simulating biodiversity ---- from random mutation to natural selection to ecological stability bo...
TRANSCRIPT
![Page 1: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/1.jpg)
Simulating Biodiversity ---- from random mutation to natural selection to ecological stability
Bo DengDept. of Math. UNLSept. ‘09
![Page 2: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/2.jpg)
http://www.geo.arizona.edu/Antevs/ecol438/lect03.html#05
Latitude Diversity Gradient
Hillebrand (2004) on 600 studies
![Page 3: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/3.jpg)
For vascular plant floras (Qian, et. al 2007)
![Page 4: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/4.jpg)
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
![Page 5: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/5.jpg)
Waide, et. al. (1999), Annu. Rev. Ecol., on 201 studies
0102030
AnimalsPlants
Summary
![Page 6: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/6.jpg)
(Scheiner & Willig 2005)
![Page 7: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/7.jpg)
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)’
![Page 8: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/8.jpg)
--- 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
![Page 9: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/9.jpg)
![Page 10: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/10.jpg)
• In Matlab syntax,,
, etc.
![Page 11: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/11.jpg)
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.
![Page 12: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/12.jpg)
![Page 13: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/13.jpg)
![Page 14: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/14.jpg)
![Page 15: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/15.jpg)
![Page 16: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/16.jpg)
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
![Page 17: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/17.jpg)
Effects of intra-specific competitions
![Page 18: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/18.jpg)
Biomass v.s. Species Richness
![Page 19: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/19.jpg)
d
r0
Biom
ass
![Page 20: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/20.jpg)
![Page 21: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/21.jpg)
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.
![Page 22: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/22.jpg)
• 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
![Page 23: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/23.jpg)
Diversity through time
http://www.geo.arizona.edu/Antevs/ecol438/lect03.html#05
![Page 24: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/24.jpg)
![Page 25: Simulating Biodiversity ---- from random mutation to natural selection to ecological stability Bo Deng Dept. of Math. UNL Sept. ‘09](https://reader030.vdocuments.mx/reader030/viewer/2022032806/56649f045503460f94c1808d/html5/thumbnails/25.jpg)
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