Mathematical model of plant growth kinetics
Kolpak Evgeny Petrovich,
Doctor of Physical and Mathematical Sciences,
Stolbovaya Maria Vladimirovna,
graduate student.
St. Petersburg State University.
Mathematical Model of Plant Growth Kinetics
Maria Stolbovaya
doctoral student, St. Petersburg State University.
Evgenii Kolpak
D.Sc, St. Petersburg State University.
The paper presents the results of studies on the study of the kinetics of plant growth. On the basis of experimental data, a mathematical model is proposed for changing the linear dimensions of plants, which is the Cauchy problem for an ordinary differential equation.
Keywords:mathematical modeling, morphogenesis, growth kinetics.
This paper describes the results of a study in the kinetics of plant growth and offers a mathematical model of changes in their dimensions based on the experimental data obtained. The model is a Cauchy problem for an ordinary differential equation.
keywords:mathematical modeling, morphogenesis, growth kinetics.
The dynamics of plant growth, apparently, was first described in the works of Sachs (1832 - 1897) - the linear size of plants over time in his experiments changed according to the "logistic" dependence. To date, numerous experimental data published in the literature, with varying degrees of accuracy, are consistent with such a nature of changes, both in linear dimensions and in the total biomass of plants. However, to describe the change in the “parameter” that characterizes both the growth of an individual plant and the accumulation of their total biomass, various approximating dependences are proposed, such as exponential, linear, parabolic, and others that do not take into account internal biological processes that cause plant growth, and external influences. such as additional nutrition, temperature changes, anthropogenic impact. The paper proposes a mathematical model of the growth of an individual plant, developed on the basis of the author's experimental data.
The analysis of plant growth kinetics was carried out on such plants as buckwheat, millet, momordica, lagenaria, lavender, chufa, tulip, etc.The research was carried out from 2000 to 2012 at the training and experimental site of the Kingisepp station for young naturalists and in the greenhouses of ZAO Raduga in the Kingisepp district. Stolbovaya M.V., Merzlyakova S.N., Likhacheva N.V. took part in the experiments.
All plants (Table 1), except for tulips, were grown in summer under natural conditions from 2000 to 2012. For tulips, forcing was carried out in winter under conditions under which the temperature of the soil and air was regulated. An area of 10 sq.m. was allocated for the cultivation of each variety. Some plants required pre-sowing treatment of seeds, growing seedlings, preparing the soil with its disinfection with a solution of potassium permanganate. They planted (sown) in a permanent place when the threat of a return of frost had passed. Additional nutrition was given to the plants in the form of top dressings with a complex mineral fertilizer. Weeding and watering was done as needed. In the process of plant growth, measurements of plant height were carried out mechanically throughout the growing season. Plant height was measured with a ruler about 1 time in 7-10 days. The temperature was measured daily.
On fig. Table 1 shows the experimental data (marked with asterisks) for buckwheat 1. Similar dependences (consistent with the data published in ) were obtained for other plants (Table 1) for the entire period of the experiment. The maximum height of plants varied from 17 cm to 110 cm. Growth time was from 80 to 110 days.
Rice. 1. Dependence "plant height - time" for buckwheat 1.
All experimental data on the growth kinetics are close to the logistic dependence. That is, to describe the dynamics of plant growth, you can use the equation:
where is the time (days), is the current height of the plant (cm), is the theoretical maximum height (cm) that the plant can reach at the end of growth, is a constant (specific growth rate, unit - 1/day). The solution to this equation is the function (− initial plant height):
.
This dependence was used to describe the obtained experimental data. TO constants and were selected using the least squares method. The results of processing experiments (constant ) for some plants are given in Table. 1. As follows from the obtained results, the constants for the studied plants varied in the range of 0.06 – 0.15. The error of their determination for three years of measurements for all cultures was no more than the remaining 5%.
Table 1.
Cultivated plants and calculated values of specific growth rates.
|
plant name |
Specific growth rate () |
plant name |
Specific growth rate () |
|
Buckwheat 1 |
0.15 |
Millet Kazan 176 |
0.07 |
|
Buckwheat 2 |
0.17 |
Tulip |
0.06 |
|
Free millet |
0.09 |
Tulip Denmark |
0.09 |
|
Millet quick |
0.08 |
Tulip Escape |
0.09 |
Temperature is one of the most important factors affecting plant growth. As follows from our experimental data, the change in temperature over time during the growing season can be described by the function
where is the minimum temperature during the growing season, and is the maximum, is the frequency of change in the maximum temperature values.
The plants with which the experiment was carried out develop if the air temperature changes in the range from (10°C in the experiment) to (30°C in the experiment). If we assume that the growth rate is maximum at a temperature 
, then the specific growth rate of the plant will be proportional to the function
if,
if or ,
where − temperature value at the current time.
This temperature function takes on zero values at And and reaches an extremum equal to 1 at . A similar approach to taking into account the effect of temperature on plant growth was used in.
The equation for the growth rate of plants, taking into account the introduced temperature regime, will take the form:
, if ,
If or .
In this model, it is assumed that the plant does not die when the temperature regime is “violated”, but only its growth stops. Numerical solution of differential equations and processing of experimental data is more convenient to implement in the programming environment of the mathematical package Matlab, which has a set of necessary built-in functions.
Thus, taking into account the temperature regime can more accurately describe the experimental data and explain the deviations of the experimental data from the logistic dependence more “biologically” justified than polynomial functions.
