It is the group of individuals of the same species at a particular area at a particular time. These also have the capacity of interbreeding. The population is dynamic. The dynamicity of the population can increase or decrease depending upon the changes in abiotic and biotic environment. In Temperate seas and lakes around the globe. The planktonic population of diatoms is high. Their number based on availability of light and abundance of nutrients.
A population is a group of individuals of same species living in a particular area in a particular unit of time. The population of different species, that are not capable of breeding with each other local population also called demes. Demes are subgroups of population, the population of organism inhabiting a particular area. Eg. - Homosapiens inhabiting hills, plains. In simple words, demes are the local population of polytypic species that actively interbreed with the same species and shares a distinct gene pool.
A population of a certain area is determined by Lincoln formula. Population ecology is the study of population and how they change over time.       

N = Total population of the particular area at a particular time.
K = Number of animals marked on the first visit.
n = Number of animals captured on the second visit.
k = Number of marked animals in recaptured animals.
3.1.    Characteristics of the population
Characteristics are statical variables of the population. A population has various characteristics. Some of these characteristics are population density, birth rate (Natality) death rate (Mortality), age distribution, biotic potential, dispersion is r-and K selected growth forms.
3.1.1.    Birth rate (Natality) : (1) It is the measurement of births rate of a population. Natality is the ability of a population to increase by reproduction. (2) It is calculated as the number of births per 1000 individuals per year. Maximum natality is the theoretical maximum production of new individuals under ideal conditions and is a constant for a given population. Natality refers to population increase under an actual or specific environmental field condition. It is not a constant for a population but may vary with the size and age composition of the population. (3) Natality rate is used to calculate the dynamics of a population. Natality is using to determining whether a population is increasing, decreasing or staying the same in size. Natality is the greatest influence on a population’s increase. Natality is generally expressed as a rate determined by dividing the number of new individuals per unit time by a unit of population.
Ex. : - A population of amoeba in a pond increase by the division to 150 in one hour. The crude natality is 100 per hour and the specific natality is 2 per hour per individual.

    B is Natality rate
    Nn – No of individual added by birth rate
    T – Unit of time
    Natality is two types.
•    Absolute Natality – It is the total birth by an individual under ideal conditions with no competition, the abundance of resources such as food and water, etc.).
•    Realized natality – It is the actual number of births which can sustain their life.
    Features of Natality
    1.    It adds new members to the population.
    2.     It increases the size of the population.
    3.     Natality adds to population density.
    4.     It maintains continuity of population.
  5.   It is high when population size is small and low when the population size is large.
The natality of a population is measured by the growth rate.
•    For wildlife management: Nt1 = Nt0 + (B − D) + (I − E) Where: 
    o    N1 = number of individuals at time t1
    o    N0 = number of individuals at time t0
    o    B = number of individuals born
    o    D = number of individuals that died
    o    I = number of individuals that immigrated
    o    E = number of individuals that emigrated between time t0 and time t1.
3.1.2.    Mortality - It is the measurement of death in a population. Mortality may be expressed as the number of individuals died in a given period. It is also called as deaths per unit time. Mortality is of two types:- Minimum mortality & Actual mortality. It is calculated by death per 1000 individuals per year. In the case of human, the rate of mortality is reduced by vaccination programs of government and by the improvement in treatment methods. 
    1.     It is the number of deaths per unit population per unit time, e.g., per one thousand individuals per year in humans.
    2.     It removes individuals from the population.
    3.     It decreases the size of the total population.
    4.     Mortality reduces the density of the given population.
    5.     It maintains the health of the population.
    6.     Mortality is low when population size is small and high when population size is large.
3.2.    Age -  
Every population is formed by the presence of different age groups in it. In a population, all members are not the same age group. Some members are young. Some are adult and some are old ages. Age distribution of a population is the proportion of individuals of different ages.
Salient features of Age Distribution 
Age distributions have a significant impact on future population growth. The age distribution is affected by many factor and mortality and natality is directly affected by age distribution. According to Bodenheimer age distribution is differential into three stages.
    A)    Pre-reproductive age.
    B)    Reproductive age.
    C)    Post-reproductive age.
Normally which population have more adult member their reproductive rate is more but lack of their parental care their mortality rate is increased. In insect population pre-reproductive age is long but real reproductive age is low. In mammals, all three age is approximately the same. In many animal and plant species, pre-reproductive age is long.
3.3.    Density – It is the number of population in per unit area. Different areas have different density of population according to the presence of resources and possibilities for a bright future.
Population density is of two types: 
Crude density: It is defined as the number of individuals or biomass per unit of the total space e.g. the number of rhinoceros living in the Kaziranga National Park. 
Specific or Ecological density: It is defined as the number or biomass per unit of the habitat space (available area or volume that can be actually colonized by the population). Generally, populations do not occupy all the space. Available to them So we may estimate the number of rhinoceros per square mile. However, some area can be avoided because of the lack of food, shelter and human habitations. Therefore, the area inhabited by the Rhinoceros actually will be its ecological density. 
The difference between crude and ecological density can be explained by taking the example of a fish pond. The density of the fish in the pond decreases as the water level drops during the summer season but the ecological density in the decreasing water of pond increases, as the fish are crowded into smaller water area. It becomes very easy for the predatory bird to catch fish at this time of the year as the ecological density of the fish is at its peak.

