized by periodic fluctuations with a fairly large amplitude around a certain average level. This is due to a number of factors that limit population growth.
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breeding potential
The components of the breeding potential of a population are: the duration of the pre-reproductive period of individuals, the multiplicity of reproduction during life, life expectancy, the number of offspring produced at a time, the duration of one reproductive cycle. All these parameters vary widely in different populations.
The pre-reproductive period (including embryonic and post-embryonic development here) can range from tens of minutes (some prokaryotes) to one and a half decades (humans, elephants, some fish, invertebrates with long larval development, many trees, etc.).
During a lifetime, the number of reproductive cycles can be definite or indefinite. The minimum number of reproductive cycles is one. This is typical for annual plants, many invertebrates, and some fish. Many plants and most vertebrates are characterized by an indefinite number of reproductive cycles, depending on the living conditions of the organism. So, long-lived trees, many fish, some reptiles, birds can breed at least several dozen times in their life.
The lifespan of organisms also varies widely - from tens of minutes (the interval between divisions of some prokaryotes) to hundreds or even thousands of years (some plants). Some of the long-lived organisms are characterized by a post-reproductive period, when in old age they lose the ability to reproduce. In others, it is absent or very weakly expressed.
At one time, a breeding individual can produce one offspring (when dividing most unicellular organisms), or even less than one (when a pair of some higher animals reproduces, in which one cub appears at a time), or a significant number of them. The record among animals here belongs to some fish, which lay tens of millions of eggs during spawning, and among plants, they reproduce by spores.
Remark 1
The duration of one reproductive cycle in different organisms ranges from tens of minutes (some prokaryotes) to 3-5 years.
The population size is total individuals in the designated area. Any population is theoretically capable of unlimited growth in numbers if it is not limited by environmental factors. Members of one population have no less impact on each other than physical environmental factors or other organisms. In populations, to one degree or another, all forms of relationships characteristic of interspecific relations are manifested, but mutualistic and competitive ones are most pronounced. Maintaining numbers under these conditions is called population homeostasis.
HYPOTHESIS OF BIOCENOTIC REGULATION OF THE POPULATIONFriederichs - the regulation of population size is a consequence of the totality of all interactions of abiotic and, especially, biotic factors at the ecosystem level.
In this case, the population growth rate will depend only on the magnitude biotic potential(theoretical maximum of descendants from one pair per unit of time). To determine the biotic potential use the formula:,
where N t is the number at time t,
N 0 - initial number.
In populations, the number varies depending on the conditions. There are the following population fluctuations: seasonal and annual (random and cyclic - depend on solar activity). AT natural conditions Periodic population fluctuations are very common. Chetverikov was the first to notice this. He called the fluctuations in the number of individuals that make up the population , population waves. Example: a change in the number of a wolf associated with a change in the number of a hare.
Selection strategies in populations(r, K - selection McArthur and Wilson 1967.) identified populations, respectively, with strategies " r- selection" (an increase in the population growth rate at its low density, the evolution of organisms in the direction of increasing the cost of reproduction) and " To-selection" (increase in survival rate and the maximum value of density in conditions of stabilized numbers with a strong negative impact - competition, predation, etc.; maintaining the life of an adult organism).
Selection is the selective reproduction of a genotype in offspring.
Individuals with certain combinations of traits are subjected to selection.
The selection strategy is the selection of individuals with a certain combination of traits.
Selection strategies according to the ratio of the costs of reproduction and maintenance of offspring.
1. K - care for a few offspring.
2. r - indifferent attitude, but maximum fertility.
Some organisms use both r and K strategies, combining them depending on conditions and seasonal cycles.
All strategies are relative depending on the species being compared.
It is clear that mortality, like fertility, has a great influence on the size of the population and the course of its changes. With the same birth rate, the higher the death rate, the lower the population size, and vice versa.
survival curves. The curves shown in Figure 3 are called survival curves. Usually, when plotting these curves, time or age is plotted along the abscissa, and the number of surviving individuals is plotted along the ordinate. Survival curves are divided into three general type. A strongly convex curve (3.1) is characteristic of species in which mortality rises sharply only towards the end of life, and before that it remains low. This type of curve is characteristic of many species of large animals and, of course, of humans.
The other extreme, a strongly concave curve (3.3), is obtained if mortality is very high in the early stages of development.
