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/

Diversity-Productivity Relationship Many shapes for this relationship have been observed in nature Rosenzweig & Abramsky (1993)

Diversity-Productivity Relationship Many shapes for this relationship have been observed in nature Rosenzweig & Abramsky (1993)

Diversity-Productivity Relationship Many shapes for this relationship have been observed in nature I. II. III. 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

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: Don’t assume a particular relationship – measure it Be wary of the independent variable used as a surrogate for “productivity”

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 A A B B A A B B B B A A A B A A B B B A A A B B B A B B A B A A A A B B B E.g., soil fertility / productivity gradient = poorest soil; species A out- competes species B = richest soil; species B out- competes species A

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, Tilman’s heterogeneity hypothesis has some empirical support

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 A B B B A A B A B A E.g., cloudiness-induced productivity gradient = lowest light availability = highest light availability How might this problem be avoided? Use an index that is insensitive to sample size

Diversity-Productivity Relationship Kyle’s 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 Resource availability, e.g., soil fertility Species 1 Species 2 Species 3 Species 4 Species 5 Species 6 Species-rich community at high end of resource gradient Species-poor community at low end of resource gradient In other words, if species’ realized niches closely track their fundamental niches, and fundamental niches overlap primarily at the high end of resource availability, then there should be a positive diversity-productivity relationship.

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

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

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?

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

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?

Diversity-Productivity Relationship (Productivity-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)

Diversity-Invasibility Relationship This is especially germane in today’s 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/~smithch/chronob/ELTO1900.htm

Diversity-Invasibility Relationship This is especially germane in today’s 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)

Diversity-Invasibility Relationship This is especially germane in today’s 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?

Diversity-Stability Relationship Initial empirical guess… MacArthur (1955) a.k.a. “complexity-stability” relationship Alternative energy pathways in complex food webs might favor more constant population sizes with reduced fluctuations, thus promoting stability

Diversity-Stability Relationship Early modeling results… May (1973) Challenged MacArthur’s 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)

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.)

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

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 isn’t 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!

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, mi=m/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 > 1, increasing k (species number) decreases the variation in biomass for the plant community”

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)<0), then the variance in the abundance of two species: s2(a+b) = 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”

Diversity-Stability Relationship Mechanisms that could generate a positive relationship between species diversity & ecosystem-level stability… McCann (2000) – Insurance effect – “An ecosystem’s 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”

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.”