Diversity-Productivity, Diversity-Invasibility,

1
Diversity-Productivity, Diversity-Invasibility,
Diversity-Stability Relationships
Warmer sea-surface temperatures (indicated by
warmer colors) higher productivity
Image from Committee on Earth Observation
Satellites (CEOS) http//www.ceos.org/
2
Diversity-Productivity Relationship
Many shapes for this relationship have been
observed in nature
Rosenzweig Abramsky (1993)
3
Diversity-Productivity Relationship
Many shapes for this relationship have been
observed in nature
Rosenzweig Abramsky (1993)
4
Diversity-Productivity Relationship
Many shapes for this relationship have been
observed in nature
III.
II.
I.
S or D
S or D
S or D
Productivity
Productivity
Productivity
Sometimes curves like I and III may arise from
sampling opposite ends of productivity gradients
in which curve II is the overall relationship
II. a.
II. b.
S or D
S or D
Productivity
Productivity
5
Diversity-Productivity Relationship
Many shapes for this relationship have been
observed in nature
Mittelbach et al. (2001) Methods
Examined the relationship between productivity
diversity for 171 studies Observations
Even though many researchers are enamored
of hump-shaped curves, the curves vary
dramatically from site-to-site, as well as within
among taxonomic groups
Suggestions and conclusions
Dont assume a particular relationship measure
it Be wary of the independent variable
used as a surrogate for productivity
6
Diversity-Productivity Relationship
Many shapes, but what are the mechanisms?
Tilman (1982, 1988), Tilman et al. (1996),
etc. Explained hump-shaped curves by the changes
in heterogeneity that sometimes accompany changes
in resource availability
A
A
B
A
B
B
A
A
B
B
B
A
A
A
B
B
A
A
A
B
B
A
B
A
A
B
B
A
B
B
A
B
A
A
A
B
B
A
B
E.g., soil fertility / productivity gradient
poorest soil species A out- competes species B
richest soil species B out- competes species A
7
Diversity-Productivity Relationship
Rosenzweig Abramsky (1993) Summarized several
mechanistic hypotheses for hump-shaped
curves Suggested that separate mechanisms
account for the rising vs. falling portions

Preferred mechanism for the rising portion
A poor environment supplies too meager a
resource base for its would-be rarest
species, and they become extinct In
other words poor environments support lower
population sizes, and population size is
inversely related to extinction probability
No well-supported mechanism for the falling
portion Provided several potential
mechanisms, but claimed that none are
well-supported by observations or experiments
even so, Tilmans heterogeneity hypothesis
has some empirical support

8
Diversity-Productivity Relationship
Stevens Carson (2001) Declining curves could
result simply from size differences if sites are
sampled with the same sized plots, more
productive sites may have fewer species because
they have fewer individuals, especially owing to
the ubiquitous clumping that occurs in natural
populations


A
A
A
A
A
A
B
A
A
A
B
B
B
A
B
A
E.g., cloudiness-induced productivity gradient
lowest light availability
highest light availability
Use an index that is insensitive to sample size
How might this problem be avoided?
9
Diversity-Productivity Relationship
Kyles conjecture If disturbance, predation,
competitive equivalence, or dispersal limitation
occur alone or in combination such that
competitive exclusion does not occur among the
recruits of species within a guild (especially
plants), then sites with conditions in which more
species are capable of surviving and reproducing
will contain more species, i.e., diversity will
increase up the resource (e.g., fertility)
gradient

10
Diversity-Productivity Relationship
A hump-shaped diversity-productivity relationship
could result in the Paradox of Enrichment
within trophic levels
Community sampled before fertilization
Community sampled after moderate-level
fertilization
Community sampled after high-level fertilization
Species diversity
Productivity
11
Diversity-Productivity Relationship
A hump-shaped diversity-productivity relationship
could result in the Paradox of Enrichment
within trophic levels
Gough et al. (2001) Methods
Examined long-term experiments from 7 Long-Term
Ecological Research (LTER) sites in
North America Observations
Nearly all demonstrated a decline in diversity
after fertilization

