Orlando Sarnelle

Resolving ecological questions through meta-analysis: Goals, metrics, and models

We evaluate the goals of meta-analysis, critique its recent application in ecology, and highlight an approach that more explicitly links meta-analysis and ecological theory. One goal of meta-analysis is testing null hypotheses of no response to experimental manipulations. Many ecologists, however, are more interested in quantitatively measuring processes and examining their systematic variation across systems and conditions. This latter goal requires a suite of diverse, ecologically based metrics of effect size, with each appropriately matched to an ecological question of interest. By specifying ecological mod- els, we can develop metrics of effect size that quantify the underlying process or response of interest and are insensitive to extraneous factors irrelevant to the focal question. A model will also help to delineate the set of studies that fit the question addressed by the meta- analysis. We discuss factors that can give rise to heterogeneity in effect sizes (e.g., due to differences in experimental protocol, parameter values, or the structure of the models that describe system dynamics) and illustrate this variation using some simple models of plant competition. Variation in time scale will be one of the most common factors affecting a meta-analysis, by introducing heterogeneity in effect sizes. Different metrics will apply to different time scales, and time-series data will be vital in evaluating the appropriateness of different metrics to different collections of studies. We then illustrate the application of ecological models, and associated metrics of effect size, in meta-analysis by discussing and/or synthesizing data on species interactions, mutual interference between consumers, and individual physiology. We also examine the use of metrics when no single, specific model applies to the synthesized studies. These examples illustrate that the diversity of ecological questions demands a diversity of ecologically meaningful metrics of effect size. The successful application of meta-analysis in ecology will benefit by clear and explicit linkages among ecological theory, the questions being addressed, and the metrics used to summarize the available information.

RESISTANCE AND RESILIENCE OF ALPINE LAKE FAUNA TO FISH INTRODUCTIONS

This paper reports on the response by amphibians, benthic macroinverte- brates, and zooplankton in naturally fishless alpine lakes to fish introductions and subsequent fish disappearance. We assessed resistance (the degree to which a system is altered when the environment changes) by comparing faunal distribution and abundance in lakes that have never been stocked with fish vs. the distribution and abundance in lakes that have been stocked and still contain fish. We assessed resilience (the degree and rate of a systems return to its previous configuration once the perturbation is removed) by comparing faunal distribution and abundance in lakes that were stocked at one time but have since reverted to a fishless condition (stocked-now-fishless lakes) vs. the distribution and abundance in lakes that have never been stocked. We quantified recovery rates and trajectories by com- paring faunal assemblages of stocked-now-fishless lakes that had been fishless for 5-10, 11-20, and .20 yr. Faunal assemblages in the study lakes had low resistance to fish introductions, but in general showed high resilience. The mountain yellow-legged frog (Rana muscosa), con- spicuous benthic macroinvertebrates, and large crustacean zooplankton (.1 mm) were dramatically reduced in distribution and abundance by fish introductions but generally recovered to predisturbance levels after fish disappearance. Inconspicuous benthic inver- tebrate taxa, small crustacean zooplankton (,1 mm), and rotiferan zooplankton (,0.2 mm) were either unaffected by fish or increased in the presence of fish. For both the benthic macroinvertebrate community and the zooplankton community as a whole, fish disappear- ance was followed by a steady change away from the configuration characteristic of fish- containing lakes and toward that of lakes that had never been stocked. Both communities remained markedly different from those in never-stocked lakes 5-10 yr after fish disap- pearance and converged on the configuration of never-stocked lakes only 11-20 yr after fish disappearance. Recovery was likely facilitated by the winged adult stages of many benthic macroin- vertebrates, resting eggs of zooplankton, and nearby source populations of frogs. However, many frog populations have disappeared since the time that lakes in this study reverted to a fishless condition, and the viability of zooplankton egg banks should decline in fish- containing lakes over time. As a result, faunal resilience may be lower in lakes that revert to a fishless condition today than is suggested by the results of our study. These findings have important implications for the restoration of alpine lake ecosystems.

Effect size in ecological experiments: The application of biological models in meta-analysis

Some of the most interesting and important questions in ecology require examination of the strength of different processes across environmental gradients and among organisms with different traits (Quinn and Dunham 1983; Tilman 1989; Cooper et al. 1990; Sarnelle 1992; Osenberg and Mittelbach 1996). Metaanalysis (see, e.g., Gurevitch et al. 1992; Gurevitch and Hedges 1993; Arnqvist and Wooster 1995; Curtis 1996) combines results from independent studies to examine patterns of effect across taxa or environments and, thus, may represent a powerful tool to test ecological theory. A meta-analysis requires that a common metric of effect size be extracted from each of the studies. Here, we focus on choosing a metric that best facilitates ecological inferences. We begin with a brief description of the standard definition of effect size in meta-analysis, as used in recent papers. We then discuss potential problems with this approach and suggest an alternative that is more explicitly tied to the dynamics of ecological systems. Using two examples drawn from predator-prey experiments, we then illustrate the limitations of the standard metric and the conceptual advantages of one ecologically based alternative. We conclude by discussing the link between metrics of effect size and ecological models.

