Scaling Up in Ecology: Mechanistic Approaches · to the simultaneous variation of multiple factors. Fluid dynamic theory of ocean waves provides an example. Wave-swept rocky shores

ES43CH01-Denny ARI 1 October 2012 11:53

Scaling Up in Ecology:Mechanistic ApproachesMark Denny1 and Lisandro Benedetti-Cecchi21Hopkins Marine Station of Stanford University, Pacific Grove, California 93950;email: [email protected] of Biology, University of Pisa, 56126, Pisa, Italy;email: [email protected]

Annu. Rev. Ecol. Evol. Syst. 2012. 43:1–22

First published online as a Review in Advance onAugust 28, 2012

The Annual Review of Ecology, Evolution, andSystematics is online at ecolsys.annualreviews.org

This article’s doi:10.1146/annurev-ecolsys-102710-145103

Copyright c© 2012 by Annual Reviews.All rights reserved

1543-592X/12/1201-0001$20.00

Keywords

criticality, dispersal distance, environmental bootstrap, extreme events,pattern formation, random walks, response function, scale transition,self-organization

Abstract

Ecologists have long grappled with the problem of scaling up from tractable,small-scale observations and experiments to the prediction of large-scalepatterns. Although there are multiple approaches to this formidable task,there is a common underpinning in the formulation, testing, and use ofmechanistic response functions to describe how phenomena interact acrossscales. Here, we review the principles of response functions to illustrate howthey provide a means to guide research, extrapolate beyond measured data,and simplify our conceptual grasp of reality. We illustrate these principleswith examples of mechanistic approaches ranging from explorations of theecological niche, random walks, and macrophysiology to theories dealingwith scale transition, self-organization, and the prediction of extremes.

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INTRODUCTION: RELATING PHENOMENA ACROSS SCALES

In a classic perspective on the role of modeling in ecology, Levin (1992) noted that “the problem ofrelating phenomena across scales is the central problem in biology and in all of science.” Currently,there are three predominant ecological perspectives on this fundamental issue. Proponents ofmacroecology (e.g., Brown 1995) begin with a search for scaling “laws” through an examinationof empirical data measured over wide ranges of scale. If substantial correlations exist—betweenbody mass and metabolic rate, for instance—macroecologists then proceed to test hypothesesconcerning the mechanisms that underlie these correlations (McGill & Nekola 2010). In theconverse of this “top-down” approach, community ecologists traditionally take a “bottom-up”perspective, using small-scale field observations and experimental manipulation to infer patternat larger scales (Underwood & Paine 2007). Both top-down and bottom-up perspectives beginwith empirical data. In contrast, ecological theorists begin with a conceptual map of how scalesmight be related. Only after these initial heuristic models have been validated qualitatively aresubsequent quantitative models tested empirically.

As distinct as they are, these perspectives are not independent. Both macroecologists andexperimental ecologists are guided by theoretical concepts, and theorists rely on these researchersto provide observations from which concepts are born and data against which models can be tested.Indeed, it is through the interaction of these perspectives that ecology can best relate phenomenaacross scales.

Interaction is easiest on common ground. Although ecologists of all stripes seem to find pleasurein promoting the differences among their approaches, there is a philosophical unity underlyingthese disparate perspectives. Each assumes that the connections of biology at one scale of timeor space to that at other scales can be described by response functions, mathematical expressionsof how systems respond to the conditions in which they find themselves. Although widely used,the concept of a response function appears under a confusing variety of names. For example, inecology, functional response describes how the rate of prey capture varies with changes in preydensity. In physiology, thermal reaction norms quantify the fitness of an organism as a function ofits body temperature. In physics, Boyle’s law specifies how the volume of a gas varies as a functionof pressure, and Newton’s second law of motion predicts how the acceleration of a mass dependson the force applied to it. Despite the differences in nomenclature, each of these mathematicaldescriptors is a response function.

Biological response functions take three general forms. Conceptual response functions—thegrist of theoretical ecology—describe, usually in a simple, abstract, and mathematically tractableform, how a system might respond in an idealized world. They are often used as the first steptoward defining connections across scales. By organizing key concepts and processes and provid-ing qualitative answers, they can be used to identify which parameters at one scale are likely tohave greatest impact at others. The second category of functions is that of measured responsefunctions, i.e., the measured response to a physical variable, as defined by Huey & Stevenson(1979). Measured response functions provide a practical means by which to connect a process atone level of organization (e.g., escape speed) to that at a higher level (e.g., survivorship). However,without a mechanistic explanation, the connection of measured response functions to processes atlower levels of organization (e.g., muscle physiology) is uncertain. To obtain full understandingof a system across multiple scales, it is therefore necessary to define and test the potential mech-anisms that account for measured responses. These are response functions in the sense of thethird category defined by Holling (1965): a mechanistic, quantitative explanation of the responseof an environmental factor, physiological process, whole organism, population, or community asa function of some physical variable. At their most fundamental, mechanistic response functions

2 Denny · Benedetti-Cecchi

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are explicit applications of the principles of physics, engineering, and chemistry; at higher lev-els, they may apply well-established principles of physiology, behavior, and statistical mechanics.Although their connections can be complex—and unexpected properties may emerge from theirinteractions—mechanistic response functions form the basis for our understanding of biology.

RESPONSE FUNCTIONS: PRINCIPLES AND CHARACTERISTICS

Two examples illustrate the formulation and utility of mechanistic response functions. The firstdescribes response to a single variable and the second to multiple variables.

Predator-Prey Response Functions

In an elegant experiment, Holling (1959) blindfolded a student and had her tap her finger on awall to locate randomly placed sandpaper discs. When a disc was located, the student removed it,set it aside, and searched again. The rate at which discs were “captured” was analyzed as a functionof their spatial density. Noting that the student’s time was divided between searching for andhandling discs, Holling derived a simple equation that accurately described how the student (a“predator”) responded to “prey” density (spatial density of disks). The resulting Type II responsefunction (Figure 1) has since been found to accurately describe the response of a wide variety ofinvertebrate predators (Maynard-Smith 1974).

The utility of the Type II function extends beyond its ability to accurately reproduce empiricalresults. For example, handling and searching times can be quantified directly and used to param-eterize a Type II model independent of field measurements of predation. If this independentlyparameterized model fits field-measured data, we can be reasonably assured that we have discov-ered the pertinent mechanisms governing prey capture, whereas deviations from measured dataprovide evidence that the simple assumptions of the Type II model are inadequate. If, for example,refuges are available in which low-density prey can hide, the response function may be sigmoidal(Type III, Figure 1) (Holling 1965). As Nisbet et al. (2000) note, “In the search for mechanisms,deviations from model predictions are at least as instructive as data that support” a model.

Prey density

Ca

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Type II

Type III

Linear extrapolation

Line

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Figure 1The rate at which predators capture prey varies with prey density in patterns that depend on the underlyingmechanics. For both the Holling Type II and Type III response functions, linear extrapolation from theresponse measured at low prey densities substantially deviates from the actual rate of capture at highdensities.

www.annualreviews.org • Mechanistic Scaling in Ecology 3

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Once it has been confirmed that a predator conforms to the assumptions of a Type II or IIIresponse, the function can be used to extrapolate prey densities outside the measured range. Thesemechanistic extrapolations can differ substantially from phenomenological extrapolations madeon the basis of field data alone. For example, at low prey density, both Types II and III responsefunctions closely approximate straight lines. Linear extrapolation to high prey density would eitheroverestimate (Type II) or underestimate (Type III) actual rates of prey capture (Figure 1).

Multiple Inputs, Single Output: Wave-Induced Hydrodynamic Force

The example above describes the response of an organism to variation in a single factor. It is oftenextremely useful to define the mechanistic response of an organism (or other physical system)to the simultaneous variation of multiple factors. Fluid dynamic theory of ocean waves providesan example. Wave-swept rocky shores are subjected to severe hydrodynamic forces, which canbreak or dislodge plants and animals, inhibit foraging, and deter settlement of larvae (e.g., Denny1988). These forces vary with the height of the waves as they reach the shore. In turn, inshorewave height is a function of wave height offshore, water depth (affected by the tides), and waveperiod. Measuring hydrodynamic force (the system’s “response”) as a function of each of thesevariables separately is a futile task because it is their interaction that matters, and there is aninfinite number of combinations that potentially impose biologically meaningful forces (Dennyet al. 2009). However, fluid dynamic theory allows one to mechanistically combine the effectsof water depth, wave height, and wave period, translating these variables into a single imposedforce (Denny et al. 2009, Helmuth & Denny 2003, Madin & Connolly 2006, Madin et al. 2006,Massel 1996, Massel & Done 1993), which can in turn be used to predict the intensity of physicaldisturbance in a wave-washed community.

Useful Characteristics

The following characteristics summarize the nature of mechanistic response functions:1. Coherence between reality and the predictions of a mechanistic response function is evidence

that the function contains all pertinent details of the process under consideration.2. If predictions differ from measured data, the form of the deviations can guide the search for

additional information.3. A validated mechanistic response function allows one to extrapolate accurately

beyond measured conditions.4. Mechanistic functions can translate multiple input variables into a single, biologically

relevant response, thereby simplifying our understanding of complex systems.We list these characteristics to highlight the utility of mechanistic response functions, but we

do not mean to imply that this utility is either universal or absolute. Only with infinite data andperfect coherence between function and reality could one be absolutely sure that all pertinentdetails have been included. Similarly, the only way to be certain that extrapolation from existingdata is valid is to test that extrapolation directly, preferably through manipulative experiments. Butto dwell here on these considerations would miss our point: Though the results may be neitherperfect nor absolute, the formulation of mechanistic response functions provides ecologists withvaluable tools that phenomenological measurements cannot.

