- population growth is the increase of decrease in the number of individuals
over time, as determined by the rate at which individuals are added to the
population through birth or immigration, or subtracted from the population
through death or emigration.
- Open: immigration and emigration occur
- Closed: ^ do not occur or are minimal
10.1: Birth and Death Rates:
- b =per capita birthrate
- d= per capita death rate (proportion of hydra dying at per unit of time)
- N(t+^t) = N(t) + bN(t)^t – dN(t)^t. Pop size
10.2: Exponential growth:
- Steady increase in population, typical in closed population with low densities
and no resource limitations.
- dN/dt = (b-d)N , describes rate of change d rep the fact that ^t (time interval)
approaches zero. Rate of growth
- r= instantaneous per capita growth rate. Intrinsic rate of increase: difference
between instantaneous per capita rates of birth and death.
- Population growth over time: N(t) = N(0)e [N0; initial population when t=0,
r>0 then increase in population.
- r is always increasing. However if rate of growth expressed as function of N,
then slope is equal to r (dN/dt = rN : limits pop. growth)
- Positive exponential growth occurs is favorable environments where
resources are not limiting, system is closed and low densities. Example:
colonization of new habitats and reestablishment after disturbance.
o Reindeer: introduces in 1911 to island of st. Paul, by 1940 pop grew to
over 2000. - geometric model: geometric models describes growth over discrete time
intervals (often a year) versus a exponential model shows population growth
on a continuous time axis. N(t)=N(0)Ϫ t
10.3: Life Tables
- life table: quantifies mortality and survival in different age classes of a
population. Construct when birth and death vary in age, like most populations.
o Cohort: group of individuals born at the same time
o nx: number of individuals in cohort alive at beginning
o Lx: survivorship: rep the probability at birth of individual to survive up to
any given age.
o qx: number of individuals that died during any given time
10.4: Mortality and Survivorship Curves
- two most common graphs: mortality curve (age-specific mortality rate vs. against age
class or develop. Stage), survivorship curve: (lx vs age class)
10.5: Fecundity Table
- demography: study of population growth
- crude birthrate: does not account for the fact that only females make babies
and that it varies in age of females.
- age and sex specific birthrate: mean number of females born to a females in
specific age group (bx) . (at age 0, girls have 0 babies thus bx = 0)
- gross reproductive rate: mean number of females born to a female in her
entire lifetime, assuming all females survive to maximum age.
- Net reproductive rate: number of females born to female in her entire lifetime,
taking in account the probability of female surviving to a specific age class.
- Fecundity table: estimates net reproductive rate: x(class), bx: amnt females
born, lx: survivorship(nx divided by total at 0), lx*bx
10.7: Logistic Growth - logistic growth: takes into account species interacting with other species and
environment, interactions may regulate growth. S shaped model in which birth
and death rate vary in density dependent manner.
- -b0 birthrate under ideal conditions (no crowding), b actual birthrate, same for
death rate; d0,d
- in exponential birth and death rate is constant
- carrying capacity: the maximum sustainable population size under the
o dN/dt = rN(1-N/K)
o as population (N) grows and reaches K, tem 1-N/K approaches 0
slowing population growth until it stops growing entirely.
o Intrinsic rate does not alter converting exp. To log. But pop increase is
affected by density dependent factors
o N small: pop increases rapidly
o Logistic model determines pop. growth, keeping in account changes in
birth and death rate w/ changing population size. Exponential keeps
10.8: Stochasticity: intrinsic and extrinsic random processes affect population
- nature is not constant. Stochastic( random) processes both internal
(demographic) and external(environmental) affect pop. dynamics .
- fact that many indiv. probability affect pop. dynamic lead to stochastic models
of pop. growth
- demographic stochasticity: random year to year variation in birth and death
rate due to intrinsic factors
- environment stochasticity: random year to year variation in birth and death
rate due to extrinsic factors such as temperature, precipitation, drought, fire
10.0: Extirpation, small pop. susceptible to extinction - extinction: when death exceeds birth rate R0 becomes less than 1 and r
becomes negative, population goes towards extinction.
- extirpation: local extinction or loss of a population as opposed to extinction of
species overall (all gone).
- caused by natural disasters, no resources, extreme tempratures
- Allee effect: decline in reproduction or survival due to low population density
- logistic growth slows as it reaches carrying capacity. Environment limits pop.
increase, resources drop to point that limits growth------because of
- Intraspecific (within species): interactions among individuals including
competition and social behaviour. These exhibit density dependence and
- density dependent: effect various with population size, intensifies as pop
reaches carrying capacity. Allows intraspecific interactions to regulate
- interspecific (between species): interactions like competition, predation and
mutualism, can also be density dependent and play role in regulating
- density independent: adverse effects that no not rely on population density to
influence population growth. Ex: natural disasters, extreme weather.
11.1: Density Dependence
- slows population by increasing death rate (density dep mortality) or decreasing
birthrate (density dep. Fecundity) or both (full density dependence)
- logistic growth involves full density dependence b( >birth) and d (