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 biodiversity-stability debate

• 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 one-predator-one-prey community”

• Diversity tended to destabilize community dynamics

May’s Model: interactions

ij measures the effect of species j’s density on species i’s rate of increase

If ij & ji = 0, then there is no effect

ij & ji are negative for competing species

ij positive & ji negative for predator (i) and prey (j)

May’s Model: set up

Set all ii = –1 (self-regulatory terms)All other values randomly assignedaverage ‘interaction strength’ (ignore 0

and sign)S = number of speciesC = connectance (the fraction of all possible

pairs of species that interacted directly)

Food webs are only likely to be stable if:

species, connectance, interaction strength instability

May’s Model: Results

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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 (ij > 0 , ji = 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 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

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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

(Naeem, 2002)

Sampling effectComplementarity

(Naeem, 2002)

Large reductions in size indicate Little resistance

Fast recovery is indicative of resilience

Diversity-dependent production can decrease stability

Pfisterer & Schmid, 2002

Effects of drought perturbation on richness-production relations

control drought

1 year later

Ratio between pre-and post-drought

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 = predatorC = consumerR = resource

a: simple food chainb: exploitative competitionc: apparent competitiond: intra-guild predation

McCann et al (1998)

Below this value the original food chain (P–C1–R) remains intact and chaotic

C2 can invade once IC2R/IC1R 0.102

Exploitative competition

Once C2 invades, dynamics become simplerOnce RIS > 0.15, the system moves towards chaos. The new C2–R interaction has become too strong and no longerdampens the system.

Above this value C1 or C2 or even P are knocked out

Simple dynamics for RIS < 0.12

Apparent competition

Weak links simplify and bound the dynamics

2 inhibitors and 3 potential oscillators => the dynamics neverreach a locally stable equilibrium.

We expect the apparent competition mechanism to inhibit the C1–R subsystem and we expect the food-chain mechanism to inhibit the C2–R subsystem.

Intra-guild predation

1. Set IC2R/IC1R = 0.112. Add the apparent competition mechanism3. P-C1 system inhibited4. Local stable solution for weak interaction strengths

Stable case

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, 794-798.

• 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?