Populations constantly change and vary in size and composition (e.g., number of males and females, number of juveniles and adults, etc.) over time. It is possible to track these changes by plotting a graph of the population size, or the number of individuals in the population, against time. The resulting plot is known as a population growth curve.
Depending on the population's growth rate, plotting the population growth curve can be easier or harder. For example, it will be easier to keep track of each new calf born to a population of whales who only reproduce every 2 or 3 years, compared to a population of bacteria growing exponentially in a matter of hours.
Exponential growth refers to an increase of a population in proportion to its current population numbers. An exponential graph results in a J-shaped curve.
In such cases, it is necessary to use a logarithmic scale instead. Logarithmic scales allow a wider range of values to be displayed on a single graph. Unlike a linear scale, the logarithmic scale does not have equal intervals between the numbers of the y-axis.
A log scale is not linear, meaning that numbers 1, 10 and 100 are equally spaced on the y-axis. Type your value and press the' log' button to convert numbers from a linear to a log scale on a calculator. The base number of the log is usually 10 on a scientific calculator.
For example, if you enter log10(10000) into your calculator, you get 4. You need to multiply your base number, which is 10, by itself 4 times to get your original number, which is 10000.
Fig. 1 - The linear scale and logarithmic scale
How does the carrying capacity affect population size?
If organisms were to reproduce continuously, their population would increase to infinity. However, real-world systems have many limitations that prevent this from happening.
Take a herd of cows in a field. If we started with only four cows, they would have plenty of space to roam and grass to consume. However, as they reproduce, the size of the population will grow, and they will require more food to survive. More cows will also take up more space. Meanwhile, the size of the field and the amount of grass available will remain the same.
The cow population might also begin to interact with other organisms in the ecosystem, decreasing or increasing the population numbers.
There may be parasites in the field that transmit diseases to cows, killing them or preventing them from reproducing. There may also be worms and insects that keep the soil healthy and promote grass growth, giving them plenty to eat.
The exact combination of conditions in an ecosystem can thus only support a specific maximum stable population size known as the carrying capacity. Beyond a certain number of individuals dictated by the carrying capacity, population growth slows down due to the limiting factors found in the ecosystem.
Fig. 2 - The carrying capacity of a population over time
What abiotic factors affect population size?
Abiotic factors involve the non-living parts of the ecosystem. Many of these factors can influence the population size in an ecosystem.
Temperature
One example is temperature. Different species operate at different optimum temperatures, and the further away an ecosystem's temperature is from a particular population's optimum, the fewer individuals will be able to survive. Temperature can significantly affect an organism's biochemistry.
In plants, cold-blooded animals (poikilotherms/ectotherms) and other organisms whose body temperatures are externally regulated, enzymes work slower when the temperature is sub-optimum (below or above the optimum conditions) and metabolic rates are reduced. Likewise, enzymes might begin to undergo denaturation at higher than optimum temperatures, reducing their efficiency.
Denaturation describes the alteration of a protein's structure (usually enzymes) and function. This change occurs because the substrate no longer complements the enzyme's active site.
Warm-blooded animals like birds and mammals (endotherms/homeotherms), on the other hand, maintain a constant body temperature regardless of the external temperature. However, they are affected by the ecosystem's temperature as well. Maintaining a constant body temperature requires energy. The further the environment's temperature is from the optimum value; the more energy organisms have to expend to maintain their body temperature through homeostasis. More energy spent on homeostasis means less energy available for growth and reproduction, limiting population growth.
Homeostasis describes the regulation and maintenance of a constant internal environment. Mechanisms of regulation include negative feedback loops and positive feedback loops.
Space
Space is another factor that can limit an ecosystem's population size. Some organisms need acres of land to roam, survive and reproduce, while others can do it within more contained areas. Habitats have a finite amount of space, which limits the number of producers that can grow there, subsequently limiting the number of consumers that can feed on them, and so on. A significant reduction in the amount of space afforded to a population can sometimes be detrimental to their survival. For more on this, see our article on Variation.
