Transcript Population growth models - Powerpoint for Oct. 2.

Population Growth Models
Ro – Net Reproductive Rate
Spruce Budworm
Spruce Budworm
Budworm defoliation
Northern Elephant Seal
• Reduced to about 20 by 1890’s
• Model of exponential recovery predicted 80 seals by
1906; 40,960 seals by 1978
• Real data – 125 seals in 1911; 60,000 seals in 1977;
today 100,000 elephant seals
Because exponential growth is seldom seen,
population growth must be constrained - two
types of constraints
1) density independent constraints - growth
constraints that are not effected by population
size - usually abiotic - weather, storms,
volcanos
2) density dependent constraints - growth
constraints whose effects change as population
size increases - usually biotic - competition,
predation, parasitism, disease
Pierre-Francois Verhulst
Raymond Pearl
Assumptions for logistic growth equation
1. The population initially has a stable age distribution
– the SAD assumption.
2. The density of the population has been measured in
the proper units. - have we included all age or size
classes?
3. The relationship between density and the rate of
increase is linear. – each individual has same effect
on r.
4. The depressive influence of density on the rate of
increase operates instantaneously without any time
lags.
Yeast Cells Budding
Growing Yeast Cells
Whooping Crane
Wildebeest
Salix cinerea
Logistic Growth in Several Species
Reasons natural population growth may not fit
logistic growth models
1. In nature, each individual added to the population
does not cause an incremental increase to r
2. In nature, there are often time lags in growth,
especially in species with complex life cycles mammals may be pregnant for months before giving
birth
3. In nature, K may vary seasonally or with climate
4. In nature, often a few individuals command many
matings
5. In nature, there are few barriers preventing dispersal
Daphnia magna – with developing embryos
General rules about population growth
1. There is a strong correlation between size and generation time
in organisms such that small organisms have shorter
generation times than large organisms - this is true for
organisms from bacteria to whales
2. Organisms with longer generation times have lower per-capita
rates of population growth
3. Therefore, larger animals have lower rates of increase, r. For
any given size, endotherms have a higher rate of increase than
do ectotherms, which in turn have a higher rate of increase
than do unicellular organisms