GUIDELINES FOR BIOLOGICAL MODELS

EQUILIBRIUM IN ECOSYSTEMS

Algorithm of the virtual laboratory

The virtual laboratory Equilibrium in Ecosystems was designed for modeling processes in ecosystems to study the basic principles of ecology. Virtual ecosystems contain an environment including different habitats, renewable food resources and several levels of consumers, which are able to exchange energy. Models created in this laboratory can be used to study predation, competition between species, maintaining biodiversity in biological communities, and population biology. The principle of cellular automata is used in modeling virtual ecosystems.

Components of virtual ecosystems

• Field – a segment of the territory inhabited by a community of species.
• Landscapes of various types, distributed on the field. The landscapes can have different rates of revegetation, water regime, intensity of disruptions, and permeability for various species.
• Renewable resources (water, plants).
• Species of plants (producers), herbivorous and carnivorous animals (consumers) with certain types of specific features.
• Reducers, which convert dead organic matter into inorganic.
• Catastrophes – disruptions, which exterminate a part of the population species.

Basic rules

Virtual organisms created in BioKit are able to move across their habitat, feed and reproduce. They expend energy to sustain life, reproduce, and lose weight. If the body mass of an individual reaches a critical point, the organism dies. Therefore, living creatures need to feed regularly in order to sustain life. Plants consume water and synthetize organic substances themselves using the energy of sunlight; herbivorous animal species feed on plants; predators catch other animals and/or eat carrion (however, carrion loses nutrients with time due to decomposition).

Resources

Water is the only regulated resource consumed by the producer plants. Plants are the food resource for herbivorous animals which in turn are food for predators.

Water is renewed in field cells at specific time intervals. The same algorithm is applied in many models for the regeneration of vegetation.

An individual can consume only the resource available in the same field cell where the individual is located. All types of food resources have identical caloric values.

Digestion efficiency

Digestion rate of the consumed resource can be calculated via the formula: mass of the digested resource = mass of the consumed resource * digestion rate.

A plant with 60% water digestion rate forms 0.6 kg of nutrients after consumption of 1 kg of water; a predator with 90% digestion rate will obtain 0.9 kg of nutrients after eating 1 kg of meat.

Usage of nutrients

All digested resources are transformed into nutrients. These nutrients are used in the following sequence:

1. sustaining body mass;
2. growth of young individuals' body mass;
3. growth of embryo mass in mature pregnant individuals;
4. relocation;
5. increase of nutrient reserves.

If the quantity of digested resources satisfies all needs, and the mass of nutrient reserves achieved the maximum possible rates, then consumption of the resource will be stopped.

In case of resource insufficiency, the organism first uses available nutrients for obligatory needs: sustaining body mass, and growth of body mass (in the young). If the amount of resources is not sufficient for obligatory needs, the individual uses its nutrient reserves; if it is too small, the individual will die.

Specialization. Probability of consumption

In the laboratory, it is possible to regulate the frequency of successful hunts for predators, and control the food preferences for herbivorous animals. A predator with 100%-successful hunting (probability of consumption) kills its prey every time; a predator with 50%-probability of consumption will leave its prey alive in 50% of cases. A predator can be easily transformed into a scavenger by setting a zero probability of successful hunts. Herbivorous animals show their consumption probability via preferring one kind of plant to others. A “picky” grass-eater will usually eat the most preferred grass species – the one with the top consumption probability.

Lifespan and life cycle

The following features have been pre-set for each species:

1. Lifecycle parameters – lifespan, age of maturity, time of forming offspring, maximal amount of offspring (for plants it also includes time of seed germination). The time in the laboratory is measured in time units.
2. Size parameters, i.e. parameters of mass: minimal mass for an adult species, minimal mass for offspring, allowable mass of nutrient reserves and initial nutrient reserves in offspring. The species will die if its mass falls below the minimal allowable mass.

All created species of animals and plants comply with the same laws of growth and reproduction. Only asexual reproduction is modeled. When a species is being created and placed onto a field, the population has individuals of various age and reproductive status.

Spatial distribution and translocation of organisms

Individuals that belong to a single species cannot occupy the same field cell in most cases due to the intraspecific territorialism.

Animals move in a specific way: they go to the field cell with the highest available food resources.

1

Prey and predator

The first model is a simple task showing the connections between ecosystem components. The virtual environment includes grass plants that are a renewable resource, a population of sheep (herbivorous animals) and a population of wolves (predators). Sheep feed on plants, whereas wolves hunt sheep. If the parameters of the species are balanced, all these components form a stable biological community.

HOW TO PERFORM A TASK

Initially, predators can not survive with the existing population of the herbivores due to the low efficiency of the predators and low biomass and density of the herbivores. To form a stable prey-predator system, you should 1) increase the digestion rate of grass by the herbivores to allow them to reach high body mass 2) increase the efficiency of predator hunting. Under these conditions, the prey population will be able to support the existence of the predators. In the stable system, the interrelated fluctuations in the quantity of predators and herbivores will be observed.

DISCUSSION

This task is useful to study a wide-known Lotka-Volterra mathematical model of the relation between the quantities of predators and prey. In this model, the diagrams of predator and prey quantities show harmonic oscillations phase-shifted against each other.

Unlike the continuous Lotka-Volterra model, which is a system of differential equations, this task deals with a different way of simulating the interrelation between predator and prey – with the help of cellular automata. The fluctuations, obtained in the course of the experiment, are not always harmonic due to a few reasons:

• fluctuations are influenced by “seasonal” processes in the created populations (periods of reproduction, maturity, etc.);
• the same system experiences fluctuations in the number of plants and herbivorous animals;
• small territory and population of species, and restrictions of animal distribution can lead to accidental, non-targeted deviations of population numbers.

The discussion can include the analysis of real indicators of predator hunting efficiency in the wild. Thus, according to some estimates, cheetahs and leopards have a 40% hunting efficiency, single lions – 15%, a group of 7 lions – 50%, a pack of hyenas – 60-80%. It can also be useful to discuss the development of predator-prey interrelations in the context of evolution, and show examples of predator-prey co-evolution.