3.4.    Distribution – Every species of a population have a tendency to develop in more than geographic area. This tendency is called population distribution. Species distribution is the manner in which a biological taxon is spatially arranged. The population can be distributed in 3 ways-
1.    Clumped distribution - When species have a group forming tendency so they form clumped distribution. The most common type of dispersion found in nature. The distance between neighbouring individuals is minimized. Social animals like ants, bee.
2.    Uniform distribution – Competition occurs so distribution is uniform/some. eg. :- Agriculture land
3.    Random distribution - Environment stage is the same but the group formation tendency is absent. eg. :- Unsocial animals

Population oscillation – The repeated changes in population from one extreme to another extreme is termed as population oscillation. It includes ups and downs again and again in a population. In a population, species member can vary by external factors but oscillation goes regular and it is a step by step process.
Two type of oscillation occurs.
i)    Seasonal – It depends on seasonal. Example:- growth in phytoplankton – in rainy season Mosquito and fly number increase.
ii)    Annual – It is because of the external and internal factor.  By internal factor, these changes are irregular but by the external factor, these changes are regular and cyclic.
3.5.    Population pyramids – 
This graphical representation is used for the determination of the age structure of a population. It represents the pre-reproductive stage, reproductive stage and post-reproductive stage of a population.
Age pyramid :
In age pyramid, different age group member draws in the successive horizontal bar. Fast dispersal population have a high rate of natality and exponentially growth in the number of the organism like bacteria, yeast, dragonfly. In a stable population, the number of individual in the post-reproductive and reproductive age group is approx equal to pre-reproductive age group so they form bell-shaped pyramid. When the number of individuals in the pre-reproductive age group is less than both the reproductive age group and post-reproductive age group then this gives an Urn shaped age pyramid.
1.    Members of pre-reproductive > reproductive > postreproductive. Pyramid shaped graph achieved which represents positive growth and a condition of the developing country
2.    Members of pre-reproductive ~ reproductive > postreproductive. Bell-shaped graph achieved.
3.    Members of pre-reproductive < reproductive > postreproductive. Urn-shaped graph achieved which represents negative growth and a condition of a developed country.

3.6.    Population Propagation :
Population propagation occurs by the interaction between biotic and abiotic factor. Population propagation is because of population density, change in the environmental factor. In population propagation, emigration and migration occur.
Emigration: The individual of particular population show emigration in order to reduce the competition for food. Shelter and reproduction. To avoid the competition individuals leave the crowded place to go to another place.
Immigration: When a displaced population come from another population and settled in new residency population. For Immigration, competition start between species for food and shelter.
Migration: In many animals, a large part of population displace for a particular time that is called migration. example: Siberian crane is migrating in Keoladeo.
The size of the population growing geometrically so this equation is modelled as Nt = No
        Nt     =     is the number of individuals at time t
        No     = the Initial number of individuals.
        L     =     Average number of offspring produced by an individual during the one-time interval.
We can use this model to project the future size of your hypothetical phlox population. The population would soon be so dense that plants would die because they lack sufficient nutrients, light and water. The population would soon spread beyond the physical limits to which a population is adapted.
3.7.    Growth curve -
3.7.1.     J shape or Exponential growth curve :

A curve on a graph that records the situation in a new environment, in which the population density of an organism increases rapidly in an exponential form but then stops abruptly as environmental resistance (e.g. seasonality in case of seasonal plants, annual plants) or some other factor (e.g. the end of the breeding phase) suddenly becomes effective. 
The J-shaped exponential growth curve has two phases.
a.     In the lag phase, growth is slow because the population is small.
b.     In the exponential growth phase, growth is accelerating. 

