Dynamics of plant communities in drylands

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The nonlinear physics of dryland landscapes
Ehud Meron Institute for Dryland Environmental
Research Physics Department Ben-Gurion
University
Physics Colloquium, Toronto, March 5, 2009
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Motivation
Innocent questions such as
how climate changes affect species diversity
(bears on ecosystem function and stability) ?
are quite complex
Focusing on the direct response of any individual
to the changing climatic conditions is
insufficient because of indirect processes at the
population and community levels that affect
species diversity
Climate change ? vegetation patterns ? resource
distributions, seed dispersal, consumer pressure
? species diversity
Climate change ? inter-specific plant
interactions ? transitions from competition to
facilitation ? species diversity
More generally, environmental changes affect
species assemblage properties by inducing
indirect processes involving various levels of
organization often across different spatial
scales.
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Motivation
Study processes of this kind by mathematical
modeling as a complementary tool to field and
laboratory experiments.
Mathematical modeling has its own limitations
Models simplify the complex reality, quite often
oversimplify it
The challenge is to propose simple models that
not only reproduce observed behaviors but also
have predictive power usually requires
identifying and modeling basic feedbacks
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Outline

• Background
• Vegetation patterns, feedbacks between biomass
  and water, and between above-ground below-ground
  biomass.
• Population level
• Introduction of a spatially explicit model for a
  plant population, applying it to vegetation
  pattern formation along a rainfall gradient and
  to desertification.
• Two-species communities
• Extending the model to two populations
  representing species
• belonging to different functional groups the
  woody-herbaceous
• system. Using it to study mechanisms affecting
  species diversity (not yet community level
  properties).
• Many-species communities
• Extending the model to include trait-space and
  use it to derive community level properties such
  as species diversity along a rainfall gradient.
• Conclusion

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Background Vegetation patterns
Aerial photograph of vegetation bands in Niger of
tiger bush patterns on hill slopes
(Clos-Arceduc, 1956)
Recent studies Catena Vol. 37, 1999 Valentin
et al. Catena 1999, Rietkerk et al. Science 2004
Salt formation in the Atacama desert (Marcus
Hauser)
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Background Biomass-water and below-aboveground
feedbacks
Both feedbacks can induce vegetation patterns
because they involve water transport ? help
patch growth but inhibit growth in the patch
surroundings
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Population level a spatially explicit model
Gilad et al. (PRL 2004, JTB 2007) Earlier
models Lefever Lejeune (1997) Klausmeier,
(1999) HilleRisLambers et al. (2000), Okayasu
Aizawa (2001) Von Hardenberg et al. (2001)
Rietkerk et al. (2002) Lejeune et al. (2002)
Shnerb et al. (2003)
Biomass
Soil-water content

Surface-water height
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Population level Vegetation states along a
rainfall gradient
Plane topography
Uniform states Bare-soil state (b 0) Fully
vegetated state (b ? 0)
Plain topography
Pattern states Spots, stripes, gaps
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Population level Vegetation states along a
rainfall gradient
Multistability of states
spot pattern Max(b)
Bistability range for any other consecutive pair
of states spots stripes, stripes gaps,
gaps uniform vegetaqtion

1. Spatially mixed patterns (240, 360)

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Population level Vegetation states along a
rainfall gradient

1. State transitions

S
Spot pattern
A dynamical-system view of desertification
B
The positive feedbacks that induce vegetation
patterns are also responsible for the
bistability range of bare soil and spots The
stronger the feedbacks the wider the bistability
range and the less vulnerable to desertification
the system is.
Many more causes and forms of desertification
gully formation by erosion, active sand dunes,
the human factor,
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Population level Observations of vegetation
patterns
Stripes of Paspalum vaginatum
Spots
Stripes
Gaps
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Population level Observations of vegetation
patterns
Rietkerk
Barbier
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Population level Soil-water patterns
Effects of the biomass-water feedbacks
Facilitation
Root augmentation (water uptake)
C10
C1.1
Competition
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Community level a model for several functional
groups
of functional groups (fg)