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Almost the only source of energy for all living organisms is the energy of the sun. Only one group of organisms can directly convert solar energy - green plants and photosynthetic organisms. We are talking about a unique natural phenomenon - photosynthesis. All other organisms absorb the energy of the sun, converted by green plants into the energy of organic substances - sugars. The main plant organ involved in photosynthesis is the leaf. Therefore, the study of plant leaves is very actual topic. Plants themselves use the produced substances as a source of nutrition. It would seem that the larger the leaf, the better, since more “food” is produced. But in the vast majority of our northern plants of forests and meadows, the leaves are medium-sized and even small. So what does the shape of the leaf depend on? We assumed hypothesis- the form depends on the conditions environment- illumination, temperature, humidity.
This question determined goal our research - find out the relationship between environmental conditions and the shape of the leaf blades of meadow and forest plants
Tasks:
Consider the features of the internal, external structure of the leaf, as the main organ of plants, its functions;
Determine how the influence of environmental conditions on the shape of the leaf blade is manifested;
Collect samples of light-loving meadow plants and shade-loving forest plants;
Conduct a study - compare the sizes, shapes of leaf blades of light-loving and shade-loving plants
An object research: green plants
Subject research: leaf blades of plants in our area.
Chapter 1
1.1. External leaf structure
The external structure of the leaf. The leaf always occupies a lateral position in the shoot, located at the nodes of the stem. In the predominant number of higher plants, the leaf has a flat shape.
A leaf is distinguished by a leaf blade, petiole, stipules and a base with which it is attached to the stem. There are plants in which the petiole and stipules are absent. Many plants have simple leaves - they have only one leaf blade (Figure 1).
Rice. one. The external structure of the sheet: 1 - leaf blade; 2 - veins; 3 - petiole; 4 - stipules; 5 - base of the sheet
There are plants in which the leaf has several leaf blades. Such leaves are called complex (Figure 2).
Rice. 2. Variety of leaves. simple leaves: 1 - lilac; 2 - Apple tree; 3 - maple; 5 - dandelion. compound leaves: 4 - Clover; 6 - rose hip; 7 - raspberries; 8 - strawberry; 9 - lupine
When studying the external structure of the leaf, it is clearly seen that the veins are clearly expressed on the leaf blade of many plants. They are represented by bundles of conductive and mechanical tissue. Through the veins, water and mineral salts enter the leaf and the organic substances formed in the leaf are discharged. In some plants, the veins are approximately the same in size and lie arcuately or parallel to each other. In others, they are represented by a pinnately branched network of small veins converging into one large central vein in the middle of the leaf. Pinnate and palmate venation is characteristic of the leaves of dicotyledonous plants, while parallel and arcuate venation is characteristic of the leaves of many monocotyledonous plants (see Appendix 1, c).
Plants have different sizes of leaves. So, in palm trees, monstera, white water lilies and yellow capsules, the leaves are very large: their length together with the petiole reaches 150-200 cm, in some palms - even 5-12 m. But in heather and needles they are very small, only 2 long -3 mm..
1.2. The internal structure of the leaf
Outside, the leaf is covered with skin. It is formed by a layer of transparent cells of the integumentary tissue, tightly adjacent to each other. The peel protects the inner tissues of the leaf. The walls of its cells are transparent, which allows light to easily penetrate into the leaf.
On the lower surface of the leaf, among the transparent cells of the skin, there are very small paired green cells, between which there is a gap. A pair of guard cells and a stomatal gap between them is called a stomata. With insufficient water supply, the stomata of the plant are closed. With the flow of water into the plant, they open (Figure 3).
Rice. 3. Participation of stomata in gas exchange and moisture evaporation
Stomata are found in the skin of all land plants. Their number in plants is huge - from 80 to 300 pieces and more per 1 mm² of leaf surface. For example, maple has 550 stomata per 1 mm2 of leaf surface, and yellow pods have 650.
Leaf tissue. Inside the leaf there are a lot of cells of chlorophyll tissue - the pulp of the leaf. Due to the large number of chloroplasts in the pulp cells, the leaf has a green color. The presence of a large number of green chloroplasts in the pulp of the leaf indicates that photosynthesis is carried out in this part, that is, organic substances are formed here.
Two types of cells are distinguished in the pulp of leaves. By appearance cells and their location in the pulp of the leaf, columnar and spongy tissues are distinguished. Columnar tissue cells contain most (about ¾) of all leaf chloroplasts. They are better lit, they form the most organic substances in the light. Through the loose spongy tissue, gas exchange and water evaporation occur (Fig. 4).
The structure of the leaf pulp is presented differently in leaves developing under different lighting conditions. In plants grown in bright light conditions, the leaves usually have two or three layers of columnar tissue - they are called light. In plants grown with a lack of light, in the shade, columnar cells form only one thin layer in the upper part of the leaf - they are called shadow cells.
Rice. 4. Scheme of the internal structure of the leaf
In most plants, stomata are located mainly on the underside of the leaf, but in some (for example, eucalyptus, cabbage) they are on both sides of the leaf. In plants with leaves floating on water (pod, water lily), stomata formed only on the upper side of the leaf, facing the air.
1.3. Sheet functions
Formation of organic substances. A green leaf performs an important function in the life of a plant - organic substances are formed here. The structure of the leaf is well suited to this function: it has a flat leaf plate, and the pulp of the leaf contains a huge amount of chloroplasts with green chlorophyll.