In Exponential growth, population display continuous growth in a favourable unlimited environment. In human or bacteria, populations can be described by the exponential model of population growth. The number of individuals increases over time logarithmically (e.g. bacterial cultures).  This type of growth is very important to the population during the establishment of a population in new environments. i.e during early succession, the pioneer community show this type of growth curve, as plenty of food and other resources are available for survival. 
a.     Biotic potential is exhibited during exponential growth. The biotic potential is defined as the maximum population growth under ideal circumstances.
b.     These circumstances include plenty of room for each member, unlimited resources (e.g., food, water), and no (e.g., predators). The exponential model is appropriate for the population which show overlapping generation because it expresses the rate of population growth in the continuous process.

Where r is constant while N is variable.

Therefore population size  N increases the rate of population increase than dN/dt also gets increased. The rate of population increases gets increased because the constant r is multiplied by a larger population size N. So during Exponential growth, the rate of population growth increases over time. When the population grow at an exponential rate, the population size at any time t can be calculated as:

Nt      =      Noen

This type of growth curve is popularly known as boom and bust growth curve. J shape is observed during algal blooms and during eutrophication. This type of population growth is termed ‘density-independent’ as the regulation of growth rate is not linked to the population density until the final crash. In Density-independent growth, the size of the population is not a factor in determining the resulting population size overall. The factor that affects the population growth is mostly abiotic like temperature, storms, floods, drought, habitat destruction.

Human Population Growth
The human population is now in an exponential part of a J-shaped growth curve. The doubling time for the human population is 53 years only. Zero population growth is when the birthrate equals the death rate and the population size remains steady. The natural population may grow at exponential rates for a relatively short period of time in the presence of abundant resource.

Exponential growth by tree population :
Tree population in the northern Hemisphere followed the retreating glaciers northward. Algal bloom exhibit exponential population growth in response to the seasonal increase in nutrients and light.     
J shaped curve is obtained by the species which have a specific breeding season or highly sensitive for environmental factors. These species starts growing in the accelerating phase and a sudden increase in its population but then it suddenly stops by any environmental or other resistance and attains its carrying capacity. It can be seen in algal blooms.
3.7.2.    Logistic population growth or S-shaped curve 
The growth of a population in a new environment in which, the population density of an organism increases slowly at the initial stage and then an exponential growth observed but after a time period growth starts to decline and slowly attains stability which is termed as carrying capacity for that species.
In addition to the lag phase and exponential growth, there is a deceleration phase where the rate of population growth slows down and a stable equilibrium phase with little if any growth, because of births equal deaths. This curve is called “logistic” because the exponential portion of the curve would plot as a straight line as the log of N.
Carrying Capacity
The carrying capacity (K) is the maximum number of individuals of a particular species that can be supported by the environment. When the number of individual N, is small, a large portion of the carrying capacity has not been utilized by the population. In this situation, the population experience the positive acceleration phase of growth but as N approaches K, population growth slows down because K−rN is nearing zero.
At carrying capacity the population size is approximately constant because the birthrate is equal to death rates. The population growth is zero at carrying capacity. The idea behind carrying capacity is that the environment can not support as many as the individual of particular species.

Overfishing from a particular pond drives a population of fish into the lag phase. The crop population show exponential phase again after reducing crop pests. Farmers can reduce the carrying capacity for a pest by alternating rows of different crops. eg. : In African buffalo carrying capacity determined by the amount of the grass available as food. Yeast population are eventually limited by there waste product alcohol. For many species carrying capacity is determined by the factors like food, parasitism, diseases and space. Population ecologists modified the logistic model by exponential growth model. It is also known as continuous growth.
-    The simplest equation of carrying capacity is 

-    Rearranging the logistic equation clearly shows the influence of population size N or rate of population growth. It is discrete growth 

-      become smaller so N = K, than the right side of the equation, become zero so population size increase. 

Logistic population growth is highest when N = K/2. In the logistic model per capita rate increases. Which is r, that depends on population size? The relationship between r and population size in the logistic model. The straight line which is shown below.