2

Shelters

The model is devoted to prey-predator relationships. It shows how stability of the predator-prey system can depend on the availability of shelters for prey in their environment. If the task is solved correctly, you can observe a stable biological community, including plants, herbivorous animals, and predators. In this case adding shelters for herbivorous animals in the environment is needed to form a stable ecosystem.

HOW TO PERFORM A TASK

Initially, predators and prey are not able to co-exist for an extended period, since predators exterminate almost all prey and then begin to starve.

However, the system can be made stable by introducing two types of habitats and making one of them inaccessible for predators (but accessible for the herbivores).

Schemes needed are shown on the pictures below. Brown and orange areas are not accessible for predators though accessible for the herbivores – they serve as shelters for them. Green areas are accessible for both species.

It makes no sense to create an island with three habitats of different accessibility.

DISCUSSION

While discussing the model it might be interesting to remember Gause’s attempts of creating a stable predator-prey system in a laboratory environment. Gause conducted experiments with two species of infusoria – predators and prey. Predator infusoria grew in numbers very fast and ate all prey infusoria; then they died out themselves. In order to extend the period of their co-existence, the researcher had to build shelters for prey using cotton wool. Thus, availability of shelters for prey in the environment can increase the stability of multi-species systems.

3

Food chain

The model is constructed for multispecies communities and the law of the ecological pyramid. If the task is solved correctly you can observe a stable community, which includes plants, herbivorous animals (first-order consumers), predators that hunt the herbivorous animals (second-order consumers), and other predators, which hunt the first predator species (third-order consumers). In accordance with the law of the ecological pyramid, the biomass of first-order consumers is significantly greater than the biomass of second-order consumers, which is in its turn higher than the biomass of third-order consumers.

The level of difficulty is higher for this assignment than it was for the previous ones; fulfillment of this assignment may require more time.

HOW TO PERFORM A TASK

The task involves constructing a stable system and including as many species as possible. It is allowed to introduce two herbivorous and two predator species.

When you first try to solve the task, you usually think of creating a four-species community where different predators hunt for different herbivorous species. However, you soon realize that Blue herbivores cannot survive even in the most favorable habitat due to the extremely low resource digestibility. Therefore, it is impossible to create a four-species community.

If you try to create a community, where both predator species hunt for White herbivores, the system turns out to be unstable. On the brown landscape the Red exterminate the herbivores too intensively; on the red landscape, the density of the herbivores is low resulting in a gradual extinction.

At the same time, in the absence of Red predators Black predators can usually co-exist with White herbivores on the brown landscape, though with significant fluctuations of population numbers. Therefore, Red predators can be turned into third-order consumers and added into the system.

If the task is solved correctly, three species can co-exist on the brown landscape rich in vegetation – White herbivores, Black predators, which hunt for White herbivores, and Red predators hunting for the Black ones only. A correct solution of the assignment is provided below. The number of herbivores should not be low in the beginning of the experiment.

DISCUSSION

The model shows the law of the ecological pyramid. The diagram shows that the number of first-order consumers is significantly greater than the number of second-order consumers, which is in its turn higher than the number of third-order consumers. If we open the model in BioKit and look at the mass of adult herbivores and predators in the laboratory editor “Equilibrium in ecosystems”, we will see that they are identical. Thus, we can assert that the biomass of third-order consumers is the smallest, and the biomass of first-order consumers is the highest. This fact complies with the law of the ecological pyramid where the biomass of the species from the chosen trophic level always exceeds the biomass of the following, higher level. It is considered that the biomass decreases by approximately 10 times during transition between the levels. This computer model does not show a very dramatic difference between the levels; however, it is obvious enough.

It is also important that only the habitat rich in the primary products can sustain a community of three tropic levels of consumers. This fact complies with the idea that resourcefulness of a habitat can affect the number of species in its communities.

4

Auto-oscillations

This model shows a self-organizing auto-oscillating system. A population of herbivorous animals is able to sustain itself on the island covered with plants that are the renewable food resource for the animals. The events that occur in the virtual ecosystem visually remind us of the Belousov-Zhabotinsky chemical reaction – the population of herbivorous animals forms the fascinating spiral spatial structures on a virtual island.

HOW TO PERFORM A TASK

In the task, you can inhabit a virtual territory with predators and herbivorous animals. Introduction of the herbivorous animals only will (in most cases) result in population extinction after the experiment has been started – the herbivores expand rapidly, capable of eating the entire food resources and die out before these resources have a chance to regenerate. Introduction of both predator and herbivorous animals makes it possible to provide for an unlimited existence of the herbivores (however, you should create an appropriate distribution of the predators and prey in the beginning of the experiment).

The system remains stable even if predators are removed from the system in the course of the experiment: the prey population will stabilize the spiral spatial structures in time. Thus, external influence on the system in the very beginning can lead to the establishment of a very stable auto-oscillating system.

DISCUSSION

Oscillation (fluctuation) is a process repeated in time. Auto-oscillations are sustained by energy from external sources; however, their parameters (amplitude, frequency) are defined by external properties of the system per se. In this model, the fluctuations of the herbivorous population numbers are caused by the continuous growth of green vegetation (it serves as a source of energy for sustaining the herbivorous population); but the character of the fluctuations is defined by the properties of the population.

Transfer of the system into the auto-oscillation mode is a good example of self-organization and stability of the system. Self-organization is an important property of living matter. Auto-wave processes are typical of many biological phenomena: nerve impulses, brain waves, muscle excitation waves, tissue differentiation and, obviously, ecosystem dynamics.

5

Ecological niches

This model shows a stable co-existence of species with separated ecological niches. If the task is solved correctly, the resulting virtual ecosystem will include two types of habitats with two different plant species and two species of herbivorous animals which differ in their feeding preferences.

HOW TO PERFORM A TASK

Initially, two herbivorous species are introduced into the territory with three plant species, where the animals compete for food. After the experiment has been launched, one plant species – wheat grass – being the strongest competitor, pushes out the others. The herbivores – donkeys and sheep – start competing for the wheat grass, which they consume with similar efficiency. With time, one of the herbivorous species will be pushed out by the other.