Nutrient Enrichment and Grazer Effects on Phytoplankton in Lakes

I derived predictions about how the magnitude of Daphnia effects on total phytoplankton biomass should vary across a gradient of enrichment (expressed as algal carrying capacity) using two, simple predator-prey models. These predictions were then compared with data from a survey of field experiments in temperate lakes. Algal responses to Daphnia manipulation were quantified as an Algal Response Factor (ARF), defined as total algal biomass in the low-Daphnia treatment divided by total algal biomass in the high-Daphnia treatment. Total phosphorus concentration (TP) was used as an index of algal carrying capacity, ranging from 10 to 460 gg/L over the 22 experiments surveyed. The Algal Response Factor ranged from 1 to 40 and was a positive, linear function of TP: ARF = -0.14 + 0.08(TP), r2 = 0.81; log ARF = -0.81 + 0.83(log TP), r2 = 0.75. Thus, algal carrying capacity, as quantified by TP, explains much of the variation in Daphnia effects on total algal biomass across lakes. The survey results supported the prediction of the simpler model, a two-species, Lotka- Volterra model of pure exploitation. Incorporating the additional complexity of inedible algae into this model did little to improve its predictive power. The conclusion that inedible algae are not of major importance to the prediction of Daphnia effects across an enrichment gradient was supported by a survey of Daphnia effects on the proportionate biomass of inedible algae. There was no evidence that Daphnia grazing typically favors dominance by inedible algae at equilibrium in highly enriched lakes. My results suggest that the well-established positive relationship between TP and equi- librium algal biomass in lakes is more likely to be a consequence of increases in Daphnias death rate with enrichment, rather than decreases in Daphnias feeding and assimilation rates. When zooplanktivorous fish are rare, Daphnia should be able to prevent phytoplank- ton biomass from responding to nutrient addition at equilibrium. As a consequence, the success of biomanipulation in eutrophic lakes should critically depend upon the effective- ness of strategies aimed at reducing zooplanktivory.

Native predators and exotic prey - an acquired taste?

Only a small proportion of exotic species invasions give rise to hyper-successful nuisance species, but those that do have dramatic negative impacts on ecosystems, such as the displacement of native species and disruption of native food webs. For a native predator, such changes may mean a major transformation in its resource base and a decline in its fitness. However, native predators may adapt to become more effective at feeding on exotic prey, either rapidly, via existing phenotypic plasticity, or more slowly, via natural selection. Despite a rapidly growing number of publications on the importance of species invasions as a driver of contemporary evolution in both invading and native species, we know little about how the arrival of exotic prey affects native predators. We propose that native predators could be important in regulating the long-term dynamics of invading species and, consequently, that the overexploitation of predators could facilitate biological invasions.

META‐ANALYSIS OF MARINE NUTRIENT‐ENRICHMENT EXPERIMENTS: VARIATION IN THE MAGNITUDE OF NUTRIENT LIMITATION

Nutrient bioassay experiments have been performed in many marine and estuarine environments around the world. Although protocols have been relatively uniform, these experiments have yielded mixed results, implicating nitrogen, phosphorus, silica, iron, and several other elements as factors limiting phytoplankton growth. Meta-analysis has the potential to explain much of this variation by exploring the relationship between the magnitude of limitation and various environmental characteristics. We quantified limitation with a simple metric, Δr, that estimates the change in the per unit growth rate of phytoplankton directly attributable to addition of a specific nutrient, such as nitrogen, iron, or phosphorus. Preliminary analyses indicated that experiments lasting ≤1 d exhibited time lags in the numerical response of phytoplankton to nutrient addition, while experiments lasting >7 d confounded nutrient limitation with processes such as increased grazing or depletion of other nutrients. Thus, we restricted th...

THE IMPORTANCE OF DATA-SELECTION CRITERIA: META-ANALYSES OF STREAM PREDATION EXPERIMENTS

The value of meta-analysis in ecology hinges on the reproducibility of patterns generated by quantitative synthesis. Meta-analysts will vary in the criteria they use to screen studies and select data within studies, even when addressing exactly the same question. We summarize some of the many decisions that an ecologist must make in deciding what data to include in a synthesis. We then show, using multiple meta-analyses taken from the same literature on stream predation experiments, that meta-analytic conclusions can be colored by selection criteria that are not specifically a function of the relevance of the data. As a consequence, we recommend that meta-analysts perform several meta-analyses using different selection criteria to examine the robustness of reported findings. We also advise ecological meta-analysts to minimize use of selection criteria that are based on judgments of study quality when extracting data from the literature, because of the potential for unconscious bias. The influence of quali...