This type of population growth is termed density-dependent since growth rate depends on the numbers present in the population. The point of stabilization, or zero growth rate, is termed the saturation value (symbolized by K) or carrying capacity of the environment for that organism. K represents the upper region of the sigmoid or S-shaped curve produced when changing population numbers are plotted over time. It is usually summarized mathematically by the logistic equation. The disease is spread more quickly in this type of population 
3.8.    Density-Dependent Factors – Factors that have a greater effect as the size or density of the population increases. Competition for space and food can modify the population size by affecting the following processes:-
1.     Behavioural responses
        A.     Cessation of mating.
        B.     Poor parental care.
     C.     Increased aggressive behavior = Contest competition / social dominance.
2.     Physiological responses
        A.     Increased spontaneous abortions.
        B.     Delayed maturation – Alter reproductive cycles.
        C.     Hormonal changes – Alter reproductive cycles.
Regulation of population growth
Population growth is affected by birth and death rate Two types of regulation 
    (i)     Density dependent .            (2)     Density  independent.
Many factors like food, shelter, rainfall, diseases, floods and predators affect the population size. When biotic factors are affected, they cause diseases and influenced by population density. The biotic factors are known as density-dependent factors. The abiotic factors are known as density-independent factors. If abiotic factors like floods or extreme temperature are affected than they can influence population density independently as their name.
3.9.    Metapopulation
Group of the population which are separated from one another by any barrier and they interact at some level are termed as a metapopulation.
In metapopulation, the two or more local populations are connected by a patch of land through which the populations can interact with each other. This interactions among the subpopulations maintain the metapopulation. Metapopulation theory is applicable for wildlife habitats as they maintain some degree of patchiness. If a population exist in the metapopulation forms. Then the chances of extinction of that population are less as the population persist in some patches. A metapopulation is the feature of the heterogeneous population. The factors that affect the animal movement within metapopulation are patch size, patch isolation, edge characteristics, and matrix characteristics.

Hanski (1997) suggests that in a population where four specified conditions are met, a Levin's-based metapopulation model is applicable.
Levin's Model
Levin's original model applied to a metapopulation distributed over many patches of suitable habitat with significantly less interaction between patches than within a patch.
Key Predictions:-
•    Metapopulation persists if e/c < 1.
•    P increases with increasing patch area this is because of decreasing extinction.
•    P increases with decreasing distance among patches because of increasing colonization.
Landscape Ecology and Metapopulation Dynamics
Exchange of individual (e.g., immigration and emigration) among patches is the feature of the population which has a patchy distribution. If the exchange rate is high and frequent, this is an indication that one species is occupying more then one patch. If each patch has a distinct and separate population then the rate of exchange is very low and infrequent.
However, in the metapopulation, there is an intermediate level of exchange between patches and having regular movement among the patches. The individual shows a dispersing behaviour moving from their natal site to another patch. 
The dynamics of metapopulation exist when species have demes in discrete habitat patches. Each deme has a finite probability of extinction. The extinction events of all demes are not synchronized. This can be imagined by the empty patches. Metapopulation theory is an important tool studying population dynamics in fragmented landscapes.
Sources and Sinks concept is used to explain the metapopulation dynamics 
When one patch has a high intrinsic growth in which the birth rate exceeded the death rate, these patches are termed as ‘’Source’’. The source is characterized by high population growth. This high growth exceeds the patch’s carrying capacity. The sink is defined as patches having less birth rate than the death rate. The individual in the population migrates from source to sink.
The knowledge of source and sink patches is critical for understanding how a particular metapopulation functions. This is called as patches occupancy.  If a critical number of the sources patches are lost, then there are very high chances that the entire metapopulation will collapse.
Localized breeding groups are also known as ‘‘demes.’’ In a typical landscape, the suitable habitat for most species exists in a patchy pattern so patches of habitat usually define the location and boundaries of demes.
These are the isolated populations which are able to interbreed and create a different gene pool in their population. After a long time of selection, they can be termed as subspecies. Various populations of gorillas can be understood by their geographical separation and have been assessed to determine distinct and disjointed gene pools.
It is the process of migration of species from one place to another, it can be of organisms for the search of food, pollens for pollination. This dispersal can be density dependent in which the increasing number of population forces an individual to migrate and another is the density-independent in which organisms use natural environmental factors and disperse randomly.
Patches, Matrix and Corridors
Patch structure of a landscape affects the spatial distribution of individuals and their movements hence influence the dynamics of populations. Patch size is the critical parameter of the landscape which is directly related to local population size. The larger patch can support a greater number of population for a long period of time as it has a great abundance of food.  
Immigration and emigration both are affected by the distance between patches. Corridors connect patches and facilitate interpatch movements. The small habitat patches which are scattered throughout the matrix act as ‘‘stepping stones’’ to promote movement between large patches. The movement of the individual of a population between habitat patches is relatively easy or difficult. This is called permeability. The spaces between habitat patches, filled by the matrix, are called gaps.  The ability of species to move across this space is called its gap-crossing ability. 
3.10.    Reproductive Strategies
Population growth dependents upon reproductive strategies. Organism develops different reproductive strategies because of environmental uncertainty. For example, some organisms are semelparity which can produce all of their offspring in a single reproductive event. This is common in insects and invertebrates and also occurs in organisms such as salmon, bamboo, and yucca plants. These individuals reproduce only once in a lifetime and die. 
Iteroparity organisms reproduce in successive years or breeding seasons. Iteroparity organism reproduces throughout life at a regular period of time. It is common to most vertebrates, perennial plants, and trees.
An organism living in the temperate region have distinct breeding seasons (seasonal iteroparity) that lead to distinct generations. individuals reproduce repeatedly and at any time of the year. An organism living in a tropical region have continuous breeding seasons (continuous iteroparity).
3.11.    Simple categorization of life history strategies: r- and K- selection
Some of the characteristics of r- and K- selected species (from Caddy, 1984).

