individual-based storage promotes coexistence in neutral communities
TRANSCRIPT
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Individual-based storage promotes coexistence in neutral communities
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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
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Vertebrates
http://frank.itlab.us/silverglen_2004/large/turtle_fish.jpg
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Protists and PlanktonProtists and Plankton
interactive.usc.edu/members/rosenblj/archives/plankton.jpg
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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
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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
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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
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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.
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• Question: Is it possible to investigate the effects of storage without the assumptions of the Storage Hypothesis?
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• Answer: Introduce a storage stage into a theory that makes no assumptions of environmental change or niche differences
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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
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Ecological Neutral Theory
• Operates via life-history processes
death
birth
Local Community, J
immigration
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Ecological Neutral Theory
Pr{Ni+1|Ni} = µ(J-Ni/J)(Ni/J-1)
Local Community, J
µ(J-Ni/J)
(Ni/J-1)
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Ecological Neutral Theory:Introducing a storage stage
death
birth
Local Community, J
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Ecological Neutral Theory:Introducing a storage stage
inactivity
birth
Local Community, J
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Ecological Neutral Theory:Introducing a storage stage
inactivity
birth
Active Pool, JA Inactive Pool, JI
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Ecological Neutral Theory:Introducing a storage stage
inactivity
birth
Active Pool, JA Inactive Pool, JI
death
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Ecological Neutral Theory:Introducing a storage stage
inactivity
birth
Active Pool, JA Inactive Pool, JI
death
activity
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Ecological Neutral Theory:Introducing a storage stage
inactivity
birth
Active Pool, JA Inactive Pool, JI
death
activity
immigrationimmigration
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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)
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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
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Time to fixation increases with initial abundance and decreased death rate, N = 2
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Time to extinction increases with initial abundance and decreased death rate, N = 6
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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
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The inactive pool oscillates within a narrow range without any explicit bounds, even when starting from zero abundance
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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
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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?
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Inactive pool reaches unrealistic abundances under low death and very high immigration
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64 species Metacommunity,local active pool (n = 1000)
γ = 1.0 , md = 0.2
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Hints at a multinomial distribution?
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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.
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Future steps in simulations
• Speciation• Spatially explicit model• Perl > Matlab• More species, larger (meta)communities
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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)]
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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
≠
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• 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
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M
J = 2
N1 N2
m