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