The formation of organic substances in the process of photosynthesis is one of the main functions of the leaf.
Evaporation of water is another important function of the leaf. Evaporation provides the relationship between the roots and leaves of the plant.
The process of evaporation of water by the leaves of a plant is regulated by the opening and closing of stomata. By closing the stomata, the plant protects itself from water loss.
Of the external factors, the work of stomata is affected by dry air, water supply conditions, light brightness and temperature. So, during a drought, most plants have stomata closed. Many plants open their stomata only in the evening and at night when the heat subsides. But in most trees, shade-tolerant plants, and many grasses, the maximum evaporation of water occurs in the daytime.
Gas exchange. Leaves, thanks to the work of stomata, also carry out such an important function as gas exchange between the plant and the atmosphere. Through the stomata, oxygen and carbon dioxide enter the leaf with atmospheric air.
Leaf fall. In the process of life, the leaves age by the end of the growing season, nutrients flow out of them, chlorophyll begins to break down, the leaves turn yellow or reddish, and waste waste substances accumulate in the leaf tissues. Aged leaves are removed due to leaf fall. This adaptation, developed in the process of evolution, provides not only the removal of substances unnecessary for the plant, but also a reduction in the surface of above-ground organs during an unfavorable period of the year.
In some plants, the leaves have acquired other functions. Many plants reproduce by leaves (vegetative propagation). Some plants store spare nutrients in their leaves, such as sedum, juvenile, aloe, cabbage, onion.
Common peas and mouse peas, along with ordinary leaves, have leaves in the form of antennae. With their help, the non-erect shoots of these plants, clinging to a support, rise higher and are carried out to the light.
In barberry, caragana, camel thorn, some leaves have become thorns that protect the shoots from animals. In cacti, the leaves have changed into sharp needles.
In nature, there are many plants that are able to catch insects with the help of leaves and digest them. Typically, such insectivorous plants grow on soils poor in minerals, especially with insufficient nitrogen, phosphorus, potassium and sulfur. From the bodies of insects, these plants receive the inorganic substances they need.
In lakes in Russia, a pemphigus plant is often found floating near the surface of the water. Among its threadlike green leaves, some are shaped like trapping bubbles (2-5 mm in diameter) with a cap. Small animals caught in them, such as daphnia, are digested and absorbed by the plant. So the plant compensates for the deficiency of minerals (especially nitrogen compounds), which are not enough in lake water.
Chapter 2
2.1. The influence of climatic characteristics on the sheet size
The modern distribution of plants on Earth is believed to be determined by climate, and thus vegetation zones almost always correspond to climatic zones. Climate and soils primarily influence external characteristics species of vegetation, which determines the external similarity of plants from areas with similar ecological conditions. Leaves, as photosynthetic organs of a plant, are optimally adapted to climatic conditions.
The shape of the leaf blade reflects the characteristics of the environment.
This assumption was confirmed by the results of research by scientists from the universities of Tübingen (Germany) and Lyon (France), who studied the dependence of the shape of the leaf blade of European trees on climatic factors. Scientists limited themselves to the study of woody vegetation. The material was collected on the territory of Europe, data were obtained on 1835 plots. At each site, tree species were grouped according to 25 indicators.
Result: leaf shape mainly depends on temperatures (average annual, total, minimum, duration of soil freezing), and to a greater extent on the minimum than on the maximum - the closest relationship is observed between the minimum temperature and the presence of a sharp base in the leaves. The relationship between the presence of entire leaves in trees and temperature is somewhat weaker, although cold can be considered as a stress factor that contributes to the formation of irregularities along the edge of the leaf blade. Precipitation-related parameters did not have a significant relationship with leaf shape parameters.
The data obtained indicate that adaptation to cold, mainly to the lowest temperatures, was of paramount importance in the evolution of deciduous flora.
2.2. The dependence of the shape of the leaf blade on the illumination
2.2.1. The influence of light on the structure of leaves
The anatomical structure of the leaves of light-loving and shade-loving plants presents important differences. The leaves of light-loving plants are often equilateral if they occupy a vertical position, while the leaves of shade-loving plants are always bilateral.
Light-loving and shade-loving (heliophilic and heliophobic) plants differ significantly from each other both in their external form and in their internal structure.
Strong lighting slows down the growth of shoots; therefore, heliophilic plants are often short-segmented and compressed, while heliophobic plants, on the contrary, are long-segmented.
The plants that make up the forest carpet are usually tall, with a long stem. The leaves of light-loving plants are usually narrow, shallow, linear or similar in shape, while shade-loving plants in the same conditions have large, broad leaves. The leaves of a two-leaved mainica, a plant that usually grows in the shade of shrubs, reach only 1/3 of their usual size in the sun.
The leaves of many plant species reach a larger size in northern countries than in more southern latitudes, which, apparently, is associated with longer duration low light period.
The leaves of light-loving plants are often folded (cereals, palm trees), or curly and tuberculate, while the leaves of shade plants are flat and smooth.
The palisade tissue of shade plants is always low (stems, poor in leaves or completely devoid of leaves, usually have a high palisade tissue around the stem); on the other hand, spongy tissue reaches a more powerful development in heliophobic plants. The leaves of typical heliophobic plants consist of only one row of cells (spiky rump). The leaves of heliophilous plants have narrow intercellular spaces, while the leaves of heliophobic plants have wide intercellular spaces.