The intermediate type (3.2) includes the survival curves of those species in which mortality changes little with age and remains more or less the same throughout the life of the group. Probably, there are no populations in nature in which mortality is constant throughout the entire life cycle of individuals (in these cases, the survival curve would be located completely on the diagonal of the graph.
The shape of the survival curve is related to the degree of care for offspring and other ways of protecting juveniles.
The shape of the survival curve very often changes with changes in population density. As the density increases, it becomes more concave. This suggests that with an increase in the number of organisms, their mortality increases.
Population growth. At first glance, it is clear that the nature of the population dynamics various kinds of organisms in a population should be associated with demographic indicators, which are also formed in the process of evolution and reflect the living conditions of the species in a particular habitat. Nevertheless, despite the fact that both fertility and mortality, and the age structure are very important, none of these indicators can be used to judge the properties of the dynamics of the population as a whole.
To a certain extent, these properties are revealed by the process population growth, which characterizes its ability to restore numbers after a catastrophe or to increase numbers when organisms populate free ecological niches.
The main stage of any microbiological production is the production cultivation of the corresponding microorganism, carried out either to increase the microbial mass - biomass, or to obtain metabolic products of a growing population of microorganisms.
Biomass is understood as the total mass of individuals of one species, group of species or community of microorganisms as a whole. It is expressed in the mass of wet or dry matter (g/m2, g/m3). From this it is clear that the task of the process engineer is to create conditions that ensure the maximum utilization of the components of the nutrient medium and the accumulation of the target product with desired properties. Naturally, theoretical basis for this are the patterns that determine the growth of the population of microorganisms, depending on the conditions for its implementation. Knowledge of the quantitative patterns of growth of populations of microorganisms in the real conditions of its implementation in capacitive equipment, expressed as the corresponding mathematical model, largely determines the transition from an empirical search to a rigorous solution of the problem of optimizing technological regimes for obtaining products of microbiological synthesis.
Batch cultivation
In the process of cultivating microorganisms in a periodic way, as mentioned earlier, several periods of growth can be distinguished (Fig. 2.19).
In the first period, after the sowing material is introduced into the medium (lag phase), the process of adaptation of the sowing culture to the new medium takes place. The population size at this time does not increase (and in some cases even decreases). The state of the population in the lag phase can be formally described as follows:
(for m lying between 0 and m1).
It is assumed that during the lag phase, microbial cells do not consume the substrate, but the metabolic activity of cells manifests itself in an increase in the content of protein and RNA (with a constant DNA content), as well as in an increase in cell volume, which in general view can be expressed using the equation
Upon reaching certain ratios between the values of the cell surface and its volume, cell division occurs, as a result of which the population begins to increase at an increasing rate, which for a given culture growth phase, called the transitional one, is described by the relation
The integral dependence describing the section of the growth kinetic curve between m1 and m2 has the form
The increase in the growth rate of populations in the transition phase goes to the limit, formally determined by the achievement of a value equal to unity by the parameter f, after which the growth rate begins to be expressed by the dependence
(for m between m2 and m3), whence the integral form represents the exponential function
This growth phase is called the exponential or logarithmic growth phase. The specific growth rate u is often used to estimate the biomass growth rate.
The terms “doubling time” and “generation time” q, calculated by the equation, are used as a characteristic of a growing culture in this phase
However, such a pattern of population growth, which in the first approximation can be described by an exponential dependence, is observed for a limited period of time, since as the biomass increases, the tendency to slow down the growth rate becomes more and more pronounced. For such a section of the kinetic curve of population growth, called the phase of damped growth of the culture, can be used differential equation for growth rate
and its integral form to describe the change in biomass concentration over time
(for the time interval between t3 and t4).
A decrease in the growth rate as X approaches the value of X4 occurs until reaching zero, which characterizes the entry of the population into the stationary phase: X = X4
(for m lying between m4 and m5).
Upon completion of the phase of stationary growth, the phase of dying off, or the phase of degeneration, of the culture begins, characterized by a decrease in the population size.