Genetic variation of the bloom-forming cyanobacterium Microcystis aeruginosa within and among lakes: Implications for harmful algal blooms

ABSTRACT To measure genetic variation within and among populations of the bloom-forming cyanobacterium Microcystis aeruginosa, we surveyed a suite of lakes in the southern peninsula of Michigan that vary in productivity (total phosphorus concentrations of ∼10 to 100 μg liter−1). Survival of M. aeruginosa isolates from lakes was relatively low (i.e., mean of 7% and maximum of 30%) and positively related to lake total phosphorus concentration (P = 0.014, r2 = 0.407, n = 14). In another study (D. F. Raikow, O. Sarnelle, A. E. Wilson, and S. K. Hamilton, Limnol. Oceanogr. 49:482-487, 2004), survival rates of M. aeruginosa isolates collected from an oligotrophic lake (total phosphorus of ∼10 μg liter−1 and dissolved inorganic nitrogen:total phosphorus ratio of 12.75) differed among five different medium types (G test, P of <0.001), with higher survival (P = 0.003) in low-nutrient media (28 to 37% survival) than in high-nutrient media. Even with the relatively low isolate survivorship that could select against detecting the full range of genetic variation, populations of M. aeruginosa were genetically diverse within and among lakes (by analysis of molecular variance, Φsc = 0.412 [Φsc is an F-statistic derivative which evaluates the correlation of haplotypic diversity within populations relative to the haplotypic diversity among all sampled populations], P = 0.001), with most clones being distantly related to clones collected from lakes directly attached to Lake Michigan (a Laurentian Great Lake) and culture collection strains collected from Canada, Scotland, and South Africa. Ninety-one percent of the 53 genetically unique M. aeruginosa clones contained the microcystin toxin gene (mcyA). Genotypes with the toxin gene were found in all lakes, while four lakes harbored both genotypes possessing and genotypes lacking the toxin gene.

Meta-analysis of cyanobacterial effects on zooplankton population growth rate : species-specific responses

We analyzed a large data set of laboratory experiments to examine the effects of cyanobacteria containing or lacking intracellular toxic metabolites and of different morphology on zooplankton population growth rates across multiple genera and species of cladocerans, rotifers and cyanobacteria. Twenty-one of the 29 zooplankton species maintained positive growth rates when fed a diet containing cyanobacteria even though cyanobacteria were a poor food source for half of the zooplankton species tested relative to a diet containing only green algae and/or flagellates. Differences among zooplankton species could not be explained by grazer species body lengths, even when experiments were restricted to those that used only filamentous cyanobacteria. Single-celled cyanobacteria were more detrimental to a larger number of zooplankton species compared to filamentous or chroococcoid colonial cyanobacteria. We also found no clear effect of putative cyanobacterial toxins on the growth of seven zooplankton species but we did detect a negative effect for the largest cladoceran species, Daphnia magna. Among the cyanobacterial genera, Microcystis had the largest negative effect on zooplankton population growth and there was no consistent difference between M. aeruginosa strains that produced microcystins and those that did not. Our results highlight the large variation in species-specific responses of zooplankton to cyanobacteria. Although cyanobacterial toxicity and mechanical interference may be important drivers in particular cyanobacteria-zooplankton interactions, we did not find general support for these mechanisms through the use of this meta-analysis.

DAPHNIA EFFECTS ON MICROZOOPLANKTON: COMPARISONS OF ENCLOSURE AND WHOLE‐LAKE RESPONSES

The effects of the herbivorous zooplankter, Daphnia, on a natural community of microzooplankton (rotifers, ciliates, and nanoflagellates) were compared in enclosures of two sizes (15 and 10000 L) and in a eutrophic lake before and after a fish kill. The magnitude of Daphnias effect on microzooplankton taxa varied quantitatively and quali- tatively between experiments. The rotifer Synchaeta pectinate and the ciliate, Didinium sp., showed extreme differences between experiments, exhibiting opposite responses in small vs. large enclosures. The relative rankings of responses for two rotifers (Polyarthra dolichoptera and Synchaeta pectinate) and two ciliates (Coleps sp. and Didinium sp.) were reversed in small vs. large enclosures. Polyarthra was depressed by Daphnia more than Synchaeta in small enclosures, while Synchaeta was depressed more than Polyarthra in the large enclosures. Didinium was depressed more than Coleps in the small enclosures, while the reverse occurred in large enclosures. Microzooplankton responses also changed over time in the large-enclosure experiment. Daphnia significantly suppressed total ciliate dry biomass, but not total rotifer biomass after 6 d, but suppressed dry biomass of both groups by the end of the 23-d experiment. This result may reflect changes in the relative importance of Daphnias predatory and competitive effects over time. Daphnias effects on the rotifers, Polyarthra and Hexarthra mira, took 3 wk to be expressed but were very strong by the end of the large-enclosure experiment, suggesting that short-term experiments may underestimate competitive effects. Polyarthras delayed response was associated with a delayed response of cryptophytes to the Daphnia manipulation. Comparisons of enclosure results with temporal correlations in lake data and with microzooplankton abundances before and after a fish kill indicated better congruence be- tween lake data and the large-enclosure results. More importantly, large-enclosure results agreed more closely with whole-lake dynamics than with small-enclosure results. Conse- quently, large-scale enclosure experiments may provide reliable predictions of whole-lake phenomena, but small-scale (microcosm) experiments may not.