Modelling structured pops Flashcards
What is demographic structure
age/stage matters for modelling because
- reproductive output varies
- dispersal behaviour varies - may be more subject to perils of new environment
- susceptibility to environment/survivability varies- eg juveniles may be more at risk.
So management varies eg harvesting certain life stages, targeting conservation according to where the threat is
Draw the population broken down as vector elements
picture of phone
Draw out matrix model and eq
Nt+1 = M.Nt
Why use matrices
In matrix form, pop models have useful properties. Matrix simple (one operation in R), so requires no more code than simple pop model
Can easily determine stable stage distribution, asymptotic growth rate, reproductive values and stage classes
Can also compute the influence of changing matrix elements eg does it make it more difference to target cons at certain points?
These parameters are known asa sensitivity and elasticity
So why use? This is a developing field, so made sensitivity then that was criticised, then elasticity and that was criticised then other approaches made like life stage analysis.
Should also consider cost, return on investment, and practicality (how adjustable these vital rates are) really any room for improvement 0.99 may be impossible to change, but 0.5 easier to change- how adjustable these things are, techniques that might inform us about where to target our management- talk about life stage simulation and pop viability ,
What is sensitivity in matrices
Effect of a small absolute change in any matrix element eg add 2
Would have a model with pre juveniles going straight to adult
What is elasticity in matrices
Effect of a small, relative change in any matrix element eg add 0.1% to each (large parameters change more)
In adults matters most in longer lived organisms bc longest life stage. In short lived organisms likely pre-juv matters most
Whats wrong with matrix models?
So far only projection matrices= what would happen given certain assumptions (eg vital rates remain unchanged)
Forcasting= what will happen, need to add things in. Need realism, complexity (eg stochasticity and DD) to consider indiv differences
Matrices or individuals
Transition probabilities are all contingent on behaviour
Behaviour is contingent on an array of individual attributes
- local characteristics of population
- local characteristics of habitat
- group characteristics
- past experience
- physiological state, if good high survival and high fecundity likely
- individual qualities, genetics, personality, eg some more aggressive
Applying models
Life stage simulation analysis
Life stage simulation analysis- can see distributions of uncertainty around pop growth rate. See how management interventions impact pop growth rate or could plot any growth rate against values for any given matrix element, see impact of uncertainty
on phone
Tells us what is actually possible to adjust
Can create a distribution of growth rate, can tells by how much a pop declines before improvements. Can see how different improvements alter growth rate
How do you do a life stage simulation analysis
recognise that vital rates are uncertain
draw matrix elements from probability distributions
estimate llamda
re-do multiple times to generate distribution of lamda
can plot lamda against vital rates to see which are most important (and hence target interventions)
or adjust parameter distributions to reflect specific interventions and determine consequences
What does a population viability analysis consist of ?
PVA is a process (Boyce 1992)
evaluation of data
modelling of population
determination of probability of persistence for some arbitrary period into the future
often relate to conservation interventions
assessing options
Related to MVP
minimum number required to ensure some probability of persistence over a given time horizon
