topic 11 - population growth Flashcards
how does population growth occur
from reproduction
what is a population
all of the individuals of a given species that live and reproduce in a particular place
what is population size
number of individuals alive at a particular time in a particular time
influenced by births, deaths, immigration, and emigration
what is the change in total number of individuals in a population
delta N/delta t = dN/dt = B-D
N = total
B = births
D = deaths
how to track per capita births and deaths
b = B/N
d = D/N
what is the per capita growth rate
r = b-d = (B-D)/N
positive r = growing population
negative r = shrinking population
how to calculate the change in pop growth
dN/dt = rN0
N0 = pop size at time 0
how to determine size of population growing exponentially
Nt = N0 (1+r max)^t
just input numbers
what is the exponential model of pop growth
under ideal conditions (organism given everything it needs)
per capita growth rate = max
intrinsic rate of increase = r max
r max = always constant and positive
(negative growth rate under these conditions = extinct pop)
how does r max vary
high in bacteria
low in animals
decreases as generation time (in days) increases
depends on life history
- r-selected = higher r max
- k-selected = lower r max
why does exponential behaviour occur in pops
new generation from t=1 can reproduce
(same as compound interest)
assumes that the same conditions are applicable to all generations and growth rate is the same over generations
what is the effect of organisms not living in ideal conditions
limits pop growth (temp, precip, disease, food availability)
what is the carrying capacity of an environment (K)
population size an environment can support
as population tends to approach carrying capacity, more and more comp, more individuals present than the environment can sustain = negative growth rate
as N tends towards K, r decreases
what is the relationship between N and K
N>K - population size too big = r<0
N=K - r=0
N<K - r>0
as N increases, r decreases
small N = close to r max
what type of equilibrium is a pop
stable equilbrium
- pop perturbed off equilibrium - tends back to K
what is the logistic model of pop growth
as pops grow, death rates increase and birth rates decrease
bigger the pop = closer to carrying capacity, the more the growth rate slows down
r influenced by the fraction of carrying capacity available
how to calculate the size of a population growing logistically
N t+1 = Nt(1+rt)
how to calculate rt
rt = r max((K-Nt)/K)
how is population growth influenced by density dependent factors
have an increasing effect as N becomes large (more individuals competing for the same things)
biotic factors:
- food
- shelter
- mates
- predation
- disease
how does crowding (density dependent) influence reproduction
directly matches logistic model
tradeoff between the resources available and number of offspring
how does crowding (density dependent) influence growth rate, adult size, and survival
growth rate (faster in lower density)
adult size (larger in lower density)
survival (longer in lower density)
how is population growth influenced by density independent factors
effect all individuals regardless of density
abiotic factors:
- temp
- population
- disturbances
how do r selected life history traits influence population growth
stay at the bottom of the curve
disturbance is common (more effected by abiotic factors)
how to k selected life history traits influence population growth
strong competition
less disturbances
better survival through extremes
