Modeling Approaches in Avian Conservation and the Role of Field Biologists

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Steven R. Beissinger University of California - Berkeley, [email protected]

Jeffrey R. Walters Virginia Polytechnic Institute and State University

Donald G. Catanzaro University of Arkansas - Main Campus

Kimberly G. Smith University of Arkansas - Main Campus

John B. Dunning Jr. Purdue University

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Beissinger, Steven R.; Walters, Jeffrey R.; Catanzaro, Donald G.; Smith, Kimberly G.; Dunning, John B. Jr.; Haig, Susan M.; Noon, Barry R.; and Stith, Bradley M., "Modeling Approaches in Avian Conservation and the Role of Field Biologists" (2006). USGS Staff -- Published Research. 688. https://digitalcommons.unl.edu/usgsstaffpub/688

This Article is brought to you for free and open access by the US Geological Survey at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in USGS Staff -- Published Research by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Authors Steven R. Beissinger, Jeffrey R. Walters, Donald G. Catanzaro, Kimberly G. Smith, John B. Dunning Jr., Susan M. Haig, Barry R. Noon, and Bradley M. Stith

This article is available at DigitalCommons@University of Nebraska - Lincoln: https://digitalcommons.unl.edu/ usgsstaffpub/688 MODELINGAPPROACHES IN AVIAN CONSERVATION AND THE ROLEOF FIELDBIOLOGISTS

Steven R. Beissinger,1 Jeffrey R. Walters,2 Donald G. Catanzaro,3 Kimberly G. Smith,3 John B. Dunning, Jr.,4 Susan M. Haig,5 Barry R. Noon,6 and Bradley M. Stith7

department of Environmental Science, Policy and Management, University of California,Berkeley, California94720, USA; department of Biology, VirginiaPolytechnic Institute and State University, Blacksburg,Virginia 24061, USA; Kenterfor Advanced Spatial Technologiesand Department of Biological Sciences, University of Arkansas, Fayetteville, Arkansas 72701, USA; ^Departmentof Forestry and Natural Resources,Purdue University, West Lafayette,Indiana 47907, USA; 5U.S. Geological Survey Forest and Rangeland Ecosystem Science Center,3200 SW JeffersonWay, Corvallis, Oregon 97331, USA; and department of Fishery and Wildlife Biology, ColoradoState University, Fort Collins, Colorado80523, USA; USA department of Wildlife Ecology and Conservation, University of Florida, Gainesville, Florida 32611,

ORNITHOLOGICAL MONOGRAPHS NO. 59 PUBLISHED BY THE AMERICAN ORNITHOLOGISTS'UNION WASHINGTON, D.C. 2006

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Lists of Tables and Figures vi From the Editor vii ABSTRACT 1 INTRODUCTION 2 THE FORM OF ECOLOGICAL MODELS 3 DETERMINISTICSINGLE-POPULATION MATRIX MODELS 4 Structure of Matrix Population Models 5 Use of Matrix Population Models in Conservation 8 STOCHASTIC POPULATION VIABILITYANALYSIS MODELS FOR SINGLE POPULATIONS 10 Structure of Stochastic Population Viability Analysis Models for Single Populations 11 Conservation Use of Stochastic Population Viability Analysis Models for Single Populations 12 METAPOPULATION MODELS 15 Structure of Metapopulation Models 15 Use of Metapopulation Models in Conservation 19 SPATIALLYEXPLICIT MODELS 20 Structure of Spatially Explicit Models 20 Use of Spatially Explicit Models in Conservation 23 GENETIC MODELS 26 Structure of Genetic Models 26 Effective-population size 26 Pedigreeanalyses 27 Use of Genetic Models in Conservation 30 SPECIES DISTRIBUTION MODELS 31 Structure of Species Distribution Models 32 Use of Species Distribution Models in Conservation 35 INTELLIGENT USE OF MODELS TO MAKE CONSERVATION DECISIONS .... 37 Attributes of Useful Models 37 Working with Multiple Models in a Decision-theoretic Framework 39 HOW FIELD BIOLOGISTSCAN INTERACT WITH MODELERS TO IMPROVE CONSERVATION DECISIONS 40 ACKNOWLEDGMENTS 41 LITERATURECITED 42

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1. Structureof the standard input file ("Me,Ma, Pa" file) used to keep studbooks, to construct pedigrees, and for gene-drop analyses 29 2. Considerationof genetic factors in common population viability models used in conservation planning 30

LISTOF FIGURES

1. Matrixpopulation models for prebreedingand postbreedinglife cycles, and elasticity calculations 6 2. Simplified example of the structureand outcomes from a stochasticsingle- population PVAmodel 11 3. DemographicPVA models with various degrees of spatial explicitness 17 4. Gene-droppedigree model and analysis for a small population 28 5. Exampleof a gap modeling process for the Ovenbird (Seiurusaurocapilla) in Arkansas 33

This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions From the Editor

Likemany membersof the AmericanOrnithologists' Union, I developed a passion for birds early in life and have been trying to make a living from this passion ever since. As you get to know fellow AOU members, particularlyover drinks, you hear stories about that moment in their lives when they discovered this incrediblefeeling about birds that could not be ignored. Some of us started at age six or seven, others in high school or college. Some of us, lacking the artisticskills of David Sibley or the humor of Pete Dunne, have had to fall back on doing research.Our field work allows us to earn a paycheck in pursuit of our passion. We get to see and catch and count birds in what are sometimes exciting, and hopefully always interesting, places. We are paid to write reports, scientific papers, and books that present our results from the field. In many cases, our work has direct or indirect implications for bird conservation. Unfortunately,we cannot simply write papers about anything that catches our fancy. Rather, we need to justify our work on the basis of prior studies and present our results using up-to-date methodologies. For many of us, this is where the ugly concepts of hypotheses, models, and statistics come into play and turn our lives of passion into actual work and sometimes drudgery.During my career,the profession has become more and more based on the testing of models, usually with associated quantitativemeasures. I took a single statistics course during eight years of college; my graduate students take at least three or four, and often more. One even has a Master's degree in statistics to go along with her MS in ecology. More and more, our field work is only as good as the model being tested, and the test only as good as the calculationsprovided. Of course, doing field work requiresa lot of skill, though usually of the "naturalhistory" category that involves details about birds, plants, and so forth. Doing modeling and developing statistical methods obviously requires a high comfort level with conceptual thinking and mathematics.Few ornithologistsare experts in both areas;field people are always trying to figure out what is currently the best way to measure their area of specialty,while modelers are trying to provide methods for the analyticalquestions posed by the field people. The goal of both groups is to develop the best science possible, with the appropriatescientific models tested with the best quantitativetechniques. All these areas within ornithologicalresearch change over time, so it is difficult for field people to stay currentwith the latest models and for modelers to ensure that field people are providing the best data possible and analyzing it properly. OrnithologicalMonograph No. 59 addresses this problemby serving as a bridge between field biologists and modelers. It provides a state-of-the-art review by a set of experts of the models they consider most relevant to currentavian conservation. It explains why these models are relevant and then shows how they can be quantitatively tested with field data. In addition, it promotes interactionbetween field workers and modelers, because models are of little use if they are not tested and supported with the right data from the field. This monographshould be of great value to beginning graduatestudents who are planning field studies and handy for us older folks who may need to catch up on things. Adding to the authors' acknowledgments, I wish to thank my students in the Avian Ecology Laboratoryat the University of Missouri- in particular,Judith Toms, she of the degrees in both stats and ecology- whose reviews greatly improved this monograph. Comments from Marissa Ahlering, Andrew Cox, and ErnestoRuelas Inzunza were helpful to the authors in making this as user-friendlyas possible. JohnFaaborg

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This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions ."^ OrnithologicalMonographs *k Volume (2006),No. 59, 1-56 ^V © The AmericanOrnithologists' Union, 2006. ^Jl?*r Printedin USA. MODELINGAPPROACHES IN AVIAN CONSERVATION AND THE ROLEOF FIELDBIOLOGISTS Steven R. Beissinger,18 Jeffrey R. Walters,2 Donald G. Catanzaro,3 Kimberly G. Smith,3 John B. Dunning, Jr.,4 Susan M. Haig,5 Barry R. Noon,6 and Bradley M. Stith7 ^Departmentof EnvironmentalScience, Policy and Management,University of California,Berkeley, California 94720, USA; department of Biology, Virginia Polytechnic Institute and State University, Blacksburg,Virginia 24061, USA; Center for Advanced Spatial Technologiesand Department of Biological Sciences, University of Arkansas, Fayetteville, Arkansas 72701, USA; ^Departmentof Forestry and Natural Resources, Purdue University, West Lafayette,Indiana 47907, USA; 5U.S. GeologicalSurvey, Forest and Rangeland Ecosystem Science Center,3200 SW JeffersonWay, Corvallis, Oregon 97331, USA; department of Fishery and Wildlife Biology, ColoradoState University, Fort Collins, Colorado80523, USA; and 7Departmentof Wildlife Ecology and Conservation, University of Florida, Gainesville, Florida 32611, USA

Abstract.- This review grew out of our realizationthat models play an increasinglyimpor- tant role in conservationbut are rarelyused in the researchof most avian biologists. Modelers are creatingmodels that are more complex and mechanisticand that can incorporatemore of the knowledge acquired by field biologists. Such models require field biologists to provide more specific information,larger sample sizes, and sometimes new kinds of data, such as habitat-specificdemography and dispersalinformation. Field biologists need to supportmodel developmentby testing key model assumptions and validating models. The best conservation decisions will occur where cooperativeinteraction enables field biologists, modelers, statisticians, and managersto contributeeffectively. We begin by discussing the general form of ecological models- heuristic or mechanistic, "scientific"or statistical- and then highlight the structure,strengths, weaknesses, and applications of six types of models commonly used in avian conservation:(1) deterministicsingle- population matrixmodels, (2) stochasticpopulation viability analysis (PVA)models for single populations, (3) metapopulationmodels, (4) spatially explicit models, (5) genetic models, and (6) species distributionmodels. We end by considering the intelligent use of models in decision-making,which requiresunderstanding their unique attributes,determining whether the assumptionsthat underlie the structureare valid, and testing the ability of the model to predict the future correctly. Received30 August 2005, accepted25 November2005.

Resumen.- Esta revision surgio al reconocerque los modelos juegan un papel cada vez mas importanteen conservacion, pero son raramenteusados en las investigaciones realizadaspor la mayoria de los biologos que trabajancon aves. En la actualidad se estan creando modelos complejos que involucran mecanismos que podrian incorporar mas del conocimiento que han adquirido los biologos de campo. Estos modelos requieren que los biologos de campo en provean informacionmas espedfica, utilicen tamafios muestrales mayores y que algunos casos provean nuevos tipos de datos, como demografia en habitats especificos e informacion sobre dispersion. Los biologos de campo deben apoyar el desarrollo de modelos a traves de en la prueba de los supuestos claves y la validacion de los modelos. Las mejores decisiones conservacion ocurriran al existir una interaccion cooperativa y efectiva entre biologos de campo, biologos que realizan modelos, estadisticos y personas que trabajanen manejo. Comenzamos discutiendo la forma general de los modelos ecologicos- heuristicos o la que describen mecanismos, "cientificos"o estadisticos- y luego destacamos estructura, las fortalezas y debilidades y las aplicaciones de seis tipos de modelos que se utilizan

8E-mail:[email protected]

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comunmenteen la conservacionde aves: (1) modelos deterministicosmatriciales de una unica poblacion, (2) modelos de analisis estocasticos de viabilidad poblacional (AVP) para una unica poblacion, (3) modelos metapoblacionales, (4) modelos espacialmente explicitos, (5) modelos geneticos y (6) modelos de la distribucionde las especies. Terminamosconsiderando el uso inteligente de modelos en la toma de decisiones, lo que requiereentender los atributos especificos de cada modelo, determinar si los supuestos que subyacen a la estructura son validos y probarla habilidad del modelo para predecir el futuro correctamente.

