simulating biodiversity ---- from random mutation to natural selection to ecological stability bo...
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Simulating Biodiversity ---- from random mutation to natural selection to ecological stability
Bo DengDept. of Math. UNLSept. ‘09
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http://www.geo.arizona.edu/Antevs/ecol438/lect03.html#05
Latitude Diversity Gradient
Hillebrand (2004) on 600 studies
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For vascular plant floras (Qian, et. al 2007)
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Left: North American Vertebrates, Nonvolant (nonflying). Right: Including reptiles, birds, etc.
http://www.geo.arizona.edu/Antevs/ecol438/lect03.html#05
Gobi Desert Rodent
Currie(1991)
Lubchenco(1978)
Herbivore Density
Pl
ant N
umbe
r
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Waide, et. al. (1999), Annu. Rev. Ecol., on 201 studies
0102030
AnimalsPlants
Summary
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(Scheiner & Willig 2005)
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Variables C = (C1, C 2, … , C n3
)’
H = (H 1, H 2, … , H n2)’
P = (P 1, P 2, … , P n1)’
R = (R 1, R 2, … , R n0)’
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--- Resource input rate
--- Resource depletion coefficient rate
--- Contact or discovery rate
--- Processing or handling time
--- Birth-to-consumption ratio
--- Per-capita death rate
--- Intra-specific competition parameter rate
--- Inter-specific competition parameter rate Trophic level: plants (k = 1), herbivores (k = 2), carnivores (k = 3)
Parameters
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• In Matlab syntax,,
, etc.
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Resource Value Plant Value Herbivore Value Carnivore Value
0.1 0.1 0.01 0.10.010.1 0.10.1 0.10.1 1 100.1 1In Matlab, e.g., , etc.
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Effects of inter-specific competitions
But when we bear in mind that almost every species would increase immensely in numbers were it not for other competing species …
Charles Darwin, On the Origin of the Species
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Effects of intra-specific competitions
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Biomass v.s. Species Richness
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d
r0
Biom
ass
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Definition: Species X is competitive in a foodweb if the time average of its per-capita growth rate dX/dt/X is positive along the steady state of the web without X.
‘Theorem’: Without inter-specific competition (c_0 = 0) but with intra-specific competition (m_0 > 0), all species will eventually become competitive and coexist at an equilibrium state as the resources become sufficiently abundant.
Stable but fragile: A competitive species X is not always competitive in every subweb of its community, i.e., the timing of its speciation or invasion to the web determines its evolutionary success.
‘Theorem’: Competitive exclusion occurs without intra-specific competition (m_0 = 0) , but the model becomes pathological in which individual organisms would have multiple lifes.
‘Theorem’: With both types of competitions, competitive species can always invade a stable foodweb without having to displace any existing species. That is, a foodweb can be both large and stable consisting of only competitive species.
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• Given the axiom of one-life rule, resource abundance is the determining factor for stability
• Resources and competitions are the determining factors for species richness
• Complexity and stability should not bear causal relationship to each other
• Because of predation, decrease in species richness is inevitable even under some ‘best’ circumstances in resource abundance
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Diversity through time
http://www.geo.arizona.edu/Antevs/ecol438/lect03.html#05
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Adapted from Waide, et. al. (1999), Annu. Rev. Ecol.(201 studies)
Unimodal
Positive
Correlati
on
Negative
Correlati
on
Insignifica
nt Corre
lation
05
101520253035
AnimalsPlants