The skin (epidermis) of light-loving plants is thick and usually does not contain chlorophyll (it is always devoid of chlorophyll on the upper side of the leaf); sometimes it is transformed by transverse cell division into a multilayer aquifer (tropical plants); her cuticle is always thickened.
The skin of shade plants is thin and single-layered, sometimes contains chlorophyll and is covered with a thin cuticle. The leaves of light-loving plants are often shiny and reflect a lot of light, as numerous tropical plants serve as an example.
The leaves of shade plants have a matte color and fade in dry air much faster than the leaves of light-loving plants. The epidermal cells of the leaves of light-loving plants, especially on the upper side of the leaf, have less wavy walls than those of the leaves of shade plants. Only the lower surface of bilateral leaves of light-loving plants is provided with stomata, or at least they are more numerous here than on the upper side (some alpine plants are an exception) and are immersed in the leaf tissue. In shade plants, the stomata are evenly distributed on both sides of the leaf, in any case, but more numerous on the underside, and at the same time lie in the same plane with the entire surface of the leaf, or even elevated above it.
The degree of hairiness is very different. Heliophilic plants, often covered with dense hairs, gray-felt or silvery-white in color, have a slight pubescence, especially on the lower surface (many plants growing on rocks, on heaths and in the steppes). The leaves of heliophobic plants are generally much less hairy, sometimes even completely bare.
Regarding the effect of light on the color of plants, it should be noted that in addition to the importance of light for the formation of chlorophyll, it can also, apparently, cause the formation of red cell sap (antokiana). Under the influence of direct sunlight, the epidermal cells of the bare parts of plants are often stained red, which apparently serves as a protection for protoplasm and chlorophyll (many young shoots, seedlings, alpine and other plants), although there are assertions that the color of the latter may depend on from the influence of the cold.
In addition, a number of researchers point out that the color of leaves, flowers and fruits of plants at higher latitudes is more intense, which may be due to the effect of almost continuous illumination.
From what has been said above, it is obvious that light has a great influence on the external form and internal structure of plants. This is also confirmed by the ability of many plants to adapt their anatomical structure and, mainly, the structure of their leaves to different lighting conditions ("plastic leaves"). A beech leaf, for example, has a different structure in the sun than a leaf of the same beech tree in the shade. The location of chlorophyll grains in the cell and the color of the leaves associated with this depend on the lighting, stronger lighting causes a less intense color, and vice versa.
2.2.2. Classification of plants in relation to light
In relation to light, all plants, including forest trees, are divided into the following ecological groups:
heliophytes (light-loving), requiring a lot of light and able to tolerate only slight shading (photophilous include almost all cacti and other succulents, many representatives of tropical origin, some subtropical shrubs);
sciophytes (shade-loving) - on the contrary, they are content with insignificant lighting and can exist in the shade (various coniferous plants, many ferns, some ornamental leafy plants);
shade-tolerant (facultative heliophytes).
Heliophytes. light plants. Inhabitants of open habitats: meadows, steppes, upper tiers of forests, early spring plants, many cultivated plants.
Small size of leaves seasonal dimorphism occurs: leaves are small in spring, larger in summer;
Leaves are located at a large angle, sometimes almost vertically;
leaf blade shiny or densely pubescent;
form scattered stands.
Sciophytes. Can't stand strong light. Habitat: lower darkened layers; inhabitants of the deep layers of water bodies. First of all, these are plants growing under the forest canopy (oxalis, hoof, goatweed).
They are characterized by the following features:
Leaves are large, tender;
Leaves are dark green
Leaves are mobile
The so-called leaf mosaic is characteristic (that is, a special arrangement of leaves, in which the leaves do not obscure each other as much as possible).
Shade-tolerant. They occupy an intermediate position. They often thrive in normal lighting conditions, but can also tolerate dark conditions. According to their characteristics, they occupy an intermediate position.
Chapter 3
For research, we took herbarium samples of meadow and forest plants that we collected at the end of June.
Study #1.Comparison of the leaf area of meadow heliophytes and shade-tolerant forest plants.
The measurement method was used. From each sample, 10 green leaves are selected by random sampling, the area is determined by the method of linear measurements along the length (L) and maximum width (W). The area of the measured leaves (S) is calculated by the formula:
where n is the number of measured leaves.
This method is suitable for cereals and other crops with linear, round leaves.
|
forest plant |
meadow plant |
||||
S (forest plants) = 87.5×45.2×0.7×10=27685mm
S (meadow plants) = 44.1 × 7.4 × 0.7 × 10 = 2284.4 mm
Output: The area of leaf blades of forest plants is more than leaf blades of meadow plants by about 13 times.
The reason is different lighting conditions.
Study #2
Comparison of meadow and forest plants according to the shape of the leaf blade (See Appendix 1, p. 23).
|
forest plants |
Record shape |
meadow plants |
Record shape |
|
bird cherry |
blunt two-serrated edge |
Alfalfa hop |
trifoliate leaf ciliary edge |
|
Stone berry |
odd-pinnate Two-toothed edge |
red clover |
trifoliate leaf The edge is simple |
|
odd-pinnate Serrated edge |
Meadow fescue |
line sheet The edge is simple |
|
|
obovate Serrated edge |
Bedstraw northern |
palm leaf Two-serrated edge |
|
|
Cotoneaster |
Oval The edge is simple |
Meadow rye |
Needle The edge is simple |
|
Oval Edge ciliary |
field bindweed |
Cordate The edge is simple |
|
|
bracken fern |
Complex odd-pinnate The edge is simple |
Reed grass |
Linear sheet, plain edge |
|
Gircha caraway |
Complex odd-pinnate vane leaf |
Velcro ordinary |
line sheet The edge is simple |
|
Cowberry |
Leaf simple obovate |
Daisy |
line sheet Serrated hay |
|
Voronet spike-shaped |
Complex odd-pinnate Bladed edge is two-serrated |
River gravel |
trifoliate leaf Two-serrated edge |
Output: In the forest, shrubs have simple leaves, while most herbs have compound leaves. Apparently, this is due to a small amount of light near the surface of the earth and the need for plants to increase the area of the leaf blade due to complex leaves.
