Density Independent Growth Flashcards
What does the potential for overproduction mean
darwin explained that on average parents produce more offspring than needed, so population have the potential to increase in number
Why is overproduction expected
Because populations that dont reproduce to replace or ONLY reproduce enough to replace, will not persist. Populations that overproduce will persist in the long run and therefore overproduction is expected and populations have the potential to increase in number
Define density-independent growth
when the growth rate of a population does not depend on the population density
What are the two types of density-independent growth and what kind of growth rate do they both have
exponential and geometric growth
per capita growth rate (per capita = per individual, and populations change by a constant proportion not number because it doesnt “increase by 2 every time” but “increases per capita, ex. doubles”)
Define exponential growth vs. geometric growth
exponential = population that is measured at any given point, is continuous
geometric = population measured at discrete intervals
When would we use exponential vs. geometric growth rate
exponential = species that are continuously reproducing
geometric = species that only reproduce at specific times
Tracking population growth equation and explanation of variables
ΔN/Δt = B – D N/t = change in population size during a time interval. B = births. D = deaths
If ΔN/Δt increase, what occurs to B and D
Both will increase
Equation to determine per capita rates and explanation of variables
ΔN/Δt = RmN ΔN/Δt = change in population size during a time interval. RmN = change in population size directly proportional to population size
Define Rm
The maximum population growth (per capita rate) of increase if no limiting of resources, etc.
What are the units of Rm
“per unit time” ex. 0.25 per day
When is Rm constant
When exploring density-independent growth
Explain the graph of change in population size vs. Population size in density dependence
ΔN/Δt on the y axis and Nt on the x-axis. It is a linear equation. The slope = Rm because its constant.
Equations to predict Nt and explanation of variables
Nt = N0λ^t. Nt = population size at a time. N0 = population size at time 0. λ = gives the finite population growth rate, that gives growth rate from one period to the next. Lamda defines the “multiplication rate”. Geometric Growth
Nt = N0^e^rmt. Exponential Growth
When is Nt = N0^e^rmt used vs. Nt = N0λ^t
Nt = N0λ^t used for geometric growth rate when they consider changes in genotype frequencies
Nt = N0^e^rmt for exponential growth because it is easier to compare growth rates in different species measured on different time scales
What is the intrinsic rate of natural increase
Rm = b-d. The number of births – the number of deaths per generation time
What occurs when making the time interval infinitesimally small
Continuous growth is achieved: dN/dt = rmN. DN/dt = rate of change at an instant in time. Rm = intrinsic rate of natural increase
Define population bomb
Populations can explode when there is nothing to limit their growth. Exponential growth can occur when resources are plentiful and is therefore temporary
An insect population is observed to increase from 6 to 15 individuals after a 2-week period. What will be the population size after 10 weeks (from time 0) if the multiplication rate stays the same?
Lambda = N1/N0 -> 15/6 = 2.5 (multiplication rate)
T = 5 (5 – 2-week intervals)
N0 = 6
N5 = N0lambda^t = 6(2.5^5)
= 586 after 10 weeks
A bacterial population has a doubling time of 20 minutes (lambda = 2). Starting with a population of 10 bacteria, what would be the population size after 12 hours.
T = 12 hours x 60 minutes = 720/20 = 36
N36 = 10(2^36) = 6.87195 x 10^11
How to determine, using data of t and Nt, if a population appears to grow exponentially over time and what the intrinsic rate of natural increase is
Plot ln(Nt) vs t and find the slope. If linear, the population is growing exponentially. Rm = the slope
A certain species of rate breeds continuously and has an estimated intrinsic rate of natural increase (rm) of 0.0143 per day. A small number invade a garbage dump where living conditions are ideal. How long will it take the population to double in size.
Nt = N0^e^rmt
Ln(nt/n0) = rmt
T = ln(nt/no)/rm
Nt/no = 2 (for doubling)
Tdouble = ln(2)/0.0143
=48.5 days
