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Population Growth (Univoltine (R0 is a multiplication constant (R0…
Population Growth
Univoltine
R0 is a multiplication constant
R0 <1 population declines to extinction
R0 = 1 population remains constant
R0 > 1 population increases geometrically
R0 multiplication dependent on N
Linear compensation function
If N > NEQ then R0 goes down
If N < NEQ then R0 goes up
Monotonic
Convergent Oscillations
Bounded oscillation
Chaotic fluctuation
Multivoltine
R0 is a multiplication constant that depends on natality (addition) and mortality (subtractions)
Probability of producing another individual
Probability of dying
Rate of change in population abundance with time
Integral form
Doubling time may be estimated from the model
rMAX used to compare mean generation time for making comparisons between taxa
Logistic Curve (accounts for Feedback mechanisms)
Integral form of Logistic Curve
S-Shaped Growth
The effect of negative feedback is limited to abundance
Geometric Growth
Assumes no limits on resources and no controlling feedbacks
Lab Tests of Logistic Theory
Gause
Peal
Sang
Chapman
Park
Field Tests of Logistic Theory
Red Foxes in Labrador
Ungulate Caribou Populations
Reindeer introduced to St. Paul Island (Alaska)
Reindeer introduced to St. George Island (Alaska)
Red Deer populations on Isle of Rhum (Scotland)
Recovering populations of Gannet on Aisla Craig Island (England)
Recovering populations of Whooping Cranes (wintering in Arkansas National Wildlife Refuge and summering in Wood Buffalo NP NWT)
Binkley & Miller
Time-Lag Models
Animals do not respond instantly to changes in their environment
Pratt's 25C Experiment
Oscillations in population - non-synchronous changes in births and deaths
Daphnia store energy when food is abundant to use during low food supplies
They continue to reproduce in low food supplies, once it is used up then the response can be seen
Pratt's 18C Experiment
Cyclical fluctuation not seen because lowering the temperature reduces Daphnia somatic growth rates and delays maturation schedules
Lower reproductive output
Stochastic Models
Deterministic model that assumes an organism reproduces with absolute certainty
More realistic, but more complex
Matrix Models
Leslie Matrix Models
Vital Rates
Age specific mortalities (P)
Age specific fecundities (F)
Stable Age Distribution
Lambda Constant
Lambda > 1
1 more item...
Lambda < 1
1 more item...
Projection matrices can become very large with long lived organisms
Lefkovitch
Grouped by life stages
Loggerhead Turtles example