Lecture 17 Flashcards
what is a population
collection of individuals living in an area
population size = N
N0 = initial population when t = 0
population density
N/area
pop size - pop abundance
why do we care about the population size
- natural resource management - how much food we have
- conservation
- heath - viruses, bacteria, understanding the risk
- predicting human population growth - is there enough resources
what did Malthus say about human population growth
an essay on the principles of population
- The human population cannot grow faster than food production
the population bomb book
saying that with explosive population growth, the human population will have catastrophic social and environmental consequences
what is the goal of population models
to predict the population growth through time using equations
Nt = individuals in a population now
Nt+1 = f (Nt)
what are time steps
t+1
using differential equations - makes time steps very small = smooth growth = continuous reproduction
using difference equations - makes time as discrete units like days, years - growth is stepwise and bump = episodic reproduction = discrete-time approaches
birth and immigration rate
both are added to the population
- ignore immigration
death and emigration
both are leaving the population
- they are equivalent so we can ignore emigration
the model = only birth and death rates = fixed constants
what does green lambda mean
multiplicative factor by which population changes over one-time unit = finite rate of increase
lambda = Nt+1 / Nt
when Lambda > 1 = births exceed deaths = pop growth
when lambda < 1 = deaths exceed births = pop decline
what is the geometric growth model
discrete-time, step function, days, years
Nt = N0 L^t
when L > 1
what is the exponential function
instantaneous per capita rates of birth and death
b - d = r = constant = intrinsic rate of increase
Nt = N0 e ^rt
- smooth function
what happens when lambda increases and decreases in a geometric growth model
1.5 = growing very fast
below 1
0.8 = very steep decline
at 1 = straight horizontal line
what happens to the r when lambda increases in an exponential model
L = 1.5, r = 0.405 = increasing rapidly
L = below 1, r = negative value = rapidly decreasing
T/F both geometric and exponential have the same outcome and can be simplified to just exponential because the L and the r are constants
true
- both constants
- grow to +/- infinity
T/F species are able to sustain exponential growth and decline for long periods of time
false
- something has to limit population growth
density dependant regulation
the GROWTH of a population depends on N - the individuals in a population
- stress, predation, disease from high number of individuals - crowded
density-independent reduction
a DECREASE in the number of individuals in a population because of other factors that are not dependent on the density
- random events, natural disasters, reverse weather, human impact
what is a logistic growth model
S-shaped curve (sigmoid) that will eventually slow down = running out of food or resources
- only s-shaped when the initial N0 is low, if it is not low it will not be S-shaped but it will still level off at K
dN/dt = rN(1/N/K)
first part = exponential = GO
second part = braking term = STOP
- makes pop density slow down when it is very close to the carrying capacity (1-1 = 0)
carrying capacity
the inflection point of the curve = K/2 = max growth rate
- the HA limit of the graph where it can not go above = K value
Pros of the logistic model
- a good model for intraspecific competition for resources (individuals in the same species fighting over food, shelter)
- simple
- can be used to consider multispecies competition
Cons for the logistic model
- too simple - only shows density dependence regulation
- gradual approach to the carrying capacity
- K is used as a constant but it may fluctuate