In order to ensure a stable co-existence of the herbivorous species, you need to separate their realized ecological niches. Wheat grass has to be removed from the plants, leaving blue grass and thistle. Since donkeys prefer thistle, and sheep mostly eat blue grass, these two species can stably co-exist on the condition that both plant species will grow on the territory.

Blue grass gradually pushes out thistle in the wet green landscape; the opposite situation is typical of the desert landscape.

Therefore, in order to solve the task successfully, you have to select a territory with equal sizes of both types of landscape, and plant this territory with blue grass and thistle. Then, sheep and donkeys will be able to co-exist for the required period of time.

DISCUSSION

Mosaic habitats can sustain the existence of more species than homogenous habitats. Mosaic habitats can provide possibilities for the specializations of different species, and their adaptation to various conditions. Thus, the forests with various tiered distribution of foliage house a greater species variety of nesting birds (MacArthur, MacArthur, 1961).

6

Cyclic succession

This model illustrates succession – a subsequent natural replacement of a vegetation community on the territory (the term succession is used mostly to describe the phytocoenosis changes, though it is applicable not only to the plants). If the task of the model is solved correctly, we can observe the disruption (the herbivores eat all the plants on the island); then, the grassless area becomes covered with one plant species, subsequently replaced with another species that results in a new disruption. That is how you can model a cyclic succession on a virtual island.

The task can turn out to be too complicated for independent work. It can be assigned as an additional task or the model can be used in demonstration mode.

HOW TO PERFORM A TASK

During initial conditions, all types of landscapes are passable and penetrable for the plants and animals in the habitat. Therefore, if you try to plant Brown island with Yellow and Violet grasses, the sheep will soon completely eat all of the Yellow grasses.

In order to protect the Yellow grasses from sheep, they can be distributed around the Red islands (which should be unavailable for other species). In order to prevent the Green and Violet grasses from replacing each other, you can for example confine Violet grasses to Brown island, and Green grasses to the Yellow continent.

Then, after the experiment has been launched, we can observe a continuous replacement of plant species on Brown island: first, it will be covered with fast-reproducing Violet grasses, then, with more competitive Yellow grasses. Later, the sheep coming from the continent will destroy the vegetation by eating all of the Yellow grasses.

DISCUSSION

There are two types of succession: primary and secondary. Primary succession occurs when a lifeless territory is inhabited “from scratch” – for example, the lava, which solidifies after a volcano eruption. Secondary succession is more common – re-vegetation of a fire-site or logging area.

Usually, community succession results in a stable (so-called “climax”) community – for example, of a bottomland hardwood forest or a wood sorrel spruce forest. However, there can be communities with cyclic succession: phytocoenosis of the final stage contains prerequisites for disruptions. A well-known example of it is a pyrogenic succession in a unique community, called chaparral – a perennial scrubland plant community that is well adjusted to endure droughts and fires. In other cases, scrub vegetation is replaced by the communities where trees prevail and the situation is quite different. Dry climate on a territory covered with shrubs results in high chances of fires, which happen once every few decades. Fires prevent the formation of tree communities; however, grass plants and shrubs regenerate after fires quickly since local plants are well adjusted to such disruptions (Odum, 1986).

PRINCIPLES OF EVOLUTION THEORY

7

Labyrinth

This model is devoted to the founder effect and the effect of the bottleneck. If the task is solved correctly, you can observe that genetic diversity of the virtual population is reduced dramatically when animals occupy new areas.

HOW TO PERFORM A TASK

A population of variously colored virtual animals called birgs has been placed into an enclosed section of the labyrinth. You have to choose the labyrinth variant where the central section will be inhabited by genetically homogenous individuals of the same color.

The picture shows a correct choice.

DISCUSSION

The founder and the bottleneck effects lead to reduced genetic diversity of populations and make them less adapted to the environment. Thus, cheetahs, a famous example of the bottleneck effect, have an extremely low genetic diversity and reduced viability.

It may also be interesting to mention that the founder effect played a major role in the formation of some human ethnic groups (e.g. the Ainu).

8

Protective coloration

There is an introductory model, devoted to the natural selection and development of protective coloration. The experiment simulates the influence of predators on the virtual population. This results in the predominant survival of individuals with protective coloration.

Unlike the ecological models, here predators, which hunt for the species, are not depicted on the field.

HOW TO PERFORM A TASK

The task is to prevent the population from extinction and to ensure that the animals change their coloration similar to the color of the environment (protective coloration). A user can change the initial quantity of the animals, control the behavior of predators, and the color of the habitat.

During initial conditions, the predators have the same influence on the prey regardless of their coloration. Besides, the initial quantity of the population is very low. A small amount of individuals can lack the necessary alleles of color. In this case, the camouflage coloration will not be adjusted during the experiment.

In order to adjust the coloration of the population to the color of the habitat, it is necessary to make sure that the predator influence is stronger on the contrasting (more visible) animals, and weaker on the inconspicuous (non-contrast) animals; the initial amount of the group should also be set relatively high. If you also reduce the period between the predator attacks, then the camouflage coloring will be developed faster.

Thus, the following parameters help the population adjust their coloration to the non-homogenous or homogenous environment during about 1000-1500 time units:

• predator pressure: attacks every 10 time units;
• predators kill 80-100% of the animals with coloration contrasting the environment,
  and 0-10% of the animals with color identical to the color of the environment (non-contrast);
• initial number of individuals: 1600.

The habitat color does not have to be changed for achieving the target. However, the students can make sure that development of protective coloration is possible in habitats of various colors.

DISCUSSION

Protective coloration as an evolutionary effect of predation is widespread in the animal world. The protective coloration is common not only among prey species, but among predators as well since they have to be able to sneak upon their prey unnoticed.

In the experiment, success of adaptability depends on the presence of the necessary color alleles in the initial population. The population, which starts with 20 individuals, will most probably fail to develop the coloration that would allow them to blend in with the environment. A bigger population will provide for many alleles of the color genes; this genetic variability will result in successful development of almost any protective coloration.

