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Ecology ch. 10
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Gravity
Terms in this set (82)
geometric growth
when a population breeds seasonally (once a year)
exponential growth
when a species reproduces almost continuously & generations overlap
curve produced by both geometric & exponential growth
j-shaped
Geometric Growth formula
N(t+1) = R0Nt
N(t+1) = population size at next generation
R0 = net reproductive rate
Nt = population size at this generation
geometric growth with more generations formula
Nt = N0R0^t
t = number of generations
N0 = number of females in population
R0 values
usually remains constant
R0 < 1, population declines to extinction
R0 > 1, population increases
R0 = 1, population at equilibrium
finite rate of increase formula
λ = N1/N0
ratio of population size from 1 year to the next
cumulative finite rate of increase formula
λ = 100(N(t+5)/Nt) - 1
average finite rate of increase
λ = (Nt/N0)^(1/t)
time to reach a certain population equation
logNt = logN0 + t(log λ)
difference b/t R0 & λ
R0 = net reproductive rate per generation
λ = finite rate of population change over a given time interval
annual breeders that live 1 yr: R0 = λ
breed for multiple years: not equal
Nt = N0R0^t where t = number of generations
Nt = N0λ^t where t = number of time intervals
grow vs decline
grow: R0 or λ > 1
decline: R0 or λ < 1
equilibrium R0 or λ = 1
exponential growth
continuous breeders
bacteria, internal parasites, humans
change in exponential population size over time
number of births per unit time interval - number of deaths per unit time interval = change in numbers / change in time
ΔN/Δt = B-D
per capita growth rate or actual rate of increase
b-d
simplified to r
to find population sizes at various times equation
Nt = Noe^rt
N0 = population size now
t = number of time intervals
R0 vs r
R0 = generational growth rate
r = instantaneous rate
r = (ln R0)/ T
intrinsic rate of increase
when conditions are optimal for the population & r is at its max rate
dN/dt = rmaxN
rmax always positive
rmax decreases as generation time increases
rmax decreases w/ body weight
r values
r < 0, population decreases
r > 0, population increases
r = 0, population remains constant; zero population growth
r and λ
r = per capita growth rate; gives instantaneous growth rate
λ = finite rate of increase over specific time period
λ = e^r
find how long it takes to double population
λ = e^rd
d = time to double
rate of 70
d = .7/r
used to calculate population doubling time
take 70 & divide it by growth rate
growth rate is cast as percentage increase in a year
at low rates of r, per capita rate of increase is roughly equivalent to finite rate of increase, λ, expressed as percentage
logistic growth
occurs where there are limited resources & thus an upper boundary for population size
can occur for both periodic & continuous breeders
carrying capacity
K
upper boundary for population time
logistic growth formula
dN/dt = rN ((K-N)/K)
dN/dt = rate of population change
r = per capita rate of population growth
N = population size
K = carrying capacity
logistic growth with small, medium & large numbers
population sizes low, even if (K-N)/K is close to 1, population so small growth = small
medium value of N, less close to 1 but population growth larger b/c larger number of females
large value of N, (K-N)/K is small & population growth small again
time lag
results from differences in the availability of resources & time of reproduction
If there is a time lag of length τ between the change in population size and its effect on population growth rate, then the population growth at time t is controlled by its size at
some time in the past, t- τ
time lag equation
dN/dt = rN(1-(N(t-τ)/K))
dN/dt = rate of population growth
rN = per capita rate of population growth
(1-N(t-τ))/ K = effect of time lag
effect of time lag
increase the population growth rate over ordinary logistic
can vary from 0-3 time periods
as length of time lag increases, population becomes unstable & fluctuations increase in size & become unstable
species with discrete generations (breed periodically)
N(t+1) = Nt + R0Nt (1-(Nt/K))
R0 values
<2 = population reaches K smoothly
2 - 2.449 = population enters stable 2-point limit cycle w/ sharp peaks & valleys
2.449-2.570 = more complex limit cycles results
>2.57 = limit cycles break down & population grows in complex, non-repeating patterns often known as "chaos"
density dependent factor
a factor whose influence varies w/ the density of the population
affect a higher proportion of individuals when population densities are higher & a lower proportion when population densities are lower
birth rates decrease as populations increase because
resources become more limited & density dependent competition for those resources increases
density dependent mortality may occur as population densities increase & competition for resources increases & causes
reduction of offspring production or survival
mortality formula
K = logN(t) - logN(t+1)
k = killing power
N(t) = population size before subject to mortality factor
N(t+1) = population size afterward
can be used to find density dependence
density independent factor
mortality factor whose influence is not affected by changes in population size or density.