Other important factors, among others, include the availability of light, humidity, and soil pH.
What biotic factors affect population size?
The biotic factors that affect population size describe the influence of the living components in an ecosystem. The main biotic factors include:
- Competition
- Predation
- Disease
- Food availability
- Waste accumulation
Competition
Competition can be split up into:
- Interspecific competition - between members of different species.
- Intraspecific competition - between members of the same species.
Ecosystems have limited resources, such as water and shelter. Species that obtain these resources more effectively have a competitive advantage over the other species. Over time, species with a competitive advantage will cause the population size of the other species to reduce drastically.
Predation
Predation occurs when another consumes one organism. The prey is a limited resource for the predator.
The predator-prey relationship displays a fluctuating pattern. This pattern happens because the predator population increases when prey is available to feed on. The prey population reduces, and as a result, the predator population also reduces as there is less food available.
Disease
Infections caused by pathogens, such as bacteria and parasites, reduce the health and fitness of organisms, negatively impacting the rate of reproduction and survival. Consequently, the population size of species that is susceptible to disease reduces.
Food availability
As we just read in the predation section, food is a limited resource in an ecosystem. When food is scarce, species will compete to obtain the limited resource.
In intraspecific competition, members of the same species will compete, and the organisms best suited to obtain food will outcompete the others. In intraspecific competition, different species will compete, and the species with the competitive advantage will outmatch the other.
Waste accumulation
When population numbers are high, organisms produce more waste, such as human sewage. The accumulation of waste can reach toxic levels, reducing the air and water quality of habitats. As a result, the reproduction and survival rate of organisms is reduced.
How can we calculate the population growth rate?
Imagine a closed population that does not interact with the outside world. There would only be two ways for the population size to change: it will increase if new individuals are born to the population, and it will decrease if individuals die. Thus, the essential factors determining the growth of the population are the birth rate and the death rate.
In the real world, populations do not exist in isolation. Most populations can interact with other populations, and there may be multiple viable habitats within the species' range of motion. This introduces the element of migration, whereby individuals move from one population to another. There are two types of migration. When an individual joins a population, known as immigration, and when an individual leaves a population, known as emigration.
If we combine these elements, we can get the basic equation for population growth. Births and immigration add to the population size, while deaths and emigration decrease the population size, giving us:
Population size = births + immigration - deaths - emigration
Over time, the population growth rate is calculated as the population change during the period divided by the population at the start of the period, times 100.
Let us calculate the growth of a mice population from January to March. In January, the population consisted of 40 mice. Ten mice died, and 40 more mice have been born since then. Assume that there is no migration. What is the population growth rate?
- Let's start by calculating the current number of mice. Ten mice died, and 40 were born, which gives us 40 - 10 + 40 = 70 mice.
- The population change is equal to the current population - the starting population. This gives us 70 - 40 = 30.
- Divide this by the population at the start of the period. 30/40 = 0.75.
- Multiply this by 100 to get the percentage. The population growth rate is 75%; in other words, the population increased by 75%.
How can we investigate population sizes in biology?
It is necessary to know the abundance and distribution of different species within their habitats to study the sizes of populations in their ecosystem. Abundance refers to the number of individuals of a species in a given area, while distribution refers to how they are spread out across a given area.
However, identifying and counting each individual in an ecosystem is a time-consuming and challenging task, particularly in vast and complex ecosystems. Thus, it is necessary to use sampling techniques that allow us to estimate the abundance and distribution of populations within ecosystems.
What are the types of sampling in biology?
There are several methods used to sample habitats in biology. Two of these methods are random sampling and systematic sampling.
As its name suggests, in random sampling, the sampling points in a specific area are chosen completely at random to reduce bias in the reported results. On the other hand, in systematic sampling, the position of the sampling points are chosen by the researcher for a particular reason.
Random sampling is often the best choice for reasonably uniform habitats. However, systematic sampling might be more appropriate when there is a clear pattern in the environment (such as a gradient in the soil pH or intensity of light).
Fig. 3 - The difference between random sampling and systematic sampling
What are the sampling methods used to estimate the size of a population?