9

Survival of the fittest

This model is devoted to natural selection. In this experimental setup, certain features of the species, being neutral or even useful in some conditions, turn harmful when these conditions change, and become eliminated from the population by natural selection. The initial population of virtual animals has eyeless and legless individuals, but if the task is solved correctly, predator pressure leads to elimination of such traits.

HOW TO PERFORM A TASK

In the initial population, the alleles responsible for the organs of vision and motion are as frequent as the alleles of “no eyes” and “no legs”. In order to eliminate the latter two alleles from the population during its evolution, it is necessary to change the conditions to make the ability for directional motion a selective advantage. This situation is possible only in a changeable environment when the animals have to look for areas where they are less noticeable for predators. Those areas are black. Hence, we have to set periodically changing conditions of the environment with a white-black gradient as color 1 and the same gradient but turned to 180° as color 2. Then the animals will have to periodically move from the upper area into the lower area to avoid predators; in the course of evolution only “eyed” and “legged” individuals survive.

DISCUSSION

Evolutionary predation results in substantial changes in both the prey species and predator species. In evolutionary (not ecological) periods of time, preys try to reduce the influence of predators and predators try to increase their hunting efficiency.

One consequence of predation, that we already know, is the development of protective (cryptic) coloration. However, the protective coloration itself is useless if animals do not try to find the areas where they can be inconspicuous. Thus, the process of evolution brings the development of cryptic behavior: individuals make themselves motionless in order not to be noticed, they take certain shapes, or rapidly move to areas where they are less noticeable to predators.

Predators contribute to the sanitation of the prey population by hunting weak and sick animals. Thus, the undesired alleles, which carry harmful features, are eliminated from the population.

At the same time, intensive adjustment to a specific environment can lead to the decrease of the populations’ genetic diversity, and, as a result, to unfavorable consequences.

10

Sexual dimorphism

This model is devoted to the role of sexual selection in the process of evolution and to the phenomenon of sexual dimorphism. If the task is solved correctly, sexual dimorphism is developed in the virtual population: females become less conspicuous (protective-colored), whereas males become more conspicuous.

HOW TO PERFORM A TASK

A green area of the habitat is populated with multicolored organisms belonging to a single species. They have three coloring genes; gene H is responsible for a hue, gene S - for saturation, gene L - for lightness. A lightness gene L is situated in the Y-chromosome and is present in males only. This gene has three alleles (l0, l50, l100) in this model; allele l0 is responsible for the black color, allele l50 is responsible for intermediary lightness (its carriers can be grey or multicolored), allele l100 is responsible for the white color. Thus females can be grey or colorful, males - black, white, grey or colorful.

In this task, the conditions have to be changed to make it possible for the females to develop green coloring, and for the males to become black in the process of evolution.

While working with the completed model, it is not necessary to know what genes and alleles exist in the population. In order to solve the first task, it is necessary to pre-set the direction of sexual selection in order to ensure that the females would prefer black males. In addition to that, the influence of predators has to be higher for contrast-colored animals than for cryptically colored (non-contrast) ones.

The following parameters of the population in most cases provide for the gradual increase of the black males percentage; the females adjust their color to the color of the environment:

• predator pressure: attacks every 40 time units;
• predators kill of 60% of the animals with coloration contrasting the environment,
  and 5% of the animals with color identical to the color of the environment (non-contrast);
• number of individuals: 400;
• coloring of “attractive” males: black is the pre-set color, the females prefer most males with color similar to the black color.

With these parameters, in about 1000-2000 days the population will mostly consist of green females and black males.

In order to solve the second task (in essence, it involves development of protective camouflage) it is enough to change the predator influence only. It is also possible to have the females prefer the green males.

Possible parameters:

• predator pressure: attacks every 40 time units;
• predators kill of 60% of the animals with coloration contrasting the environment,
  and 5% of the animals with color identical to the color of the environment;
• number of individuals: 400;
• the attractive color: not specified.

With these parameters, the population will consist of primarily green females and males in about 1000 days.

DISCUSSION

After solving the task of developing protective coloration in the previous model “Protective coloration”, a reasonable question may arise: if it is so advantageous to be inconspicuous for both prey and predators, then why is bright coloring so common among many species? Sexual selection can prevent the protective coloration from spreading: many species show higher preference of brighter and more noticeable males to less noticeable ones with plain coloring. Sexual selection is a powerful evolution factor, as you can see in the model.

Development of sexual dimorphism is thought to be directly connected to different involvement of different genders in nurturing the offspring. Females of many species are more involved in offspring nurturing than their males. Females more often have the right of selecting a mating partner. Therefore, the process of evolution leads to sexual dimorphism: males develop brighter colors, and females became less conspicuous in order to nurture their offspring safely.

In the case of birds, we see a dependence of the degree of sexual dimorphism on the level of offspring nurturing. Thus, wood grouses have a high sexual dimorphism and, consequently, females take care of their offspring. On the other hand, in the case of the blackcap, males and females have similar colorings and both participate in offspring nurturing.

11

Heterozygosis

This model is devoted to inbreeding – a factor, which reduces the genetic diversity of a population. When the rate of interbreeding (mating between close relatives) increases, the amount of heterozygous individuals in the population is reduced. One of the ways to increase the rate of interbreeding is to restrict mobility of individuals.

HOW TO PERFORM A TASK

The experimental setup involves studying how the level of dispersion of organisms can influence the level of their genetic variability. Students have to compare the relative frequency of heterozygotes in a population where all individuals are constantly on the move, and in a population of non-motile individuals. The level of genetic diversity is lower in the population of non-motile individuals since interbreeding there occurs among neighbors, which are often closely related.

In order to compare the heterozygote frequency in motile and non-motile groups, it is necessary to be able to change the genotypes of the virtual animals. According to the task conditions, the population includes red and green individuals. To ensure the motility of all individuals and their offspring, you have to select the alleles MM for the first and second genotypes of the population. To ensure the non-motility of the individuals and their offspring, the alleles mm should be selected.

After the experiment has been launched, it turns out that in the case of motility, the relative share of yellow animals (heterozygotes on coloring gene) is higher than in the case of non-motility. Multiple runs of the experiment can confirm this.

