Population Growth

Factors Affecting Population Growth Populations grow and shrink in response

to abiotic and biotic factors. Abiotic – physical & chemical factors

such as water & light availability, soil structure, salinity, pH, etc.

Biotic – factors having to do with living organisms, like competition & predation.

Population Growth Models We can study the way populations grow

by using models. What happens when resources are

unlimited? What limits population growth?

Example – Waterhemp Waterhemp

populations can grow quickly. When it occurs in soybean fields, it can reduce the crop of soybeans available to harvest.

Geometric Growth When there are plenty

of resources, the population can grow very rapidly. As the population

grows, there are more individuals available to reproduce, so it grows faster.

Geometric Growth If the estimated

growth rate is 2.0, each individual will produce 2 offspring each year. 2,4,8,16,32,64 etc

Geometric Growth A simple measure of

population growth is the ratio of the population size at one time (Nt+1) to the population size in the previous time step (Nt

). This is known as the finite rate of increase, denoted by lambda (λ).

Geometric Growth The geometric

population growth model: Nt = N0λt

Population that reproduce all at once sometimes follow this growth model. Sockeye salmon

Exponential Growth Some organisms can reproduce multiple

times throughout the year. We need to adjust our growth equation.

r=lnλ

Exponential Growth dN/dt = rN N= population size t = time r = intrinsic rate of increase So, change in population size over time is

the population size times r. Populations grow increasing fast due to

increase in reproductive individuals. Positive feedback

Exponential Growth When conditions

are optimal, with unlimited resources, the population can grow at its maximum rate. rmax

Exponential Growth The human

population is growing exponentially.

Logistic Growth In reality,

populations usually can not sustain exponential growth for long. Resources

become limiting.

Logistic Growth Carrying Capacity (K) – the number of

individuals the environment can support. The population grows exponentially, then

levels off as K is reached and resources start to run low.

Logistic Growth Example: sheep in

Tasmania (southern Australia) Introduced in 1810 Reached carrying

capacity around 1860 Fluctuates around

carrying capacity

Logistic Growth Equation Adds a carrying

capacity component to the exponential growth equation: dN/dt = rN (1-

N/K)

Factors that Affect Population Growth Density dependent factors will affect

population growth more when there are more individuals in a given area. Disease / parasites Food Light Space Predation

Factors that Affect Population Growth Density independent factors affect

population size in the same way regardless of population density. Storms Falling trees Natural disasters

Example - Aphids Aphid populations will increase until

they reach the carrying capacity. This is determined by limited resources –

soybean leaves for example. When the population nears the carrying

capacity, some individuals will get enough food to survive & reproduce, some get enough to just survive, and some will starve.

Aphids Is food limitation an example of a

density-dependent factor or a density-independent factor?

Density-dependent Density-independent

Dispersal and Metapopulations

Growth Rate Growth rate = births – deaths

We must also account for immigration and emigration.

Growth rate = births – deaths + immigration – emigration r = b-d + i-e

Immigration If a habitat patch is

small, it may not be able to permanently support a population. Immigrants from other

patches can come in and rescue the population periodically.

Source-Sink Populations Immigrants usually come

from a neighboring population. If there is a large population surrounded by smaller populations, the small ones may be constantly re-populated by immigrants from the large one. 

Source-Sink Populations Population size and distance

between ponds affects the probability of California tiger salamanders colonizing one pond from another in a system of ponds in Monterey County, CA. Trenham and colleagues estimated how far rescue effects from source ponds extend to other ponds that might be sinks, based on dispersal patterns and pond characteristics. Dispersal estimates are shown by arrows. Ponds with many emigrants, such as LC, are sources, while ponds that primarily have immigrants but not emigrants, such as CRP, are sinks.

Dispersal Dispersal is important to help small

populations avoid extinction. Allows organisms to escape competition,

find mates, find new resources, etc. Take advantage of new space opened up

after a landslide etc.

Metapopulations A metapopulation is a

set of subpopulations connected via dispersal. A metapopulation inhabits a shifting set of occupied and empty patches that together sustain the metapopulation for much longer than any one patch sustains a subpopulation.

Variability in Populations Environmental stochasticity - refers

to seemingly random variability in resource availability, ecological community composition, predation pressure, weather events, etc., which often causes fluctuations in a population's growth rate.

Variability in Populations Demographic Stochasticity -

Population growth rate is determined by birth and death rates. By chance, there could be many births in a row, leading to a higher population growth than you would expect. Or by chance, there could be a number of deaths in a row, leading to unexpected extinction.

Variability in Populations The Allee effect

occurs when populations reproduce at a slower rate than expected at low population densities. Meerkats form social

groups where only one pair reproduces.

Variability in Populations All of these sources of variability can

make modeling and predicting population dynamics challenging.