RESPONSE FUNCTIONS: A SECOND LOOK

Simple response functions suffice for many applications. However, the complexity of somebiological systems requires that additional factors be taken into account.


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Uncertainty

The response functions of Figure 1 are deterministic, that is, exact. In reality, there is alwayssome uncertainty (noise) in how a system responds, and this uncertainty can be incorporated in atleast two ways.

First, in addition to specifying a deterministic response, one can specify the probabil-ity distribution of the system’s noise. In this case, calculation of response proceeds throughtwo steps. For a given value of the input variable, one first calculates the expected (average)response. A value is then chosen at random from the noise distribution and added to the expec-tation to give one random realization of the actual response. This approach forms the basis forwide-ranging theoretical studies in population dynamics (e.g., Lande et al. 2003, Melbourne &Hastings 2008), and is a standard approach to the study of turbulent fluid dynamics (Tennekes& Lumley 1972). Gaylord et al. (1994) and Denny (1995) used two-part response functionsof this sort to quantify the force required to break intertidal organisms as a function of theirsize.

Second, in some extreme examples, the system under consideration is driven by chance alone.In turbulent flow, for example, small particles (e.g., gametes, seeds, spores, or phytoplankton)move in a random walk, and the distance they travel as a function of time can only be describedstatistically (Berg 1984, Denny & Gaines 2000, McNair et al. 1997). Alternatively, random walkscan be driven by an organism’s behavior (e.g., de Jaeger et al. 2011, Viswanathan et al. 2000).In both cases, the response function relating distance to time is an explicit probability function,specifying (exactly) what the probability is that, after a given period, an object will have traveledless than a certain distance.

Change Through Time

Response functions often change through time. Thermal tolerance in animals can shift, for in-stance, as repeated exposure to sublethal high temperatures result in an increase in lethal temper-ature (Angilletta 2009). Similarly, response can change through time due to evolution (Schoener2011, Whitehead 2012). For example, as the climate warms, arctic red squirrels give birth earlierin the year, an effect due in part to a shift in gene frequencies (Berteaux et al. 2004). In such cases, itis necessary to specify the time at which a response function is to be applied or to express responseas an explicit function of both time and the input variable.

Hysteresis

The simple functions of Figure 1 imply that response is independent of the direction of changein input variable, but this is not always true. For example, the response of plants to sunlight canexhibit hysteresis (Cullen et al. 1992, Long et al. 1994). Prolonged exposure to irradiance abovea threshold can damage cells; as a result, photosynthesis follows a lower trajectory as irradiancedeclines (Figure 2). Other examples abound: Metabolic rate increases as an organism’s bodytemperature rises, but if temperature is sufficient to cause damage to ATP-producing machinery,metabolic rate may take a different, lower trajectory as temperature subsequently falls. Likewise,the response of a desert community to gradually increasing rainfall can take a different path thanthat followed as rainfall subsequently decreases (Gutschick & BassiriRad 2003), and recovery ofmussel beds from disturbance can take a different path than that followed as beds are disturbed(Guichard et al. 2003).


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Irradiance

Ph

oto

syn

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rate

Figure 2Photosynthetic rate increases with increasing solar irradiance, but above some limit, increased irradiancedamages cells. Because of this damage, if irradiance subsequently declines, the rate of photosynthesis isreduced below that of undamaged tissue.

Models

When complexities such as uncertainty, temporal evolution, and hysteresis are incorporated, thedistinction between a response function and a mechanistic “model” becomes blurred. Indeed,there is really no need to make a formal distinction between the two: Response functions are asimple form of model, and models are often, in essence, compound response functions.

A central issue for mechanistic models is the trade-off between mechanistic detail and heuristicgenerality (Baskett 2012, Rastetter et al. 2003). A model based on mechanistic response functionscan be so parameter rich that it applies only to a specific organism; generality is gained onlyby making the model more abstract. This trade-off is exemplified by bioenergetic models, inwhich individual response functions (both measured and mechanistic) are combined to predict therate and allocation of energy flow through an organism. The proximal goal of such models is toconstruct a whole-organism response function that takes as its inputs environmental variables suchas temperature and food concentration and gives as its outputs predictions for growth rate, ultimatebody size, age of reproductive maturity, and lifetime reproductive output (Nisbet et al. 2000). Todate, this effort has been carried farthest by a variety of dynamic energy budget (DEB) models(reviewed by Kooijman 2000, Nisbet et al. 2000, van der Meer 2006), but this progress has comeat the expense of mechanistic detail—DEB models depend on a set of simplifying assumptionsand incorporate variables that cannot be measured directly. Efforts are under way to retain thegenerality of DEB models while incorporating mechanistic details (Nisbet et al. 2012).

SCALING UP

Having outlined the nature of mechanistic response functions, we now review six examples inwhich they can assist ecologists’ efforts to scale up from knowledge of small-scale interactions tothe prediction of large-scale patterns. These examples are drawn from a broad array of systems(Table 1). However, we draw added insight by highlighting the diverse response functions oper-ating within a common system—the intertidal zone of wave-washed shores.

Mechanism versus Correlation: The Ecological Niche

The concept of the niche has been central in ecology since the 1950s (Hutchinson 1957, MacArthur& Levins 1967), and it has recently been used to predict species range limits (Buckley et al. 2008,


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Table 1 Representative applications of mechanistic response functions

Response function(s) Representative application Complexity Key referencesFunctional response of predators tovarying density of prey

Predator-prey interactions Individualresponsefunctions

Compoundresponsefunctions

Holling 1959

Mechanistic scaling relationship ofmetabolism with body mass

Explaining macroecologicalpatterns in body and range size

Chown & Gaston 1999, Chown et al.2007, Gaston et al. 2009, Kozlowskiet al. 2003, West et al. 1997

Probabilistic response functions Modeling of chance events suchas return times, distancetraveled, disturbance

Gaylord et al. 2006; Katul et al. 2005;Levin et al. 2003; McNair et al. 1997;Nathan 2006; Nathan et al. 2002, 2005;Zimmer et al. 2009

Fluid dynamic theory translatingmultiple physical variables into asingle hydrodynamic force

Physical disturbance onwave-swept rocky shores

Denny 1988, Denny et al. 2009,Helmuth & Denny 2003, Madin &Connolly 2006, Madin et al. 2006,Massel 1996, Massel & Done 1993

Response functions describing localpopulation processes (e.g.,competition, predation)

Scale-transition theory:predicting large-scale dynamicsthrough nonlinear averaging

Benedetti-Cecchi et al. 2012, Chessonet al. 2005, Melbourne & Chesson2006, Melbourne et al. 2005

Response functions describing localpopulation processes (e.g.,disturbance, recruitment)

Self-organization: predictinglarge-scale patterns and systemstability

de Jaeger et al. 2011, Guichard et al.2003, Pascual & Guichard 2005, Sole &Bascompte 2006

Bioenergetic models (e.g., dynamicenergy budget or heat-budgetmodels)

Prediction of organism’s vitalrates as a function of itsenvironment (e.g.,temperature, foodconcentration)

Bell 1995; Campbell & Norman 1998;Denny & Harley 2006; Gates 1980;Helmuth 1998; Kooijman 2000; Nisbetet al. 2000, 2012; van der Meer 2006

Fluid dynamic theory translatingmultiple physical variables into asingle hydrodynamic force,heat-budget models

Predicting ecological andevolutionary extreme events inthe presence of stochasticenvironmental fluctuations

Denny & Dowd 2012, Denny et al. 2009

Heat-budget models, dynamicenergy budget models, measuredresponse functions for locomotion

Delineation of the ecologicalniche

Kearney et al. 2008, 2010, 2012

2010; Kearney et al. 2010, 2012). In this approach, a suite of measured environmental variablesis correlated with presence or absence of a given species, and the resulting “climate envelope” isused to delineate the species’ potential range. For example, the toxic cane toad Bufo marinus wasintroduced into northeastern Australia in 1935 and has spread worrisomely south and west. Climateenvelope models suggest that toads might eventually reach the urbanized southeastern coast ofAustralia (Urban et al. 2007). However, by relying on correlation rather than mechanism, climateenvelope models can miss the true causes of range limitation (Davis et al. 1998, Elith & Leathwick2009, Gaylord & Gaines 2000, Kearney & Porter 2009). In the case of cane toads, Kearney et al.(2008) combined response functions for the animal’s interactions with its environment to calculatethe rate at which adult toads could invade new territory. Due primarily to the animal’s temperature-dependent ability to hop, the rate of invasion is predicted to approach zero as toads move intothe cooler south, a prediction that matches the measured rate of southerly range extension. Adulttoads could live on the southern coast if they were accidentally (or intentionally) introducedthere—and hence, climate envelope models include the coast in the toad’s potential range—but


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mechanistic analysis reveals that toads do not have the locomotory capacity to reach those locations.Furthermore, by identifying the most relevant axes of the niche, the mechanistic approach sets thestage for measurement of an organism’s ability to evolve in response to the limiting factor (e.g.,Kuo & Sanford 2009).

