Population Biology I: Population Growth

A population is agroup of organisms of a single species that live and reproduce in the same area.

Types of variables
State variable: ratio
Rate variable: how fast a state variable changes

Single species model
Starts out with continuous exponential growth.
Exponential growth is the first principle of population dynamics. A population will grow exponentially as long as the environment remains constant.
A continuous model implies rapid feedback, continuous births, and overlapping generations. Uses differential equations.
A discrete model implies births in specific periods, non-overlapping generations, and uses difference equations.

Nt = population size (number of individuals) at a certain time 't'.
N0 = initial population size (at time 0)
B = Total Births
D = Total Deaths
I = Immigration
E = Emigration

Nt = N0+B+I-D-E

Assuming a closed system, there will be no I nor E, thus Nt = N0+B-D
Nt - N0 = B - D
∆N = B-D

b = birth rate per capita
d = death rate per capita
r = intrinsic rate of increase; r is species-specific and can change within a species
r = b-d

∆N = B-D
∆N = bN-dN
∆N = (b-d)N
∂N/∂t = (b-d)N
∂N/∂t = rN

Nt = N0e^(rt)

Doubling time: time it takes to double the population

tdouble = ln(2)/r

Discrete exponential growth

lambda = Nt/N0 (N at a future time/initial population)
lambda = finite rate of increase
lambda > 1.0 population increases
lambda = 0 population constant
lambda < 1.0 population decreases

Best estimate of lambda occurs when the population reaches a Stable Age Distribution (SAD).
SAD: relative proportion of individuals in each class remains constant

Nt = lambdaN0

Two models converge when the time step (interval) in the discrete model becomes shorter. It allows conversion from one model to the other.

lambda = e^r
r = ln(lambda)

Probability of extinction
Pex can be seen as a function of N0
Pex=(d/b)^N0
A lower initial population increases the probability of extinction.
Highlights the importance of population size for persistence of populations.

Policies and their Effect on Human Population

The objective of this activity is to discuss how international and national development policies and cultural influences can affect human population development and growth.

The following outline presents a comparison between the countries of Australia and United Kingdom in terms of sustainability policies and the effect on their respective populations.

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Australia
Population facts

• Ageing population (Baby boomers are growing old)
• High levels of immigration into the country
• Consistent growth, but uneven across the different regions
• Great majority of population lives in urbanized areas

Aims

• Economic stability
• Address labor shortages
• Prepare accordingly for when the population pyramid finally inverts
• Sustainability across the country
• Improve connections between regions
• Improve infrastructure
• Increase food production without compromising the environment
  

Policies

• Immigrants on work visas will face a much more simplified process.
• Infrastructure development projects will focus on those areas that present the most growth.
• Economic policies are working to strengthen connections with international companies.
• Agricultural policies are working to increase food production, but limiting the amount of additional resources that are used. (Target: Low input, high yield)
• Working to relocate people in order to limit the growth of urbanized areas so as to protect biodiversity and avoid the habitat degradation and loss.

United Kingdom
Population facts

• Aging population (Baby boomers)
• Growing population
• Population divided by regions
• There is a certain level of immigration

Aims

• Control population growth
• Manage population segments before the population pyramid inverts
• Protect natural resources
• Achieve high employment levels
  
• Sustainability through education
  

Policies

• Government support will help provide jobs and training.
• Prevent emigration by creating communities where people will want to live and work.
• Provide family planning services
• Work toward social inclusion of all citizens
• Focusing on education and sustainability through educating the population
• Work together with international organization to determine sustainability policies
• Health care available to increase the population's well-being.
  

Conclusions
It can be seen in both cases, the policies are made according to the population conditions. This means that policies issued are based on the needs identified in a specific population. At the same time, the policies have an effect on the people, so it goes both ways. For example, Australia has a high immigration rate and the growth of its own population is constant but not enough to cause significant problems. This is why Australia focuses on taking advantage of immigration to target labor shortages which will become an increasing problem as the population ages. United Kingdom also has an aging population, but it is focusing more on retaining its current population and training them to address the labor shortages.

Both countries are focusing on achieving sustainability, but each of the policies are made considering the culture, geography, and needs of each country's population.

Population Pyramids

Population pyramids show how many individuals are alive in different age groups of a certain region in a given year. These are made up of bars, and the x-axis shows the population numbers while the y-axis shows the age group. The length of the bars shows relative proportion, shown as a percentage of the total population.

These pyramids shows population distribution and can help make predictions on population change.

Types of Pyramid Shapes
There are four stages in the population pyramids.

