Define population.
Gotelli: “A group of plants, animals, or other organisms, all of the same species that live together and
all of the same species, that live together and reproduce.”
Ricklefs
Ri
kl f (Economy of Nature): “The group of organisms of (E
f N t ) “Th
f
i
f
a particular species that inhabit a particular area.”
Curtis & Barnes (Biology): “Any group of individuals of one species that occupy a given area at the same time.
time.”
Begon et al. (Population Ecology): no definition given.
Characteristics of a population
•
•
•
•
•
size
spatial extent
spatial extent
genetic composition
gender ratio
many more…
How do we measure population size?
• Individuals, biomass, stems
How do we measure population size?
• Individuals, biomass, stems
• Density vs. absolute numbers
Mathematical models for population growth
Notation: N denotes population size
Discrete time: difference equations
Discrete time: difference equations
Nt 1  Nt  ...
Mathematical models for population growth
Notation: N denotes population size
Continuous time: differential equations
Continuous time: differential equations
dN(t )
 ...
dt
Processes that change population size
•
•
•
•
birth
death
immigration
emigration
• A population is “closed” if there is no immigration and emigration.
Exponential growth: The first law of population dynamics
“There is a reasonable consensus among ecologists that the exponential law is a good candidate for the first principle of population dynamics (e.g., Ginzburg
l ti d
i (
Gi b
1986 B
1986, Brown 1997, 1997
Berryman 1999). My formulation of this principle is as follows: ‘‘a population will grow (or decline) exponentially as long as the environment experienced by all individuals in the population remains constant’’. Environment here refers to all environmental influences affecting vital rates of individuals
environmental influences affecting vital rates of individuals, including abiotic factors, the degree of intraspecific crowding, and density of all species in the community that could interact with the focal species.”
ith th f l
i ”
‐ Peter Turchin (2001) Does population ecology have general laws?
Unbounded population growth in continuous time:
Exponential growth
Exponential growth
• Closed population in continuous time
p p
• Birth, death rates are constant on a per‐capita basis
dN
 rN
dt
r = instantaneous rate of increase
i t t
t fi
• Solution: N(t )  N((0))e
rt
• Population doubling time = ln(2)/r