Natural selection in favour of:-    
    (1)     Rapid development.
    (2)     The high rate of population increase.
    (3)     The high rate of egg production.
    (4)     Small body size.
    (5)     Single reproduction. 
 (6)  Less emphasis on behavioural and morphological characteristics to increase individual survival habits.
    (1)     Slow development.
    (2)     The low rate of population increase.
    (3)     The low rate of egg production.
    (4)     Large body size.
    (5)     Multiple reproductions.
    (6)     Behaviour and morphology assure good individual survival, e.g., territorial behaviour, spines, special dentition and special feeding habits.
3.12.    Survivorship curves : 
In population mortality of species is described by survivability curve. Survivorship curve is drawn against the time of survival organism. In a population, three types of the survival curve. Different types of survivorship curves on the basis of Survivors and age.
(i)    Diagonal Curve – In all types of ages, the mortality rate is constant and straight Curve is obtain. Ex. : - Hydra, Birds. & Rats
(ii)    Convex curve – When organism spend her complete life period up to the old age and then they are so this is convex type curve.  Ex. : - Human, Rabbit and another mammalian.
(iii)    Concave curve: When organism does not spend her complete period they become dead in short life so the concave curve is obtained. Ex. : - Oysters & fishes.

A survivorship curve is a graph showing the number or proportion of individuals surviving to each age for a given species or group (e.g. males or females). Survivorship curves can be constructed for a given cohort (a group of individuals of roughly the same age) based on a life table. The numbers of densities (on the vertical axis) are almost always plotted on a log scale. Survivorship schedules (Sx) is used to calculate in order to understand survivorship curves. There are three parameters of survivorship schedules. {standardized survivorship (lx), age-specific survivorship (gx), and life expectancy (ex)}. 
Standardized Survival Schedule (lx)
Because we want to compare cohorts of different initial sizes, we standardize all cohorts to their initial size at time zero, S0. We do this by dividing each Sx by S0. This proportion of original numbers surviving to the beginning of each interval is denoted lx.
We can also think of lx as the probability that an individual survives from birth to the beginning of age x. Because we begin with all the individuals born during the year (or other intervals), lx always begins at a value of one (i.e., S0/S0), and can only decrease with time. At the last age, k, Sk is zero.
Type I curve represents higher reproductive mortality and it attains a maximum lifespan. Type II curve represents a constant decline in the survivability of individuals with the increasing age of the organism. Type III curve represents a sharp decrease in the number of population of individual and few of them survive which attains the maximum life span.
3.13.    Life Tables - 
A life table is a record of survival and reproductive rates in a population, broken out by age, size, or developmental stage (e.g., egg, hatchling, juvenile, adult). Ecologists and demographers (scientists who study human population dynamics) have found life tables useful in understanding patterns and causes of mortality, predicting the future growth or decline of populations, and managing populations of endangered species.
A tabular form of a survivorship curve. First developed for human populations, e.g. actuarial tables for life insurance companies.
The significance of the Life Table
1.    Population age structure: It gives insight into No of young v/s no. of old individuals in the population.
2.    Reproductive age individuals.
3.    Population growth rate can be measured ( How fast the population size growing or shrinking.
4.    Population survivorship patterns.
    There are two varieties of life table
3.13.1.    Cohort life table 
A cohort is the total individuals born, hatched, or recruited into a population during a particular time interval. Normally cohorts are defined and calculated of cohorts is on the annual basis. eg.:- all individuals born in 2015. A cohort life table follows the survival and reproduction of all members of a cohort from birth to death. 
3.13.2.    A static life table 