• Stage 1: Expanding - High CBR, rapid fall in each upwardage group due to high CDR, short life expectancy.
• Stage 2: Expanding - High CBR, fall in CDR as more individuals live to middle age, slightly longer life expectancy.
• Stage 3: Stationary - Declining CBR, low CDR, more individuals live to old age.
• Stage 4: Contracting - low CBR, low CDR, higher dependency ratio (those that cannot work), longer life expectancy.

LEDCs tend to be stage 1 or 2

MEDCs tend to be stage 3 or 4

Population Growth

Population growth can be defined in terms of birth rate, death, doubling time, migration, and fertility rate.

The total fertility rate (TFR) is the average number of children that each woman has over her lifetime. Calculating this helps show the potential for population change in a country.

TFR > 2.0 = population increase
TFR < 2.0 = population decrease
TFR = 2.0 = stable population

Factors that impact our environment apart from population size, is the amount and distribution of wealth as well as the resource desire and need.

Population Growth and Food Shortages

There are two opposing theories on this subject: one by Thomas Malthus, and the other by Ester Boserup. Malthus states that the population is increasing geometrically while the food supply increases aritmethically. This means that the population will surpass the amount of food available, causing excess individuals to die off.
Boserup on the other hand states that while the population keeps growing it will develop the technology needed to meed the food demand. While Malthus is too pessimistic, Boserup is too optimistic. I think we need to find a middle ground. Also, population keeps growing and each country's demands are different. Will the population grow so much that it will cause a dramatic dieback? Have we surpassed our carrying capacity?

Measuring Population Change

There are 4 main factors affecting population size:

1. Birth rate
2. Death rate
3. Immigration
4. Emigration

To measure population change one needs to know:

1. Crude Birth Rate
2. Crude Death Rate
3. Doubling Rate
4. Natural Increase Rate

The Crude Birth Rate (CBR) is the number of births per one thousand individuals in a population per year. It is calculating by dividing the number of births by the total population size and multiplying by 1000.

CBR=[(Number of Births)/(Population Size)]*1000

The Crude Death Rate (CDR) is the number of deaths per 1000 individuals. It is calculated the same as the CBR.

CDR=[(Number of Deaths)/(Population Size)]*1000

The Natural Increase Rate (NIR) is a percentage found by calculating

NIR=(CBR-CDR)/10

Doubling Time is the time in years it takes for a population to double its size.

Doubling Time= 70/NIR

Human Development Index

The Human Development Index is a measure adopted by the United Nations Development Program as a way of calculating a country's well-being. It combines measurements of life expectancy, standards of living, education and GDP into one single value, which can be used to rank countries.

Taking this into consideration, two broad classifications can be used into which countries can be placed:

• MEDCs: Most economically developed countries
  
• LEDCs: Least economically developed countries

MEDCs are industrialized countries that have high GDPs. Their population is relatively rich and has a relatively low growth rate. These countries also have a high level of resource use.

On the other hand, LEDCs are less or not at all industrialized. These countries may have high natural capital, but it is usually exported to MEDCs where it is processed. LEDCs have lower GDPs and have higher poverty rates. Their population is large and has poor standards of living along with a high population growth rate.

Limiting Factors and Population Growth

Populations can change over time due to many different variables, known as limiting factors. These keep populations in check and can be classified into

• Density dependent factors
• Density independent factors

Density dependent factors are those that, as its name implies, depend on population density. This means that the impact these factors have depends on how many individuals there are. These are usually biotic factors, such as biomass, predation, competition.

Density independent factors are those that affect a population regardless of its size. These are usually abiotic factors. Some examples are pH, temperature, salinity, and also natural disasters such as tornadoes, earthquakes, volcanic explosions.

GROWTH CURVES

Growth rate can be graphed. There are two different types of curves:

• J-curve
• S-curve

Each shows a different type of population growth.

J-curves show exponential growth. The population grows exponentially and then crashes or suffers what is known as a dieback. This is because the population overshoots and exceeds the carrying capacity (K), which is the maximum amount of individuals an ecosystem can support without being affected. This is known as a boom and bust pattern. This growth rate is common in organisms.

S-curves start out as exponential growth, but then stabilize as the population reaches its carrying capacity. This growth rate is consistent with density dependent factors. This is known as a logistic curve.

S- and J-curves are idealized. In nature, both types of limiting factors act on the same population and the result is a combination of both curves.

And what about humans?

Human population seems to be growing exponentially, but in my opinion, seeing the conditions our planet is in, it seems as if we have surpassed our carrying capacity. Is the human population heading for a dieback? How much longer before the population crashes?