Suggestions conclusions The
results have utility for similar situations, but
little relevance to natural
productivity gradients, since species
distributions along natural gradients
are influenced by long-term ecological
evolutionary processes, e.g., species
may preferentially colonize or originate within
sites of high productivity, giving
rise to a positive relationship
12
Diversity-Productivity Relationship(Productivity-
Diversity)
So far we have considered productivity gradients
due to gradients in resource availability, e.g.,
physical gradients What happens when we reverse
the axes, and ask how diversity in a given site,
i.e., one set of physical conditions, influences
productivity?

13
Diversity-Productivity Relationship(Productivity-
Diversity)
Examples from artificial communities
Loreau et al. (2001) Biodiversity and
Ecosystem Functioning Methods
Compiled data from a variety of field, Ecotron
other mesocosm experiments in which S
or D were varied experimentally
Observations

Sites of high intrinsic resource availability
Productivity
Sites of low intrinsic resource availability
S or D
14
Diversity-Productivity Relationship(Productivity-
Diversity)
Examples from artificial communities
Loreau et al. (2001) Biodiversity and
Ecosystem Functioning Conclusions
A monotonic or saturating curve almost always
results from experimental settings
examining the influence of diversity on
productivity

At least two mechanisms can
create a positive relationship between
diversity and productivity 1.
Complementarity species use complementary niche
space 2. Sampling random
sampling a large species pool is more likely to
select a key (highly
productive) species than sampling a small pool
How might these two mechanisms differ in
their implications for conservation,
global change, etc., especially with respect to
redundancy?
15
Diversity-Productivity Relationship(Productivity-
Diversity)
Diversity
Latitudinal gradient
Productivity
Diversity
Biomass gradient
Productivity
Productivity
Diversity
Experimental diversity gradient
Diversity
Productivity
For plants, the relationship may change with
scale (see Mittelbach et al. 2001) Experimental
manipulations of plant diversity within
habitats generally yield positive relationships
Figure from Purvis Hector (2000)
16
Diversity-Invasibility Relationship
This is especially germane in todays world of
rampant spread of exotic species, i.e., the
homogenization of biodiversity
Charles Elton first proposed that more
diverse communities should be less invasible
Photo of Charles Elton from http//www.wku.edu/sm
ithch/chronob/ELTO1900.htm
17
Diversity-Invasibility Relationship
This is especially germane in todays world of
rampant spread of exotic species, i.e., the
homogenization of biodiversity
Fargione et al. (2003) Methods
Experimental, grassland plots containing mixtures
of plants from four functional
guilds C3 (cool-season) grasses, C4
(warm-season) grasses, legumes,
non-N-fixing forbs Experimentally
introduced seeds of representatives of each guild
Results and conclusion C4
grasses exhibited the greatest inhibitory effect
on introduced species (i.e., they were
competitive dominants) established species from
each functional guild most strongly
inhibited species from its own guild
Diversity reduces invasibility, both by
increasing the chances of encountering
established plants of the same guild (close
competitors cannot invade), as well
as established plants of the dominant guild (a
sampling effect)
18
Diversity-Invasibility Relationship
This is especially germane in todays world of
rampant spread of exotic species, i.e., the
homogenization of biodiversity
Levine (2000) Methods Removed
non-Carex species from sedge tussocks along
streams in California, and
subsequently added 1, 3, 5, 7, 9 native species,
but kept the total cover of plants
identical After one year, added 200
seeds of 3 exotic species to each tussock
Results and conclusion Fewer
exotic seedlings established on more species-rich
tussocks Increased diversity provides
increased immunity to invasion
Levine also found that diversity of native
species was positively related to diversity
of exotics in unmanipulated tussocks
In light of his experimental results, how
could this happen?
19
Diversity-Stability Relationship
Initial empirical guess
MacArthur (1955) a.k.a. complexity-stabilit
y relationship Alternative energy pathways
in complex food webs might favor more constant
population sizes with reduced fluctuations,
thus promoting stability
20
Diversity-Stability Relationship
Early modeling results
May (1973) Challenged MacArthurs intuition
verbal arguments with mathematical models