Static (or time specific) life table count all individuals alive at a given time and record the age of each records the number of living individuals of each age in a population and their reproductive output. Life tables (whether cohort or static) that classify by age are called Age-based life tables. 
Size-based and stage-based life tables classify individuals by size or developmental stage, rather than by age. It is more useful. This type of curve is characteristic of species that produce a large number of offspring. This includes most marine invertebrates
The different columns of a life table are as follows:-
X     =     age interval or age class.
nx     =     number of survivors at the start of age interval x.
lx     =     proportion of organisms surviving to start age interval x. 
dx     =     the number or proportion dying during age interval x to x+ 1.
qx     =     rate of mortality during the age interval x to x+ 1.
Lx     =     number of individuals alive on the average during the age interval x to x+ 1. 
Tx     =     total years to be lived by individuals of age x in the population.
ex     =     mean expectation of life for individuals alive at the start of the age interval x.    
A cohort table provides more information. A static life table is built by determining the age of dead individuals of a cross-section of the population. The static life table does not directly show the survivorship or fecundity of that population as it matures, experiencing changes in the environment. Instead, these numbers must be derived using the assumption that the mortality experienced by a cohort at any age stays constant. On the downside, following a cohort over many years is usually difficult.
Life table symbols and definition of terms:-
x     =     age class or interval
lx     =     proportion of the population that began the generation that survived to age class x
Fx     =     average number of female offspring produced by individuals during age class x (usually only females are tabulated in life tables, males are superfluous)
Hypothetical example: Imagine 2 species of mice. Both live a maximum of 5 years with the same survivorship. Species A produces two offspring in year 2 and none after that, species B produces 5 offspring (1 in year 3, and 2 in each of years 4 and 5). Which species has a higher growth rate?

1)     If K were infinity, N[t]/K would be zero and the population growth would follow the equation for exponential growth. 
2)     If the population size, N[t] were much smaller than carrying capacity K then N[t]/K would be small. In this case, the population would grow nearly exponentially (until the population size were no longer much smaller than K).
The Lotka-Volterra equations are used to Express a population change based upon growth and maximum population size. 
The relationship is normally expressed as a differential equation:

In this equation, the expression dN/dt represents the rate of change of the number of organisms, N, with time, t, and r is a growth term (units time-1) and K is the carrying capacity (same units as N). 
It is clear that for small values of N, N/K is very small so that (1-N/K) is approximately equal to one, and the equation is effective:

As N increases, (1-N/K) becomes smaller, effectively reducing the value of r. This is termed density-dependence and is an example of negative feedback because of the larger the population, the lower the growth rate.
This equation can be re-written in a form that can be evaluated for any value of N at two times t and (t+1), giving the equation:

Notice that this equation contains new parameters R and a. These are related to r and K by:

Exponential phase:
1.    The rapid increase in population growth.
2.    Natality rate exceeds the mortality rate.
3.    Abundant resources are available. (food, water, shelter)
4.    Diseases and predators are rare.
Traditional phase:
1.    Natality rate starts to fall and/or the mortality rate starts to rise.
2.    There is a decrease in the number of resources.
3.    An increase in the number of predators and diseases.
4.    The population still increasing but at a slower rate.
Plateau phase:
1.    No more population growth, population size is constant. 
2.    Natality rate is equal to the mortality rate.
3.    The population has reached the carrying capacity of the environment. 
4.    The limited resources and common predators and diseases keep the population numbers constant.

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