Community succession Vacant space Pioneer species i Intermediate - - PowerPoint PPT Presentation

Community succession Vacant space Pioneer i species Intermediate Climax community Disturbance community

Markov models of succession

(list of assumptions from Gotelli) ( p )

• Communities can be classified into discrete states
• Time is measured in discrete units
• Time is measured in discrete units
• Transition probabilities among states do not change

as time passes p

• No spatial structure
• No density dependence
• Large number of patches
• No time lages

A change from Gotelli: Define the stage vector to be the proportion of patches in each community type, not the proportion of patches in each community type, not the absolute number.

Two (equally valid) interpretations of the equilibrium stage vector: stage vector:

• At any point in time, the (average) proportion of

patches in each community type patches in each community type

• The proportion of time that each patch will spend in

each community type in the long run

O O G O G G G G G G G G S F O O F F O O F F O O O O O O O O O O F O O G G G G G G G G G G S S F F O O O G G G G G G S G O O O O O F F O O O O G G G G G S O G O F O F G G G O O O O O O G S G G G G G G G G O O O F F G G O O G G G G O O O F O F F F F F G G G G G O O O O O F G G G O F O G G G O O O O F O O O F O G O G O O F O G S S F S F F F O F S S F F O O O O G O G S G G G G O F O O G G G G G G G G S G G S S S G G G G S F O O O O O O G O O O F F G G G G G G G G S G G S S S G G G G S F O O O O O O G O O O F F G O O O O G G G G O O F G G G G G O O O G G G G G G G O O O F F F F G G O F F S S G O F O O O O O F F O O O G O F G S F O O O O O O O O O O G G G G G S S F F S F O G O O O O F S F O O F G G G G G S G G G G O O F F S F O G G G G G G G S F F O F F S F F F O O F G G O G S S S O O G G G G O O O O O O G G G G G G G G G S O O O F F O O O F F G G S G O O O G G S F S S S F O O O F S S O O O O O G G G G O O F F F F O O O O F S G G G G G G G O O O F F F O O O G G G G O O F F F F O O O O F S G G G G G G G O O O F F F F S G S S O G O F F O O O G O F F O F F F O O O F O O G O O G G

Additional analysis of the transition matrix The turnover time is the (random) amount of time that a patch spends in a given community type before transitioning to another community type The expected transitioning to another community type. The expected (average) turnover time for each community type is: 1 1

i ii

p    where pii is the diagonal element of the transition matrix associated with community type i. associated with community type i.

Additional analysis of the transition matrix The recurrence time is the (random) amount of time between a patch leaving a given community type and its first return to that type The expected (average) its first return to that type. The expected (average) recurrence time for each community type is:

 

1 1

i i i ii

w w p     where wi is the component of the equilbrium stage vector associated with community type i. vector associated with community type i.

Additional analysis of the transition matrix The damping ratio is a measure of how quickly a collection of patches returns to the equilibrium stage vector following a widespread disturbance The vector following a widespread disturbance. The damping ratio is

1 2

    where G (always =G) and S are the largest and second largest eigenvalues of the transition matrix, second largest eigenvalues of the transition matrix,

• respectively. Larger values of  indicate more rapid

return to the equilibrium stage vector.