If the animals are motile, then within 200 time-units after the launch of the experiment they normally distribute around the area more or less evenly (however, overpopulation reduces the frequency of heterozygotes below 50% - which is expected in accordance with the Hardy-Weinberg principle).

If the individuals are non-motile, local agglomerations of homozygote animals are formed. The heterozygotes frequency is lower due to the high frequency of interbreeding among closely related animals.

This regularity also can be observed when only yellow individuals inhabit the field in the beginning of the simulation.

Thus, the conclusion can be made that reduction of the level of dispersion leads to a lower level of the heterozygosis in a population.

Distribution of motile organisms:

Distribution of non-motile organisms:

DISCUSSION

Non-motility, restricted mating, restricted distribution (interbreeding only among neighboring animals, relocation of individuals only to the neighboring cells of the field) result in the higher frequency of inbreeding and, consequently, to the higher homozygosis of the population.

A high level of homozygosis of the population is considered an unfavorable feature, which reduces the stability of the population and its chances for survival. Cheetahs are a typical example of a species with a high level of homozygosis: different species are so genetically close to each other, that skin transplants between them (non-relatives) are not rejected. Cheetahs have a very low level of offspring survivability, which is directly related to high homozygosis, including that of undesired alleles.

12

Types of reproduction

This model shows the advantage of sexual reproduction over asexual reproduction. Novel combinations of alleles result in revealing new traits in offspring, which may be useful in current conditions. Therefore, sexual reproduction allows a population to adapt to a changing environment. If the task is solved correctly, you can see the appearance of individuals with novel bright coloration in an initial population.

HOW TO PERFORM A TASK

In the task, a multicolored area is inhabited with individuals of the same species. They have a pre-set coloring, which is inherited. Every individual carries a gene of a coloring hue (responsible for development of red, yellow, blue, green, cyan or violet coloring); however in most cases the coloring is not revealed due to the influence of other genes.

The task calls for changing the initial conditions in order to have the population develop and maintain their types of coloring. This would ensure a high similarity to a multicolored environment.

In order to develop protective coloration, you can inhabit the environment with the predators that will hunt the most conspicuous prey. In the process of evolution, the population will gradually adjust to the environment – the animals will develop protective coloration.

During initial conditions, animals reproduce via asexual reproduction (monogenesis), and fail to achieve a close similarity to the color of the environment (initially, the population has no individuals of required colorings). The required degree of similarity can be reached by changing the type of reproduction into a sexual reproduction (gamogenesis). In the case of sexual reproduction, the recombination of the alleles will lead to the birth of brightly colored individuals, which will occupy the areas of corresponding colors.

DISCUSSION

Asexual reproduction allows the species to reproduce faster without spending time searching for a mating partner, thus turning it into an advantage in certain conditions. However, asexual reproduction makes the offspring genetically identical to the parent, and limits the ability of the population to inhabit new areas. Sexual reproduction provides for the recombination of parent gene pools; the offspring carry unique sets of features, which can be adaptive. Therefore, sexual reproduction, unlike the asexual one, provides for the wide range of possibilities for adjustment to a changing environment and spreading to new habitats.

13

Taking over territory

This model shows the effect of population quantity in interspecies competition. Two species that compete for the territory interact with each other. A species which occupies the area first, will effectively prevent the other species to take the same territory – even in cases when the other species is better adapted to the environment.

HOW TO PERFORM A TASK

The area is inhabited by two species with different coloring (red and yellow). Initially, they occupy the areas which they are mostly adjusted to. Predators eat the most conspicuous animals; that is why a red habitat is most suitable for the red species, and yellow areas – for the yellow species.

Besides, the habitat has areas of orange color which initially is not taken by any species. The red and yellow species are equally adjusted to this environment.

After the launch of the experiment, you can see that both red and yellow animals try to occupy the orange hills. However, two species cannot inhabit the same hill for a long time. The winner is the species, which was the first to occupy a new area and achieved high numbers before coming into contact with the other species. Thus the size of the population plays a major role in suppressing the competitor.

In order to help one species occupy two orange hills, you need to choose a landscape where these hills are closer to the initial habitat of this species.

When the red area is inhabited with the yellow species, and the yellow one – with the red species, the populations prevent the fittest species from taking over the territory for a long time. Thus, the effect of the initial population size is quite significant in the interspecies competition.

DISCUSSION

The advantage of the species, which was the first to take over the territory, is shown in the experiment with Bromus plants – Bromus rigidus and Bromus madriensis. When two grass plant species were planted on the available territory simultaneously, the lead was taken by Bromus rigidus; however, Bromus madriensis, if planted first, took over the competitor (Begon, Harper, Townsend, 1989).

EVOLUTIONARY STABLE STRATEGIES

14

Fighting for food

This is a simple introductory model, developed for learning to work in experimental setups of the laboratory “Evolutionary stable strategies”. Virtual territory is inhabited by aggressive and cowardly animals that belong to one species. They compete for food, mate and reproduce. Aggressive animals always fight for food, cowardly animals yield their food to their competitors. In an experiment you can see that only one of these strategies, the one that is more successful than the other, remains in the population after some period of time. Such a strategy is called «evolutionary stable».

HOW TO PERFORM A TASK

There are representatives of only two behavior strategies on the field. Aggressive animals always fight for food, while cowardly animals always yield their food to their competitors. The individuals with different strategies belong to the same species and can mate. Behavior strategies are inherited: an offspring's strategy matches the strategy of one of the parents.

In the course of evolution, aggressive individuals begin to prevail by suppressing the coward individuals until extinction. In this case, the initial proportion of numbers does not determine the success of aggressive strategy: even if there are fewer aggressors in the beginning of the experiment, their strategies eventually help them win.

DISCUSSION

Using this model, you can introduce the concept of an evolutionary stable strategy – a behavior that prevents other types of behavior from developing in this population. In this case, the strategy of aggressors appears evolutionary stable – the only other possible strategy – cowards – can neither spread in the population nor sustain its numbers.