Introduction days earlier. Nonetheless, most presenters at both meetings employed a statistical model to Avian biologists involved in conservation test the significance of, or evaluate patterns in, activities encounter formal mathematical and their data. Talkingabout models with ornitholo- simulation models ever more frequently and in gists evokes strong reactions, as evidenced by ever more diverse forms.Models are constructed the responses of AOU meeting attendees to the to act as descriptions of ecological systems question:"What is the first thing that you think (MaynardSmith 1974).As in other sciences, such of when I say the words 'model or ecological models have driven the development of certain model'?".Answers included "hot air," "money concepts in conservationbiology, such as popu- for someone else," "predictingthe future,""I go lation viability and metapopulation dynamics. right to the Discussion and hope that they know Mathematicaland simulation models (hereafter what they are doing," "peoplewho haven'tbeen "models")have been used to predict outcomes in the field enough,""computers," "assumptions based on past, current,or projected conditions, and generalizations,""reality?," and "something and they serve a useful role in synthesizing I don't understandat all." knowledge and guiding research. To make a Models, unlike statistics, are not universally model, one is forced to state explicitly the rela- accepted as serious tools by field biologists, tions between external factors and the state of perhaps because models are perceived as more the system, and this quickly reveals the limits of difficult to test definitively than other kinds of our understanding. More significantly,models hypotheses (Aber 1997). When models perform have become importanttools that are applied to poorly, they are typically modified by chang- policy decisions, and their use will continue to ing assumptions or input values, rather than expand as desktop computing power grows and rejected. This reduces confidence in model user-friendlysoftware makes modeling increas- predictions or conclusions. Models, by their ingly accessible. Models, however, are neither a nature, are simplifications of and hypotheses panacea nor the only useful kind of analysis for about complex natural systems and can never making conservation decisions. Intelligent use capture all of a system's dynamics. To avoid of models in decision-making requires under- oversimplification and to make models more standing their unique attributes, determining useful in resolving conservationproblems, one whether the assumptions that underlie the increasesthe number of parametersthat need to structureare valid, and testing the ability of the be sampled, but this is likely to result in poor model to predict the future correctly. estimation of many parameter values. Poor The present review, and a symposium at an parameter estimation, like oversimplification, AmericanOrnithologists' Union (AOU) meeting causes field biologists to question the value sponsoredby the AOU ConservationCommittee, of models. Because models are simplifications grew out of our realizationthat models play an and abstractionsof nature, all are expected to important role in conservation but are rarely be "wrong"to some degree, which makes them incorporated in the research of most avian obvious targetsfor attackwhen they become the biologists. For example, at a recent AOU meet- basis of controversialdecisions- as in the debate ing, only -4% of 317 papers presented or tested over conservation planning for the Northern models, compared with -21% at a meeting of SpottedOwl (Strixoccidentalis caurina; Noon and the Ecological Society of America held a few McKelvey1996a, Noon and Murphy 1997).

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Despite these problems, their usefulness for those that address optimal foraging (Stephens making predictions ensures that models will and Krebs 1986), life history (Charnov 1993), continue to be importantin decision-making.In population dynamics (Maynard Smith 1974, conservation,predicting the future behavior of Caswell 2001), and game theory (Maynard a population or system under differentmanage- Smith 1982). Models come in many shapes and ment programsis of paramountinterest, and no sizes, however, and there are multiple typolo- credible prediction is possible without a formal gies of ecological models relevant to avian or informal model of the system. Increaseduse ecology (Jorgensen and Bendoricchio 2001, of mathematicalmodeling in conservation is a Nichols 2001, Gertsevaand Gertseva2004). One manifestationof the maturationof conservation typology classifies models as either heuristic biology as a science. As improved computing or mechanistic (Pielou 1981). Heuristic models power facilitatesthe development of ever more capture the essence of a system using a few, realistic models, their appeal to field biologists sometimes abstract,variables to predict future grows, as do demands on field biologists to pro- system behavior, but such models provide no duce data for parameterestimation. As a result, causal explanation for the model outcomes avian biologists need to be able to understand expected to occur. In contrast, mechanistic and evaluate models, and modelers need to models are designed to capture the key pro- interact with field biologists. The opportunity cesses and relationships among variables as exists for a productive synergism between these they exist in nature, and to provide an expla- two groups to improve conservationdecisions. nation for expected outcomes. Models used to This monographreviews a set of models that project forest growth illustrate this contrast. avian biologists are likely to encounter in con- Traditionalmodels of forest growth and yield servation. As scientists who are both modelers are heuristic- they use regression equations to and field biologists, we offer a perspective on predict future forest growth on the basis of past, models in conservation that is grounded in empirically estimated, relationships (Pielou theory, application, and natural history. We 1981, Davis et al. 2001). The form of these equa- begin by discussing the general form of eco- tions and the regression coefficients may not logical models. We then highlight the struc- have direct biological interpretations. In con- ture, strengths, weaknesses, and applications trast, forest succession models are mechanistic of six types of models. Our goal is to present and attempt to projectfuture tree structureand a diverse typology of model applications used composition on the basis of known aspects of in avian conservationand to indicate the kinds the survival process, physiological tolerance of information required for each, so that avian to shading, competitive ability to obtain light biologists may become more aware of the types and water, and recruitment dynamics based of data that will improve the realism, precision, on dispersal and propagule number (Shugart and accuracyof modeling efforts. We conclude 1984, Huston 1992). These models require an by examining how models can be used intel- understanding of mechanistic processes, and ligently to make conservation decisions, and therefore depend on experimental studies of how field biologists and modelers can interact processesby field biologists. All the model types to improve the decision-makingprocess. we discuss in this monograph containboth heuristic and mechanistic elements, but they vary The Form of Ecological Models in relative emphasis. As a model's complexity increases,it can incorporatemore key processes Modeling natural processes consists of and becomes more mechanistic. The popula- constructing a plausible symbolic representation models we discuss generally represent an tion of the dynamics of a system in the form increasingly complex, increasingly mechanistic of mathematicalequations or rule sets (Pielou series (deterministicsingle-population, stochas- 1981). Ecological models can take many forms, tic single-population,metapopulation, spatially but most models are closely related to a priori explicit). hypotheses about how a system functions. In Another useful characterization of models this sense, models project the consequences distinguishes between scientific and statisti- of hypotheses (Nichols 2001). Many types of cal models (Nichols 2001, Williams et al. models are relevantto avian research,including 2002). Scientific models are used to project the

This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions 4 ORNITHOLOGICAL MONOGRAPHS NO. 59 consequences of a hypothesis of how a system is that any forecast of the consequences of an works, usually expressed in mechanistic terms. action is inherently based on some model of For example, a scientific model may predict how the system works. This includes the pre- how the reproductive output of a certain bird diction of "no adverse consequences," which species will be affectedby weather,habitat, and also is based on some mental construct of the their interaction during the breeding season system. The great advantage of an intelligible (Franklin et al. 2000). Statistical models (and mathematical or simulation model is that it hypotheses) follow logically from their cor- makes explicit the structure, assumptions, and responding scientific models; they project how relationships among the system's variables. measurable quantities or data should appear if For example, a population model can include consistent with the scientific model. various factors believed to affect survival and A final useful partition of ecological models fecundity, such as habitat quality, habitat dis- is based on whether their objectiveis to describe tribution, annual variation in food supply, and biological processes or to facilitatemanagement predation rate. With an explicit model, one can decisions (Taylor 1995). Biological models are assess the importance of different assumptions often mechanistic, but are not constrained in about relationships among factors, incorporate their design (i.e. their input parameters and new information about processes, and test and outputs) to reflectthe concernsof managers.For refine the ability to predict population dynam- example, a key parameter whose value would ics. Models may, unfortunately, also lead to trigger a management response is not required wrong decisions when they do not incorporate in optimal-foraging models. Management important processes or unintentionally use models, in contrast, are specifically designed incorrectparameter estimates (Emlen1989). The to facilitatedecision-making even in the context criticalquestion is to what extent a conservation of great uncertainty (Williams et al. 2002, Dale decision will benefit from considering the 2003). Such models should be based on param- results of a particular model. The answer eters that are easily estimated and relevant to depends on the model's attributes. managers. Differences in the construction of In the following six sections, we discuss the biological and management models may limit attributes of biological models that have been the value of some biological models for man- transformed into management models and agement decisions. All the models we examine describe their structures,assumptions, and uses below exhibit characteristicsof both biological in conservation. We conclude with a return to and managementmodels. the general topics of (1) intelligent use of mod- It is important to recognize that the model els in conservation and (2) interactionsof field types discussed above are not mutually exclu- biologists with modelers. sive and that we have not exhaustively discussed all possible characterizations.In addition, most Deterministic Single-population Matrix models treated in this monograph can be classi- Models fied within one or more typologies. For a discussion of other useful characterizationsof model Deterministicsingle-population matrix mod- types relevant to management and conserva- els (hereafter"matrix population models") are tion, see Williams et al. (2002). among the simplest demographicmodels. They Inherent differences between the predic- are descriptions of population dynamics con- tions or outputs of a biological model and the sisting of a set of equations (one for each age or factors affected by management often inhibit stage class) that predict population size at time conservationdecisions. In the policy arena, our t + 1 from informationon the survival, growth, limited understanding of ecological processes and reproduction of individuals at time t. The and the uncertaintiesassociated with projected equations are often formulated into a matrix, consequences of environmental change are which is a rectangular array of numbers or often used to inhibit action and protect the symbols. Matrices have mathematical proper- status quo. Those who oppose costly conserva- ties discussed below that are directly related tion decisions find complex models based on to important measures of population dynam- simplifying biological assumptions to be easy ics, and they are very convenient for analysis targets. What they fail to recognize, however, with computers. Matrix population models