Two functional groups b1 - woody, b2 -
herbaceous
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Community level Competition vs. facilitation
Inter-specific interactions along a rainfall
gradient
Woody species alone Ameliorates its
micro-environment as aridity increases.
Woody patches can buffer species diversity loss
as aridity increases
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Community level Competition vs. facilitation
Inter-specific interactions and pattern
transitions
Woody alone
Clear cutting on a slope in a bistability range
of spots and bands
Species coexistence and diversity are affected by
global pattern transitions. Coexistence appears
as a result of bands ? spots transition.
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Large communities
Current form of model cannot provide information
about species assemblage properties such as
species diversity.
Extend the space over which biomass variables are
defined to include a trait subspace
and use this trait space to distinguish
among different species within a functional group.
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Deriving community-level properties
Pulse solutions provide information on species
assemblage properties
B
?
Small plants, long roots
Big plants, short roots
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Species diversity along a rainfall gradient
Stationary pulse solutions at increasing
precipitation rates
As precipitation rate increases

1. Species diversity (width) increases
2. Abundance (height) increases
3. Average composition moves to lower ? values, i.e.
   to species investing more in above-ground biomass
   and less in roots.

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Conclusion

• Eco-physical phenomena involve various levels of
  organization, different time scales and different
  spatial scales. This results in many indirect
  processes that bear on the questions that we ask,
  including
• Bottom-up processes
• plant interactions ? vegetation pattern
  formation
• Top-down processes
• pattern transitions ? plant interactions

Various aspects of this complexity can be
addressed using a single platform of nonlinear
mathematical models that capture basic feedbacks
between biomass and water and between
above-ground and below-ground biomass.
Theoretical results are consistent with many
field observations, but controlled experiments
are needed!
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Acknowledgement
Jonathan Nathan
Hezi Yizhaq
Jost von Hardenberg
Erez Gilad
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Funded by
Israel Science Foundation James S. McDonnel
Foundation (Complex Systems program) The Center
for Complexity Science Israel Ministry of
Science (Eshcol program)
References

1. J. Von Hardenberg, E. Meron, M. Shachak, Y.
   Zarmi, Diversity of Vegetation Patterns and
   Desertification Phys. Rev. Lett. 89, 198101
   (2001).
2. E. Meron, E. Gilad, J. Von Hardenberg, M.
   Shachak, Y. Zarmi, Vegetation Patterns Along a
   Rainfall Gradient, Chaos Solitons and Fractals
   19, 367 (2004).
3. E. Gilad, J. Von Hardenberg, A. Provenzale, M.
   Shachak, E. Meron, Ecosystem Engineers From
   Pattern Formation to Habitat Creation, Phys.
   Rev. Lett. 93, 098105 (2004).
4. H. Yizhaq, E. Gilad, E. Meron, Banded
   vegetation Biological Productivity and
   Resilience, Physica A 356, 139 (2005).
5. E. Meron E. Gilad, Dynamics of plant
   communities in drylands A pattern formation
   approach, in  Complex Population Dynamics
   Nonlinear Modeling in Ecology, Epidemiology and
   Genetics, B. Blasius, J. Kurths, and L. Stone,
   Eds. , World-Scientific, 2007.

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References

1. E. Gilad, J. Von Hardenberg, A. Provenzale, M.
   Shachak, E. Meron, A mathematical Model for
   Plants as Ecosystem Engineers, J. Theor. Biol.
   244, 680 (2007).
2. E. Gilad, M. Shachak, E. Meron, Dynamics and
   spatial organization of plant communities in
   water limited systems , Theo. Pop. Biol. 72,
   214-230 (2007).
3. E. Meron, E. Gilad, J. Von Hardenberg, A.
   Provenzale, M. Shachak, Model studies of
   Ecosystem Engineering in Plant Communities, in
   Ecosystem Engineers Plants to Protists , Eds K.
   Cuddington et al., Academic Press 2007.
4. E. Sheffer E., Yizhaq H., Gilad E., Shachak M.
   and Meron E., Why do plants in resource
   deprived environments form rings? Ecological
   Complexity 4, 192-200 (2007).
5. E. Meron, H. Yizhaq and E. Gilad E., Localized
   structures in dryland vegetation forms and
   functions, Chaos 17, 037109 (2007)
6. Kletter A., von Hardenberg J., Meron E.,
   Provenzale A., "Patterned vegetation and rainfall
   intermittency", J. Theoretical Biology 2008.
7. Shachak M., Boeken B., Groner E., Kadmon R.,
   Lubin Y., Meron E., Neeman G., Perevolotsky A.,
   Shkedy Y. and Ungar E., " Woody Species as
   Landscape Modulators and their Effect on
   Biodiversity Patterns", BioScience 58, 209-221
   (2008).

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Biological soil crusts
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Desertification induced by drought
Remains of a spot pattern of Noaea mucronata in
the northern Negev
Moshe Shachak (2009)