It is also useful to introduce a concept of reproductive success. In this situation, one strategy pushes out the other, since the individuals with this behavioral strategy get better food and reproduce more often than others. That is why only the animals with a more successful strategy remain in the population in the course of evolution.

Pay attention to the way to define the behavioral strategy. When a user creates animals with a specific strategy, he needs to answer the following questions: “Whether to start a fight?”, “Whether to accept a fight?”. The mark “+” means “yes”, the mark “-“ means “no”, a “?” – means “not defined”. Aggressors both initiate fights and take them; cowards never initiate fights and never take them. Thus, fights occur when two aggressors meet; when an aggressor meets a coward, no fight happens, but the aggressor wins the conflict and takes over the food; when two cowards meet, the food is distributed at random to one of them.

After completing the main task, you can optionally change the behavioral strategies of virtual animals and learn how their behavior will change in this case. For example, if you change the strategy of cowards with the strategy “I never initiate fights but will take them”, then the green animals with this strategy will push out the red aggressors. A possibility of changing the strategies allows learning to control the behavior of virtual animals.

It is better not to use question marks while changing the strategies in the tasks, since in this case the user will not know the behavior of the animals.

15

Repulsing aggressors

This model illustrates the possibility of successful co-existence between animals of different behavioral strategies. In this case, none of the strategies is evolutionary stable.

The population includes representatives of different behavioral strategies. Initially, aggressors enter the territory of cowards and exterminate them. By changing the landscape of the habitat, you can place individuals with different behaviors with the cowards and see what strategy helps the cowards to survive after the aggressors' invasion.

HOW TO PERFORM A TASK

The successful strategy is the strategy of peaceful animals which never initiate conflicts by trying to take over food from their neighbors. However, if anybody tries to take their food, they are able to resist. In these circumstances, the strategy of peaceful animals will be more successful than the strategy of aggressors.

The cowards can live undisturbed and reproduce among the peaceful animals in the population: in the absence of aggressors, both peaceful and coward individuals exhibit similar behavior and have no advantage over each other. There are no fights; any of the two animals in the cell can acquire food.

While conducting the experiment, you can see that the strategy of cunning individuals turns out to be the second successful strategy, which provides for a numerical advantage over aggressors (cunning individuals fight only with smaller animals when they have more chances to win). However, the cowards cannot survive together with the cunning animals and rapidly die out.

DISCUSSION

The model shows the possibility of co-existence of different behavioral strategies in the population.

A behavioral strategy does not necessarily prevail and remain resistant to other strategies (evolutionary stable). Quite often, several behavioral strategies remain and co-exist in the course of evolution.

In this task, the final proportion of cowards and peaceful animals depends on their proportion at the time of elimination of aggressors from the population (so that the behavior of cowards and peaceful animals becomes similar).

Absence of the single evolutionary stable behavioral strategy reflects the principle of behavioral heterogeneity of the individuals in the population. In the wild, representatives of the same population can have completely different forms of behavior in similar situations (for example, rats can be either aggressive or friendly; show curiosity about new objects or avoid them; perform an active search for a solution or passively wait in a problem situation, etc.)

In this task, you should pay attention to the fact that the success of a behavioral strategy is determined both by external conditions of the environment and by the presence of different strategies in the population.

You can see that if you observed a mixed population of cowards and peaceful animals for a rather long time period, then at some point, one of the strategies (either peaceful, or cowardly animals) will push out the others. It can be explained by the genetic drift in a small population. Random fluctuations in numbers can lead to the elimination of a strategy even if it does not yield to the others.

16

Environmental conditions

The model shows that success of a behavioral strategy depends on environmental conditions. Environmental conditions can be either “external” for the population – for example availability and distribution of food on the territory, or “internal” – the presence of a species with different behavioral strategies.

In initial conditions, several isolated groups of animals, which follow different strategies, inhabit the area. After launching the experiment, the aggressive group dies out very fast. If the task is solved correctly, aggressors can live and prosper for a very long time.

HOW TO PERFORM A TASK

In order for the aggressors to survive, it is possible to take one of the following steps: a) to increase the amount of food available in field cells; b) to decrease the cost of fighting by making them less slaughterous; c) to combine the areas of aggressive and bully or cowardly individuals. Though the group of aggressors is not able to sustain its existence in isolation for a long time, they feel comfortable among cowards and bully individuals. Thus, one strategy can support a different behavioral strategy in a population.

It has to be explained to the students how to find better solutions of the tasks. They can achieve their goals by changing one of the parameters available. In order to look for a different solution, they have to go back to the initial conditions of the assignment by refreshing the page in their browser.

DISCUSSION

During discussion, it is possible to emphasize that some behavioral variants can exist in a population only thanks to other variants.

After performing the assignment, the possibility of competition for resources in natural conditions, the manifestation of this competition, and the nature of resources have to be discussed. Intra-specious competition for food, territory and mates can often be observed in wild nature. Suggest the students to remember how the competing species behave: they use different threatening postures; resort to different fighting techniques; show submission to a rival after losing a fight, etc. Behavior in intra-species competition is often ritual. It is important that even strong competition for food or mating rarely leads to serious clashes between rivals. The conflicts are often almost bloodless: one of the rivals retreats after expressing a threat without engaging in real fighting. It does not necessarily show dissimulation – the animal can yield the resource to its rival after admitting its victory in a bloodless fight. This model explains how similar forms of behavior might have developed: the strategy of aggressors turns out inefficient if they engage in fighting that will cost a lot of energy.

While performing the task, the students can notice that in previous assignments the aggressors exterminated the cowards. Suggest the students to create the same situation in this model. In order to achieve that, they can, for example, reduce the cost of fights to a single point and place the aggressors with the cowards.

They also can create an opposite situation when cowards defeat aggressors. When the food quantity goes up to 30, the cowards, which avoid fighting, slowly push the aggressors out of the population. Therefore, the success and stability of a behavioral strategy depend on environmental conditions.

17

Rock-scissors-paper

This model shows a stable co-existence of three behavioral strategies in the same population. After the experiment has been launched, you can see that bullies, cunning animals, and aggressors can co-exist for an indefinitely long time. Their interactions between strategies (based on the principle of “rock, scissors, paper”) can be revealed while working with the model.