This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions MODELS IN AVIAN CONSERVATION 5 have long been used in ecology (Leslie 1945, al. 2002). When the capture data are viewed in 1948; Lefkovitch 1965; Getz and Haight 1989; a forward manner, the model estimates annual Caswell 2001), and they have been employed to local survival ((f)^the probability that an indi- make management recommendationsfor birds vidual in the population in year t will survive since the late 1960s.Applications have included and remain in the population in year t + 1); endangered species, such as the Whooping when viewed backwards, the model estimates Crane (Grusamericana; Miller and Botkin 1974) the seniority probability (yj the probability and CaliforniaCondor (Gymnogyps californianus-, that an individual did not enter the popula- Mertz 1971), as well as seabirds (Leslie 1966) tion between years t and t - 1). Lambda at time and game birds (Geis et al. 1969, Anderson t (A,)is estimated by <\>tI yt +v Neither of these 1975, Nichols et al. 1995). They became further approaches is reviewed here, because they are established as a tool for making population essentially statistical rather than demographic management decisions with the incorporation models and as yet do not allow incorporation of sensitivity analysis (e.g. elasticity, discussed of mechanistic processes (Nichols et al. 2000, below) (Crouse et al. 1987, Crowder et al. 1994, Nichols and Hines 2002, Williams et al. 2002). Doak et al. 1994, Silvertown et al. 1996). Nevertheless, they can have important conser- It is not appropriateto use matrix models to vation applications (Dreitz et al. 2002, Cam et make long-term population projections unless al. 2003, Franklinet al. 2004). Both approaches it is assumed that long-term averages for the calculate direct estimates of lambda, whereas vital rates will experience little change. Matrix matrix population models yield an asymptotic models can be used to estimate the geometric rate of population change based on an expected rate of population growth (lambda, or A); to rate of population change modeled from an indicate population characteristics,such as the observed set of vital rates (Caswell 2001). distribution of individuals among age classes Sandercockand Beissinger (2002) showed that (stable age distribution) or the reproductive all three approaches can yield consistent esti- value of age classes; and (as it is often used in mates of lambda. Matrix population models conservation)to evaluate the influence of demo- have the advantage of incorporatingmore bio- graphic rates on population change (sensitivity logical processes, but the disadvantageof some- analysis) (McDonaldand Caswell 1993, Caswell times yielding unrealistic values of lambda, 2000). If the relationship between proposed because of either poor estimates of vital rates or management actions and demographic rates a mismatch between the actual and asymptotic can be determined, the ability of different man- stable age distribution. agement actions to produce positive population change under current conditions can be com- Structure of Matrix Population Models pared. Thus, a matrix population model might indicate whether management actions that Matrixpopulation models are the least data- increase nesting success will be more effective demanding of the models reviewed here (Fig. than management actions that increase adult 1), though years of field study are needed to survival, even though the model may not accu- construct and parameterize them well. These rately projectpopulation size over time. models require only: (1) an understanding of Methods other than matrix population age, stage, or social structure(to determineages models can be used to estimate lambda. The or stages for analysis); (2) identification of age traditional approach uses the geometric mean or stage of first reproduction;and (3) estimates of the ratios of population size (N) estimates for of reproductive success and survivorship for consecutiveperiods (A= Nt+1/Nt)calculated from the different ages or stages. Ideally the deci- a time series (Morrisand Doak 2002,Williams et sion of how many stages to use and their al. 2002),whereas a newer approachis based on composition should be closely tied to variation mark-recapturedata using the temporal sym- in demographic parameters (Sauer and Slade metry method of Pradel (1996). The temporal 1987, Caswell 2001, Pfister and Wang 2005). In symmetry method fits mark-recapturemodels practice, however, ages or stages of long-lived for open populations to capture data viewed organisms are often collapsed into a few classes simultaneously in a forward and backwards because field studies are rarely long enough to manner (Nichols and Hines 2002, Williams et measure age-specific rates. Nevertheless, many

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Fig. 1. Matrixpopulation models for (A) prebreedingand (B) postbreedinglife cycles, and elasticity calculations (modified from Beissingerand Westphal1998). Life-cycle diagrams are presentedwith nodes for four age classes: 0 (juvenilesthat are young of the year), 1 (subadults,hatched in the previous year, and up to 1 year of age), 2 (subadultsfrom 1 to 2 years of age), and 3 (adults >2 years old). Individuals of each age class (indicated by subscripts)survive with a probabilityof P, but only adults reproducewith a fecundityof m. No juvenilenode occurs in the prebreedinglife-cycle diagram,because censuses are conductedjust prior to the breeding season, when surviving young have alreadybecome 1-year-oldsat a juvenile survival probabilityof Pj this appearsin the prebreedinglife-cycle diagramin the first row of the matrix.The postbreedinglife cycle and matrixhave an extra node and row, respectively,for juveniles,because censuses are conducted immediatelyafter the breeding season. The first row of the postbreedingmatrix models reproductionas a product of fecundity and subadult (P2)or adult survival (P3).The reasonis that only a portionof these individuals will survive from the postbreed- ing census until the beginning of the next breeding season, increase in age by one year, and then reproduce. Basic matrix calculations can easily be solved using commerciallyavailable mathematicssoftware by one of two methods. The power method (McDonaldand Caswell 1993) raises the matrix to a high power (e.g. A128), which causes the rows and columns of the matrix to converge on proportionsthat do not change. The stable age distribution is calculated from the proportions of the coefficients of the columns; the coefficients of the rows converge on reproductivevalue, which is found by dividing each coefficientby the value of the first coefficient in its row. Lambda(A,), the geometricrate of annual population growth, is found by dividing any cell in A128by the same cell in A127.Alternatively, matrix algebra (Caswell 2001) can be used to calculatethe stable age distribution(right eigenvector), reproductive value (left eigenvector),and lambda (dominantor largestpositive eigenvalue or latent root of the matrix).Elasticity requires calculating the derivativeof the log of lambda with respect to the log of a matrixelement («„)situated in the ith row and ;th column of the matrix.The formulafirst requirescalculation of the sensitivity (s/y.)of the element, which is the partialderivative of lambda with respect to the element. The term (vw) is the product of the reproductivevalue and stable age distributionassociated with the row and column address of a particularelement, whereas the term is the sum of all the element by element products of the stable age distributionand reproductivevalue.

This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions MODELS IN AVIAN CONSERVATION 7 birds have complex social structures, which is the expected contributionof an individual in may include subadults that have yet to reach a particularage- or stage-class to future popu- the age of first breeding, nonbreeding adults lation growth. Nevertheless, the mathematical old enough to breed (e.g. helpers), senescing terminology and processes involved in matrix adults, etc. An understanding of social struc- algebra can be confusing to those unfamiliar ture is critical to determining the underlying with them (Caswell 2001). An introduction structureof the matrix (McDonaldand Caswell to the calculations is provided in Figure 1; 1993,Harcourt 1995). Estimates of age- or stage- McDonald and Caswell (1993) and Morris and specific rates of fecundity and survivorship Doak (2002) give more detailed, but readable, are usually the most important components of presentations. matrix population models, and the accuracyof Sensitivity can be analyzed in several ways their estimation is likely to have a large effect (Caswell 2000, 2001), but elasticity is employed on model outcomes. Most matrix population most frequently (Fig. 1). Elasticity is the pro- models of vertebrates are constructed only portional change in annual population growth for females, because male fecundity is often (lambda) resulting from a proportional change unknown. Thus, rates are usually expressed on in a matrix element (de Kroon et al. 1986; de a per-femalebasis. Nevertheless, two-sex mod- Kroon et al. 2000). Elasticity values for the ele- els can be built (Caswell 2001). ments of matrix population models have the Caswell (2001) and McDonald and Caswell convenient propertyof summing to 1.0 and give (1993) present detailed treatments of the a proportionalcontribution to the total sensitiv- structureof matrix population models and the ity of lambda. Thus, small changes in the vital calculations involved, so we summarize these rates that compose a matrix element having only briefly here. The underlying structure of a large elasticity value will produce a much a matrix model is the life cycle of the organ- greater effect on the rate of population growth ism, which can be depicted in a diagram as a than equally small changes in the vital rates that set of nodes for stages and arcs for transitions comprise a matrix element having a small elas- between stages (Fig. 1). In the matrix, a row ticity value. However, the first row of matrixele- is required for each stage- or age-class of the ments is calculatedas a product of both survival modeled population, and columns track the and fecundity (Fig. 1). Thus, lower-level elas- contribution of each stage or age to the row. ticities must be calculated to partition elasticity The first row of the matrix accounts for rates of among survival and fecundity (Wisdom and vital rate is production and recruitment of young into the Mills 1997, Caswell 2001). When a such as population, and the other rows present rates of found on more than one matrixelement, survival within stages or the transitionfrom one adult survival, lower-level elasticity values can value for the stage to another.Correct construction of matrix be added to obtain a total elasticity models critically depends on the time at which vital rate,but the elasticity values will no longer the population is censused in relation to the sum to 1.0. For all demographicsubcomponents time of reproduction(Noon and Sauer 1992). found only on the same element, lower-level value. Many matrix analyses are easily done elasticity values will take on the same is using commercially available mathematics In birds, for example, fecundity frequently software (e.g. MATLAB,MATHEMATICA, and calculated as a product of the proportion of MATHCAD) requiring only the input of the females breeding, proportion of nests fledging matrix followed by a few commands (Caswell young, and number of female young fledged 2001, Morrisand Doak 2002).Once the matrixis per successful nest. This can limit the useful- constructed,it is easy to calculate (1) the annual ness of elasticity in instances where the goal is a rate of population growth (lambda), which to understandthe effect of changing particular describes the rate of change for each stage- subcomponent of reproduction(e.g. proportion class and the population once the population of nests fledging young). has reached a stable age distribution; (2) the Two less frequently used but equally valu- the stable age distribution, which is the propor- able approaches to analyzing sensitivity tion of individuals in each age- or stage-class if of matrix population models are the life-table the rates of survival and reproduction remain response experiment (LTRE) and life-stage The LTRE is an unchanged; and (3) reproductive value, which simulation analysis (LSA).

This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions 8 ORNITHOLOGICAL MONOGRAPHS NO. 59 analytical approach that extends elasticity by the ratio of juveniles to after-hatch-yearbirds, incorporating specific changes to vital rates which is an indirect estimate of recruitment (Caswell 1996b,2000). It compares the contribu- (Peery et al. 2006a), with model estimates of tions of specific changes in particularvital rates productivity needed for stable populations with differences in lambda between a "mean" (Beissinger 1995a, Beissinger and Nur 1997, or "control"matrix and a "perturbed"or "treat- Peery et al. 2006b).Matrix models were used to ment" matrix.The LTREdoes this by taking the evaluate acceptable rates of mortality required product of the change in the vital rate caused to re-establish viable populations of California by perturbation and the sensitivity of lambda Condors (Meretskyet al. 2000), to analyze risks to changes in that rate (Caswell 2000, Mills and of decline in and effects of long-line fisheries on Lindberg 2002). Thus, LTREcan compare the AmsterdamAlbatrosses (Diomedea amsterdamen- effects on lambda of the overall contributionof sis; Inchaustiand Weimerskirch2001), to specify changes in vital rates.Although frequentlyused the effects of feral cats on island-nesting Black- to analyze plant population dynamics (Bruna vented Shearwaters(Puffinus opisthomelas; Keitt and Oli 2005, Brys et al. 2005, Griffith and et al. 2002), and to determine habitat-specific Forseth 2005), LTREhas rarely been applied to differences in population growth in Peregrine birds; for a notable exception, see Cooch et al. Falcons (Falcoperegrinus; Kauffman et al. 2003) (2001).Life-stage simulation analysis is a simu- and ptarmigans (Lagopusspp.; Sandercock et lation-based approach to sensitivity analysis. al. 2005). Matrix models have also been used It evaluates the effect on lambda of changes in to compare the efficacy of population control vital rates by constructinghundreds of replicate options for Snow Geese (Chen caerulescens; matrices randomly drawn from specified distri- Mills and Lindberg 2002) and Brown-headed butions for each vital rate (Wisdom and Mills Cowbirds (Molothrusater, Citta and Mills 1999). 1997,Wisdom et al. 2000). Lambdais calculated In these two applications, as well as in the for each matrix, and the coefficient of deter- GreaterPrairie Chicken example (Wisdom and mination (r2) between the value of each vital Mills 1997), LSA was employed as an alterna- rate and lambda is found; this reveals which tive form of sensitivity analysis to indicate how vital rate accounts for the greatest variation in potential variation in vital rates was affecting the growth rate for all simulations when rates the population dynamics. Hoekmanet al. (2002) change simultaneously. also used multiple approaches to explore the sensitivity of Mallard (Anas platyrhynchos)life- Use of Matrix Population Models in cycle stages. Cooch et al. (2001) used LTREto Conservation analyze the demographic responses of Lesser Snow Geese (Anserc. caerulescens)to changes in Use of deterministic matrix population food abundance. models in management decisions has grown Although matrix population models require rapidly since the development of elastic- the least data of all the modeling approaches ity analysis. Matrix analyses were used to reviewed here, developing accurateand precise estimate rates of population growth for log- estimates for vital rates and constructing the gerhead sea turtles (Carettacaretta) to compare matrixis not a trivial matter.First, accurate esti- the effects of different management options; mates of fecundity and survival based on long- these indicated that turtle-excluder devices term studies are rarelyavailable for endangered are more effective than in situ and ex situ egg species (Noon and Sauer 1992, Beissinger and protection (Crouse et al. 1987, Crowder et al. Westphal 1998). Survivorship is often the most 1994, Grand and Beissinger 1997). Similarly, difficult demographic rate to measure accu- analyses of elasticity were used to evaluate the rately, because it must be distinguished from effects of proposed management techniques on the probability of resighting (Nichols 1992). lambda in Red-cockadedWoodpeckers (Picoides Complex statisticaltechniques have been devel- borealis; Heppell et al. 1994) and Greater oped to yield accurate estimators of survival Prairie Chickens (Tympanuchuscupido pinnatus; and to test for differences among age- or stage- Wisdom and Mills 1997). Matrix models were classes (Lebretonet al. 1992). Unless the prob- applied to Marbled Murrelets (Brachyramphus ability of resighting is very high, they usually marmoratus)to estimate lambda and to compare require large samples of marked individuals