flat line in mortality vs density
physical factors:
weather, drought, freezes, floods, fires
inverse density dependent factor
source of mortality that decreases w/ increasing population size
mortality vs density = negative slope
life history strategies
sets of physiological & behavioral features that incorporate not only reproductive traits but also survivorship, length of life characteristics, preferred habitat type, & competitive ability.
have important implications for how populations grow & for reproductive success of populations & species
types of life history strategies:
iteroparity vs semelparity
continuous vs seasonal iteroparity
R & K selection
Grime's triangle
iteroparity vs semelparity
semelparity:
when offspring produced in single reproductive event; in insects & invertebrates
if the environment is stable, then selection favors single act of reproduction b/c organism can devote all energy to making offspring & not maintaining own body
iteroparity = the pattern of repeated reproduction at intervals throughout the life cycle; in vertebrates & perennial plants
if survival of juveniles is very poor & unpredictable, selection favors repeated reproduction & long reproductive life to increase chance that juveniles will survive
continous iteroparity
individuals reproduce repeatedly & at any time of year
primates, tropical species, & parasites
seasonal iteroparity
birds, mammals, or temperate forest trees; distinct breeding seasons lead to distinct groups of individuals all born at same time
K selected species
stable populations adapted to exist at or near the carrying capacity K of the environment
r-selected species
high rate of per capita population growth, r, but poor competitive ability
Grime's Triangle components
ruderals
competitors
stress tolerators
Ruderals
adapted to take advantage of habitat disturbances
annual plants adapted to colonizing disturbed areas
competitors
adapted to live in highly competitive but benign environments
tree species
stress tolerators
adapted to cope with extreme environmental conditions such as high soil salt or temperatures that exist in salt marshes & deserts
mangroves & cacti
demographic interpretation of Grime's triangle
fecundity, growth & survival can be more accurately measured than position of a species along relatively ambiguous stress gradient
Population Viability Analysis
technique that provides an estimate of the minimum population size needed to preserve a species
the probability that a population will go extinct w/in a given number of years
takes into account the effects of chance events on populations
calculate a minimum viable population that has a 99% chance of remaining intact for 1000 years
demographic transition
shift from high birth & high death rates to low birth & low death rates
age structure
relative numbers of individuals of each defined age class. commonly displayed as a population pyramid
which of the following is an assumption of logistic models of population growth?
population has limited resources
if the age structure diagram of a population has parallel sides, the population size will
remain the same
the earth's global population growth over last 250 yrs can best be described as
geometric
which of the following population growth models specifically takes into account density dependent limits to population growth
logistic
which of the following refers to the max number of individuals of a given species that the environment can support
carrying capacity
according to geometric models for a continously breeding population, the per capita rate of population growth (r) will decerase if
r <0
approximately ow much is a population of squirrels growing with the following parameters: r = .25, N = 536, K = 710
6%
the lifespan of a species is typically inversely related to which one of the following life history characteristics
intrinsic rate of population growth
use of natural enemies and/or pathogens to regulate the population of pert organisms is referred to as
none of the choices
according to the r-K continuum, which of the following is likely to be characteristic of the african elephant/
low intrinsic rate of population increase
which of the following terms refers to a reproductive stategy in which individuals of a species reproduce multiple times over their lifespan?
iteroparity
geometric or exponential growth curves are described as
j shaped
which of the following best describes a population in stage 1 of demographic transition?
high birht rate & high mortality rate
if population of annual plant has net reproductive rate (r0) = 1.15, how much will it increase in the next year?
15%
a populations growth rate is said to be at equilibrium when what?
R0 = 1
E.O. Wilson & R. McArthur
r-K continuum
R. M ay
time lags in population growth
P. Grimes
stress, disturbance, competition & plant life histories
M. Schaffer
population viability analysis
M. Wackernagle
human ecological footprint
If R0 = 1.1 and Nt = 1,000, what is N(t+1)?
1100
max number of individuals a certain area can sustain is known as
carrying capacity
which of the following factors may change carrying capacity over time
weather, other species, deforestation, soil chemistry
max rate of population growth for a continously breeding population
intrinsic rate of increase
if r=.1, K =100, and N = 50, what is dN/dt?
2.5
age structure refers to
relative number of individuals in each age group
current human population on earth is
6.7 billion
amount of land necessary for survival for each person in sustainable world is known as
ecological footprint
if b = .55, d = .45, N = 1000, dN/dt =
100
what is the minimum condition needed to prevent a continuously breeding population from going extinct
r>0
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