HOW TO PERFORM A TASK

If you perform paired introductions of strategies, you can notice that:

• cunning animals always push out aggressors;
• bullies always push out cunning animals;
• aggressors prevail in numbers over the bullies (although they do not push them out completely).

Thus, the interaction of strategies is similar to the system of winning in the game “rock, scissors, paper”. When three strategies are included into the population, their numbers become interrelated: an increase in the number of cunning animals will lead to an increase of bullies, and, as a consequence, to an increase in the number of aggressors.

DISCUSSION

Species heterogeneity is typical of natural populations. It also concerns behavior; for example, rats, great tits, and finches: some animals behave actively and fearlessly in similar situations, others behave passively and carefully, displaying a fear of new objects and phenomena. The diversity of behavioral strategies can be attributed to the absence of a single evolutionary stable variant. A principle of “rock, scissors, paper” can be one of the mechanisms of sustaining this diversity.

18

Hunting together

This model is devoted to the phenomenon, which is known in social biology as “a prisoner’s dilemma”. The dilemma is that interaction of population representatives with different strategies can result in an evolutionary stable strategy, which fails to ensure the maximum possible profit (after the majority of the population individuals takes it). Thus, the strategy, which is less profitable for the species, pushes out the strategy, which is more profitable for the species.

HOW TO PERFORM A TASK

In the course of this experiment, two animals in the same field cell hunt together and equally share the prey. But some individuals honestly cooperate with their partners, while others (cheaters) deceive them, preferring to pass all hunting responsibilities to the partner.

After the experiment has been launched, the available resources are most efficiently used by the strategy where the animals always cooperate with each other. However, if the landscape is changed and animals with different strategies meet each other, the less efficient strategy of the cheaters prevails.

The “prisoner’s dilemma” calls for the following condition: a deceitful individual gets maximum profit if the other cooperates in hunting; an honest individual gets a little less profit in case of mutual cooperation; mutual deceit brings even less profit, and the least goes to the honest animal, which was deceived during hunting together. These parameters are pre-set in the experiment as initial conditions.

DISCUSSION

During discussion, it is necessary to emphasize that the cheater strategy, which is less profitable for the population as a whole, can push out the strategy of the honest animals, since a maximum award is obtained by the cheater, which interacts with the honest one.

The phenomenon of “prisoner’s dilemma” comes from court cases where the punishment for group crimes is more severe than for the same crime committed by an individual person. Imagine two criminals were detained almost simultaneously for similar offenses. There are reasons to believe that they acted in conspiracy. They are being interrogated separately and offered the following conditions:

• If one criminal gives evidence against the other, and the other keeps silent, then the first one is released for cooperating with the prosecution, while the silent one is sentenced to 10 years in jail.
• If the criminals testify against each other, each of them is sentenced to two years in jail.
• If both of them keep silent, each of them is sentenced to six months in jail.

The third option would be the most optimal solution in terms of “mutual profit”. However, each criminal would consider it more logical to betray his partner: in this case, it’s either freedom or two years in prison. As neither of them knows what his partner will do, they both pursue the strategy of betrayal and testify against each other.

It is important, that in this model the individual does not remember the outcome of the previous encounters with other individuals (i.e. this experiment is identical to the non-iterated “prisoner’s dilemma”). In case animals have multiple contacts with each other and remember the previous behavior of individuals – deceived or cooperated – the award could be given to more complicated strategies (see “Eye for an eye” model).

19

Eye for an eye

This model is devoted to the classic problem of the game theory – “iterated prisoner’s dilemma”. While working with the model, you can see that in the course of multiple interactions the individuals get more profit sticking to the principle of “eye for an eye”: to return evil for evil and good for good.

Initially, a population includes both honest animals and cheaters. The cheaters deceive their partner while hunting together; the honest ones cooperate. After the experiment has been launched, cheaters suppress the strategy of the honest completely. If the task is performed correctly, the addition of animals with the third strategy will defend honest animals.

HOW TO PERFORM A TASK

The honest individuals can be protected by introducing individuals with a fair behavioral strategy. These animals stick to the principle of “eye for an eye”: if their partner previously deceived them, they will deceive him as well; if the partner behaved honestly, they will cooperate. Fair individuals will successfully resist the cheaters and have no influence on the survival of the honest.

DISCUSSION

It may be interesting to discuss the cases in nature, which are considered identical to the iterated prisoner’s dilemma. Thus, vampire bats can regurgitate food, sharing with others whom they recognize individually. Such interactions are multiple. Supposedly, these cases of mutual feeding are identical to the multiple cooperation of the neighboring individuals in the model. Pied flycatchers help their neighbors scare off owls from the nest if their neighbors come to help them in return. This demonstrates the strategy of “eye for an eye”.

PRINCIPLES OF GENETICS AND SELECTION

20

Length of fur

This is an introductory model specially developed for the initial study of the “Principles of genetics and selection” virtual laboratory. It is a classic task to perform a monohybrid cross. A male and a female cat are sitting in the cage. The male cat has long hair and the female cat has short hair. Mating animals and crossing their offspring help to figure out, that short hair is a dominate trait in cats.

HOW TO PERFORM A TASK

On the left hand side of the field, there is a virtual cage divided into several sections. The section of “Breeders” house one male cat (to the left) and one female cat (to the right). The female cats always take the right section of the cage; the male cats take the left side.

The animals can be mated. A double click on each animal will depict the male and female cats in the "Cross" section. You can also simply drag the animal into this section using a mouse.

Below there are buttons to perform virtual crossing. If you place a cursor on the button, you will see a helping hint describing the function of this button.

If you press “Cross”, the offspring kittens will be depicted in the lower section of the cage: the males to the left, the females to the right.

If you press the button “Cross” again, the kittens of the previous interbreeding will disappear and be replaced with the new breed.

The kitten can be dragged with the mouse into the section of “Offspring” or even into the section of “Breeders” if we want to use them later in breeding. Remember: in the section “Breeders” the same cell can be taken by one species only; in the section “Offspring” the same cell can be occupied by animals with the same phenotype.

