ecology
the study of how organisms interact with one another and with their physical environment
why does population ecology matter
sometimes we
... [Show More] either want to prevent or promote population growth
4 keys to population change (only 4 things can change pop size)
1. birth
2. immigration
3. death
4. emigration
population dynamics
The study of how complex interactions between biotic and abiotic factors influence variations in population size
changes in population size reflect...
the SUM of births, deaths, immigration, and emigration
N sub 1
number of individuals at time 1 (future)
N sub 0
number of individuals at time 0 (now)
B
number of births between times 0 and 1
D
number of deaths between times 0 and 1`
I
number of immigrants arriving between times 0 and 1
E
number of emigrants leaving between times 0 and 1
"BIDE" are...
the vital rates
- the raw numbers
geometric population growth
population growth described over discrete time intervals
geometric rate of increase
Lambda
when lambda > 1
pop are growing
when lambda = 1
pop are stable
when lambda < 1
pop are shrinking
is lambda = 1.0156, what does that mean
pop growing by 1.56%
lambda
- the geometric rate of increase
- can use to predict one time step (this yr to next yr)
- can use to predict several time steps
population's growth rate
the change in the number of individuals in the population (delta N) per unit time (delta t)
when considering the rate of change over a very, very short interval, we typically use:
dN/dt, rather than (delta N/delta t)
discrete pop growth
- lambda expresses a pop growth rate over for example, 1 day or 1 year
- amount of time is much longer
- domain has an infinite set of values
- ex: malaria parasite pop increases every 7 days
continuous (exponential) pop growth
- infinitely smaller time intervals
- rate of change in pop size for continuous growth known as intrinsic rate of increase
- populations grow exponentially when reproduction is continuous
- domain has infinite number of STEPS and form a continuum
intrinsic rate of increase
rmax
how are Lambda and rmax related
for continuously growing populations:
Lambda= e^rmax
rmax= ln Lambda
per capita vital rates
(lower case)
- per individual/ per person
- ex: b=B/N (per capita birth rate = # of Births/ # of individuals at time 1)
rmax
maximal rate of increase of the population for a given set of abiotic conditions
- intrinsic rate of growth
r
"little r"
"real r"
- per capita growth rate
- almost always LESS THAN rmax, NEVER greater than rmax
when does r reach rmax
when b is as high as possible and d is as low as possible
what is Lambda's magic number
1
what is r's magic number
0
populations are growing when
lambda > 1
or
r>0
populations are stable when
Lambda = 1
or
r=0
populations are shrinking when
Lambda < 1
or
r< 0
when pop size is increasing exponentially, rmax or Lambda is constant, BUT the number added per day is...
increasing
you can figure out the population at any time, as long as you know WHAT?
the initial population size and the rule (model)
emigration
Migration from a location
exponential growth
Growth pattern in which the individuals in a population reproduce at a constant rate
geographic range
the area inhabited by a population
immigration
Migration to a new location
intrinsic rate of increase (rmax)
The rate at which a population will grow under optimal conditions (i.e., when birthrates are as high as possible and death rates are as low as possible). Compare with finite rate of increase.
per capita growth rate (r)
In population models, the average individual's contribution to total population growth rate.
population
A group of individuals that belong to the same species and live in the same area
population size (N)
the number of individuals in a population
Vital rates, b, i, d, and e
birth, immigration, death, emigration
Is r changing or constant when a population is undergoing exponential growth?
When a population is undergoing exponential growth, r is constant. Consider dN/dt = rN. This is the exponential growth equation. This is saying that the instantaneous per capita rate of growth is constant, but the rate of growth (dN/dt) increases, because the factor that r is multiplied by (N, population size) is increasing. [Show Less]