This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions MODELS IN AVIAN CONSERVATION 9 followed over at least three years to estimate low sensitivity. Moreover, sensitivity analy- the probability of resighting and survivorship sis does not indicate the degree to which it is for a single year. It is unfortunate that sur- feasible to influence a vital rate with different vival estimates can be problematic, because management options and does not incorporate sensitivity analyses suggest that population the cost per unit change in lambda of particu- change in most long-lived vertebrates is often lar management options, a metric that may be most affected by changes in adult survivorship important to decision-makers (Nichols and (Lande1988b, Pfister 1998). For example, Saether Hines 2002). and Bakke (2000) compared elasticities of 49 Elasticity analysis has also been criticized species of birds and found that adult survival because it can lead to inconsistencies in evalu- tended to have the greatest effect on population ating demographic rates, depending on how growth, though the contribution of fecundity they are scaled (Link and Doherty 2002). The increased with increasing clutch size. Second, proportional changes of an elasticity analysis the structure and values in the matrix depend are unitless and calculated on a log-log scale. on whether it is parameterizedas a prebreeding However, demographic rates are measured on or postbreedingmodel, or as a birth-flow(births differentscales (e.g. annual survival varies from occur continuously over the projectioninterval) 0 to 1, whereas annual fecundity values may or birth-pulse (births occur during a short exceed 10 in ducks and thousands in fishes and breeding season within the interval) model invertebrates).Link and Doherty (2002) argue (Noon and Sauer 1992, Caswell 2001). The larg- that the log-log scale is mainly appropriate est differences are in the calculation of realized for transformation of probabilities (bounded fecundity,in the first row of the matrix (Fig. 1). by 0 and 1), but should be replaced with Matrixpopulation models are often employed variance-stabilizedtransformations when ana- to recommend management strategies, but lyzing matrices that contain elements outside results need to be interpreted sensibly. These that range. See Doherty et al. (2004)for a recent models are simple descriptions of population application of this approach with a seabird. dynamics. Matrix population models rarely Because of these and other limitations, Norris attempt to incorporate processes that produce and McCulloch(2003) and Norris (2004)recom- the observed survival and reproductive rates, mend a greatly reduced role for elasticity analy- and and they often ignore the effects of uncertainties sis in influencing management decisions, feasible effects in parameter estimation (Wisdom et al. 2000), instead suggest analyzing the covariation among vital rates (van Tienderen of management on vital rates and the resulting 2000), density dependence (Grant and Benton population growth rates. This kind of scenario 2000), and stochasticity (de Kroon et al. 2000). analysis provides a direct way to evaluate the This limits the appropriateuses of these models effects of management on population growth. in several ways. First, sensitivity analyses can However, the validity of the insights depends indicate which vital rates or stages most affect upon the ability of management to achieve the model outcomes or requiremore study for better demographic improvements specified in the parameterestimation, and they can be used to scenariosbeing evaluated. anal- identify the managementstrategy that may lead A second limitationon use of sensitivity to the fastest population recovery. However, yses is that they are not value-free, but depend sensitivity analyses do not indicate which fac- on the vital rates used in the matrix (Caswell matrix tors are causing populations to decline (Green 1996a). Changes in values used in the and Hirons 1991, Beissinger and Westphal may sometimes shift the rankings of elasticity 1998).The latter informationrequires compara- results (Mills et al. 1999, Wisdom et al. 2000). tive, behavioral and experimental approaches Furthermore,if a demographicrate is depressed matrix (Lande 1988b,Caughley and Gunn 1996, Norris by the effects of a limiting factor, its value. 2004, Peery et al. 2004), or comparisonof model element(s) will have a smaller elasticity that factors or asso- trajectories with real population trajectories This does not mean stages for (Hitchcockand Gratto-Trevor1997, Peery et al. ciated with this element are less important 2004). In addition, recovery will require more management than other elements. For example, Crow time in populations that are declining because elasticity values for the Mariana (Corvus of limiting factorsthat operate on elements with kubaryi)on Guam indicated an overwhelming

This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions 10 ORNITHOLOGICAL MONOGRAPHS NO. 59 importance of adult survivorship, but success- 50, 100, or more years into the future by allow- ful reproductionhas rarely occurredduring the ing lambda or demographic rates to change for past decade because of nest predation by the each time step (usually one year); the method brown tree snake (Boiga irregularis)(National is Monte Carlo, which samples rates randomly Research Council 1996, Beissinger 2000). The from predetermineddistributions (Fig. 2). Each model was based on low fecundity values run of a stochastic model follows a unique tra- observed under current conditions, not the jectory and yields a differentending population presumably higher but unobserved values that size, because the lambdas or demographicrates prevailed before the invasion of the snakes. change randomly with each time step. Whereas Recovery strategies that addressed only adult a deterministic matrix population model survivorship would miss the main cause of produces a single-population projection that decline, which was poor reproduction caused changes at the rate of lambda, stochasticsingle- by snake predation on eggs and nestlings. population models yield probabilistic results. A third limitation is that population estima- Models must be run 500-1,000 times to explore tors derived from deterministicmatrix analyses the full range of parametervalues so that results assume that demographicrates are constant, an portraythe distributionof possible ending pop- assumption that is violated to some extent in all ulation sizes (Harriset al. 1987, Burgmanet al. matrixapplications. For example, ecosystems can 1993, Morrisand Doak 2002). experience severe environmental fluctuations Results from stochastic single-population on relatively short cycles as compared with models can be summarized in several ways the generation time of birds (e.g. El Nino), and (Burgmanet al. 1993, Beissinger and Westphal these can greatly affect demography (Beissinger 1998). The most common for evaluating popu- 1986, 1995b;Grant 1986). The effects of violating lation viability is the proportion of runs that this assumption depend on how much varia- end at population size zero ("extinction"rate), tion in demographic rates occurs from year to or at a small size, such as <25 individuals year (Wisdom and Mills 1997, Caswell 2001). In ("quasi-extinction"rate). No standard interval addition, positive population growth rates do or extinction rate defines a viable population, not indicate that a population is secure, because but intervals of 50-100 years and extinction environmental variation and catastrophes can rates <5%are commonly used (Rails et al. 2002, cause large fluctuations in population size and Reed et al. 2002). A second result computes result in a high chance of extinction (Goodman the expected "time to extinction," which is the 1987,Tuljapulkar 1989, Lande 1993,Mangel and mean or median year of extinction for popula- Tier 1994, Saetheret al. 2005). Stochasticsingle- tions that went extinct. A third approach is to population models are a more complex alterna- calculate the mean and standard deviation for tive to deterministicmodels, and they are more population size at each interval. Perhaps the realistic in that they incorporate variation in most complete descriptor of model results is demographicrates. to plot the cumulative probability function for ending population size (Fig. 2D). This is Stochastic Population Viability Analysis known as the quasi-extinction function and Models for Single Populations is a basic form of risk analysis (Ginzburg et al. 1982, Burgman et al. 1993). The minimum Stochastic demographic models of single viable population size (MVP) can be found by populations are another way to describe popu- changing the initial population size to find the lation dynamics. These models usually do not smallest size that had a 95%chance of remain- incorporatethe processes that produce particu- ing extant at the end of the period evaluated lar rates of survival and reproduction, but to in the simulation (Shaffer 1981, Soule 1987). some extent they simulate the effects of these Minimum viable population sizes from mod- processes by including annual variationin vital els are rarely used in management contexts, rates or lambda. Stochastic models are used to because of the difficulty in accurately forecast- make long-term population projections, espe- ing risks of extinction (Rails and Taylor 1997, cially in the context of population viability anal- Reed et al. 2002), though estimates sporadically ysis (PVA; Shaffer 1981, 1987; Beissinger and appear in the published literature (Harcourt McCullough2002). A population is projectedfor 2002, Reed et al. 2003).

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Fig. 2. Simplified example of the structure and outcomes from a stochastic single-population PVA model (fromBeissinger and Westphal1998). (A) The prebreedinglife-cycle diagram gives the model age or stage structure (see Fig. 1). (B) The basic flow of events of the prebreedinglife cycle structuresthe model. Rates for fecundity (w) and survival (P) are randomlychosen anew for each time step (from predetermineddistributions) and used in matrixcalculations to projectthe population size at the next census (i.e. year). (C) The initial population is projectedover many years in a single iterationof the model, as shown by any of the trajectories.Projections are repeated 500-l,000x to simulate differentpossible population trajectories.(D) Outcomes for various management options (e.g. current conditions or "as is," increasing fecundity, or decreasing mortality) are determined, such as the quasi-extinctionfunction, extinction rate, time to extinction, and average population size. The quasiextinctionfunction incorporatesthe population size from all projectionsat a specified interval and is determinedby calculatingthe cumulativeprobability for populations ending less than or equal to a particular size at the specified time interval.The extinctionrate is where the function intersectsthe y-axis.