Macrophysiology

At the interface between physiology and macroecology, macrophysiology explores variation inphysiological traits at large spatial and temporal scales. When based on mechanistic responsefunctions, macrophysiological results can have ecological implications regarding patterns in bodysize, abundance, range size, and species richness (Gaston et al. 2009). For example, the mecha-nistic basis for the increase in range size with latitude—Rapoport’s rule—involves physiologicaladaptations to increased climate variability toward the poles (Gaston et al. 2009). Reductionsin metabolism at the elevated temperature of low latitudes allow species to reduce range sizewhile preferentially allocating resources to growth and development (Chown & Gaston 1999). Incontrast, elevation of metabolic rates as an adaptation to low temperatures has been postulated toenable species, particularly insects, to maintain high growth rates (thereby requiring larger ranges)in regions where the growing season is short, such as at high latitudes (Chown & Gaston 1999).

Macrophysiological investigations have also used mechanistic scaling relationships ofmetabolism to explain macroecological patterns in body size (Chown & Gaston 1999, Chownet al. 2007). Competing physiological models make distinct predictions for the scaling exponentof metabolism as a function of mass, such that, in principle, it should be possible to discriminateamong theories using metabolic scaling data. For example, the nutrient supply network model ofthe metabolic theory of ecology predicts that metabolic rate scales as mass3/4 (West et al. 1997).This prediction—based on the assumption that nutrients are supplied through space-filling fractalnetworks—in theory applies generally from molecules to organisms. An alternative model positsthat body size changes as a consequence of variation in cell size and/or number under naturalselection pressure and predicts an exponent of 3/4 for interspecific scaling relationships and valuesof 2/3 to 1 for intraspecific scaling relationships (Kozlowski et al. 2003). The precise value ofthe intraspecific exponent depends on the relative contribution of variation in cell size and cellnumber to body mass. Isometric scaling (an exponent of 1) is expected when changes in body sizeare determined entirely by variation in cell number, whereas an exponent of 2/3 is expected fromthe exclusive contribution of variation in cell size.

Chown et al. (2007) compared these models using metabolic rate data from 391 species ofinsects. They found a scaling exponent of 3/4 at the interspecific (phylogenetic) level and 1 atthe intraspecific level, results more consistent with the cell-size model than the nutrient supplynetwork model, although large confidence intervals associated with estimated scaling exponentscomplicate definitive distinction between models.

Macroecological consequences may accrue from these macrophysiological results if develop-mental processes underlying variation in cell number and size have prevalence over other proximatedeterminants of body mass. For example, to maintain a constant energy budget, cell size shoulddecrease with increasing temperature. Therefore, if variation in cell size is not compensated bychanges in cell number, as the results of Chown et al. (2007) suggest, one may predict a decreasein body size with increasing temperature (Chown & Gaston 2010).

Scale-Transition Theory

A potentially important role for mechanistic response functions has been formalized by Chessonand coworkers in scale-transition theory (Chesson et al. 2005, Melbourne et al. 2005, Melbourne &


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Ra

te o

f ca

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re X

X Y1

Y2

Y1 < Y2

Type II

Prey densityPrey density

a

XX

Y1

Y2

Y1 > Y2

Type III

b

Figure 3Examples of Jensen’s inequality. (a) The Holling Type II response function decelerates such that an increase of X in prey density resultsin a relatively small increase in capture rate (Y1). In contrast, a decrease of X in density results in a relatively large decrease in capturerate (Y2). Thus, if prey density varies at ± X around an average value (solid dot), then the overall rate of prey capture is less than ifdensity remained at that average. (b) At low prey density, the Holling Type III response function accelerates. In this case, variation of± X results in a net benefit to the predator because Y1 > Y2.

Chesson 2006), a scaling “recipe” stemming from recognition that response functions are typicallynonlinear and that interaction of local nonlinearities with spatial or temporal variation distorts theprediction of large-scale patterns. Consider a heuristic example. As we have seen, capture rate canvary nonlinearly with prey density (Figure 1). For each predator, there is a particular prey densityat which energy input from prey just offsets energy expended in respiration. At this compensationdensity, the predator’s growth rate is zero. Consider, now, a scenario in which the spatial averageof prey density equals compensation density, but density varies from place to place. If the responsefunction is Type II, capture rates decelerate with increasing prey density (i.e., the second derivativeof the function is <0). In this case, if predators wander randomly across the landscape, the increasedenergy influx from encounters with above-average prey density is small compared to the reducedenergy influx from periods spent sampling below-average densities (Figure 3a). Thus, even inan area where average density equals compensation density, a predator will eventually starvewhen confronted with sufficient variance in prey availability. In contrast, at low prey densities, aType III response function accelerates (the local second derivative is >0; Figure 3b). In this case,if it experiences sufficient variation in density, a predator can actually grow even though averageprey density equals only compensation density.

These phenomena are examples of Jensen’s inequality ( Jensen 1906): For any monotonic (butnonlinear) function f, the function of the mean value f (x) (e.g., capture rate at mean populationdensity) differs from the mean value of the function f (x) (e.g., the “true” capture rate averagedacross individuals as they encounter variation in prey density). In these examples, because the TypeII response decelerates, f (x) < f (x). At low prey density, the Type III response accelerates, sowithin this range, f (x) > f (x). Ruel & Ayres (1999) and Benedetti-Cecchi (2005) provide otherecological examples of Jensen’s inequality.

Often, the variation that invokes application of Jensen’s inequality depends on the scale at whicha process occurs. For example, the variation in prey density described above depends on temporalpatterns of foraging and spatial scale(s) of prey distribution. Scale transition theory provides a


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Power law: a functionwith the form y = axb ;taking the logarithm ofeach side of thisequation yields a linearfunction of the formlog y = log a + b log x

means to combine these scale-dependent factors with mechanistic descriptions of local dynamicsto accurately predict an average response at large scales.

The procedure starts with a definition of the response function for the process in question.Parameters of the function are estimated at small scale from empirical (mensurative or experi-mental) data. Large-scale predictions are then expressed as the sum of the local-scale average (theso-called mean field model) and correction terms that take into account distortion introduced bynonlinear processes (the scale-transition terms). In its simplest form (Chesson et al. 2005),

f (x) ≈ f (x) + 12

f ′′(x)Var(x). 1.

Here, f (x) is the mean field estimate, f ′′(x) is the second derivative of f (measured at the mean,x), and Var(x) is the variance in x (spatial or temporal) at the largest scale of interest.

Continuing our predator-prey example, if the nonlinearity of capture rate is due to densitydependence, one needs to estimate how much variance in prey density occurs at the largest scaleover which a prediction is required. This quantity is then used to correct the inaccurate predictionobtained by simply averaging local measurements. Consider a comparison between Type II andIII responses to prey density (Figure 4a). In this hypothetical example, the Type II response ismore effective at uniform low densities, but less effective at uniform high densities. Increasingthe variance of prey density decreases the advantage of a Type II response at low densities, butreduces the advantage of the Type III response at high densities (Figure 4b).

This simple example ignores the effects of predation on prey density. If consumer and resourceinteract, one needs to estimate the covariance between consumer location and resource density atthe large scale and use this covariance to correct the average obtained from local measurements.Melbourne et al. (2005) and Melbourne & Chesson (2006) illustrate this process with examplesbased on empirical data, focusing largely on nonlinear population and community processes. Butthere is a formidable opportunity to apply the theory to other levels of biological organization(e.g., the physiological level) and to physical processes (e.g., disturbance and thermal stress).

Case studies illustrating the application of scale-transition principles typically focus on discretespatial scales. For example, Melbourne et al. (2005) show how the dynamics of periphyton algaeon individual cobbles can be scaled up to an entire stream, and how metacommunity dynamics ofintertidal crabs and desert annual plants depend on variation at discrete small scales. Benedetti-Cecchi et al. (2012) illustrate how the dynamics of algal turfs and their interactions with canopy-forming algae can be scaled up from individual plots (20 cm × 20 cm) to an entire island (tens ofkilometers). Scale-transition theory can, however, be extended to incorporate continuous measuresof environmental variance, enabling great flexibility for scaling up local dynamics over multiplespatial or temporal scales. This may prove particularly useful when, for example, deciding uponthe size of a network of protected areas (e.g., McLeod et al. 2009). In this case, the ability to scaleup local dynamics as a function of network size may constitute a valuable decision-making tool.

Self-Organization

Ecological literature is replete with examples of pattern at spatial scales much larger than individualorganisms: waves, spirals, and labyrinthine clumps in arid vegetation (e.g., Couteron & Lejeune2001, Klausmeier 1999, Rietkerk et al. 2002); power-law distributions of gap sizes in forests(e.g., Malamud et al. 1998); and traveling waves of lynx, voles, and bud moths (Bjørnstad et al.2002, Kaitala & Ranta 1998, Ranta & Kaitala 1997, Ranta et al. 1997). These patterns can havefunctional advantages for the organisms involved, increasing their productivity and stability invariable environments. Efforts to explain these emergent patterns and their ecological role(s) have


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Figure 4A hypothetical example of the effect of spatial variation in prey density on the rate of predation. (a) In theabsence of spatial variability, the Type III response results in higher rates of prey capture at all but the lowestprey densities. (b) The difference between Type II and Type III capture rates differs depending on spatialvariability in prey density. The higher the variance (set equal to a given fraction of the mean density), thesmaller the difference between the types of response.