that showed no theoretical basis for the
relationship to necessarily be in any
particular direction (all possibilities could be
obtained)
21
Diversity-Stability Relationship
Back to empiricism, with potential reasons for
differences of opinion
Pimm (1984 1991) Three levels of organization
at which to measure stability
Population Community (especially community
composition) Ecosystem (especially biomass,
energy flux, or the flux of matter,
e.g., C, N, etc.)
22
Diversity-Stability Relationship
Back to empiricism, with potential reasons for
differences of opinion
Pimm (1984 1991) Five definitions for
stability
Stability (in the strict mathematical
sense) a system is stable if, and only if,
the variables all return to equilibrium
conditions after displacement from them
Resilience the rapidity with which a
variable that has been displaced from
equilibrium returns to it
Persistence the duration that a
variable maintains a given value until it
changes to a new value
Resistance the degree to which
other variables change when a given variable
is permanently changed to a new value
Variability the degree to which
a variable varies over time
23
Diversity-Stability Relationship
Back to empiricism, with potential reasons for
differences of opinion
Pimm (1984 1991) At least three definitions
for complexity Species richness S
Connectance the degree to which all nodes
interconnect with other
nodes in a food web Relative
abundance D and this isnt an
exhaustive list!
(3 levels of ecological organization) x (5
definitions of stability) x (3 definitions of
complexity) at least 45 different
questions that could be asked about the
relationship between community complexity
stability!
24
Diversity-Stability Relationship
Mechanisms that could generate a positive
relationship between species diversity
ecosystem-level stability
McCann (2000)
Averaging effect Assume covariances between
species are zero and variance (si2) in abundance
of individual species i in a plant community is
equal to cmiz, where c and z are constants and mi
is the mean density of species i. Given that all
k species in a community are equal in abundance
and sum to m (that is, mim/k), then the
coefficient of variation (CV) of community
abundance can be determined as CV 100s/m
100(c/k)1/z For the case z gt 1, increasing k
(species number) decreases the variation in
biomass for the plant community
25
Diversity-Stability Relationship
Mechanisms that could generate a positive
relationship between species diversity
ecosystem-level stability
McCann (2000)
Negative-covariance effect If covariances
between species (say, species a and b) are
negative (that is, cov(a,b)lt0), then the variance
in the abundance of two species s2(ab) sa2
sb2 2cov(a,b) will be less then the sum of
the individual variances (that is, sa2 sb2),
and so will decrease overall biomass variance in
the plant community
26
Diversity-Stability Relationship
Mechanisms that could generate a positive
relationship between species diversity
ecosystem-level stability
McCann (2000)
Insurance effect An ecosystems ability to
buffer perturbations, loss in species and species
invasions is dependent on the redundancy of the
species having important stabilizing roles, as
well as on the ability of the species in the
community to respond differently to
perturbations. Increasing diversity increases
the odds that such species exist in an ecosystem.
This idea has been extended to suggest that the
greater the variance of species responses in a
community then the lower the species richness
required to buffer an ecosystem. increasing
diversity increases the odds that at least some
species will respond differentially to variable
conditions and perturbations greater diversity
increases the odds that an ecosystem has
functional redundancy by containing species that
are capable of functionally replacing important
species taken together, these two notions have
been called the insurance hypothesis
27
Diversity-Stability Relationship
Mechanisms that could generate a positive
relationship between species diversity
ecosystem-level stability
McCann (2000)
Weak-interaction effect Weak interactions
serve to limit energy flow in a potentially
strong consumer-resource interaction and,
therefore, to inhibit runaway consumption that
destabilizes the dynamics of food webs. In
addition, the weak interactions serve to generate
negative covariances between resources that
enable a stabilizing effect at the population
community level. The negative covariances ensure
that consumers have weak consumptive influences
on a resource when the resource is at low
densities.