Structure of Stochastic Population Viability from a time series of counts or estimates of Analysis Models for Single Populations population size for consecutive periods (A = Nt +JNt) or from the log of the counts (Morris Stochastic single-population PVAs can be and Doak 2002, Williams et al. 2002); the latter built as either unstructuredor structuredmod- measure is used to calculate the stochastic rate els. Unstructured models use estimates of the of population growth (u), which is equivalent mean and varianceof lambda to projectpopula- to r (exponential rate of increase) rather than tion fluctuations into the future by employing lambda (geometric rate of increase). The mean Monte Carlo techniques to sample lambdas and variance of u can be used in analytical randomly from predetermined distributions. models to yield estimates of the probabilitythat They contain no structure or information a population of a given size will reach any size about individuals (e.g. ages, stages, or sizes). threshold at some number of years in the future Unstructuredmodels are usually parameterized based on the diffusion approximation (Dennis

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et al. 1991, Foley 1994, Holmes 2004). Although capacity, or a population ceiling size may be the concepts behind these applications of sto- designated that acts as an upper boundary for chastic calculus are sophisticated, Morris and population trajectories (Burgman et al. 1993, Doak (2002) provide very accessible details for Foley 1994,Sabo et al. 2004).Structured stochas- doing the calculations. tic single-population models can also incorpo- Parameterizingstructured single-population rate stochastic processes that may occur when models requiresabout twice as many rates to be populations become small, such as Allee effects estimated than are needed for matrix popula- (Courchampet al. 1999, Stephens et al. 1999) or tion models (Beissinger and Westphal 1998), inbreeding (Charlesworth and Charlesworth though many of the additional rates can be 1987, Lande 2002). Catastrophes are a form derived from the same field data. The basic skel- of environmental variation that can be distin- eton of structuredstochastic population models guished from environmental stochasticity by is similar to that of deterministicmatrix models, the magnitude of effects on demography.They so they require the same estimates of mean age- may result in large population declines and or stage-specificsurvival and fecundity.In addi- can greatly increase the chance of extinction tion, to model the effects of demographic and (Mangel and Tier 1994),but are not necessarily environmental stochasticity, models require rare events. Physical forces that strongly affect estimates of variance in fecundity and survival demography, such as droughts and floods, for each age- or stage-class. Demographic can occur in short intervals (e.g. 5-7 years) stochasticity refers to chance events in birth or and in predictable cycles (Beissinger 1986). death rates attributableto population size. For Determining the predictability of important example, the probabilityof survival for a partic- environmental factors (Colwell 1974, Stearns ular age-class may be 60%,but each individual 1981, Beissinger and Gibbs 1993) is required to either lives or dies. The variability that results assess whether models should allow demogra- from this process represents demographic phy to vary entirely stochastically or with an stochasticity.Demographic stochasticity can be underlying form of quasiperiodicity. modeled by choosing the numberof draws from a binomial distributionequal to the population Conservation Use of Stochastic Population size, with probabilities chosen from a range Viability Analysis Models for Single of realistic values for the demographic rate Populations of interest. Environmental stochasticity refers to changes in demographic parameter values Stochastic single-population models have caused by fluctuations in the environment frequently been used to estimate the likelihood that affect all individuals similarly (e.g. annual of extinction for wild populations and, on that variation in weather or resources;Lande 2002). basis, to make management recommendations. Accuratemodeling of environmentalstochastic- Shaffer (1981, 1983) first used PVA on Grizzly ity is difficult;it requiresknowledge of the rela- Bears (Ursus arctos) in Yellowstone National tionship between environmentalconditions and Park,though stochastic population models had vital rates and their varianceover the full range occasionally been used to explore the demog- of conditions encountered. raphy of endangered and harvested birds Stochastic single-population models should (Nichols et al. 1980, 1995).A structuredstochas- also include additional complexities, namely tic single-population model was used to predict some method of incorporating density depen- that Red-cockadedWoodpeckers in the Georgia dence and carrying capacity and the frequency Piedmont and Piping Plovers (Charadriusmelo- and effects of catastrophes. Carrying capacity dus) in the Great Plains had high likelihoods of sets an upper limit on how large populations extinction within 100 years (Ryan et al. 1993, can grow and density dependence affects popu- Maguire et al. 1995). These models have also lation growth rates. Models without such lim- been used to evaluate the necessity of removing its often overestimate population persistence Puerto Rican Parrots(Amazona vittata) from the and underestimate maximum growth rates wild for captive breeding (Lacy et al. 1989),the (Ginzburget al. 1990, Sabo et al. 2004). Various viability of captive and reintroduced popula- density-dependent functions can be used to tions of Bearded Vultures (Gypaetusbarbatus) in model the effects of approaching carrying the Alps (Bustamante1996), threats to an island

This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions MODELSIN AVIANCONSERVATION 13 population of Capricorn Silvereyes (Zosterops among input parametersand changes to model lateralls chlorocephala;Brook and Kikkawa 1998), structure. Cross and Beissinger (2001) recom- the effect of fisherieson AmsterdamAlbatrosses mended employing several kinds of sensitivity (Inchaustiand Weimerskirch2001), and risks to analyses to understand how input parameters BalearicShearwaters (Puffinus mauretanicus; Oro affect model outcomes, but suggested compar- et al. 2004). Unstructured single-population ing management scenarios to evaluate the effi- models have been used to examine life-history cacy of potential managementoptions. correlatesof time to extinction in birds (Saether Stochastic models provide a more flex- et al. 2005); and a variation of this approach, ible approach than deterministicones, because the population prediction interval (Saetherand demographic rates need not be restricted to Engen2002), has been used to examine risks to a current conditions. For example, the effects of declining population of BarnSwallows (Hirundo silviculturalpractices on a threatenedmammal rustica)in Europe (Engen et al. 2001). were examined to estimate how the likelihood Like deterministicmatrix models, structured of extinctionwas affectedby changes in carrying stochastic models of single populations are capacity (Lindenmayerand Possingham 1996). most useful for examining the effects of dif- Similarly,stochastic modeling examinedhow the ferent management options (Fig. 2D). This is interval between low water conditions affected often done by comparing population projec- the viability of Snail Kites (Rostrhamussociabilis) tions of different management scenarios and in the Florida Everglades (Beissinger 1995b). by sensitivity analysis, which, unlike deter- Demographic rates were partitioned among ministic matrix models, cannot be calculated differentenvironmental states (i.e. drought, lag, analytically.The conventional method of sen- and flood years), and the periodic sequence of sitivity analysis for stochastic PVA models is environmentalstates dictatedvital rates. to determine the change in the probability of Results from stochastic single-population extinction (or another model output) in relation models should be interpreted carefully, of to fixed-percentagechanges in a model param- course. Although PVA models supplied with eter (Beissinger 1995b).This involves adjusting adequate data have the potential to track the model parameters one at a time, conducting average short-term trajectory of a population many iterationsfor each new parameterset, and with accuracy(Brook et al. 2000b),these models comparingthe resultswith the averageoutcome, are unlikely to produce accurate predictions which is calculated by setting all input param- of the likelihood of extinction (Ludwig 1996, eters to their mean value. For example, Reed 1999;Beissinger and Westphal1998; Groom and et al. (1998) constructed a structured stochastic Pascual 1998; Fieberg and Ellner 2000). First, PVA model for the Hawaiian Stilt (Himantopus demographic data are often inadequate, and mexicanusknudseni) and found that popula- estimates of vital rates are frequently imprecise tions were unlikely to go extinct. Sensitivity and are based on studies too limited in duration analysis indicated that model outputs were to estimate properly the mean and variance. most affectedby changes in nesting failure and Analyses of long-term data sets of a variety of adult survival- factors that managers could animals have shown that asymptotic estimates minimize by maintaining predator control and of the variance in population size, if they occur limiting water-level fluctuations. Furthermore, at all, may requireat least 8-20 years of sampling the results were insensitive to changes in the (Pimm and Redfearn 1988, Pimm 1991, Arino probability of catastrophe and density depen- and Pimm 1995) Reasonable estimates of vari- dence. In addition to conventional sensitivity ance in vital rates for birds probably require at analysis, sensitivity can be evaluated by exam- least several generations of study, which could ining the effect on model outputs of changing easily exceed 10-20 years for many species. each model parameterby a fixed percentage of Second, estimates of variance in vital rates and its range (relative sensitivity), and by analyz- lambda derived from field studies include sam- ing the impacts of input parameter values on pling error,which should be discarded because the likelihood of extinction or quasi-extinction it is caused by errorsin parameterestimation, as using logistic regression (Cross and Beissinger well as the annual (environmental)variation of 2001). The latter approach is perhaps the most interest (Nichols et al. 1994, Staples et al. 2004). useful, because it can examine interactions Studies of Semipalmated Sandpipers (Calidris

This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions 14 ORNITHOLOGICAL MONOGRAPHS NO. 59 pusilla) found that sampling error contributed Taken together, these concerns strongly sug- nearly as much to the total variance in annual gest that one should place limited confidence survivorship as temporal variation (Hitchcock in the extinction estimates generated by these and Gratto-Trevor1997). Methods are avail- models. Stochastic single-population models able to partition a vital rate's total variation are best employed in conservation decisions into components caused by sampling error and by comparing the differences in relative rates process error (Gould and Nichols 1998, White among management options incorporated et al. 2002). into the model rather than basing policies Third,the primaryprediction from stochastic on the absolute rates of extinction predicted single-population models, the probability of (Beissingerand Westphal1998, Reed et al. 2002, extinction, is difficult to validate because these McCarthyet al. 2003, Lottset al. 2004).This was models incorporate stochastic processes. We the basis for comparing conservationstrategies cannot know which of the hundreds of simu- based on different sizes and configurations of lated population trajectorieswill most resemble reserves for the Northern Spotted Owl in the the trajectoryof the actual, unreplicated popu- PacificNorthwest (Noon and McKelvey 1996b). lation. Comparing the model's average popula- Populationviability analysis models also benefit tion projection with a time series of historical from incorporating uncertainty directly, using population trends provides a way to examine Bayesian techniques (Goodman 2002, Taylor how well the model captures the short-term et al. 2002, Wade 2002) or exploring the role dynamics of the system (Brook et al. 2000b). of estimation error and uncertainty on model But it does not verify the value of stochasticity outcomes (Parysow and Tazik 2002). They also or other variables used in the model that are benefit from using an explicit decision analysis responsible for differences among model runs. framework (Possingham et al. 2002, Drechsler Furthermore,acceptable levels of risk always and Burgman 2004). Rails et al. (2002) provide occur at one tail of the distribution of possible an importantset of guidelines for using PVAin outcomes (e.g. <5%chance of extinction in 100 conservationdecisions. years), which makes the accuracyof predictions The additional complexity of stochastic particularlydifficult to evaluate (Ludwig 1996, single-population models compared with 1999). Model assumptions or secondary predic- deterministic matrix population models is an tions, such as population size or estimates for example of a tradeoff that we will revisit fre- means and variancesof vital rates, are more fea- quently.On the one hand, stochasticmodels are sible to test (McCarthyet al. 2001, Lindenmayer more appealing to field biologists because they et al. 2003). Fourth, differences in model struc- are more realistic and include more processes; ture can have strong effects on management therefore, they can incorporate more of what recommendationsresulting from model output. field biologists know or hypothesize about Models with different structurescan reproduce the system. On the other hand, not only are the same population dynamics in the absence of estimates of demographic rates required, as in management, but may predict different effects matrix population models, but also mechanis- of management regimes (Pascual et al. 1997, tic relationships between the environment and Gerber and VanBlaricom2001, La Montagne demography (e.g. rates and intensities of catas- et al. 2002). Also, different computer programs trophes, long-term trends in carrying capacity, can produce different estimates of viability and forms of density dependence) must be from the same data because of differences in documented. Finally, the accuracy with which the ways of modeling density dependence and demographic rates are depicted should be sex ratio (Mills et al. 1996, Brook et al. 2000a). determined through model-validationstudies. Incorporatingdensity dependence may increase Even with this added complexity, stochas- model realism, but requires additional valida- tic single-population models do not consider tion to determine whether density dependence several factors that commonly occur in nature is modeled accurately.Even when data appear and may affect extinction rates. Immigration to be adequate, stochastic single-population and dispersal are rarely incorporatedin single- models can make large errors in estimating the population models but can have important rate of extinction (Taylor 1995, Ludwig 1999, effects on population dynamics (Stacey and Belovsky et al. 2000, Fiebergand Ellner2000). Taper 1992). Individuals may often be found