Drag: hydrodynamicforce acting in thedirection of relativeflow between an objectand the surroundingfluid

been led by theoretical ecologists drawing on insights from developmental biology and physics(Sole & Bascompte 2006). We review two examples.

Facilitation-inhibition models. In 1952, Alan Turing outlined a theory in which facilitationand inhibition interacted at different spatial scales to produce wave- or spot-like patterns. Turing(1952) developed his theory in the context of organismal development, but the principles applyequally well in ecological contexts. Patterns observed in bed-forming mussels provide an instruc-tive example. When growing on soft substrata, young Mytilus edulis form distinctive rows or clustersof near-uniform size and spacing (Figure 5a). van de Koppel et al. (2005, 2008) propose that thislarge-scale pattern is due to the small-scale, local response of individual mussels to both hydrody-namic forces and suspended food concentrations. They posit that it is advantageous for mussels toadhere to each other in clusters to avoid dislodgment by drag (facilitation at the individual scale),but it is disadvantageous to be in the middle of too large a clump because the available food hasalready been eaten by mussels on the periphery (inhibition at the group scale). van de Koppel et al.(2008) demonstrated the efficacy of their explanation through field observations and experiments:The predicted pattern of clusters matched that observed, and cluster size increased when foodwas artificially provided to mussels in the center. Furthermore, per capita growth rate was higherfor observed patterns of clustering than it was for either solitary mussels (which are susceptibleto disturbance) or a continuous bed (in which many mussels are underfed). Increased growth rate


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log branch size

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Figure 5(a) Mussels on the soft substratum of Menai Straight (Wales) form characteristic clumps and rows indicative of self-organizationthrough the interaction of facilitation and inhibition (photo by J. Widdows). The scale and pattern of clumps and rows depend on flowspeed, food availability, and the properties of the substratum (van de Koppel et al. 2005, 2008; Widdows et al. 2009). (b) A notionalexample of scale independence: the frequency of snowflake branches decreases with increasing branch size. When plotted on log-logaxes (as we have done here), the power function indicative of self-organized criticality forms a straight line.

of clumped mussels thus provides a potential selective factor in the evolution of cluster-formingbehavior. De Jaeger et al. (2011) showed that rapid formation of clumps is abetted by the tendencyof mussels to crawl in Levy walks (a particular form of random motion) and that this behaviorforms an evolutionarily stable strategy. Similar large-scale patterns are found in the vegetation ofarid ecosystems, although the mechanism of pattern formation is different (Rietkerk et al. 2002).

Criticality. At the critical temperature of 0◦C, water can abruptly change from liquid to solid.The mechanics of this and similar threshold transitions is such that, near the critical point (thatis, at criticality), small-scale (in this case, molecular) interactions result in large-scale patterns (forreviews, see Pascual & Guichard 2005, Sole & Bascompte 2006). For instance, snowflakes, whichform near water’s critical temperature, have delicate branching patterns visible to the naked eye,i.e., at scales far removed from those of individual molecules. In many systems, the patterns thatemerge at criticality are characterized by scale independence. For example, the branching patternin one small “twig” of one arm of a snowflake is similar to the branching pattern of the whole arm,which itself may be repeated between arms. If one were to take an entire snowflake and record thenumber of branches of different sizes, scale independence of pattern would emerge as a power-lawrelationship between frequency and size (Guichard et al. 2003, Sole & Bascompte 2006): The ratioof the number of branches at one size to that n times that size is constant regardless of the sizechosen, a relationship that produces a straight line on a log-log plot (Figure 5b). In this example,the system’s behavior is related to temperature, but the same ideas apply for critical values of anyfactor.

Because the capacity for small-scale interactions to produce scale-independent patterns is man-ifest only at criticality, presence of a scale-independent pattern might signal that a biological sys-tem (a population or community) is poised near a threshold and, therefore, susceptible to abruptswitches between alternative states or large temporal swings, either of which presents challengesfor conservation and management. However, recent work suggests that under certain conditions


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Lift: hydrodynamicforce actingperpendicular to thedirection of relativeflow between an objectand the surroundingfluid

scale-independent patterns can be formed in systems that are resistant to abrupt shifts in state(Pascual & Guichard 2005). Indeed, in these cases of robust criticality the mechanisms that leadto pattern formation can contribute to the system’s overall stability.

Mussel beds serve as a model system for investigating robust criticality. On wave-swept rockyshores, gaps are produced in otherwise continuous mussel beds as hydrodynamic lift dislodgesmussels (Denny 1987, Paine & Levin 1981). The size distribution of resulting gaps follows thepower-law relationship indicative of a process near its critical point, and Guichard et al. (2003)have devised a model that accounts for this observation. In short, when one mussel is dislodged,adjacent mussels are initially weakened and regain their adhesive strength only after a periodof susceptibility. As a result, once a gap is initiated, it can grow from its edges if waves applysufficient force within the period of susceptibility. Conversely, gaps can shrink as mussels recruitat gap edges. Empirical estimates of the period of susceptibility and rates of recruitment andgap formation showed that for mussels in Oregon disturbance and recovery occurred at similartemporal and spatial scales. When Guichard et al. (2003) parameterized their model with thesemeasured values they were able to accurately recreate the observed distribution of gap sizes,suggesting that their model indeed captured the dynamics of the system.

Furthermore, they note that a scale-independent pattern of gaps has the tendency to maintainthe system near its critical point. In their model, if the shore is initially uniformly covered withcontiguous mussels, the first gap formed can rapidly propagate through the entire bed as onesusceptible mussel after another peels off at the gap’s edges. Once all mussels are removed, thebed cannot recover because there is no edge to which mussels can recruit. In contrast, a bedwith a distribution of gap sizes is relatively stable because the emergent pattern of gaps inhibitspropagation of catastrophic disturbance, allowing time for sufficient recruitment. Models suggestthat this tendency toward stability is inherent in systems in which disturbance and recovery arelocal in space and intermittent in time and have the same spatial and temporal scales (Pascual &Guichard 2005).

The role of mechanism. In the past two decades, predictions of large-scale, self-organizedpatterns (as outlined above) have moved swiftly from formulation of abstract theories to theirdemonstration in the field. The next step—prediction of when and where a given type of patternformation will manifest—requires the sort of mechanistic approach we espouse here. Again, con-sider mussel beds. In one environment, mussels form uniform-sized clusters and rows indicativeof facilitation-inhibition dynamics; in another, cluster size is distributed in the scale-independentpattern indicative of criticality. In their examinations of mussel dynamics, Guichard et al. (2003),van de Koppel et al. (2008), and de Jaeger et al. (2011) were content to demonstrate that theirtheories worked for a given set of environmental conditions, refraining from speculation as to howdifferences in the environment might favor one model over the other or when and where thosedifferent conditions might occur. It is here that the mechanistic approach can play an importantrole.

We know a great deal about the mechanics of mussels’ attachment to the substratum (e.g.,Carrington 2002a,b; Carrington et al. 2008, 2009; Moeser & Carrington 2006; Moeser et al.2006) and the hydrodynamics of mussels in beds (Denny 1987). Similarly, fluid dynamic theory canaccount for the ability of mussels to reduce the local density of suspended food (e.g., Frechette et al.1989). Application of this information allows one to predict when and where the aforementionedmodels are operative.

The mechanism proposed by van de Koppel et al. (2008) requires flow slow enough that musselsresting on mud or sand can resist hydrodynamic forces. Denny (1987) has shown that in mussel


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Turbulent mixing:eddies and swirls ofturbulent flow thatmove water in randompatterns, therebymixing the fluid

beds, lift FL (in newtons) is the dominant hydrodynamic force:

FL ∼= 451U 2 A, 2.

where A is the area of bed occupied by a mussel (in square meters) and U is velocity (in metersper second). For mytilid mussels, A ∼= 0.08L1.77,where L is the maximum length (in meters) ofthe mussel shell (M. Denny, personal observation). Thus,

FL ∼= 36U 2 L1.77. 3.

For a mussel on unconsolidated substratum, the primary force resisting lift is the mussel’s weightin water, W, which (from unpublished measurements) is

W (in N ) ∼= 354L2.93. 4.

Combining Equations 3 and 4 and solving for U, we find that, for a typical mussel 5 cm long,velocities greater than 0.55 m s−1 are sufficient to dislodge the organism from the substratum.Mussels’ byssal attachment to mud or sand might provide some slight added resistance to lift, butthe critical value at which U disrupts a bed should nonetheless be less than approximately 1 m s−1.Indeed, the organized pattern of mussels is disrupted during winter storms (van de Koppel et al.2005). To resist higher velocities, mussels must attach to solid substrata—that is, to rock—with aconcomitant stepwise increase in resistance. Minimum force per area required to dislodge a bedmussel from rock is approximately 4 × 104 N m−2 (Denny et al. 2009), which, in conjunction withEquation 2, implies that velocities greater than approximately 10 m s−1 are required to dislodgemussels from rock.

These calculations thus suggest that the mechanism of van de Koppel et al. is viable only whereU < 1 m s−1 and that of Guichard et al. (2003) only where U > 10 m s−1. A mechanistic approachto the process of self-organization thus confirms the results of existing models, but in additionpredicts that there is a range of conditions—mussels attached to rock with 1 m s−1 < U < 10 ms−1—under which neither model of self-organization should apply.

