Individual-based storage promotes coexistence in neutral communities

Plants• MastMast– Trees hold seeds across reproductive seasonsTrees hold seeds across reproductive seasons

• SeedbanksSeedbanks– Seeds accumulate in soil without reproducing Seeds accumulate in soil without reproducing

each seasoneach season

www.grazulis.com

Vertebrates

http://frank.itlab.us/silverglen_2004/large/turtle_fish.jpg

Protists and PlanktonProtists and Plankton

interactive.usc.edu/members/rosenblj/archives/plankton.jpg

ProkaryotesProkaryotes

• May persist for thousand to millions of years May persist for thousand to millions of years in dormant stagesin dormant stages

• Most bacteria in natural systems are inactiveMost bacteria in natural systems are inactive

blogs.discovermagazine.com/discoblog/files/2008/04/bacteria.jpg

Periods of delayed growth and reproduction:

• Storage Effect: The interaction between variable recruitment and high, less variable, adult survivorship that allows populations to be maintained over long periods by relatively few but large reproductive events

Storage Effect, proper

• Requires• Individual-based species differential responses to

environmental change• Overlapping generations or long-lived reproductive

stages• Increased intraspecific competition with increased

species abundance

Problems with the Storage Effect• Requires explicit assumptions of competitive asymmetries and

niche differences• Relies on environmental change to maintain a compositional

species equilibrium• Does not account for speciation and does not allow for extinction.

• Question: Is it possible to investigate the effects of storage without the assumptions of the Storage Hypothesis?

• Answer: Introduce a storage stage into a theory that makes no assumptions of environmental change or niche differences

Ecological Neutral Theory

• All individuals of all species are assumed to be equivalent in life-history probabilities

• Demographic change occurs stochastically and is only influenced by the effect of relative abundance on dispersal, speciation, and extinction

• All species can go extinct• Models effects of speciation

Ecological Neutral Theory

• Operates via life-history processes

death

birth

Local Community, J

immigration

Ecological Neutral Theory

Pr{Ni+1|Ni} = µ(J-Ni/J)(Ni/J-1)

Local Community, J

µ(J-Ni/J)

(Ni/J-1)

Ecological Neutral Theory:Introducing a storage stage

death

birth

Local Community, J

Ecological Neutral Theory:Introducing a storage stage

inactivity

birth

Local Community, J

Ecological Neutral Theory:Introducing a storage stage

inactivity

birth

Active Pool, JA Inactive Pool, JI

Ecological Neutral Theory:Introducing a storage stage

inactivity

birth

Active Pool, JA Inactive Pool, JI

death

Ecological Neutral Theory:Introducing a storage stage

inactivity

birth

Active Pool, JA Inactive Pool, JI

death

activity

Ecological Neutral Theory:Introducing a storage stage

inactivity

birth

Active Pool, JA Inactive Pool, JI

death

activity

immigrationimmigration

Ecological Neutral Theory:Introducing a storage stage

Pr{Ni+1|Ni} = µ(NiA/JA)*γ(JI-NiI)/(JI+1)*NiA/(J-1) =

µ(NiA/JA)

NiA/(J-1)

Active Pool, JA Inactive Pool, JI

γ(JI-NiI)/(JI+1)

Simulations in Perl

• Simulate times to extinction or monodominance for isolated communities

• Simulate growth of the inactive pool– Not explicitly constrained– Begins from zero abundance

• Simulate immigration from a metacommunity using a spatially implicit approach

Time to fixation increases with initial abundance and decreased death rate, N = 2

Time to extinction increases with initial abundance and decreased death rate, N = 6

Time to fixation for a given death rate is not affected, or is barely affected, by species richness

Ja = 100 Ja = 500

0.6

0.8

1.0

The inactive pool oscillates within a narrow range without any explicit bounds, even when starting from zero abundance

Size of the inactive pool is highly influenced by death rate and size of the active pool. Fluctuating behavior of the inactive pool is apparently

not affected by species richness

Spatially Implicit Metacommunity

• Migration into Inactive Pool– Is not competitive, assume a constant rate

• Migration into Active Pool– Is competitive, assume a constant probability

• Question:– Do we observe different distributions than Hubbell’s

model? For J, Ja, and Jd?– Does migration cause the inactive community to grow

unrealistically?

Inactive pool reaches unrealistic abundances under low death and very high immigration

64 species Metacommunity,local active pool (n = 1000)

γ = 1.0 , md = 0.2

Hints at a multinomial distribution?

When immigration into the inactive pool decreases to 0.1 and death rate is at 1.0, the distribution resembles a log-series; even though the

parameters are approaching Hubbell’s model.

Future steps in simulations

• Speciation• Spatially explicit model• Perl > Matlab• More species, larger (meta)communities

Transition Probabilities:

Focal species Ni in an isolated local community

Pr{Ni +1|Ni} = µ*Nia(Ja-1)/Ja(J-γ)*(1-γNiI/JI)

Pr{Ni -1|Ni} = µγ*(NiI/JI)*(Nia(1-Ja)/Ja(J-γ) +1)

Pr{Ni |Ni} = 1- [(µ*Nia(Ja-1)/Ja(J-γ)*(1-γNiI/JI) + (µγ*(NiI/JI)*(Nia(1-Ja)/Ja(J-γ) +1)]

Markov Tables representing transition among states of abundance (0 to J), for species Ni

M =

Rows: abundance at time TColumns: abundance at time T+1Matrix entries: probabilities of transitioning from between abundance states

Entries on the diagonal represent the probability of maintaining the same abundance across time steps

≠

• Model the interaction of two or more synchronized stochastic processes– Change in active pool, change in inactive pool

• Useful when abundance states can grow rapidly and when processes are only partially dependent

M

J = 2

N1 N2

m