This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions MODELS IN AVIAN CONSERVATION 15 not in a single panmictic population, but rather Techniques employed include radiotelemetry, in spatially distinct subpopulations distributed and enclosures and experimental releases to widely across the landscape and connected by elucidate the role of dispersal and emigration infrequentdispersal events. In addition, demo- in population dynamics. Modern mark-recap- graphic rates and their variances may vary ture methods, especially multistrata models, spatially among different habitats or subpopu- are becoming increasingly important for esti- lations (Pulliam 1988). Typically,other types of mating movement and demographic param- models are used to address these complexities, eters in marked populations (White et al. 2002). namely metapopulation models and spatially Robust statistical techniques recently have explicit models. been developed to estimate patch occupancy while accounting for imperfect detection rates Metapopulation Models and missing data (MacKenzieet al. 2002, 2003, 2006).A complicatingfactor for metapopulation Metapopulationmodels have become impor- modeling is whether the focal species inhab- tant tools for understanding the relationships its a highly dynamic landscape or a "shifting between landscape structure and population mosaic" of patches, because most metapopula- dynamics.By incorporating spatial characteristics tion models assume that the configurationand of local populations, metapopulation models quality of habitat patches are relatively static provide a means of analyzing and predicting (Wiens 1997;but see Hastings 2003, Hanski and the response of individual species to habitat Gaggiotti 2004). For example, Fleishman et al. fragmentationand other features of landscape (2002)found that occupancy and turnoverwere structure.They also provide a degree of realism better modeled by measures of habitat quality that appeals to managersand researchers. than by patch area or isolation. When present, Whether a metapopulation or single- strong temporal changes may dominate the population model is the more appropriateway dynamics of a system, and accounting for such to describe population dynamics depends on changes in habitat quality in a metapopulation what is known, or believed, about population model may be difficult (Thomas and Hanski structure and the importance of landscape- 2004). Even if a landscape is nearly static, the dependent processes. Faced with the need to population dynamics within a system may not model a species living in a patchy landscape,it is fit a metapopulationframework. For example, if importantto determine whether the additional a system is functioningas a single population or with processes that metapopulation models incor- as a collection of independent populations model porate are important and necessary to depict no migration, use of a metapopulation population dynamics accuratelywith respect to may be inappropriate(Harrison 1994, Harrison the objective of the modeling exercise (Hanski and Bruna1999). 2002, Harrison and Ray 2002). A key question Recent years have seen a proliferation of is how fragmentedthe system is relative to the metapopulation models. Below, we outline and dispersal ability of the species being modeled. some of the characteristicsof these models Several types of evidence can be suggestive discuss the merits of different models from a of metapopulation dynamics. Turnover,or the conservationperspective. extinction and recolonization of local populations, is the most widely cited (Hanski 1992)but Structure of Metapopulation Models is not a necessary condition for a population to be treated as a metapopulation (Kareivaet al. Metapopulation models can be grouped 1997,Hanski and Gaggiotti2004). Unfortunately, into three classes: theoretical, occupancy, and and long-termdata on turnoverare rarely available, patch models. Theoreticalmodels (Hanski and turnovermay not be observed in metapopu- Gaggiotti 2004) typically make simplifying lations that are driven more by "rescue"than assumptions about the spatial characteristics by recolonization(Stacey et al. 1997). Rigorous of patches- for example, assuming equal of approachesto investigating processes that pro- patch size or uniform distribution patches duce metapopulation dynamics are reviewed (Lambersonet al. 1992, Gilpin 1996). They may lattice by Ims and Yoccoz (1997) and exemplified for use "neutral landscapes" (With 2004), various taxa in Hanski and Gaggiotti (2004). models (Hanski and Gaggiotti2004), or method

This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions 16 ORNITHOLOGICAL MONOGRAPHS NO. 59 of moments or other mathematicalapproaches A rapidly growing list of species has been (Bolker 2004). These models typically do not studied using occupancy models, but bird stud- use site-specific information; consequently, ies are notably rare.Hanski and Gaggiotti(2004) their purpose is to provide general insights searched literaturepublished from 1996 to 2000 into metapopulation processes. These models and found that birds were the least-studied tend to be very general in nature, and they have taxa, compared with mammals, fish, butterflies, made fundamental contributionsto our under- and plants. Avian examples include Neotropical standing of metapopulationdynamics. migrants(Villard et al. 1992),Pacific Island birds Occupancy models have been developed (Cook and Hanski 1995), and the European and popularized by Hanski (1994a, b), who Nuthatch (Sittaeuropaea; ter Braak et al. 1998). used incidence functions to model metapopu- The paucity of patch-occupancymodels for bird lations. Hanski's approach has been modified studies may reflect the relative scarcityof unoc- and elaborated into a class of models com- cupied suitable habitat or turnover, perhaps monly referred to as "stochastic patch occu- in part because of the greater dispersal ability pancy models" (SPOMs;Hanski and Gaggiotti and longevity of birds as compared with other 2004). Etienne et al. (2004)provide an overview organisms. of different types of SPOMs. The incidence Patch models are perhaps the most widely function approach combines the pattern of used metapopulation models (Fig. 3B). In patch occupancy with relationships derived patch-based models, the smallest unit in which from biogeography to estimate colonization population size is trackedis the individual habi- and extinction rates (Hanski 1999), whereas tat patch. Individuals reside only within these the patch-turnoverapproach is based on docu- patches and may move or disperse among them, menting patch colonizations and extinctions but they are not permittedto survive in the sur- (Sjogren-Gulve and Ray 1996, Kindvall 2000, rounding landscape. Thus, metapopulation Sjogren-Gulve and Hanski 2000). A key char- models incorporatespatial relations in a rather acteristic of SPOMs is their reliance on simple restricted manner, because spatial data are presence-absence data obtained from single or limited to a matrix of interpatchdistances and multiple surveys to estimate the probability patch sizes. Neither the location of individuals that a patch is occupied and to model meta- within a patch nor the types of landscapematrix population dynamics (Hanski 1998, Thomas that surround a patch are included; however, and Hanski 2004). Morris and Doak (2002) both may affect survival or reproduction and provided computer algorithms for developing are often included in spatially explicit models occupancy models using maximum-likelihood (Fig. 3C, D). Population dynamics within each (ML) techniques or logistic regression, and patch are usually modeled as in stochastic Moilanen (2004) and Grimm et al. (2004) have single-population models, with the additional created generic software to develop occupancy steps of determining the numbers of individu- models. Grimm et al. (2004) also provide an als that will disperse from and migrate to each example for Capercaillie (Tetraourogallus). An patch. Patch models are popular because easy- important recent advance for parameterizing to-use software packages are readily available occupancy models was made by MacKenzie (Lindenmayeret al. 1995). et al. (2002, 2003). They extended mark-recap- The choice of model type may depend, in part, ture statistical approaches to estimate patch on the availabilityof data needed to parameter- occupancy, colonization, and extinction ize the model. Data requirementsfor metapopu- rates that account for imperfect detection. lation models vary considerably,ranging from These techniques have been implemented in a few parameters for some theoretical models the programs MARK and PRESENCE (see to dozens of parameters for complex patch Acknowledgments). Once parameterized from models (Beissinger and Westphal 1998, Grimm field data, an occupancy model can then be et al. 2004, Moilanen 2004). Theoreticalmodels applied to other metapopulations of the same typically have fewer input variables, requiring species or used to simulate metapopulation only very coarse, general data. For example, dynamics by substituting new patch-area and Levins's (1969)model that introduced the meta- patch-isolation data in a simulation model population concept had only two key param- (Hanski 1999). eters, extinction and colonization rates, which

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Fig. 3. DemographicPVA models with various degrees of spatial explicitness, modified from Gilpin (1996) and Beissingerand Wesphal(1998). (A) The landscape includes four patches of forest (shaded gray and num- bered 1-4) surroundedby a matrixof agriculturallands (shaded white) and dissected by a river (shaded black) that acts as a barrierto dispersal. (B) Patch metapopulationmodel for the landscape in (A) showing linkages between patches by dispersal indicated by arrows. Each patch has its own internal population dynamics. (C) Spatiallyexplicit cellularautomata or grid model for the landscapein (A). The landscapeis now represented by grid cells, each with its own population size, immigrationand emigrationrate, and fecundity and survival ratebased on the grid-habitatcharacteristics and the habitatcharacteristics of surroundinggrid cells. Occupied cells have stars, dashed lines indicate influences of neighboring cells, and arrows show potential dispersal among patches. (D) Individuallybased model where the movement path, mortality(indicated by an "X"),and reproductionof each animal (star) is trackedacross the landscape. Survival and fecundity may differ between the matrixand the patches, as well as within the patches in relationto distance from the edge. predicted the fraction of occupied patches. interpatchdistances. Some of these parameters Occupancy models have a fairly standardized require informationthat is nearly impossible to set of input parameters (Morris and Doak obtain in the field (e.g. rate of mortality during 2002, Grimm et al. 2004). These include simple migration), but techniques that require a few field data consisting of patch area, occupancy, simplifying assumptions are available to esti- interpatch distances, and several parameters mate them from readily obtainable field data that are typically estimated using nonlinear (Hanski 1994b, 1999). Accurate estimates of ML regression or related techniques. Examples some parametersmay be unimportant to over- of the latter include parametersexpressing the all model accuracy(Hanski 1994a),but Ims and effect of distance on migration rate or the rela- Yoccoz (1997) suggest that precise and unbi- tionship between emigration rate and popula- ased estimates of emigration, migration, and tion density. For example, a model by Hanski colonization rates may be especially important (1994b) included eight parameters: carrying for systems with high rates of transfer among capacity, density-independent growth rate, patches. This argues for the importance of strength of density dependence, demographic applying statistical techniques that incorporate stochasticity, environmental stochasticity, uncertaintyin detection when estimating move- emigration rate, migration mortality rate, and ment and occupancy rates (White et al. 2002,