Random Walks and Dispersal

The ability to disperse is often a key aspect of the interaction among species. For example, if thecompetitive dominant in a community cannot disperse sufficiently to occupy patches of new spacecreated by physical disturbance, competitive inferiors with superior dispersal strategies can persist(Rees et al. 2001, Tilman 1994; but see Clark et al. 2004). Furthermore, the rate and scope ofdispersal govern the magnitude of gene flow between populations, thereby affecting populationgenetics and the potential for local evolution.

In recent years, researchers have combined engineering theories of turbulent mixing and flowwith statistical theories of random walks to construct detailed mechanistic models that use small-scale motion to predict the large-scale distance traveled by propagules such as seeds, pollen,ballooning spiders, and aquatic larvae and spores (e.g., Gaylord et al. 2006; Katul et al. 2005; Levinet al. 2003; Nathan 2006; Nathan et al. 2002, 2005; Zimmer et al. 2009). These studies provideinsight into a wide variety of ecological and evolutionary processes, from the rate of species’advance to community assembly (Levin et al. 2003). In each case, the output of the model—a formof mechanistic response function—is a probability distribution that quantifies the likelihood thata propagule released at a certain point in space will first impact the substratum at a given distance.

These random-walk models are noteworthy in two respects. First, because they are derivedfrom basic physical principles, they are generalizable. The same approach that leads to accuratepredictions for seeds in air (Nathan 2006; Nathan et al. 2002, 2005) leads to accurate predictions


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for algal spores in seawater (Gaylord et al. 2006). Furthermore, models for both air and water leadto similar surprising results. In both media, and across a wide variety of propagules, the probabilitydistribution of impact distances has a “fat tail,” meaning that it is considerably more probable thanpreviously assumed that propagules travel great distances from their point of release. The abilityto predict the likelihood of this long-distance dispersal has practical importance in many aspects ofecology, e.g., the rate of range extension for an invading species or pathogen (Kinlan et al. 2005),the persistence of “fugitive” species in disturbed patches, and recolonization following extremeevents (Morritt et al. 2010, Phillips et al. 2010, Platt & Connell 2003). For example, severe winterstorms can locally extirpate kelp populations. If kelps are to reestablish, they must be “seeded”by spores from other less-impacted locations. Knowledge of the dispersal characteristics of kelpspores (Gaylord et al. 2006) allows designers of marine protected areas to bolster the stabilityof their ecosystems by spacing kelp-bed refugia close enough together to ensure reestablishmentafter storms (Gaines et al. 2010). Note that dispersal distance predicted by these models dependsin mechanistic fashion on relevant variables of the physical environment. As these variables—suchas wind and current speeds—change (Solomon et al. 2007), new predictions can be made even forenvironmental conditions that do not currently exist.

Mechanistic approaches have been used to quantify the dispersal of propagules at even largerscales. For example, high-resolution models of wind- and current-driven water motions have beenused to predict the pattern of dispersal of reef-fish larvae in the Caribbean Sea, and these predictionshighlight the effect of larval behavior on dispersal distance (Cowen & Sponaugle 2009; Cowenet al. 2000, 2006). Absent behavior, fish larvae are likely to be swept hundreds of kilometers fromtheir natal locations. However, when larvae actively adjust their depth (a mechanistic response),their dispersal can be severely limited, and this can have drastic effects on the “connectedness”of populations among islands. Depth-adjustment behavior can similarly affect local retention ofinvertebrate larvae (e.g., Morgan & Fisher 2010).

Extreme Events and the Environmental Bootstrap

Extreme events play critical roles in ecology and evolution (e.g., Gaines & Denny 1993, Katz et al.2005), potentially shifting communities between alternate stable states (e.g., Barkai & McQuaid1988, Paine & Trimble 2004, Petraitis et al. 2009). Some extreme events are due to simple, unitarycauses—factors that either happen or not, such as earthquakes and volcanic eruptions—and theyare consequently difficult to predict. Many extreme ecological events, however, are due not tothe imposition of a single environmental stressor, but rather to the simultaneous imposition ofseveral, individually benign stressors (Paine et al. 1998), and these compound events are open toprediction. Building on recently developed resampling theory (Efron & Tibshirani 1993), Dennyet al. (2009) devised a statistical technique (the environmental bootstrap) that takes as its inputa relatively short time series of environmental data—5–10 years—and produces an ensemble ofhypothetical year-long realizations of how the environment might by chance have played outdifferently. Using this technique, it is possible to estimate the probability that even extremely rareevents might occur by chance alone, and the environmental bootstrap thus provides a tool to movefrom short-term measurements to long-term predictions.

Implementation of this tool requires mechanistic response functions. For example, resamplinga short record of tidal height, wave height, and wave period can provide an extensive ensemble ofhypothetical time series for ocean “waviness.” However, as described above, this information mustbe interpreted by a mechanistic response function to provide biologically meaningful data about thedistribution of maximum hydrodynamic forces imposed during hypothetical years. When coupledwith the organism’s structural response function (the probability of being dislodged by a given


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Figure 6(a) The fraction of mussels killed by hydrodynamic forces differs dramatically among sites with differentwave exposures, but varies little through time. (b) In contrast, the fraction of limpets killed by thermal stressvaries substantially with both habitat (the orientation of the rock surface: tilted to the north, east, west, orsouth) and time. Redrawn from Denny et al. (2009).

Heat-budget model:a method forcalculating bodytemperature by takinginto account all theways in which heat canenter or leave anorganism

hydrodynamic force), this distribution allows one to estimate the likelihood that the organism willbe killed by an extreme wave event in a year chosen at random.

Denny et al. (2009) applied this analytic process to predict rates of dislodgment in mussels.In this case, the physics of ocean waves [specifically, the topographically imposed limit to heightat breaking (Helmuth & Denny 2003)] renders mussel beds “immune” to extreme events. Riskvaries among sites of differing wave exposure (Figure 6a), but at a given site, extreme dislodgmentlikely to be encountered in a century or millennium is only slightly greater than that likely to beencountered in a decade. In other words, substantial spatial variation is the norm, but catastrophescannot occur. This immunity to catastrophe may help to explain mussels’ widespread competitivedominance, and accords with the study by Guichard et al. (2003) regarding the stability of intertidalmussel beds.

A similar analysis can be carried out using heat-budget models (Bell 1995, Campbell & Norman1998, Gates 1980, Helmuth 1998) to predict the probability of extreme thermal events. Based onthe heat-budget model of Denny & Harley (2006), Denny et al. (2009) used an environmentalbootstrap to examine the effect of extreme temperatures on the distribution of a species of intertidallimpet. In contrast to mussels, which are immune to hydrodynamic catastrophes, Lottia giganteais subject to thermal catastrophes. In an average year, the species is unlikely to be thermallystressed by its environment (Figure 6b). However, every decade (on average) greater than 90%of limpets on south-facing rocks will be killed by the chance imposition of a stressful combinationof environmental factors. In contrast, it is predicted that limpets on north-facing rocks will notencounter stressful conditions even if they wait a hundred years. Given their rarity, it is not


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surprising that thermal catastrophes of the type predicted by Denny et al. (2009) have not beendirectly observed for L. gigantea in nature, but their existence is consistent with the measureddistribution of limpets high on the shore: Limpets are rare or absent on south-facing rocks butabundant on north-facing rocks (Miller et al. 2009). Building on these studies, Denny & Dowd(2012) used the bootstrap predictions for L. gigantea’s body temperature to explore the evolutionof thermal tolerance, concluding that it is rare extreme events that set the “safety margin” for thesegastropods. The mechanistic approach afforded by the combination of an environmental bootstrapand a heat-budget model thus allows for the prediction of effects that occur on timescales beyondthose available for (or at least convenient for) direct measurement. To date, this approach hasbeen applied only in marine habitats, but ample opportunity exists for its extension to terrestrialsystems.

The ability to predict the probability of extreme events may prove useful as we explore theeffects of global climate change. For example, if field measurements record two extreme thermalevents in quick succession when none have been recorded for some time previously, the tendencymight be to attribute the increased frequency of events to global warming. The environmentalbootstrap, coupled with a heat-budget model, provides a means for testing this hypothesis. Byallowing one to estimate the mean probability of extreme events, one can calculate the probabilityof two such events happening in quick succession by chance alone (Denny et al. 2009). If thisprobability is unacceptably high, encountering two such events in quick succession cannot beunequivocally attributed to a change in environment.

We emphasize that practical use of the environmental bootstrap requires a mechanistic ap-proach. For example, in their assessment of the probability of thermal death in limpets, Dennyet al. (2009) examined 53 million data points for each of six environmental factors. It would beimpractical to test empirically the effect of each possible combination of these factors. But a heat-budget model allows for efficient translation of all possible combinations into a single biologicallyrelevant output—body temperature—the effects of which can be readily quantified.

CONCLUSIONS

The mechanistic approach to ecological scaling we advocate here provides a methodological frame-work to unravel the interplay among processes operating at different scales and how these inter-actions contribute to the diversity of ecological patterns in nature (Carpenter & Turner 2000,Holling 1992). Cross-scale interactions are becoming more likely in a world that is increasinglyconnected through the flow of materials and organisms and by climate instabilities (Peters et al.2004, 2008). Increasing connectivity implies that fine-scale processes, such as point-source pol-lution, exotic invasions, and epidemics, can propagate to influence large-scale areas. Broad-scaledrivers operating at the regional or continental scale (e.g., trends in climate-related variables suchas sea-surface and atmospheric temperature and CO2) can magnify or overwhelm local events(Peters et al. 2008). By linking ecological phenomena across scales, mechanistic response func-tions have a great potential to explain and ultimately predict how populations and communitiesrespond to the compound effects of scale-dependent, interacting processes.