The above system of equations can only be used to describe a specific kinetic growth curve obtained as a result of the experiment, but is not able to serve as a basis for predicting the process, since in the given dependences as parameters (X1, ..., X4; m1, . .., t5), final values of biomass concentration and time are introduced. At present, there is still no generally accepted mathematical model of population growth that would accurately describe the kinetics of biomass accumulation under conditions of periodic cultivation and would contain the minimum number of empirical coefficients. To the greatest extent, these requirements are met by the model of N. I. Kobozev, the use of which in the study of the kinetics of population growth gives encouraging results. The integral form of the equation he proposed, which describes the kinetic curve of population growth, has the form
This equation is the most general expression for population growth, and depending on particular conditions (reversible or irreversible reproduction, population growth with the depletion of the substrate or while maintaining its quantity at a constant level), the equation takes on an appropriate form and gives a different expression for the biomass concentration.
The main disadvantage of the periodic method is the cyclicity and constant change in cultivation conditions, which makes it difficult to control and regulate the process parameters.
Great opportunities for increasing the efficiency of production lie in the continuous method of cultivation.
Continuous cultivation
The essence of the method is to maintain constant environmental conditions, and thus the microorganism-producer in a certain physiological state. With the continuous method in education final product during the entire fermentation process, almost the entire population of microorganisms is involved, which is facilitated by optimal conditions cultivation.
With continuous cultivation, an open dynamic system, in which microorganisms multiply continuously at a rate dependent on the influx of nutrients and other nutritional conditions. A part of the volume of the culture liquid continuously flows out at the same rate as the medium is fed into the apparatus, and the number of microorganisms supporting the continuous process remains constant in the fermenter. Under sterile conditions, the continuous method ensures the preservation of the culture in a physiologically active state for a long time.
The rate of increase in biomass in the duct is expressed by the equation
The value D=F/V is known as the dilution rate. It characterizes the flow rate per unit volume. F - medium flow rate, ml/h (m3/h); V is the volume of the fermenter, ml (m3).
If in steady state dX/dt = 0, then u = D. This means that the concentration of cells is unchanged. Most often this happens at D = 0.01 ± 0.25.
Under conditions of continuous cultivation, when the culture is in a state of dynamic equilibrium (at u = D), turbidostatic and chemostatic processes are distinguished.
In turbidostat culture, the medium flow rate is controlled so that the cell concentration remains constant. In chemostatic cultivation, a constant concentration of cells in the medium is maintained using a constant concentration chemical compounds, in particular a limiting substrate (for example, sources of carbon, nitrogen, vitamins, etc.).
The dependence of the specific culture growth rate on the substrate concentration is determined by the Monod equation
In full culture medium Ks in relation to S is an insignificant value and can be neglected, then from the equation u = umax S/S = umax it can be seen that in a complete nutrient medium, the specific growth rate of the culture does not depend on the concentration of the limiting factor. For bacteria growing in a nutrient medium with carbohydrates, the Ks value is a few tenths of a milligram per 1 liter of medium, and for microorganisms growing on media with amino acids, it is several micrograms per 1 liter, and 5 is several grams per 1 liter. Low Ks values were obtained for yeast grown on glucose. It should be noted that the S/(Ks+S) value is close to unity as long as the substrate concentration is not too low. Since the required concentration of carbon source for most fermentation processes is expressed in g/l, the Ks in 10-100 mg/l of sugar can only cause a decrease in the specific growth rate by a few percent compared to umax. In this regard, the value of the specific growth rate under these conditions should not decrease below 90% of the maximum growth rate.
Substrate concentration is not the only factor limiting the growth rate of microorganisms. N. D. Ierusalimsky came to the conclusion that the specific growth rate depends on the density of the population and that at a high concentration of cells, metabolic products can retard growth. The specific growth rate can be calculated from the equation
To maintain the culture in a state of maximum reproduction rate, a constant influx of fresh substrate and the removal of metabolic products are necessary.
When determining the growth of microorganisms during the cultivation period, it is assumed that the contents of the fermenter are well aerated and mixed, that the population of microorganisms is homogeneous and its properties are practically constant at a high concentration of the growth-limiting substrate, i.e., at S > Ks. Other substances that affect growth are also in constant excess. Then the specific growth rate u should be considered close to umax.
In the case of periodic cultivation of microorganisms, the dependence of the change in the concentration of microorganisms over time is described by the differential equation
The economic coefficient expresses the quantitative needs of microorganisms in nutrients. If the system is in equilibrium, then u = D. The equilibrium can be disturbed by changing the flow rate u > D or u< Д или изменяя концентрацию субстрата среды S. Так как выход Y определяется из соотношения между образовавшейся биомассой и потреблением субстрата, то уравнение принимает вид
It should be noted that the productivity of the process is determined by the product of the dilution rate and the concentration of microorganisms DX, i.e., the amount of biomass obtained per unit volume of the fermenter per unit time. The maximum productivity of the process is always associated with an increased concentration of the substrate in the resulting medium.