In the meadow - the leaves are linear (in cereals), less often - simple and complex.
Study #3
The study of forest and meadow plants by the color of the leaf blade (visually).
Comparing the leaves of meadow and forest plants, we saw that the leaves of meadow plants have a bright green color (cereals, meadow geranium, field loach, blue cyanosis, grass carnation, gravel and others), some light green, sometimes resembling plaque (gray-green hiccups , wormwood, five-lobed motherwort, silver cinquefoil).
The leaves of forest plants have a bright green and dark green color, almost all (blueberries, cotoneaster, ferns, mountain ash, bird cherry, strawberries, lingonberries and others).
Output- forest plants have darker leaves with more chloroplasts due to the lack of light under the forest canopy.
Conclusion
At the beginning of the work, we set ourselves the goal of finding out the relationship between environmental conditions and the shape of leaf blades of meadow and forest plants. After reviewing the work of other authors on this topic and conducting our own research, we can conclude:
The leaf occupies a lateral position in the shoot; in most higher plants, the leaf has a flat shape. The flat shape of the leaf provides the greatest contact of the plant surface with the air and sunlight.
A leaf is a special organ containing cells that capture the sunlight necessary for photosynthesis (air nutrition). In addition, the leaf is involved in gas exchange and transpiration - the evaporation of moisture.
Leaves, as photosynthetic organs of a plant, are optimally adapted to climatic conditions. The shape of the leaf mainly depends on temperatures, and to a greater extent from low temperatures than from high ones. There is a relationship between the presence of entire leaves in trees and temperature. Precipitation does not affect the shape of the leaf blade (in the temperate zone).
Light has the greatest influence on the external shape and internal structure of plants. The location of chlorophyll grains in the cell and the color of the leaves associated with this depend on the lighting, stronger lighting causes a less intense color, and vice versa.
We conducted research comparing meadow and forest plants, and came to the conclusion that the leaves of meadow plants have a smaller leaf blade area, lighter in color, the leaves are mostly simple than those of forest plants. They identified the reason - a different level of illumination. Light is the main factor affecting plants.
We consider our hypothesis - the shape of the leaves depends on environmental conditions - light, temperature, moisture, to be confirmed.
Information sources
Biology textbook grade 6. Electronic version (http://blgy.ru/biology6/leaf)
http://agrosbornik.ru/innovacii1/106-2011-10-09-15-29-31.html
http://eco-rasteniya.ru/svet-kak-ekologicheskij-faktor.html
http://lektsii.com/1-100601.html
http://botanical_dictionary.academic.ru/5917
https://ru.wikipedia.org/wiki/
dic.academic.ru/dic.nsf/bse/74352/
Attachment 1
The difference between leaves in shape, edge of the leaf blade, venation
Leaf Shape:
Fan-shaped: semi-circular, or in the form of a fan
Bipinnate: Each leaf is pinnate
Deltoid: leaf is triangular, attached to the stem at the base of the triangle
Lateform: Divided into many lobes
Pointed: wedge-shaped with a long apex
Needle: thin and sharp
Cuneiform: the leaf is triangular, the leaf is attached to the stem at the apex
Spear-shaped: sharp, with spines
Lanceolate: the leaf is long, wide in the middle
Linear: the leaf is long and very narrow
Bladed: with multiple blades
Spatulate: spade-shaped leaf
Unpaired: pinnate leaf with apical leaflet
Reverse lanceolate: top part wider than the bottom
Reverse heart-shaped: leaf in the form of a heart, attached to the stem at the protruding end
Obovate: in the form of a tear, the leaf is attached to the stem at the protruding end
Oval: the leaf is oval, with a short end
Oval: leaf is oval, ovoid, with a pointed end at the base
Single-bladed: with one leaf
Rounded: round shape
Palmate: the leaf is divided into finger-shaped lobes
Parapinnate: pinnate leaf without apical leaf
Pinnatisected: a simple dissected leaf in which the segments are arranged symmetrically about the axis of the sheet plate
Pinnate: two rows of leaves
Attachment 1
Reniform: kidney-shaped leaf
Dissected: the leaf blade of such a leaf has cuts reaching more than two-thirds of its half-width; parts of the leaf blade of a dissected leaf are called segments
Rhomboid: diamond-shaped leaf
Crescent: in the form of a sickle
Heart-shaped: in the form of a heart, the leaf is attached to the stem in the region of the dimple
Arrowhead: A leaf shaped like an arrowhead, with flared blades at the base
Three-pinnate: each leaf is in turn divided into three
Trifoliate: the leaf is divided into three leaflets
Subulate: in the form of an awl
Thyroid: leaf rounded, stem attached from below
leaf edge
Round-toothed - with undulating teeth, like a beech.