DISCLOSURE STATEMENT

The authors are not aware of any affiliations, memberships, funding, or financial holdings thatmight be perceived as affecting the objectivity of this review.


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ACKNOWLEDGMENTS

This is contribution 383 of PISCO, the Partnership for Interdisciplinary Studies of CoastalOceans, a consortium funded by the Gordon and Betty Moore Foundation and the David andLucile Packard Foundation. We thank the Friday Harbor Working Group (in particular M.Baskett, C.D.G. Harley, P. Jonsson, H. Nepf, and R. Zimmerman) for stimulating discussionsand J. Widdows for kind use of his photograph. L.B.C. acknowledges support from the EuropeanCommunity under the FP7 projects VECTORS and CoCoNET.

LITERATURE CITED

Angilletta MJ. 2009. Thermal Adaptation: A Theoretical and Empirical Synthesis. New York: Oxford Univ. PressBarkai A, McQuaid CD. 1988. Predator prey role reversal in a marine benthic ecosystem. Science 242:62–64Baskett ML. 2012. Integrating mechanistic organism-environment interactions into the basic theory of com-

munity and evolutionary ecology. J. Exp. Biol. 215:948–61Bell EC. 1995. Environmental and morphological influences on body temperature and desiccation of the

intertidal alga Mastorcarpus papillatus Kutzing. J. Exp. Mar. Biol. Ecol. 191:29–55Benedetti-Cecchi L. 2005. Unanticipated impacts of spatial variance of biodiversity on plant productivity. Ecol.

Lett. 8:791–99Benedetti-Cecchi L, Tamburello L, Bulleri F, Maggi E, Gennusa V, Miller M. 2012. Linking patterns and

processes across scales: the application of scale-transition theory to algal dynamics on rocky shores.J. Exp. Biol. 215:977–85

Berg H. 1984. Random Walks in Biology. Princeton: Princeton Univ. PressBerteaux D, Reale D, McAdam AG, Boutin S. 2004. Keeping pace with fast climate change: Can arctic life

count on evolution? Integr. Comp. Biol. 44:140–51Bjørnstad ON, Peltonen M, Liebhold AM, Baltensweiler W. 2002. Waves of larch budmoth outbreaks in the

European Alps. Science 298:1020–23Brown JH. 1995. Macroecology. Chicago: Univ. Chicago PressBuckley LB, Rodda GH, Jetz W. 2008. Thermal energetic constraints on ectotherm abundance. Ecology 89:48–

55Buckley LB, Urban MC, Angilletta MJ, Crozier LG, Rissler LJ, Sears MW. 2010. Can mechanism inform

species distribution models? Ecol. Lett. 13:1041–54Campbell GS, Norman JM. 1998. An Introduction to Environmental Biophysics. New York: Springer-VerlagCarpenter SR, Turner MG. 2000. Hares and tortoises: interactions of fast and slow variables in ecosystems.

Ecosystems 3:495–97Carrington E. 2002a. Seasonal variation in the attachment strength of blue mussels: causes and consequences.

Limnol. Oceanogr. 47:1723–33Carrington E. 2002b. The ecomechanics of mussel attachment: from molecules to ecosystems. Integr. Comp.

Biol. 42:846–52Carrington E, Moeser GM, Dimond J, Mello JJ, Boller ML. 2009. Seasonal disturbance to mussel beds: field

test of a mechanistic model predicting wave dislodgment. Limnol. Oceanogr. 54:973–86Carrington E, Moeser GM, Thompson SB, Coutts LC, Craig CA. 2008. Mussel attachment on rocky shores:

the effect of flow on byssus production. Int. Comp. Biol. 48:801–7Chesson P, Donahue MJ, Melbourne B, Sears AL. 2005. Scale transition theory for understanding mechanisms

in metacommunities. In Metacommunities: Spatial Dynamics and Ecological Communities, ed. M Holyoak,MA Leibold, RD Holt, pp. 279–306. Chicago: Univ. Chicago Press

Chown SL, Gaston KJ. 1999. Exploring links between physiology and ecology at macro-scales: the role ofrespiratory metabolism in insects. Biol. Rev. 74:87–120

Chown SL, Gaston KJ. 2010. Body size variation in insects: a macroecological perspective. Biol. Rev. 85:139–69Chown SL, Marais E, Terblanche JS, Klok CJ, Lighton JRB, Blackburn TM. 2007. Scaling of insect metabolic

rate is inconsistent with the nutrient supply network model. Funct. Ecol. 21:282–90Clark JS, Shannon L, Ibanez I. 2004. Fecundity of trees and the colonization-competition hypothesis.

Ecol. Monogr. 74:415–42


Ann

u. R

ev. E

col.

Evo

l. Sy

st. 2

012.

43:1

-22.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

gby

Sta

nfor

d U

nive

rsity

- M

ain

Cam

pus

- L

ane

Med

ical

Lib

rary

on

07/1

5/13

. For

per

sona

l use

onl

y.


Couteron P, Lejeune O. 2001. Periodic spotted patterns in semi-arid vegetation explained by a propagation-inhibition model. J. Ecol. 89:616–28

Cowen RK, Lwiza KMM, Sponaugle S, Paris CB, Olson DB. 2000. Connectivity of marine populations: openor closed? Science 287:857–59

Cowen RK, Paris CB, Srinivasan A. 2006. Scaling connectivity in marine populations. Science 311:522–27Cowen RK, Sponaugle S. 2009. Larval dispersal and marine population connectivity. Annu. Rev. Mar. Sci. 1:

443–66Cullen J, Neale P, Lesser M. 1992. Biological weighting function for the inhibition of phytoplankton photo-

synthesis by ultraviolet radiation. Science 258:646–50Davis, AJ, Jenkinson LS, Lawton JH, Shorrocks B, Wood S. 1998. Making mistakes when predicting shifts in

species range in response to global warming. Nature 391:783–86de Jaeger M, Weissing FJ, Herman PMJ, Nolet BA, van de Koppel J. 2011. Levy walks evolve through

interaction between movement and environmental complexity. Science 332:1551–53Denny MW. 1987. Lift as a mechanism of patch initiation in mussel beds. J. Exp. Mar. Biol. Ecol. 113:231–45Denny MW. 1988. Biology and the Mechanics of the Wave-Swept Environment. Princeton: Princeton Univ. PressDenny MW. 1995. Predicting physical disturbance: mechanistic approaches to the study of survivorship on

wave-swept shores. Ecol. Monogr. 65:371–418Denny MW, Dowd WW. 2012. Biophysics, environmental stochasticity, and the evolution of thermal safety

margins in intertidal limpets. J. Exp. Biol. 215:934–47Denny MW, Gaines S. 2000. Chance in Biology. Princeton: Princeton Univ. PressDenny MW, Harley CDG. 2006. Hot limpets: predicting body temperature in a conductance-mediated

system. J. Exp. Biol. 209:2409–19Denny MW, Hunt LJH, Miller LP, Harley CDG. 2009. On the prediction of ecological extremes.

Ecol. Monogr. 79:397–421Efron B, Tibshirani RJ. 1993. An Introduction to the Bootstrap. Boca Raton: Chapman and Hall/CRCElith J, Leathwick JR. 2009. Species distribution models: ecological explanation and prediction across space

and time. Annu. Rev. Ecol. Evol. Syst. 40:677–97Frechette M, Butman CA, Geyer WR. 1989. The importance of boundary-layer flows in supplying phyto-

plankton to the benthic suspension feeder, Mytilus edulis L. Limnol. Oceanogr. 34:19–36Gaines SD, Denny MW. 1993. The largest, smallest, highest, lowest, longest and shortest: extremes in ecology.

Ecology 74:1677–92Gaines SD, White C, Carr MH, Palumbi SR. 2010. Designing marine reserve networks for both conservation

and fisheries management. Proc. Natl. Acad. Sci. USA 107:18286–93Gaston KJ, Chown SL, Calosi P, Bernardo J, Bilton DT, et al. 2009. Macrophysiology: a conceptual reunifi-

cation. Am. Nat. 174:595–612Gates DM. 1980. Biophysical Ecology. Mineola, NY: DoverGaylord B, Blanchette C, Denny MW. 1994. Mechanical consequences of size in wave-swept algae.

Ecol. Monogr. 64:287–313Gaylord B, Gaines SD. 2000. Temperature or transport? Range limits in marine species mediated solely by

flow. Am. Nat. 155:769–89Gaylord B, Reed DC, Raimondi PT, Washburn L. 2006. Macroalgal spore dispersal in coastal environments:

mechanistic insights revealed by theory and experiment. Ecol. Monogr. 76:481–502Guichard F, Halpin PM, Allison GW, Lubchenco J, Menge BA. 2003. Mussel disturbance dynamics: signatures

of oceanographic forcing from local interactions. Am. Nat. 161:889–904Gutschick VP, BassiriRad H. 2003. Extreme events as shaping physiology, ecology, and evolution of plants:

toward a unified definition and evaluation of their consequences. New Phytol. 160:21–42Helmuth BST. 1998. Intertidal mussel microclimates: predicting the temperature of a sessile invertebrate.