The productivity of a continuous growing process can be expressed by the equation
Comparing the productivity of batch and continuous cultivation processes in the production of fodder yeast, we assume that the batch process will end in 10 hours, so n = 1/10. For the chosen value u = 0.3 we get D = 1/10 (1-1/3) = 0.095. With continuous production D = 0.3. It follows from this that at the same concentration of microorganisms, the productivity of the process of periodic cultivation is three times lower than that of continuous cultivation. When the goal of cultivation is to obtain metabolic products P, the following equation is used to describe the process and determine the biosynthetic activity K of a microorganism:
This indicates that the rate of metabolite biosynthesis over time dt is directly proportional to the amount of biomass and specific activity K of the microorganism. K can be determined from the equation
With continuous cultivation, mutations can form. If the number of mutations during one generation is expressed through Q, the number of generations per hour D/ln2, the specific rate of reproduction of mutants through ux and their concentration in the fermenter through Xm, then the equation will take the form
This equation can be used to calculate the concentration of mutants in the fermenter.
Biological synthesis is based on enzymatic processes. The dependence of the enzymatic reaction rate on the substrate is expressed according to the Michaelis-Menten equation
In a continuous process, u = D. For the formation of the product, it is necessary to establish a limiting factor and factors that limit the growth of the culture (temperature, pH, repressors, inhibitors, etc.).
In a homogeneous-continuous process, where u = D
It follows from this that the amount of product depends on the concentration of biomass, the activity of the culture and the dilution rate D.
The material balance of a homogeneous-continuous process on the substrate is expressed by the equation
It can be assumed that the biomass yield does not depend on the concentration of the component. Then, according to the equation S = S0 – X/a, one can determine the concentration of the substrate in the outflowing culture liquid. With a decrease in the dilution rate D, the difference between the concentration of the substrate in the inflow and outflow increases, since the concentration of biomass in the medium increases.
Growth - this is an increase in the total mass in the process of development, leading to a constant increase in the size of the organism. If the organism did not grow, it would never become larger than a fertilized egg.
Growth is provided by the following mechanisms: 1) an increase in cell size, 2) an increase in the number of cells, 3) an increase in non-cellular substance, the products of cell vital activity. The concept of growth also includes a special shift in metabolism, which favors the processes of synthesis, the intake of water and the deposition of intercellular substance. Growth occurs at the cellular, tissue, organ and organism levels. The increase in mass in the whole organism reflects the growth of its constituent organs, tissues and cells.
There are two types of growth: limited and unlimited. Unlimited growth continues throughout ontogenesis, until death. Such growth is possessed, in particular, by fish. Many other vertebrates are characterized by limited growth, i.e. quite quickly reach a plateau of their biomass. The generalized curve of the dependence of the growth of an organism on time with limited growth has an s-shaped shape (Fig. 8.18).
Rice. 8.18. Generalized growth-time curve
Before development, the organism has some initial dimensions, which practically do not change for a short time. Then begins a slow, and then a rapid increase in mass. For some time the growth rate may remain relatively constant and the slope of the curve does not change. But soon there is a slowdown in growth, and then the increase in the size of the body stops. After reaching this stage, a balance is established between the consumption of material and the synthesis of new materials that provide an increase in mass.
Rice. 8.19. Changes in growth rate depending on the stage of development of the human body.
BUT- in the fetus and in the first two years after birth, B- at the beginning of the postnatal period
The most important characteristic of growth is its differentiality. This means that the growth rate is not the same, firstly, in different parts of the body and, in - second, at different stages of development. Obviously, differential growth has a huge impact on morphogenesis.
Not less than important feature is such a growth property as equifinality. This means that, despite the emerging factors, the individual tends to reach the typical size of the species. Both differential and equifinal growth point to the manifestation integrity developing organism.
The rate of overall growth of the human body depends on the stage of development (Fig. 8.19). The maximum growth rate is typical for the first four months of intrauterine development. This is due to the fact that the cells at this time continue to divide. As the fetus grows, the number of mitoses in all tissues decreases, and it is generally accepted that after six months of intrauterine development, there is almost no formation of new muscle and tissue. nerve cells except for neuroglial cells.
