topic 11 - deterministic vs stochastic models Flashcards
Deterministic models
Outcome determined solely by inputs (nothing left to chance)
• Geometric, Exponential, Logistic,
Leslie/Lefkovitch Matrix models,
Lotka-Volterra models
why use stochastic models
But natural word includes
uncertainty
describe stoch models
Stochastic: “involving chance or probability” • Population parameters (e.g., R, r, b, d) vary according to specified frequency distribution (probabilities) based on real data • Can be applied to all model types above • Two types of stochasticity commonly modeled: environmental & demographic
Environmental Stochasticity - unpreditable events, good vs bad yrs
Yearly variability in population growth caused by unpredictable
events
– Weather, natural disasters, etc.
– Interspecific interactions: natural enemies, competition, etc.
• Good & bad years for population growth
– Good years: b > d, population increases (r > 0)
– Bad years: b < d, population declines (r < 0)
• Without specifying causes of “Good” & “Bad” years, we can still
model populations using stochastic models
when is a year good? when is it bad?
Good & bad years for population growth
– Good years: b > d, population increases (r > 0)
– Bad years: b < d, population declines (r < 0)
why can we calc mean and varience. what are we assuming
“r” varies yearly, so you can calculate mean & variance
Assuming a normal distribution
Generate frequency distribution of
probabilities that particular r values will
appear in next generation
what can we generate w the stochastic model
r (instantaneous rate of increase)
Probabilities that particular r values will appear in the next
generation (based on mean & variance of r)
r value in the next generation
how does the stoch model pick r values
A stochastic model randomly selects an r value (from the probability
distribution below) to be used for each time interval of the projection
The probability distribution defines the sample of r values from which the
random selection is mad
omputer simulation of stochastic exponential growth - no two models will be the same
Approximates exponential growth (although slower), but fluctuates considerably``
Variance in N t over time is proportional to r & σ 2r
Populations growing rapidly or that have a more variable growth rate will
fluctuate MORE than slow growing populations or those with relatively constant
growth rates
Still a stochastic model if σ2r=0?? why?
no! it is a deterministic model
random Birth rate variation?
Birth rate variation
• Average birth rate may be 2 offspring/female, but individuals may have 0, 1,
2, 3 or 4+
• By chance, reproduction may be higher or lower than average
random death rate variation?
Death rate variation
• Average death rate may be 0.6
• Individuals either survive or die (1 or 0)
• By chance, many consecutive deaths may occur (0000010111)
what do we specify instead of avgs for birth and death rate?
probabilities.
limit to persistence?
Limit to how much the population can vary in size and still persist
If N fluctuates too much, the population could crash to zero
Extinction from environmental stochasticity is nearly certain when:
σ 2r > 2r
Adding Stochasticity- presumes? is each run the same? what are we interested in for Nt?
Presumes that growth rate varies over time according to some
distribution
• Even with same r & σ 2r each model run is unique
• We are not interested in the values of Nt for a single run, but in the
distribution of Nt values