Ecol. Monogr. 68:51–74Helmuth BST, Denny MW. 2003. Predicting wave exposure in the rocky intertidal zone: Do bigger waves

always lead to larger forces? Limnol. Oceangr. 48:1338–45Holling CS. 1959. Some characteristic of simple types of predation and parasitism. Can. Entomol. 7:385–98Holling CS 1965. The functional response of predators to prey density and its role in mimicry and population

regulation. Mem. Entomol. Soc. Can. 45:1–60


Ann

u. R

ev. E

col.

Evo

l. Sy

st. 2

012.

43:1

-22.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

gby

Sta

nfor

d U

nive

rsity

- M

ain

Cam

pus

- L

ane

Med

ical

Lib

rary

on

07/1

5/13

. For

per

sona

l use

onl

y.


Holling CS. 1992. Cross-scale morphology, geometry, and dynamics of ecosystems. Ecol. Monogr. 62:447–502Huey RB, Stevenson RD. 1979. Integrating thermal physiology and ecology of ectotherms: a discussion of

approaches. Am. Zool. 19:357–66Hutchinson GE. 1957. Concluding remarks. Cold Spring Harb. Symp. Quant. Biol. 22:415–27Jensen JL. 1906. Sur les functions convexes et les inequalites entre les valeurs moyennes. Acta Math. 30:175–93Kaitala V, Ranta E. 1998. Travelling wave dynamics and self organization in a spatio-temporally structured

population. Ecol. Lett. 1:186–92Katul GG, Porporato R, Nathan R, Siqueira M, Soons MB, et al. 2005. Mechanistic analytical models for

long-distance seed dispersal by wind. Am. Nat. 166:368–81Katz RW, Brush GS, Parlange MB. 2005. Statistics of extremes: modeling ecological disturbances. Ecology

86:1124–34Kearney M, Matzelle A, Helmuth B. 2012. Biomechanics meets the ecological niche: the importance of

temporal data resolution. J. Exp. Biol. 215(8):1422–24Kearney M, Phillips BL, Tracy CR, Christian KA, Betts G, Porter WP. 2008. Modeling species distributions

without using species distributions: the cane toad in Australia under current and future climates. Ecography31:423–34

Kearney M, Porter W. 2009. Mechanistic niche modeling: combining physiological and spatial data to predictspecies ranges. Ecol. Lett. 12:334–50

Kearney M, Simpson SJ, Raubenheimer D, Helmuth B. 2010. Modelling the ecological niche from functionaltraits. Philos. Trans. R. Soc. B 365:3469–83

Kinlan BP, Gaines SD, Lester SE. 2005. Propagule dispersal and the scales of marine community process.Divers. Distrib. 11:139–48

Klausmeier CA. 1999. Regular and irregular patterns in semiarid vegetation. Science 284:1826–28Kooijman SALM. 2000. Dynamic Energy Budget Theory for Metabolic Organisation. Cambridge, UK: Cambridge

Univ. PressKozlowski J, Konarzewski M, Gawelczyk AT. 2003. Cell size as a link between noncoding DNA and metabolic

rate scaling. Proc. Natl. Acad. Sci. USA 100:14080–85Kuo ESL, Sanford E. 2009. Geographic variation in the upper thermal limits of an intertidal snail: implications

for climate envelope models. Mar. Ecol. Progr. Ser. 388:137–46Lande R, Engen S, Saether BE. 2003. Stochastic Population Dynamics in Ecology and Conservation. Oxford, UK:

Oxford Univ. PressLevin SA. 1992. The problem of pattern and scale in ecology: the Robert H. MacArthur Award lecture. Ecology

73:1943–67Levin SA, Muller-Landau HC, Nathan R, Chave J. 2003. The ecology and evolution of seed dispersal: a

theoretical perspective. Annu. Rev. Ecol. Evol. Syst. 34:575–604Long S, Humphries S, Falkowski P. 1994. Photoinhibition of photosynthesis in nature. Annu. Rev. Plant

Physiol. Plant Mol. Biol. 45:633–62MacArthur RH, Levins R. 1967. The limiting similarity, convergence and divergence of coexisting species.

Am. Nat. 101:377–85Madin JS, Black KP, Connolly SR. 2006. Scaling water motion on coral reefs: from regional to organismal

scales. Coral Reefs 25:635–44Madin JS, Connolly ST. 2006. Ecological consequences of major hydrodynamic disturbances on coral reefs.

Nature 444:477–80Malamud BD, Morein G, Turcotte DL. 1998. Forest fires: an example of self-organized critical behavior.

Science 281:1840–42Massel SR. 1996. Advanced Series on Ocean Engineering, Vol. 11. Ocean Surface Waves: Their Physics and Prediction.

Singapore: World Sci. 508 pp.Massel SR, Done TJ. 1993. Effects of cyclone waves in massive coral assemblages on the Great Barrier Reef:

meteorology, hydrodynamics and demography. Coral Reefs 12:153–66Maynard-Smith J. 1974. Models in Ecology. Cambridge, UK: Cambridge Univ. PressMcGill BJ, Nekola JC. 2010. Mechanisms in macroecology: AWOL or purloined letter? Towards a pragmatic

view of mechanism. Oikos 119:591–603


Ann

u. R

ev. E

col.

Evo

l. Sy

st. 2

012.

43:1

-22.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

gby

Sta

nfor

d U

nive

rsity

- M

ain

Cam

pus

- L

ane

Med

ical

Lib

rary

on

07/1

5/13

. For

per

sona

l use

onl

y.


McLeod E, Salm R, Green A, Almany J. 2009. Designing marine protected areas networks to address theimpact of climate change. Front. Ecol. Environ. 7:362–70

McNair JN, Newbold JD, Hart DD. 1997. Turbulent transport of suspended particles and dispersing benthicorganisms: how long to hit bottom? J. Theor. Biol. 188:29–52

Melbourne BA, Chesson P. 2006. The scale transition: scaling up population dynamics with field data. Ecology87:1476–88

Melbourne BA, Hastings A. 2008. Extinction risk depends strongly on factors contributing to stochasticity.Nature 454:100–3

Melbourne BA, Sears ALW, Donahue MJ, Chesson P. 2005. Applying scale transition theory to metacommu-nities in the field. In Metacommunities: Spatial Dynamics and Ecological Communities, ed. M Holyoak, MALeibold, RD Holt, pp. 307–30. Chicago: Univ. Chicago Press

Miller LP, Harley CDG, Denny MW. 2009. The role of temperature and desiccation stress in limiting thelocal-scale distribution of the owl limpet, Lottia gigantea. Funct. Ecol. 23:756–67

Moeser GM, Carrington E. 2006. Seasonal variation in mussel byssal thread mechanics. J. Exp. Biol. 209:1996–2003

Moeser GM, Leba H, Carrington E. 2006. Seasonal influence of wave action on thread production in Mytilusedulis. J. Exp. Biol. 209:881–90

Morgan SG, Fisher JL. 2010. Larval behavior regulates nearshore retention and offshore migration in anupwelling shadow and along the open coast. Mar. Ecol. Progr. Ser. 404:109–26

Morritt DM, Nilsson C, Jansson R. 2010. Consequences of propagule dispersal and river fragmentation forriparian plant community diversity and turnover. Ecol. Monogr. 80:609–26

Nathan R. 2006. Long-distance dispersal of plants. Science 313:786–88Nathan R, Katul GG, Horn HS, Thomas SM, Oren R, et al. 2002. Mechanism of long-distance dispersal of

seeds by wind. Nature 418:409–13Nathan R, Sapir N, Trakenbrot A, Katul GG, Bohrer G, et al. 2005. Long-distance biological transport

processes through the air: can nature’s complexity be unfolded in silico? Diversity Distrib. 11:131–37Nisbet RM, Jusup M, Klanjseek T, Pecquerie L. 2012. Integrating dynamic energy budget (DEB) theory with

traditional bioenergetic models. J. Exp. Biol. 215(7):1246Nisbet RM, Muller EB, Lika K, Kooijman SALM. 2000. From molecules to ecosystems through dynamic

energy budget models. J. Anim. Ecol. 69:913–26Paine RT, Levin SA. 1981. Intertidal landscapes: disturbance and the dynamics of pattern. Ecol. Monogr.

51:145–78Paine RT, Tegner MJ, Johnson EA. 1998. Compounded perturbations yield ecological surprises. Ecosystems

1:535–45Paine RT, Trimble AC. 2004. Abrupt community change on a rocky shore—biological mechanisms contribut-

ing to the potential formation of an alternative state. Ecol. Lett. 7:441–45Pascual M, Guichard F. 2005. Criticality and disturbance in spatial ecological systems. Trends Ecol. Evol.