Rice. 8.20. Growth curves of individual organs and tissues
compared to the generalized growth curve (see text for explanation)
The further development of muscle cells is that the cells become larger, their composition changes, and the intercellular substance disappears. The same mechanism operates in some tissues and in postnatal growth. The growth rate of the organism in postnatal ontogenesis gradually decreases by the age of four, then remains constant for some time, and at a certain age again makes a jump, called pubertal growth spurt. It has to do with puberty.
The difference in the growth rate of organs and tissues is shown in fig. 8.20. The growth curves of most skeletal and muscular organs follow the general growth curve. The same applies to changes in the size of individual organs: the liver, spleen, kidneys. However, the growth curves of a number of other tissues and organs differ significantly. On fig. 8.20 shows the general growth curve of the body and most of the other organs ( III), the growth of external and internal organs breeding ( IV), the growth of the brain, as well as the skull, eyes and ears ( II), growth of lymphatic tissue of the tonsils, appendix, intestines and spleen ( I).
The significance of different growth rates of organs and tissues for morphogenesis is clearly seen from Fig. 8.21. Obviously, in the fetal and postnatal periods, the growth rate of the head decreases compared to the growth rate of the legs.
Rice. 8.21. The proportions of the human body in embryogenesis and after birth
Rice. 8.22. Forms of proliferative growth.
BUT - multiplicative; B - accretionary (see text for explanation)
The pubertal growth spurt characterizes only humans and monkeys. This allows us to evaluate it as a stage in the evolution of primates. It correlates with such a feature of ontogeny as an increase in the time interval between the end of feeding and puberty. In most mammals, this interval is small and there is no pubertal growth spurt.
As mentioned above, growth is driven by cellular processes as an increase in the size of cells and an increase in their number. There are several types of cell growth.
Auxiliary - growth by increasing the size of cells. This is a rare type of growth seen in animals with a constant cell count, such as rotifers, roundworms, insect larvae. The growth of individual cells is often associated with polyploidization of nuclei.
proliferative - growth proceeding by cell multiplication. It is known in two forms: multiplicative and accretionary.
Multiplicative growth is characterized by the fact that both cells that have arisen from the division of the parent cell again enter into division (Fig. 8.22, BUT). The number of cells grows exponentially: if n- division number, then N n=2 n. Multiplicative growth is very effective and therefore almost never occurs in its pure form or ends very quickly (for example, in the embryonic period).
accretionary growth lies in the fact that after each subsequent division, only one of the cells divides again, while the other stops dividing (shaded, Fig. 8.22, B). In this case, the number of cells grows linearly. If a P - division number, then N n=2 n. This type of growth is associated with the division of the organ into cambial and differentiated zones. Cells move from the first zone to the second, maintaining constant ratios between the sizes of the zones. Such growth is typical for organs where the renewal of the cellular composition takes place.
The spatial organization of growth is complex and regular. It is with it that the species specificity of the form is largely associated. This manifests itself in the form allometric growth. Its biological meaning is that the organism in the course of growth must preserve not a geometric, but a physical similarity, i.e. do not exceed certain ratios between body weight and the size of the supporting and motor organs. Since with the growth of the body, the mass increases to the third degree, and the sections of the bones to the second degree, so that the body is not crushed by its own weight, the bones must grow in thickness disproportionately quickly.
Growth regulation is complex and diverse. Great importance have a genetic constitution and environmental factors. Almost every species has genetic lines characterized by the maximum size of individuals, such as dwarf or, conversely, giant forms. Genetic information is contained in certain genes that determine the length of the body, as well as in other genes that interact with each other. The realization of all information is largely due to the action of hormones. The most important of the hormones is somatotropin, secreted by the pituitary gland from birth to adolescence. The thyroid hormone - thyroxine - plays a very important role throughout the entire period of growth. FROM adolescence growth is controlled by steroid hormones of the adrenal glands and gonads. From environmental factors highest value have food, season, psychological influences.
Interesting is the dependence of the ability to grow on the age stage of the organism. Tissues taken at different stages of development and cultivated in a nutrient medium are characterized by different speed growth. The older the embryo, the slower its tissues grow in culture. Tissues taken from an adult organism grow very slowly.
