Fill in the blanks for lecture 5 Flashcards
_______ and _________ increase population size (_), _______ and ___________ decrease population size.
Births and immigration increase population size (N), deaths and emigration decrease population size.
The geometric growth of a population has two assumptions:
1)
2)
1) A closed system
2) Population growth is continuous
In the geometric growth of a population equation,
N is ________ ________
r is -
t is ____
N- population density
r - per capita population growth rate
t - time
The _________ growth equation is given by dN/dT = rN.
exponential
The exponential growth model (single species) assumes what?
1)
2)
3)
1) unlimited food and space to grow
2) No predators
3) Closed system (no immigration/emigration)
What is the integrated form of the exponential growth equation?
N(t) = No*e^(rt) where, N(t) = population density at time t No = initial population density t = time r = per capita population growth rate (intrinsic growth rate)
Assume you are rearing a population of insects in the lab. You start with 100 individuals and the intrinsic growth rate is 0.2 insects/week. Assume that growth is continuous.
What would the population of insects be in 6 weeks?
N(t) = No*e^(rt) N(t) = 100*e^(0.2*6) N(t) = 332
________ is also called the Verhulst model.
Logistic
When comparing the prediction of Verhulst, using the first 5 U.S censuses, he predicted the population growth, and it was found to be?
Nearly identical to the actual census data.
Logistic population growth - As a population increases in size (increased density), its growth rate will decline due to:
1)
2)
3)
1) Depletion of resource
2) Aggressive interactions among individuals (competition of resources)
3) Increased wastes
________ ________ is a negative feedback between density and per capita growth rate.
Density dependence
Logistic population growth assumes?
Closed system: no immigration/emigration
Density dependent per capita birth and death rate varies with ________ ______ (______).
Population size (density)
The carrying capacity K, is the point at which birth and death rate are _________.
equivalent
logistic (or verhulst) single species model - growth in a ________ _________.
limited environment
What is the equation for the logistic growth model, and what do each of the variable mean?
dN/dT = rN ((K - N)/K) where, dN/dt = change in numbers/change in time r - intrinsic rate of increase K - carrying capacity N - population size
Calculate the % growth for a population with:
K - 4 000
r = 0.1 individuals/year
N - 4 500
Thus, since N is larger than K, the % growth must be negative.
dN/dT = rN ((K-N)/K)
dN/dT = 0.1 * 4500 * ((4000-4500)/4000)
dN/dt = -56.25 individuals per year
Then, convert to percentage.
-56.25 individuals/year * 100%/4500 individuals
= -1.25% growth per year
Instead of getting a perfect fit of the logistic growth model in nature, we often get _________ around the carrying capacity.
oscillations
The logistic growth equation predicts sigmoidal population growth through time. The population size (density) reaches a _______ maximum at K, __ _______ ________.
Stable maximum at K, the carrying capacity
Visualize how population growth rate (dN/dt) varies as a function of population size. The peark of the dN/dt corresponds to the _______ ____ in the dN/dt vs. time curve.
inflexion point
The inflexion point in the dN/dt vs. time curve corresponds to / K.
1/2
dN/dt declines with _________ population size (N).
declines
Assumptions of the logistic equation are _________.
unrealistic
The assumptions of the logistic growth model are: (4).
CEO SorA
1) Closed
2) no Oscillations/time lags.
3) External environments has no effect on dN/dt,
4) if an individual can reproduce, there is no size or age effect