20:88–95Peters DPC, Groffman PM, Nadelhoffer KJ, Grimm NB, Collins SL, et al. 2008. Living in an increasingly

connected world: a framework for continental-scale environmental science. Front. Ecol. Environ. 6:229–37Peters DPC, Pielke RA Sr, Bestelmeyer BT, Allen CD, Munson-McGee S, et al. 2004. Cross-scale interactions,

nonlinearities and forecasting catastrophic events. Proc. Natl. Acad. Sci. USA 101:15130–35Petraitis PS, Methratta ET, Rhile EC, Vidargas NA, Dudgeon SR. 2009. Experimental confirmation of

multiple community states in a marine ecosystem. Oecologia 161:139–48Phillips BL, Kelehear C, Pizzatto L, Brown GP, Barton D, Shine R. 2010. Parasites and pathogens lag behind

their host during periods of host range advance. Ecology 91:872–81Platt WJ, Connell JH. 2003. Natural disturbances and directional replacement of species. Ecol. Monogr. 73:507–

22Ranta E, Kaitala V. 1997. Travelling waves in vole population dynamics. Nature 390:456Ranta E, Kaitala V, Lindstrom J. 1997. Dynamics of Canadian lynx populations in space and time. Ecography

20:454–60Rastetter EB, Aber JD, Peters DPC, Ojima DS, Burke IC. 2003. Using mechanistic models to scale ecological

processes across space and time. BioScience 53(1):68–76


Ann

u. R

ev. E

col.

Evo

l. Sy

st. 2

012.

43:1

-22.

Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

gby

Sta

nfor

d U

nive

rsity

- M

ain

Cam

pus

- L

ane

Med

ical

Lib

rary

on

07/1

5/13

. For

per

sona

l use

onl

y.


Rees MR, Condit R, Crawley M, Pacala S, Tilman D. 2001. Long-term studies of vegetation dynamics. Science293:650–55

Rietkerk M, Boerlijst MC, van Langevelde F, HilleRisLambers R, van de Koppel J, et al. 2002. Self-organization of vegetation in arid ecosystems. Am. Nat. 160:524–30

Ruel JJ, Ayres MP. 1999. Jensen’s inequality predicts effects of environmental variation. Trends Ecol. Evol.14:361–66

Schoener TW. 2011. The newest synthesis: understanding the interplay of evolutionary and ecological dy-namics. Science 331:426–29

Sole RV, Bascompte J. 2006. Self-Organization in Complex Ecosystems. Princeton: Princeton Univ. PressSolomon S, Qin D, Manning M, Chen Z, Marquis M, et al., eds. 2007. Contribution of Working Group I to the

Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Cambridge, UK: CambridgeUniv. Press. 996 pp.

Tennekes H, Lumley JL. 1972. A First Course in Turbulence. Cambridge, MA: MIT PressTilman D. 1994. Competition and biodiversity in spatially structured habitats. Ecology 75:2–16Turing A. 1952. On the chemical basis of morphogenesis. Philos. Trans. R. Soc. B 237:37–72Underwood AJ, Paine RT. 2007. Two views on ecological experimentation. Bull. Br. Ecol. Soc. 38(3):24–30Urban MC, Phillips BL, Skelly DK, Shine R. 2007. The cane toad’s (Chaunus [Bufo] marinus) increasing ability

to invade Australia is revealed by a dynamically updated range model. Proc. R. Soc. B 274:1413–19van de Koppel J, Gascoigne JC, Theraulaz G, Rietkerk M, Mooij WM, Herman PMJ. 2008. Experimental

evidence for spatial self-organization and its emergent effects in mussel bed ecosystems. Science 322:739–42van de Koppel J, Rietkerk M, Dankers N, Herman PMJ. 2005. Scale-dependent feedback and regular spatial

patterns in young mussel beds. Am. Nat. 165:E66–77van der Meer J. 2006. An introduction to dynamic energy budget (DEB) models with special emphasis on

parameter estimation. J. Sea Res. 56:85–102Viswanathan GM, Afanasyev V, Buldryrev SV, Havlin S, da Luz MGE, et al. 2000. Levy flights in random

searches. Physica A 282:1–12West GB, Brown JH, Enquist BJ. 1997. A general model for the origin of allometric scaling laws in biology.

Science 276:122–26Whitehead A. 2012. Comparative genomics in ecological physiology: toward a more nuanced understanding

of acclimation and adaptation. J. Exp. Biol. 215:884–91Widdows J, Pope ND, Brinsely MD, Gascoigne J, Kaiser MJ. 2009. Influence of self-organised structures on

near-bed hydrodynamics and sediment dynamics within a mussel (Mytilus edulis) bed in the Menai Strait.J. Exp. Mar. Biol. Ecol. 379:92–100

Zimmer RK, Fingerut JT, Zimmer CA. 2009. Dispersal pathways, seed rains, and the dynamics of larvalbehavior. Ecology 90:1933–47


Ann

u. R

ev. E

col.

Evo

l. Sy

st. 2

012.

43:1

-22.

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nloa

ded

from

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w.a

nnua

lrev

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s.or

gby

Sta

nfor

d U

nive

rsity

- M

ain

Cam

pus

- L

ane

Med

ical

Lib

rary

on

07/1

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l use

onl

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ES43-FrontMatter ARI 1 October 2012 13:46

Annual Review ofEcology, Evolution,and Systematics

Volume 43, 2012Contents

Scalingy Up in Ecology: Mechanistic ApproachesMark Denny and Lisandro Benedetti-Cecchi � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 1

Adaptive Genetic Variation on the Landscape: Methods and CasesSean D. Schoville, Aurelie Bonin, Olivier Francois, Stephane Lobreaux,

Christelle Melodelima, and Stephanie Manel � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �23

Endogenous Plant Cell Wall Digestion: A Key Mechanismin Insect EvolutionNancy Calderon-Cortes, Mauricio Quesada, Hirofumi Watanabe,

Horacio Cano-Camacho, and Ken Oyama � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �45

New Insights into Pelagic Migrations: Implications for Ecologyand ConservationDaniel P. Costa, Greg A. Breed, and Patrick W. Robinson � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �73

The Biogeography of Marine Invertebrate Life HistoriesDustin J. Marshall, Patrick J. Krug, Elena K. Kupriyanova, Maria Byrne,

and Richard B. Emlet � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �97

Mutation Load: The Fitness of Individuals in Populations WhereDeleterious Alleles Are AbunduantAneil F. Agrawal and Michael C. Whitlock � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 115

From Animalcules to an Ecosystem: Application of Ecological Conceptsto the Human MicrobiomeNoah Fierer, Scott Ferrenberg, Gilberto E. Flores, Antonio Gonzalez,

Jordan Kueneman, Teresa Legg, Ryan C. Lynch, Daniel McDonald,Joseph R. Mihaljevic, Sean P. O’Neill, Matthew E. Rhodes, Se Jin Song,and William A. Walters � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 137

Effects of Host Diversity on Infectious DiseaseRichard S. Ostfeld and Felicia Keesing � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 157

Coextinction and Persistence of Dependent Species in a Changing WorldRobert K. Colwell, Robert R. Dunn, and Nyeema C. Harris � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 183

Functional and Phylogenetic Approaches to Forecasting Species’ Responsesto Climate ChangeLauren B. Buckley and Joel G. Kingsolver � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 205

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ES43-FrontMatter ARI 1 October 2012 13:46

Rethinking Community Assembly through the Lens of Coexistence TheoryJ. HilleRisLambers, P.B. Adler, W.S. Harpole, J.M. Levine, and M.M. Mayfield � � � � � 227

The Role of Mountain Ranges in the Diversification of BirdsJon Fjeldsa, Rauri C.K. Bowie, and Carsten Rahbek � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 249

Evolutionary Inferences from Phylogenies: A Review of MethodsBrian C. O’Meara � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 267

A Guide to Sexual Selection TheoryBram Kuijper, Ido Pen, and Franz J. Weissing � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 287

Ecoenzymatic Stoichiometry and Ecological TheoryRobert L. Sinsabaugh and Jennifer J. Follstad Shah � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 313

Origins of New Genes and Evolution of Their Novel FunctionsYun Ding, Qi Zhou, and Wen Wang � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 345

Climate Change, Aboveground-Belowground Interactions,and Species’ Range ShiftsWim H. Van der Putten � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 365

Inflammation: Mechanisms, Costs, and Natural VariationNoah T. Ashley, Zachary M. Weil, and Randy J. Nelson � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 385

New Pathways and Processes in the Global Nitrogen CycleBo Thamdrup � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 407

Beyond the Plankton Ecology Groug (PEG) Model: Mechanisms DrivingPlankton SuccessionUlrich Sommer, Rita Adrian, Lisette De Senerpont Domis, James J. Elser,

Ursula Gaedke, Bas Ibelings, Erik Jeppesen, Miquel Lurling, Juan Carlos Molinero,Wolf M. Mooij, Ellen van Donk, and Monika Winder � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 429

Global Introductions of Crayfishes: Evaluating the Impact of SpeciesInvasions on Ecosystem ServicesDavid M. Lodge, Andrew Deines, Francesca Gherardi, Darren C.J. Yeo,

Tracy Arcella, Ashley K. Baldridge, Matthew A. Barnes, W. Lindsay Chadderton,Jeffrey L. Feder, Crysta A. Gantz, Geoffrey W. Howard, Christopher L. Jerde,Brett W. Peters, Jody A. Peters, Lindsey W. Sargent, Cameron R. Turner,Marion E. Wittmann, and Yiwen Zeng � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 449

Indexes

Cumulative Index of Contributing Authors, Volumes 39–43 � � � � � � � � � � � � � � � � � � � � � � � � � � � 473

Cumulative Index of Chapter Titles, Volumes 39–43 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 477

Errata

An online log of corrections to Annual Review of Ecology, Evolution, and Systematicsarticles may be found at http://ecolsys.annualreviews.org/errata.shtml

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