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MacKenzieet al. 2003). Sensitivity analysis and of patches that are occupied. Grimmet al. (2004) comparativesimulation experimentscan also be recommend "intrinsicmean time to extinction" used to evaluate model uncertainty (Grimm et (Grimmand Wissel 2004) as the primaryoutput al. 2004). from their generic model. Once an adequate Patch models typically require more detailed occupancy model is created for a species, it can data than theoretical or occupancy models be applied to other landscapes to make predic- (Akcakaya 2000a, b; Hanski and Gaggiotti tions about the equilibrium occupancy rate for 2004). Simple patch models may require patch new sets of patches (Hanski 1999, Hokit et al. carrying capacities, population growth rates, 1999). Also, by changing the number or con- and immigration and dispersal rates among figuration of patches, the relative importance patches. More complex models may have of each patch to metapopulationpersistence can many input requirementsin common with the be evaluated (Hanski 1994a, 1999). Thus, these matrix or stochastic single-population models models can be used to evaluate the suitability discussed above. For example, age- or stage- of a landscape for a species and the conserva- structured vital rates may be required, with tion value of particularhabitat patches. Because the added twist that these parametersmay vary they are based on presence-absence data and among patches. are designed to predict patch occupancies, Patch models also require parameters occupancymodels generallyare not used to pre- related to spatial structure. These include dict population densities or actual population whether rates of dispersal and immigration size. Patch models have an advantage here; in are dependent on density within a patch and, addition to turnoverrates and equilibriumoccu- most importantly, the degree of correlation pancy,they also provide population trajectories, among patches for environmental stochastic- risk of population extinction or decline, and ity (Lindenmayer et al. 1995, Beissinger and related measures of population size (Akcakaya Westphal 1998). Environmental stochasticity and Atwood 1997,Hokit et al. 1999). is typically assumed to be perfectly correlated Estimates for parameters, such as dispersal among patches, meaning that all patches simul- or the correlationof vital rates among patches, taneously experience the same good or bad are often based on sparse data. Also, there is conditions. This assumption reduces the influ- often little basis for choosing among different ence of processes important to metapopulation structures for modeling dynamic processes, dynamics, such as the rescue effect (Morris such as conditions that cause individuals to and Doak 2002). If vital rates within patches migrate from one patch to another. Sensitivity vary synchronously and if vital rates do not analysis can reveal how importanta parameter vary greatly among patches, the metapopula- or assumption is to the output of a model; this tion behaves much like a single population; indicates how much the reliability of model but if they vary asynchronously, the dynam- output is compromised by difficult-to-estimate ics of a metapopulation can be very different parametersor by the particularway a process is from those of a single population (Stacey et al. modeled (Beissingerand Westphal1998, Grimm 1997). Such variables are extremely difficult to et al. 2004).With metapopulationmodels, sensi- measure in the field, yet they may have a major tivity analysis is used primarilyfor this purpose effect on model results and population behav- ratherthan to determine the best parametersto ior. Sensitivity analyses are especially important alter through management efforts; the latter is when using models with poorly known param- done with matrixpopulation models. For exam- eters (Beissinger and Westphal 1998, Mills and ple, Akgakayaand Atwood (1997) found large Lindberg2002). differences in sensitivity among 17 parameters Outputs from the various metapopulation in their patch-based metapopulation model of models differ greatly and may also be a deter- the CaliforniaGnatcatcher (Polioptila californica). mining factor in the choice of model type. Such findings may provide assurancethat some Because theoretical models may differ greatly poorly known parametersare relatively unim- in their underlying assumptions, few gener- portant compared with other, better-known alizations can be made about their output. ones. This allows field biologists to focus on Occupancy models usually yield estimates for measuring the parameters that matter most turnover rates and the equilibrium proportion (Dunning et al. 1995).

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Compared with stochastic single-population approaches (Akcakaya and Atwood 1997, models, metapopulation models increase Beissinger and Westphal 1998, Reed et al. 2002, demands on field biologists for data to param- Grimmet al. 2004). eterize and validate (Beissinger and Westphal 1998). The ability to validate metapopulation Use of Metapopulation Models in models by comparing simulated and observed Conservation data varies among model types. Theoretical models are rarelyintended to mimic a particular Metapopulation models differ significantly system accurately;therefore, comparing model in their potential for use in conservation. output with actualfield data usually serves little Theoretical metapopulation models are usu- purpose. Occupancy and patch models usually ally designed to derive a better understanding are applied to particular situations, making of general conservation principles about how validation a possibility. Occupancy models are metapopulations work (Hess 1996a, b; With often validated by using a model developed 1997, 2005; With and King 2001), though they for one metapopulation to make patch-occu- can be designed to model specific situations. pancy predictions for another metapopulation, Occupancymodels are highly practical,because which are then tested against the actual patch- they directly incorporatesite-specific field data; occupancy data (Hanski 1994a, Hokit et al. they can make short-termpredictions about the 1999).Patch models can also be validated by this patch occupancy of a given species for differ- approach and by comparing predicted popula- ent configurationsof patches, imagined or real. tion trends with actual population trends. For Thus, occupancy models can be useful in man- example, Wooton and Bell (1992) found a good aging landscape structure. An important criti- fit between the population increase of Peregrine cism of occupancy models is that they assume - Falcons predicted by a model and the observed "quasistationarity" in other words, that the increaseover an eight-yearperiod. data used to parameterizethe model came from Usually, however, managers and research- a system with no increasingor decreasingtrend ers are interested in predicting the likelihood in patch occupancy (Hokit et al. 2001, Hanski of extinction too far into the future for valida- 2002). Many present-day landscapes may be tion to be feasible. Also, field situations that far from equilibriumbecause of recent human- provide true replicates to develop a probabil- induced fragmentation.However, recent studies ity of extinction are exceedingly rare (but see suggest that occupancy models may be fairly Hanski [1999]for possible examples). Data sets robust to violations of this assumption (Hanski with trajectory or extinction information are 1999,Hanski and Gaggiotti2004), and modifica- often too limited in spatial or temporal extent tions to occupancy models have relaxed this to compare with model output, making strong assumption (Moilanen1999, Etienne et al. 2004). statistical validation of these models difficult. Patch models are less vulnerable to this One approachis to develop different models of problem,because they rely on measurementsof the same system independently and then com- vital rates that do not necessarily assume equi- pare the models for concordant output (Noon librium conditions (Hokit et al. 2001, Morris and McKelvey1996b, Kindvall 2000, Hokit et al. and Doak 2002). For example, a metapopula- 2001).Another approachis to test specific com- tion model was developed for the California ponents or assumptions of the model (Thomas Gnatcatcher in a rapidly changing landscape et al. 1990).Such tests are valuable, but they do in Orange County, California (Akgakaya and not demonstrate the model's overall accuracy Atwood 1997). The model projected a rapid in predicting the future. Consequently, many population decline and a high risk of extinction researchersdiscourage reliance on predictions in most simulations. An important implication projected far into the future from these simu- was that the results were strongly divergent, lation models. Instead, they recommend using depending on the lengths of time used in the the models for other purposes. These include simulations. Simulations identified a critical identifying variables that are likely to be most time horizon of 30-40 years, at which predicted and Bell important, elucidating system dynamics, gen- extinction rates were greatest. Wooton erating new hypotheses, and evaluating the (1992) used a patch model of the Peregrine relative effectiveness of different management Falcon to identify the northern population as

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a source and the more critically endangered locations of individuals within each habitat southern population as a sink. They concluded patch or kinds of habitatsurrounding the patch, that intensive recovery actions on the southern each of which may affectdemography. population were probably misplaced, and that Spatially explicit population models often the same effort directed at the source population include individuals as objects,which are placed in the north would eventually strengthen the in known locations in space and assigned southern population through the source-sink habitat-specific demographic traits based on dynamics linking the two populations. Because these locations(Fig. 3). The models then total the patch models partly rely on underlying biologi- resultsof all individualsto obtainpopulation sta- cal mechanisms,they may be applicableto more tistics, such as population size at a specific time, widely different situations than occupancy population trajectories,or time to extinction. models (Hokit et al. 2001). However, estimating Thus, SEPMsare often individual-basedmodels demographic rates and numerous other param- (IBMs),but their main outputs are population eters needed for these models greatly increases characteristicsand processes. Spatially explicit the demand on field biologists for demographic models can be used to model movementsof indi- data, and increased model complexity also viduals across a diverse landscape(Cooper et al. brings greater risk of error propagation caused 2002) or responses of populations to changing by poor parameter-estimation(Conroy et al. landscapestructure (Akcakaya 2000b). 1995, Beissinger and Westphal1998, Morrisand Individual-based models have several Doak 2002). advantages over the aggregate population models discussed above. They can describe Spatially Explicit Models population traits with distributionsrather than mean values, explicitly represent individual An especially complex type of simulation performance, incorporate local interactions, model, spatially explicit models incorporate and yield a mechanistic ratherthan descriptive exact spatial and temporal locations of objects. approach to modeling (DeAngelis and Rose Objects might include patches of habitat, indi- 1992). Individual-based models appeal to field vidual organisms,different populations, or barri- biologists, because they simulate important ers to dispersal (Fig. 3). Spatiallyexplicit models processes in the lives of individual organisms, have been used to study a variety of large-scale the scale at which population dynamics are ecological patternsand processes, such as deter- determined. Thus, IBMs may be employed as mining the distribution of suitable habitat at population models without a spatial compo- multiple scales (Hattenand Paradzick2003) and nent, as, for example, in modeling larvalrecruit- predicting regions of future human-wildlife ment in fisheries, where such models have been conflicts (Treveset al. 2004). Their primary use employed with great success (DeAngelis et al. in ornithologyhas been in the study of regional 1993, Rice et al. 1993). However, IBMs require population dynamics. We concentrate on spa- extensive data on behavior and its demo- tially explicit population models (SEPMs)in this graphic consequences. Habitat-basedIBMs, for review.Spatially explicit population models may example, require that variation in the expected be built for entire metapopulationsor for single values of birth, death, and movement rates be populations, depending on what objects are explicitly related to habitat variation. Spatially included and how they are distributed. explicit IBMs are the most complex means of Some models are considered "spatially representingpopulation dynamics and are most implicit" if they include measures of landscape appealing for species that have complicatedlife composition, such as proportions of different histories and inhabit heterogeneous landscapes habitats in a landscape (Dunning et al. 1992, (DeAngelis and Rose 1992, Murdochet al. 1992, Donovan et al. 1995, McGrathet al. 2003). For Walterset al. 2002). example, the metapopulationmodels reviewed above are spatiallyimplicit, because they include Structure of Spatially Explicit Models some spatial information, such as patch size and distances between patches. However, those Spatially explicit population models typi- models are not completely "spatially explicit," cally take one of two forms (Fig. 3C, D). Grid-or because they operate without tracking specific cell-based models trackpopulation sizes in cells

