Biodiversity and Stability
Dr. Mathew Williams
Complexity and stability
• Does a cellular process need all those
processes?
• Must an organism have so many genes?
• Does an ecosystem need all those species?
• Are more diverse (complex) ecosystems
more or less stable?
Forms of stability
• Resilience describes the speed with which a
community returns to its former state after
perturbation
• Resistance describes the ability of a
community to avoid displacement in the
first place
Resistance and Resilience to
Change
• Subsistence farmers plant diverse crops to
decrease chance of crop failure
• Diversity may reduce pest outbreak risks by
diluting host availability
• Microbial microcosms show less variability
in communities with greater species
richness (Naeem & Li, 1997)
Resistance to Invasions
• Theoretical models suggest that species-poor
communities have more empty niches and so are
more vulnerable to invasion
• Studies of intact ecosystems show both –ve and
+ve correlations between species richness and
invasion
• Vulnerability is probably strongly governed by
traits of resident and invading species rather than
species richness per se
• Absence of parasites is often critical for invasive
success
History of the biodiversitystability debate
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Early ideas of Elton and MacArthur
The models of May and others
Combinatorial biodiversity experiments
New approaches to modelling
MacArthur’s ideas (1955)
• If a population has diverse predator and
prey species, then…
• Changes in overall population abundance
are buffered against declines in the density
of individual species
• Insurance hypothesis: more diverse
communities can express a greater range of
responses to environmental perturbation
Elton’s observation
• “simple communities are… more easily
upset… than richer ones, that is, more
subject to destructive oscillations in
populations and more vulnerable to
invasions” (Elton, 1958)
Elton’s arguments
• Models of 2 interacting species are unstable
• Lab communities of 2 or few species are
difficult to maintain
• Islands (species-poor) are more vulnerable
to invasions than continents
• Crop monocultures are vulnerable to pests
• Species-rich tropical forests are less noted
for insect outbreaks than boreal forests
Counter arguments
• May has disproved the modelling
assumption
• Multi-species lab communities crash
(BIOSPHERE II)
• Introduced species can become pests on
continents
• Natural monocultures (salt marsh, bracken)
seem stable
• Insect abundance does fluctuate markedly in
tropical forests
May’s Model (1973)
• Created randomly constructed simulated
communities with randomly assigned
interaction strengths
• “we consider a simple mathematical model
for a many-predator-many-prey system, and
show it to be in general less stable, and
never more stable, than the analogous onepredator-one-prey community”
• Diversity tended to destabilize community
dynamics
May’s Model: interactions
bij measures the effect of species j’s density
on species i’s rate of increase
If bij & bji = 0, then there is no effect
bij & bji are negative for competing species
bij positive & bji negative for predator (i)
and prey (j)
May’s Model: set up
Set all bii = –1 (self-regulatory terms)
All other b values randomly assigned
b = average ‘interaction strength’ (ignore 0
and sign)
S = number of species
C = connectance (the fraction of all possible
pairs of species that interacted directly)
May’s Model: Results
Food webs are only likely to be stable if:
b(SC)<1
 species,  connectance,  interaction
strength   instability
Model versus Nature
• "the balance of evidence would seem to
suggest that, in the real world, increased
complexity is usually associated with
greater stability. There is no paradox
here....The real world is no general
system. Nature represents a small and
special part of parameter space [shaped
ultimately by evolutionary forces acting
on individuals]“ (May)
Interpretation
• real ecosystems "develop" by adding, and
losing, species over time, not by
randomly sampling ecological
possibilities.
• But there are no necessary, unavoidable
connections linking stability to
complexity
Random versus real
• Randomly assembled foodwebs can be
biologically unreasonable (e.g. loops)
• Reasonable foodwebs :
– Are more stable than unreasonable ones
(studies by Lawlor and by Pimm)
– Do not have a sharp transition zone from
stability to instability
Bottom-up controls
• Bottom-up or donor control: consumer
populations are affected by food supply,
but not vice versa (bij > 0 , bji = 0)
– Stability is unaffected by or increases with
complexity (DeAngelis, 1975)
• Examples are detritivores, seed-eaters,
parasitoid-host systems
Response to Perturbations
• Pimm (1979) created 6-species
communities (2 predators, 2 intermediate,
2 basal species)
• Varied connectance (i.e. complexity)
• Removal of top predator  stability
decreased with increasing complexity
• Removal of “basal” species (plants) 
stability increased with increasing
complexity
Is there supporting evidence
for May’s model?