There are three main methods used to sample population size:
- Quadrats (point and frame)
- Transects
- Mark-release-recapture
Quadrats
There are two frequently used quadrats: the point quadrat and the frame quadrat.
A point quadrat is a horizontal bar supported by two legs with holes at set intervals. A long pin is dropped at each of the holes, and each species that the pin touches is recorded as a sample. On the other hand, a frame quadrat is a quadrat frame divided into equally sized quadrats by string or metal wire. The abundance of different species in each quadrant is recorded.
Quadrats are very useful sampling methods for plant and fungi species and non-motile or slow-moving animals that do not move away when approached.
How can we calculate the frequency of a species?
The abundance results from the quadrats can be used to determine the frequency or the likelihood that a particular species occurs in a given area. This is normally used for species that are easily countable.
To calculate frequency, the number of squares in which the species is present is divided by the total number of squares multiplied by 100. The formula is as follows:
Species frequency = (number of squares species is present in ÷ number of squares) x 100
If a species of insect were found in 20 out of 50 squares, the species frequency would be ((20/50) x 100 =) 40%.
How can we calculate the percentage cover of a species?
Quadrats can also be used to determine the percentage cover or portion of a given area that a particular species occurs in. This can be useful when it is difficult to identify individual organisms, such as grasses, mosses, and fungi.
The quadrat is divided into 100 smaller squares, and the number of squares the species occurs in is equivalent to its percentage cover To calculate this, . Expressed as a formula, this gives us:
Percentage cover = number of squares species is present in ÷ 100
If moss is found in 15 out of the 100 smaller squares within the quadrant, and grass is found in 30 of the squares, the percentage cover of moss is 15% and the percentage cover of grass is 30%.
Belt transects
Some areas show a distinguishable pattern of change in their physical conditions. In these cases, systematic sampling methods like belt transects are more appropriate to use.
A transect is a line along which samples of the population are taken. Quadrats are placed at regular intervals along the line - for instance, at every ten-meter increase in altitude or at every 0.5 increase in pH - and the number of species in each square is recorded. This provides us with continuous samples that we can use to determine if changes in the distribution and abundance of species correspond to changes in the physical conditions.
Fig. 4 - A transect line displaying quadrats at even intervals corresponding to soil pH
What is mark-release-recapture?
Most animals move too quickly to be counted using the methods outlined above. Mark-release-recapture methods are used to account for these species.
A given number of animals are captured and marked with an identifier (for example, with different colours of animal-safe waterproof paints) and released into the wild to mix with the population. After some time, another sample of individuals in the population is collected, and the number of marked individuals within the recaptured sample is recorded.
This method makes the following assumptions:
- The marked individuals have mixed fully and randomly with the main population.
- The capture and marking process has not affected the survival rates of any individuals.
- The markings made have remained in place.
- The population has not grown or decreased significantly between the first and second samples.
From this, we can estimate the population size (N) by multiplying the number of individuals in the first (n1) and second (n2) samples and dividing it by the number of marked individuals recaptured (m). The equation is as follows:
N = (n1 x n2) / m
If we were to investigate the abundance of butterflies in a patch of meadow, we could use nets to capture and mark a sample of butterflies on their wing or abdomen and release them into the wild. One day later, we can recapture another large sample and count how many are marked.
Let n1= 200, n2 = 213, and m = 50. Plugging these into the equation above gives us (200 x 213) / 50 = 852. There are approximately 852 butterflies in the meadow.
Population Size - Key takeaways
A population growth curve plots the changes in the size of a population over time. This can be plotted on a linear or logarithmic scale.
The carrying capacity of a population is determined by a combination of abiotic and biotic factors.
To sample the size of a population, researchers use random or systematic sampling. In random sampling, the sampling points are chosen completely at random, while in systematic sampling, the position of the sampling points is chosen by the researcher for a particular reason.
Quadrats (point and frame) or belt transects are useful sampling method techniques that are less motile. The mark-release-recapture method is most commonly used for highly motile species.
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