Fine-toothed - with fine teeth
Two-pronged - each clove has smaller teeth
Finely serrated - with small asymmetrical teeth
Full edge - with a smooth edge, without teeth
Ciliated - with fringe around the edges
Toothed - with cloves, like a chestnut. The step of the clove can be large and small.
Lobed - rugged, with notches that do not reach the middle, like many oaks
Serrated - with asymmetrical teeth directed forward towards the top of the leaf, like a nettle.
Notched - with deep, wavy cutouts, like many species of sorrel
Spiny - with inelastic, sharp ends, like some hollies and thistles.
Leaves are simple and complex. complex A leaf is one whose petiole has several leaf blades. They are attached to the main petiole with their own petioles, often on their own, one by one, fall off and are called leaflets. Examples of a complex leaf are hemp, lupine, clover, horse chestnut, walnut. Simple The leaf has one plate. From a simple to a complex leaf, there are various transitional forms, distinguished by the nature and degree of indentation of the plate.
Simple leaves according to the outline of the plate are oval, ovoid, obovate, kidney-shaped, oblong, lanceolate, xiphoid, linear etc.
If the edges of the leaf blade do not have any notches, the leaf is called whole. If the notches along the edge of the sheet are shallow, the sheet is called whole. Whole leaves are distinguished by the nature of the notches and protrusions between them. So, if the notches are sharp and the protrusions are rounded, the sheet crenate(as in sage, budry, etc.); if the recesses are wedge-shaped, and the protrusions are sharp, triangular, the sheet jagged(in beech, hazel, etc.); if the protrusions are oblique and sharp, it turns out serrated leaf (of a pear).
According to the shape of the top of the plate, the leaves are: blunt, sharp, pointed And pointed.
According to the shape of the base of the plate, the leaves are wedge-shaped, heart-shaped, spear-shaped, arrow-shaped, etc.
In addition to the listed categories of a whole sheet, there are also bladed, separate And dissected leaves. A leaf is called lobed, in which the cuts along the edges of the plate reach one quarter of its width (for oak), and with a greater depth, if the cuts reach more than a quarter of the plate's width, the sheet is called separate(at the poppy). The blades of the split sheet are called shares. Dissected call a leaf in which cuts along the edges of the plate reach almost to the midrib, forming plate segments.
Separated and dissected leaves can be palmate And pinnate, double-fingered And doubly pinnate etc.
Concerning complex leaves, then among them are distinguished ternary, palmate And pinnate. If a complex leaf consists of three leaflets, it is called ternary or ternary (in clover, alfalfa, soybean, pueraria, etc.). If the petioles of the leaflets are attached to the main petiole as if at one point, and the leaflets themselves diverge radially, the leaf is called palmate complex(in lupine, hemp, horse chestnut). If on the main petiole the lateral leaflets are located on both sides along the length of the petiole, the leaf is called pinnate. If such a leaf ends at the top with an unpaired single leaflet, it turns out odd-pinnate leaf (in sainfoin, white acacia, mountain ash, etc.). If a tendril develops instead of the upper single leaflet (on the wiki), then the leaf belongs to unpaired. If there is no terminal leaflet or tendril, the leaf is called paired(in peanuts, carob). Sometimes, in an unpaired leaf, all lateral leaflets are reduced and only the terminal, strongly developing unpaired leaflet remains, so that the leaf seems simple, not pinnate (in an orange).
The main part of an ordinary sheet is its plate. leaf blade- this is an expanded flat formation that performs the functions of photosynthesis, gas and water exchange. In addition to the lamina, the leaves often have petiole- an elongated cylindrical stem-like part, with the help of which the plate is attached to the stem. If there is a petiole, the leaf is called petiolate, and if it is absent, it is called sessile. The bottom of the sheet is base- can grow and cover the stem in the form of a tube. This formation is called a leaf sheath. Quite often, at the base of the leaf, there are special outgrowths at the petiole - stipules. Stipules are paired, of various shapes and sizes, green or colorless, free or fused with petiole. Stipules may or may not fall as the leaf grows.
Leaves are called simple if they have one leaf blade on the petiole, and in a complex leaf, several plates, called leaflets, are attached to one petiole.
Simple sheet. The leaf blade of a simple leaf can be whole or, on the contrary, dissected, i.e. in varying degrees, indented, consisting of protruding parts of the plate and notches. To determine the nature of dissection, the degree and shape of the indentation of leaf blades and the correct name of such leaves, first of all, it should be taken into account how the protruding parts of the blade are distributed - lobes, lobes, segments - in relation to the petiole and to the main vein of the leaf. If the protruding parts are symmetrical to the main vein, then such leaves are called pinnate. If the protruding parts come out as if from one point, the leaves are called palmate. According to the depth of cuts of the leaf blade, leaves are distinguished: lobed, if the recesses (the depth of the cuts) do not reach half the width of the half-plate (the protruding parts are called lobes); separate, with a depth of cuts that go deeper than half the width of the half-plate (protruding parts - lobes); dissected, with a depth of incisions reaching the main vein or almost touching it (protruding parts - segments).
Complex sheet. Compound leaves, by analogy with simple ones, are called pinnate and palmate with the addition of the word "complex". For example, pinnate, palmate, ternary, etc. If a compound leaf ends with one leaflet, the leaf is called odd-pinnate. If it ends with a pair of leaflets, then it is called paro-pinnate.
