Chapter 12 Lecture 1 Flashcards
under ideal conditions…
populations can grow rapidly
demography
the study of populations
growth rate
in a population, the number of new individuals that are produced per unit of time minus the number of individuals that die
Intrinsic growth rate (r)
the highest possible per capita growth rate for a population.
what do individuals experience under ideal conditions
maximum r (i.e., maximum reproductive rates and minimum death rates
what does the strength of a reproductive population depend on
- the number of individuals of reproductive age
- the availability of resources such as food and mates
- the presence or absence of predators, disease, etc.
how may individuals be added to populations
- continuous reproduction
2. discrete reproductive periods
what does the periodicity with which offspring are produced result in
important differences in the way in which population growth is conceptualized mathematically
in many species, young are added only during certain times of the year during…
discrete reproductive periods - such populations undergo geometric growth
in geometric growth
the rate of increase is proportional to the number of individuals present in the population at the beginning of the discrete reproductive period
what is the typical form of population growth in the wild
geometric growth
species that reproduce continually
they can add young at any time of the year
what do populations with continual reproduction undergo
exponential growth
exponential growth model
a model of population growth in which the population increases continuously at an exponential rate
what equation describes the exponential growth model
Nt+ N0e^rt
Nt
future population size
N0
current population size
r
intrinsic growth rate
t
time over which a population grows
e
2.7183
J-shaped curve
the shape of the exponential growth when graphed
the rate of a population’s growth at any point in time is the derivative of this equation
dN/dt = rN
e^r
the factor by which the population increases during each unit of time, and is sometimes symbolized with a lambda
exponential growth
results in a continuous curve of increase (or decrease, when the rt term is negative) whose slope varies in direct relation to the size of the population
the rate of increase of a population undergoing exponential growth at a particular instant in time, the instantaneous rate of increase =
dN/dt = rN
dN/dt = rN
this equation encompasses two principles (A)
- the exponential growth rate (r) expresses the population increase (or decrease) on a per individual basis
dN/dt = rN
this equation encompasses two principles (B)
- the rate of increase (dN/dt) varies in direct proportion to the size of the population (N)
the rate of the change in population size equals
the contribution of each individual to population growth times the number of individuals in the population
the individual contribution (per capita) to population growth is the difference between
the birth rate (b) and the death rate (d) calculated on a per capita basis
dN/dt = bN - dN or
dN/dt = (b-d)N
since r is the difference between birth rate and death rate (b-d),
dN/dt (rate of increase) = rN
when the death rate exceeds the birth rate…
r is negative, and the population declines
what equation represents exponential population growth
Nt = N0e^rt
when young are added to populations during certain time frames (discrete population growth), what is the best way to represent growth
geometric growth model
which growth is most common among wild populations
discrete
overall, within each year, the population growth rate of a discretely growing population varies with
seasonal changes in the balance of birth and death processes
seasonal
discrete
why do populations initially grow slowly
because there is a small number of reproductive individuals
what does growth rate increase with
the number of reproductive individuals
what kind of breeding seasons do most species have
discrete
geometric growth model
a model of population growth that compares population sizes at regular time intervals
expressed as a ratio of a population’s size is one year to its size in the preceding year (lambda)
geometric growth model
when lambda is greater than 1
population size has increased
when lambda is less than 1
population size has decreased
lambda cannot be…
negative
growth in populations with discrete breeding seasons is treated somewhat differently than…
growth in populations with continual growth
the size of the populations with discrete breeding seasons must be measured consistently at…
a particular time of the year to have any meaning
when populations are augmented periodically…
it is most convenient to express the growth rate as a ration of the population in one year to that of the preceding year (N1/N0)
demographers have assigned lambda to N1/N0 and call it
the geometric growth rate
lambda =
N1/N0
lambda represents
a factor of population increase
if one wants, then to project the size of a population into the future (t=1), it could be written as
N(t+1) = N (1) lambda
in order to project the growth of a population…
the original number N(0) is multiplied by the geometric growth rate lambda once for each unit of time passed
N(t) =
N(0) lambda^t
the equation for geometric growth is identical to the one for exponential growth, except that…
lambda, the geometric growth rate, takes the place of e^r (the amount of exponential growth accomplished in one time period)
N(t) =
N(0) lambda ^t
exponential and geometric growth models are identical except
e^r takes the place of lambda
when a population is decreasing
lambda < 1
r < 0
when a population is constant
lambda = 1 r = 0
when a population is increasing
lambda > 1
r >0
decreasing populations have…
negative exponential growth rates and geometric growth rates greater than 0 but less than 1
increasing populations have
positive exponential growth rates and geometric growth rates that are greater than 1
doubling time
the time required for a population to double in size
how can doubling time be estimated
by rearranging the exponential growth model
Nt = N0e^rt —>
e^rt = Nt/N0
When a population doubles, Nt/N0 =
2
for the geometric model, the equation for doubling time is
t2 = loge2/loge(lambda)
