Density Independent Growth

Question 1

What does the potential for overproduction mean

Answer 1

darwin explained that on average parents produce more offspring than needed, so population have the potential to increase in number

Question 2

Why is overproduction expected

Answer 2

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

Question 3

Define density-independent growth

Answer 3

when the growth rate of a population does not depend on the population density

Question 4

What are the two types of density-independent growth and what kind of growth rate do they both have

Answer 4

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”)

Question 5

Define exponential growth vs. geometric growth

Answer 5

exponential = population that is measured at any given point, is continuous
geometric = population measured at discrete intervals

Question 6

When would we use exponential vs. geometric growth rate

Answer 6

exponential = species that are continuously reproducing
geometric = species that only reproduce at specific times

Question 7

Tracking population growth equation and explanation of variables

Answer 7

ΔN/Δt = B – D N/t = change in population size during a time interval. B = births. D = deaths

Question 8

If ΔN/Δt increase, what occurs to B and D

Answer 8

Both will increase

Question 9

Equation to determine per capita rates and explanation of variables

Answer 9

ΔN/Δt = RmN ΔN/Δt = change in population size during a time interval. RmN = change in population size directly proportional to population size

Question 10

Define Rm

Answer 10

The maximum population growth (per capita rate) of increase if no limiting of resources, etc.

Question 11

What are the units of Rm

Answer 11

“per unit time” ex. 0.25 per day

Question 12

When is Rm constant

Answer 12

When exploring density-independent growth

Question 13

Explain the graph of change in population size vs. Population size in density dependence

Answer 13

ΔN/Δt on the y axis and Nt on the x-axis. It is a linear equation. The slope = Rm because its constant.

Question 14

Equations to predict Nt and explanation of variables

Answer 14

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

Question 15

When is Nt = N0^e^rmt used vs. Nt = N0λ^t

Answer 15

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

Question 16

What is the intrinsic rate of natural increase

Answer 16

Rm = b-d. The number of births – the number of deaths per generation time

Question 17

What occurs when making the time interval infinitesimally small

Answer 17

Continuous growth is achieved: dN/dt = rmN. DN/dt = rate of change at an instant in time. Rm = intrinsic rate of natural increase

Question 18

Define population bomb

Answer 18

Populations can explode when there is nothing to limit their growth. Exponential growth can occur when resources are plentiful and is therefore temporary

Question 19

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?

Answer 19

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

Question 20

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.

Answer 20

T = 12 hours x 60 minutes = 720/20 = 36

N36 = 10(2^36) = 6.87195 x 10^11

Question 21

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

Answer 21

Plot ln(Nt) vs t and find the slope. If linear, the population is growing exponentially. Rm = the slope

Question 22

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.

Answer 22

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