• If we assume b is constant, then
species rich communities (high S) must
have less connectance (C) to remain as
stable
• Field data show that C can increase,
fall or stay the same with changes in S
b(SC)<1
Experimental Approaches
• Combinatorial methods are commonly used
to investigate all types of complexity
• The process is to deconstruct biological
systems into their separate parts…
• …and then systematically reconstruct arrays
of replicate systems that vary in
combinations of parts
Combinatorial biodiversity
experiments
Complex ecosystem,
8 species
(Naeem, 2002)
Biomass (plot size)
Varies among replicates
Complementarity
Sampling effect
(Naeem, 2002)
Large reductions in size indicate
Little resistance
Fast recovery is indicative of resilience
(Naeem, 2002)
Diversity-dependent production
can decrease stability
Pfisterer & Schmid, 2002
Effects of drought perturbation on
richness-production relations
 control
 drought
Ratio between preand post-drought
1 year later
Pfisterer & Schmid, 2002
Rearranging the insurance
hypothesis?
• Hypothesis: species-rich systems are more
productive because of niche-complementarity
• Perturbation disrupts complementarity
• Perturbed diverse communities thus suffer
more than simple communities lacking
complementarity
Conclusions?
• Problems with this experiment:
– small, short term, does not include other contributors to
the food web, such as herbivores or decomposers,
looked only at drought
• Problems with the conclusions:
– sampling could still be an issue
• Key output: the relationship between diversity and
stability may be determined by pre-stress
relationship between diversity and productivity
New approaches to modelling
• Use empirical measures of interaction
strength
• Non-equilibrium dynamics
• Food webs consistent with nature
• Biomass is the model currency
• Consumption rates become saturated as
resource density increases
Coupled oscillators
• Food chains can be seen as coupled
oscillators (e.g a consumer & a resource)
• Cyclic dynamics result when oscillators are
commensurate
• Quasi-periodic or chaotic dynamics
result when the oscillators are
incommensurate
Corollories
• Stabilizing all the underlying oscillators
eliminates the occurrence of cyclic or
chaotic dynamics in the full system
• Reducing the amplitude of the
underlying oscillators reduces the
amplitude of the dynamics of the full
system.
• Therefore, inhibiting strong consumer–
resource interactions within a food web
promotes persistence in food webs.
Three mechanisms inhibit
oscillatory subsystems
• Apparent competition mechanism (a
consumer preys on multiple resources)
• Exploitative competition mechanism (two
consumers compete for the same resource)
• Food-chain-predation mechanism (top
predator reduces consumer’s attack rate on
resource item)
P = predator
C = consumer
R = resource
a: simple
food chain
b: exploitative
competition
c: apparent
competition
d: intra-guild
predation
McCann et al (1998)
Exploitative competition
C2 can invade once
IC2R/IC1R  0.102
Below this value
the original food
chain (P–C1–R)
remains intact and
chaotic
Once C2 invades, dynamics become simpler
Once RIS > 0.15, the system moves towards chaos.
The new C2–R interaction has become too strong and no longer
dampens the system.
Apparent competition
Simple dynamics for
RIS < 0.12
Above this value C1
or C2 or even P are
knocked out
Weak links simplify and bound the dynamics
Intra-guild predation
We expect the apparent
competition mechanism to
inhibit the C1–R subsystem
and we expect the foodchain mechanism to inhibit
the C2–R subsystem.
2 inhibitors and 3 potential oscillators => the dynamics never
reach a locally stable equilibrium.
Stable case
1. Set IC2R/IC1R = 0.11
2. Add the apparent
competition mechanism
3. P-C1 system inhibited
4. Local stable solution for
weak interaction strengths
Testable predictions
• Relatively weak interactions coupled to strong
interactions reduce oscillations
• Food webs with many weak interactions should be
less chaotic
• Generalist dominated food webs should exhibit
less variable dynamics than specialist dominated
webs
• Depauperate food webs should be more oscillatory
than reticulate webs
• Data suggest a strong skew towards weak
interactions
Random versus actual
communities
• Compiled food-web relationships with
plausible interaction strengths are more
stable than randomly constructed food webs
• This suggests that interaction strength is
critical for stability
What you should have learned
today
• A history of the biodiversity-stability debate
• The utility of combinatorial experiments
• The insights that modelling brings to the
debate
• And that the debate continues.
References
• McCann K, Hastings A, Huxel GR (1998) Weak trophic
interactions and the balance of nature. Nature, 395, 794798.
• McCann KS (2000) The diversity–stability debate. Nature,
405, 228-233.
• Naeem S (2002) Biodiversity equals instability? Nature,
406, 23-24.
• Pfisterer AB, Schmid B (2002) Diversity-dependent
production can decrease the stability of ecosystem
functioning. Nature, 416, 84-86.
Reading from last week
• Pfisterer. A.B. & B. Schmid. 2002. Diversity-dependent
production can decrease the stability of ecosystem
functioning. Nature 416 84-86
– what insights does this experiment provide?
– what are the criticisms of the approach?
• McCann, K., A. Hastings G. R. Huxel. 1998. Weak trophic
interactions and the balance of nature. Nature 395 794-8
– what insights does the modelling provide?
– what are the criticisms of the approach?