The dismemberment of the plate of a simple leaf, as well as the branching of parts of a complex leaf, can be multiple. In these cases, taking into account the order of branching or dismemberment, they speak of double-, thrice-, four-pinnate or palmate, simple or complex leaves.
The main forms of the leaf blade
Types of division of simple leaf blades and classification of compound leaves
Main types of sheet edge
1 - whole; 2 - notched; 3 - wavy; 4 - prickly; 5 - gear; 6 - double-toothed; 7 - serrated; 8 - gorodchaty
Top shapes The shape of the top, base and edge of the leaf blades are also features used in the description and definition of plants.
The main forms of the top of the leaf blade
Forms of the base of the leaf blade
Main types of leaves
The leaf is a vegetative organ of plants, is part of the shoot. The functions of the leaf are photosynthesis, water evaporation (transpiration) and gas exchange. In addition to these basic functions, as a result of idioadaptations to various conditions of existence, leaves, changing, can serve the following purposes.
- Accumulation of nutrients (onion, cabbage), water (aloe);
- protection against being eaten by animals (thorns of cactus and barberry);
- vegetative propagation (begonia, violet);
- catching and digesting insects (dew, venus flytrap);
- movement and strengthening of a weak stem (pea tendrils, wikis);
- removal of metabolic products during leaf fall (in trees and shrubs).
General characteristics of a plant leaf
The leaves of most plants are green, most often flat, usually bilaterally symmetrical. Sizes from a few millimeters (duckweed) to 10-15m (in palms).
The leaf is formed from the cells of the educational tissue of the growth cone of the stem. The leaf rudiment is differentiated into:
- leaf blade;
- petiole, with which the leaf is attached to the stem;
- stipules.
Some plants do not have petioles, such leaves, unlike petioles, are called sedentary. Stipules are also not found in all plants. They are paired appendages of various sizes at the base of the leaf petiole. Their form is diverse (films, scales, small leaves, spines), their function is protective.
simple and compound leaves distinguished by the number of leaf blades. A simple sheet has one plate and disappears entirely. The complex has several plates on the petiole. They are attached to the main petiole with their small petioles and are called leaflets. When a compound leaf dies, the leaflets fall off first, and then the main petiole.
Leaf blades are diverse in shape: linear (cereals), oval (acacia), lanceolate (willow), ovate (pear), arrow-shaped (arrowhead), etc.
Leaf blades are pierced in different directions by veins, which are vascular-fibrous bundles and give the sheet strength. The leaves of dicotyledonous plants most often have reticulate or pinnate venation, while the leaves of monocotyledonous plants have a parallel or arcuate venation.
The edges of the leaf blade can be solid, such a sheet is called whole-edge (lilac) or notched. Depending on the shape of the notch, along the edge of the leaf blade, there are serrate, serrated, crenate, etc. In serrated leaves, the serrations have more or less equal sides (beech, hazel), in serrated ones, one side of the tooth is longer than the other (pear), crenate - have sharp notches and blunt bulges (sage, budra). All these leaves are called whole, since their recesses are shallow, do not reach the width of the plate.
In the presence of deeper recesses, the leaves are lobed, when the depth of the recess is equal to half the width of the plate (oak), separate - more than half (poppy). In dissected leaves, the recesses reach the midrib or to the base of the leaf (burdock).
Under optimal growth conditions, the lower and upper leaves of the shoots are not the same. There are lower, middle and upper leaves. Such differentiation is determined even in the kidney.
The lower, or first, leaves of the shoot are the scales of the kidneys, the outer dry scales of the bulbs, the cotyledon leaves. The lower leaves usually fall off during the development of the shoot. The leaves of the basal rosettes also belong to the grassroots. Median, or stem, leaves are typical for plants of all kinds. Upper leaves usually have smaller sizes, are located near flowers or inflorescences, are painted in various colors, or are colorless (covering leaves of flowers, inflorescences, bracts).
Sheet arrangement types
There are three main types of leaf arrangement:
- Regular or spiral;
- opposite;
- whorled.
At the next arrangement, single leaves are attached to the stem nodes in a spiral (apple, ficus). With the opposite - two leaves in the node are located one against the other (lilac, maple). Whorled leaf arrangement - three or more leaves in a node cover the stem with a ring (elodea, oleander).
Any leaf arrangement allows plants to capture the maximum amount of light, since the leaves form a leaf mosaic and do not obscure each other.
Cellular structure of the leaf
The leaf, like all other plant organs, has a cellular structure. The upper and lower surfaces of the leaf blade are covered with skin. Living colorless cells of the skin contain the cytoplasm and nucleus, are located in one continuous layer. Their outer shells are thickened.
Stomata are the respiratory organs of a plant.
In the skin are stomata - gaps formed by two trailing, or stomatal, cells. Guard cells are crescent-shaped and contain cytoplasm, nucleus, chloroplasts, and a central vacuole. The membranes of these cells are thickened unevenly: the inner, facing the gap, is thicker than the opposite.
Changing the turgor of the guard cells changes their shape, due to which the stomatal opening is open, narrowed or completely closed, depending on environmental conditions. So, during the day, the stomata are open, and at night and in hot, dry weather they are closed. The role of stomata is to regulate the evaporation of water by the plant and gas exchange with the environment.
Stomata are usually located on the lower surface of the leaf, but there are also on the upper, sometimes they are distributed more or less evenly on both sides (corn); in aquatic floating plants, stomata are located only on the upper side of the leaf. The number of stomata per unit leaf area depends on the plant species and growth conditions. On average, there are 100-300 of them per 1 mm 2 of the surface, but there can be much more.