In order to perform crossings several times it is more convenient to use the button of multiple crossings. One click generates 10 consecutive crossings; the kittens are automatically transferred into the section “Offspring”.

Any selected animal can be deleted by pressing a special button. Besides, there are buttons for a complete cleanup of the “Offspring” section and the button of returning to the initial conditions of the experiment.

The bar chart reflects the numbers of animals of various phenotypes located in the section “Offspring”. The input field below the chart helps to find out which phenotype ratio occurs among the hybrids of the first and second generation. A proper analysis requires: a) all animals in the section “Offspring” should have the same parents; b) the number of offspring has to be sufficiently large.

In this task, the animals in the cage – a female cat and a male cat – have only one difference – the length of the hair, coded by the L-gene. The male cat with the ll-genotype has long hair, the female cat with the LL-genotype has short hair. All first generation hybrids (Ll) are short-haired, and the proportion of the features is 3 to 1 among the second generation hybrids.

DISCUSSION

This task allows to analyze the phenotypic ratio of first generation hybrids and second generation hybrids in the case of the monohybrid cross, where one allele of the gene completely dominates the other.

Though gene responsible for the hair length has only two alleles, there are even three types of cat breeds – long-haired, semi long-haired and short-haired. Short-haired breeds include British, Russian Blue, Abyssinia, and Siam; semi long-haired cats – Siberian, Norway Forest, and Somalian; long-haired – only Persian cats. Both Persian and semi long-haired cats have recessive ll genotypes. The unusually long hair in Persian cats is a qualitatively inherited feature caused by polygenes (this is not simulated in the virtual laboratory).

21

Black pigment

A task of increased complexity is devoted to multiple allelism. Cats of three different colorings are sitting in a cage. Crossing them will help you to define the principle of inheriting a black, chocolate, and cinnamon coloring.

HOW TO PERFORM A TASK

The following regularities can be found during interbreeding:

• mating a black male cat and a chocolate female cat: the first generation hybrids will be black; the second generation hybrids will have a 3 to 1 phenotype ratio;
• mating a black male cat and a cinnamon female cat: the first generation hybrids will be black; the second generation hybrids will have a 3 to 1 phenotype ratio;
• mating a chocolate male cat and a cinnamon female cat: the first generation hybrids will be chocolate; the second generation hybrids will have a 3 to 1 phenotype ratio.

Thus, we can assume that the B-gene has three alleles. The B-allele of the black coloring dominates the alleles of the chocolate and cinnamon coloring; the b-allele of the chocolate coloring dominates the bl-allele of the cinnamon coloring.

If we breed the animals with Bbl genotype (black coloring) and bbl-genotype (chocolate coloring) and cross them, we will get all types of colorings.

DISCUSSION

This task is useful for studying the multiple allelism – a situation when one gene has more than two alleles. The gene B that is responsible for the amount of black pigment in the hair has three alleles, which are responsible for three different coat colors in cats. Multiple allelism is also typical of the C-gene, which codes the lighter coloring of the body of Siamese and Burmese cats.

22

Smokey tiger cat

This task is for test crossing. In order to figure out the genotype of the phenotypically identical black smokey male cats, it is necessary to cross them with the female cats – carriers of recessive features. To minimize the number of crossings you should choose the most appropriate female cat for crossings.

HOW TO PERFORM A TASK

The most optimal way is to select a chocolate marbled female cat without a smokey coloring. This female cat carries recessive traits only and thus is the best choice for performing test crossings.

Here is the right solution of the task.

DISCUSSION

The task involves the I-gene, which is responsible for the shaded coloring when there is no pigment at the base of the hair. The types of shaded colorings are quite diverse. The degree of color intensity is most probably defined by polygenes. If the majority of the hair is colored, the coloring is called smokey; if only the tips are colored – chinchilla; the intermediary variant is shady. Smokey cats are a little lighter than the cats of ordinary colorings; chinchilla cats can look almost white.

It is interesting to see the interrelation between eye color and shady coloring. The shady-colored carriers of the dominant alleles of the I-gene usually have green eyes, which you can see on the icons of virtual animals.

CELL BIOLOGY

23

Autotroph

This model involves studying the metabolism typical of the organisms with autotrophic type of feeding. A virtual plant cell is constructed in the course of the experiment.

HOW TO PERFORM A TASK

Initially, the environment does not contain organic substances; it contains oxygen, carbon dioxide and ammonia. In these conditions, a cell cannot obtain glucose by any other means than synthesizing it from the inorganic substances. An emerging cell needs chloroplast for photosynthesis. Other important organelles include a cell membrane, a mitochondria (otherwise, a cell will not have enough energy for substance synthesis), organelles for protein synthesis (nucleus, endoplasmic reticulum, ribosomes), vacuole, and cell wall. In this experiment, the cell wall efficiently prevents the cell from bursting (the parameters are set to make a cell hypertonic in relation to the environment). The vacuole is required to take osmotic-active substances (in this case, the glucose) from the cytosol. Without the vacuole, the metabolic process slows down so much that the cell dies.

The following cytosolic enzymes have to be introduced into the cell: glycolysis and fat synthesis enzymes, the enzymes for structured polysaccharides synthesis and the enzymes for nucleotide synthesis. Including of ethanol fermentation enzymes in the cell is a mistake.

DISCUSSION

While performing the task, a user creates a virtual plant cell with typical organelles, which make it different from the animal cell: cell wall, plastids, vacuole. It is better to discuss together with the students which functions are carried out by these organelles in real cells and which of these functions are presented in a virtual cell. It is recommended to give examples of the unicellular eukaryotic organisms, which have similar cell compositions (for example, chlorella).

This experiment can be used to discuss the types of organism’s nutrition. The created unicellular organism is autotrophic – it can independently synthesize organic substances from the inorganic ones. The photoautotrophs use energy from light for their photosynthesis; the chemoautotrophs (for example, sulfur bacteria) – the energy of chemical bonds. Heterotrophs are not capable of synthesizing organic matter.