Leaf pulp (mesophile)
Between the upper and lower skin of the leaf blade is the pulp of the leaf (mesophile). Under the top layer is one or more layers of large rectangular cells that have numerous chloroplasts. This is a columnar, or palisade, parenchyma - the main assimilation tissue in which photosynthesis processes are carried out.
Beneath the palisade parenchyma are several layers of cells irregular shape with large intercellular spaces. These layers of cells form a spongy, or loose, parenchyma. Spongy parenchyma cells contain fewer chloroplasts. They perform the functions of transpiration, gas exchange and storage of nutrients.
The flesh of the leaf is permeated with a dense network of veins, vascular-fibrous bundles that supply the leaf with water and substances dissolved in it, as well as remove assimilants from the leaf. In addition, the veins perform a mechanical role. As the veins move away from the base of the leaf and approach them to the top, they become thinner due to branching and gradual loss of mechanical elements, then sieve tubes, and finally tracheids. The smallest branches at the very edge of the leaf usually consist only of tracheids.
Diagram of the structure of a plant leaf The microscopic structure of the leaf blade varies significantly even within the same systematic group of plants, depending on different growth conditions, primarily on lighting conditions and water supply. Plants in shaded places often lack palisade perenchyma. The cells of the assimilation tissue have larger palisades, the concentration of chlorophyll in them is higher than in photophilous plants.
Photosynthesis
In the chloroplasts of the pulp cells (especially the columnar parenchyma), the process of photosynthesis takes place in the light. Its essence lies in the fact that green plants absorb solar energy and create complex organic substances from carbon dioxide and water. This releases free oxygen into the atmosphere.
Organic substances created by green plants are food not only for the plants themselves, but also for animals and humans. Thus, life on earth depends on green plants.
All oxygen contained in the atmosphere is of photosynthetic origin, it accumulates due to the vital activity of green plants and its quantitative content is maintained constant due to photosynthesis (about 21%).
Using carbon dioxide from the atmosphere for the process of photosynthesis, green plants thereby purify the air.
Evaporation of water from leaves (transpiration)
In addition to photosynthesis and gas exchange, the process of transpiration occurs in the leaves - the evaporation of water by the leaves. The stomata play the main role in evaporation, and the entire surface of the leaf also partially takes part in this process. In this regard, stomatal transpiration and cuticular transpiration are distinguished - through the surface of the cuticle covering the leaf epidermis. Cuticular transpiration is much less than stomatal: in old leaves, 5-10% of total transpiration, but in young leaves with a thin cuticle, it can reach 40-70%.
Since transpiration is carried out mainly through the stomata, where carbon dioxide also enters for the process of photosynthesis, there is a relationship between the evaporation of water and the accumulation of dry matter in the plant. The amount of water that a plant evaporates to build 1g of dry matter is called transpiration coefficient. Its value ranges from 30 to 1000 and depends on the growth conditions, type and variety of plants.
The plant uses an average of 0.2% of the passed water to build its body, the rest is spent on thermoregulation and transport of minerals.
Transpiration creates a suction force in the cell of the leaf and root, thereby maintaining the constant movement of water throughout the plant. In this regard, the leaves are called the upper water pump, in contrast to the root system - the lower water pump, which pumps water into the plant.
Evaporation protects the leaves from overheating, which has great importance for all life processes of a plant, especially photosynthesis.
Plants in dry places, as well as in dry weather, evaporate more water than in conditions of high humidity. Evaporation of water, except for stomata, is regulated by protective formations on the skin of the leaf. These formations are: cuticle, wax coating, pubescence from various hairs, etc. In succulent plants, the leaf turns into spines (cacti), and the stem performs its functions. Plants of wet habitats have large leaf blades, there are no protective formations on the skin.
Transpiration is the mechanism by which water is evaporated from the leaves of a plant. With difficult evaporation in plants, guttation- the release of water through the stomata in a drop-liquid state. This phenomenon occurs in nature usually in the morning, when the air approaches saturation with water vapor, or before rain. Under laboratory conditions, guttation can be observed by covering young wheat seedlings with glass caps. After a short time, droplets of liquid appear on the tips of their leaves.
Isolation system - leaf fall (leaf fall)
The biological adaptation of plants to protection from evaporation is leaf fall - a massive fall of leaves in the cold or hot season. In temperate zones, trees shed their leaves for the winter when the roots cannot supply water from the frozen soil and frost dries out the plant. In the tropics, leaf fall is observed during the dry season.
Preparation for shedding leaves begins with a weakening of the intensity of life processes in late summer - early autumn. First of all, chlorophyll is destroyed, other pigments (carotene and xanthophyll) last longer and give the leaves an autumn color. Then, at the base of the leaf petiole, parenchymal cells begin to divide and form a separating layer. After that, the leaf comes off, and a trace remains on the stem - a leaf scar. By the time of leaf fall, the leaves are aging, unnecessary metabolic products accumulate in them, which are removed from the plant along with the fallen leaves.
All plants (usually trees and shrubs, less commonly herbs) are divided into deciduous and evergreen. In deciduous leaves develop during one growing season. Every year, with the onset of adverse conditions, they fall. Leaves of evergreen plants live from 1 to 15 years. The death of part of the old and the appearance of new leaves occurs constantly, the tree seems evergreen (coniferous, citrus).