This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions MODELSIN AVIANCONSERVATION 21 that are typically the building blocks of larger The population model that is linked to the habitat patches. Cells do not have to be equal landscape map can take different forms, depend- in size (Walters et al. 2002). Cells are influenced ing on the simulations being done. A typical by the inputs and outputs of neighboring cells. format is a life-history simulator that classifies Grid-based models can be used to monitor sepa- each individual in the model by sex and age and rate populations in each cell, especially when the then takes it through an annual cycle of breed- modeled populations are so large that following, survival during the nonbreeding season, ing each individual may be impracticable. Such and dispersal. Ideally, individuals are assigned population-based models are commonly used habitat-specific demographic traits, depending for abundant organisms such as plants, insects, on where they are located on the landscape or rodents (Bradstock et al. 1996, Price and grid. Their life history may also depend on loca- Gilpin 1996). McCarthy et al. (2000) presented tion. For example, the likelihood of successful an avian example of a population-based model. dispersal may depend on proximity to vacant They constructed a spatial PVA model of two areas of suitable habitat. In models that treat the Australian treecreepers (family Climacteridae) sexes separately, reproductive success may be in 39 remnant patches of native habitat. The related to the spatial distribution of individuals model simulated population dynamics in each of the opposite sex. More complex social and occupied patch, and allowed dispersers to link reproductive strategies, such as obligate flock- between-patch dynamics. Most avian SEPMs are ing and cooperative breeding, have recently individual-based models that track the location been incorporated in SEPMs (Cooper et al. 2002, of every individual and calculate population Walters et al. 2002). In all these cases, the model sizes from counts of individuals in each location. sums across individuals and landscape patches In these models, population dynamics are the to calculate population characteristics at vari- outcome of processes that occur at the level of the ous time steps. individual. Individual-based models have been Most published SEPMs for bird species are used to simulate responses to regional manage- developed for species that are rare, endangered, ment practices (Boone and Hunter 1996), to eval- or of strong management interest. Typically uate translocation options (Akcakaya et al. 1995), these species are not migratory. These species and to simulate the effects of forest management characteristics are partly attributable to the policies (McKelvey et al. 1993, Lamberson et al. extensive data needs of SEPMs. Endangered 1994, Liu et al. 1995, Walters et al. 2002). species programs are more likely than other The crucial part of spatially explicit modeling research groups to have the necessary funds data. is linking a population model to a landscape and logistical support to collect such models are map (Akgakaya 2000a). The map can be as sim- Spatially explicit population ple as a set of patches, some defined as suitable extremely data-hungry. Ideally, they require habitat and others as unsuitable for a particu- extensive data on the distributions of habitat habitat- lar species. More complex maps can include types and quality across landscapes, habitat variables that contribute to classifying specific demography from the landscape, and habitat suitability for each location. All models, an accurate idea of dispersal patterns and move- Some however, require a mapping of the locations ment rules. Such detail is rarely available. can be of good and poor habitat from the standpoint of the needed data gathered relatively GIS databases can of the species considered. The development easily; for instance, existing the of extensive Geographic Information System provide the habitat distributions. However, often need (GIS) databases for conservation has allowed maps generated from GIS systems the areas. of the incorporation of real-world landscapes into to be verified by visiting Maps are useless without eco- spatial models. When a GIS-database includes habitat distributions the distribution of habitat patches, a landscape logical knowledge of how habitat quality affects and survival. grid can be created by overlaying a grid of cells reproduction Long-term survey estimates of on top of the original map and then assigning data can provide habitat-specific habitat characteristics from the original map to density, but locally accurate demographic and each cell. This works most easily if the grid cell dispersal data are generally not available for data these models size is considerably smaller than the polygons most species. To provide the must their of the original map. require, field biologists partition

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demographicdata by habitat quality (Krementz is striking. In concept, the development of a and Christie 1999) and acquire extensive data SEPM for a migratory species on its breeding on dispersal and movement patterns. grounds is straightforward,except for the dis- Like most models, SEPMs conform to the persal routines.Migrants show differencesfrom "garbage in, garbage out" rule. The reliability permanent residents in how they disperse to of the model depends on realism of structure, initial breeding sites; these differences present validity of the coding algorithms, and accuracy challenges to model developers. of the data used to initialize the simulations. In the life-historysimulator in a typical SEPM In building a model of a real-world landscape, designed for a permanent resident, individuals the physical layout of the landscape can be (both adult and juvenile) are subject to mortal- confirmed with remote sensing data, and ity during the nonbreeding period and then thus is usually not the limiting factor in the disperse to find suitable breeding locations. model. Larger problems are usually presented Typical models allow surviving adults to be by attempting to connect habitat suitabilities site-faithful to previous breeding locations, to various patch types, parameterizing the and juveniles to inherit natal sites when their population model, and building realistic dis- parents do not survive or to start dispersing persal rules. For each of these steps, there is no from their natal patch. For permanent resident substitute for accuratenatural-history informa- species, therefore, the number and location of tion for the region and species under study. potential dispersing individuals is easily deter- Ruckelshaus et al. (1997) constructed an mined for each year of a simulation- they are SEPM of hypothetical populations to deter- based on the results of mortality during the mine the consequences of parameter error in preceding nonbreedingperiod. general model performance. Large errors in For a migratoryspecies, however, these basic model predictions resulted from inaccurate components of the dispersal subroutine are not parameterization of dispersal characteristics. trivial decisions for the model developer. First, Errors in landscape classification had smaller field studies of migratory birds have demon- effects on model performance. Wennergrenet strated that few locally produced offspring al. (1995) also found that model results were return to breed close to their natal territory highly influenced by error associated with (Nolan 1978). Thus, each year, the potential dispersal parameters. If these results are cor- new breeders that search for available breed- rect, they suggest caution in widespread use of ing positions are not local birds and do not SEPMs,because the models were most sensitive have specific locations from which to begin the to errors in parameters that are typically the dispersal phase. The modeler must decide how most difficult to estimate. Mooij and DeAngelis to place these individuals on the landscape grid (1999), however, argue that Ruckelshaus et al. at the start of dispersal. Are the new dispersers (1997) greatly overestimated the inaccuracies placed at random into any grid cell or only into of error propagation in these models. They suitable-habitatcells? Are they initially placed also showed through a simulation exercise in the southernmostcells, to imitate a migratory that SEPMs may suffer less from uncertainty movement from southern wintering grounds? in parameter estimates than simpler models Field studies of how migratorybirds make their (Mooij and DeAngelis 2003) and proposed a initial habitat choices provide few guidelines. strategy of model development to reduce the Perhaps more important for model results, chance of significanterror propagation. the model developer must determinehow many The second main theme apparent from a dispersers to recruit into the population each review of published avian SEPMsis that nearly year. For closed populations of permanentresi- all models have been developed for permanent dents, the number of dispersers is determined resident species. In part, this may reflectthe fact by survival of local adults and juveniles from that many species of management interest are the previous year. But this is not necessarily resident species (e.g. Northern Spotted Owls). true for migratoryspecies, unless the production But some rare and endangered species are fully and survival of local individuals is correlated migratory (e.g. Whooping Crane and Golden- with regional populations- that is, if results of cheeked Warbler [Dendroica chrysoparia]),so the the model from the previous year can be used relative lack of SEPMs for migratory species as a guide to regional population dynamics.

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Although this may be true in some cases, there recommendationsthat this habitat type be pro- are many cases where local demographywould tected and increased where possible. not be a good guide. For instance,if the local site The second use of spatially explicit models being modeled is a sink population, then the is in the study of effects of specific changes in numberof juveniles produced locally would not land use on individual species in particular be a good measure of regional productivity.If landscapes. Perhaps the unique contributionof the local populationis a consistentsource popu- SEPMsis the ability to examine how a proposed lation, then productivityand survival may vary management action in an actual landscape much more outside the local population than might affect a given population. To answer this within it. Pulliam et al. (1995)demonstrate that, concern, the actual landscape is usually incor- even at the landscape scale, the relative quality porated into the modeling exercise, because of local sites can have strong effects on local general simulations on hypothetical landscapes dynamics in surroundingregions. Conceptually, do not have the necessary specificity. there are ways to overcome these problems;but Spatially explicit models of Bachman's so far,no SEPMsfor migratoryspecies have been Sparrow have been used to examine the long- published.King et al. (2000)developed a spatially term consequences of timber management in explicit model that they used to assess the status southeastern pine forests. Bachman'sSparrows of Henslow's Sparrows (Ammodramushenslowii) occupy temporary successional stages of man- in a highly fragmented landscape. Using the aged pine forest and are strongly affected by results of modeling the sparrow population on creation of such habitat through timber-harvest a hypotheticallandscape, they were able to make programs. Pulliam et al. (1992) and Liu et al. management recommendationsfor reversing a (1995)used the model to study landscape effects severe populationdecline in this species. in this poorly dispersing species and to make recommendationsconcerning specific manage- Use of Spatially Explicit Models in ment plans in a particular forested landscape. Conservation One recommendation was to increase suitable habitat for Bachman's Sparrows by altering Spatially explicit models can be used in the habitat structure of 40- to 50-year-old pine several conservation contexts. Hypothetical forest (which they generally would not use) to populations can be modeled on artificiallygen- mimic that of the mature forests the species pre- erated landscapes to determine the likelihood fers. This recommendation was implemented, of population response to a general change in and Bachman'sSparrows quickly colonized the landscape structure. For example, Pulliam et modified stands (Dunning et al. 2000). al. (1992) used an SEPMof Bachman'sSparrow Spatially explicit IBMs have also been (Aimophilaaestivalis) to determine the impor- developed for several threatened or endan- tance of a rarehabitat type, longleaf pine (Pinus gered cooperative breeders, including the palustris) forest, in the sparrow's population Florida Scrub-Jay(Aphelocoma coerulescens; Stith dynamics. A series of simulations was done, et al. 1996) and the Red-cockadedWoodpecker in which the amount of the rare habitat type (Letcheret al. 1998, Walterset al. 2002). In both was varied in a hypothetical landscape, and cases, this approach was used because of the a population model based on the life-history spatially restricted dispersal behavior of help- characteristicsof the sparrow was run on these ers, which cannot be incorporatedinto simpler differentlandscapes. The population responded models. The Red-cockadedWoodpecker model disproportionatelyto increases or decreases in was later modified for a study of the effects longleaf pine forest, which suggests that this of landscape change on another cooperative habitat played a more important role in popu- breeder, the Brown Treecreeper (Climacteris lation dynamics, compared with other habitat picumnus) of Australia (Cooper et al. 2002). were also types in the species' range, than its relative rar- Spatially explicit population models decisions for ity would have suggested (Pulliam et al. 1992). importantin making management Because this rare habitat type contained other the NorthernSpotted Owl (McKelveyet al. 1993) decisions in species of management interest, most notably and in guiding land-management the endangered Red-cockadedWoodpecker, the southern California that affect the endangered model results were used to bolster management CaliforniaGnatcatcher (Akcakaya 2000a).

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Spatial models have been influential in the (2005)compared results of a model of dynamics research and management decisions involved developed for one population of Red-cockaded in restoring the Florida Everglades (Sklar et Woodpeckers to the dynamics of a different al. 2001, 2005). Models have been developed population. In this case, the model proved to be to track the changes in regional hydrology accuratein predicting most population param- throughout the Everglades as restoration is eters of the second population, though Schiegg implemented, as well as changes in associated et al. (2005) concluded that better estimates of ecological factors such as the distribution of some aspects of dispersal behavior would fur- natural fires within the system (Lockwood et al. ther improve the model. 2003).Avian models were used to evaluate how Another approach is to predict short-term changes in hydrology and fire regimes in the patternsthat can be tested against field data. In Everglades would affect population dynamics the Bachman'sSparrow model, for instance, Liu of Cape Sable Seaside Sparrows (Ammodramus (1993) used a randomization procedure to ini- maritimus mirabilis; Pimm and Bass 2002, tialize population distributionsonto a map sim- Lockwood et al. 2003), Snail Kites (Curnutt et ulating part of the Savannah River Site, South al. 2000, Mooij et al. 2002), and wading birds Carolina. This procedure was based on field (Fleming et al. 1994, Curnutt et al. 2000). The data of habitat use in a single year. Liu (1993) models typically ranked alternative manage- then produced predicted distributions of bird ment scenarios with a goal of comparing the density across different-aged stands in future relative responses. Although no single manage- years. When distributions were documented in ment alternativeis beneficial to all studied spe- subsequent years, the fit between predicted and cies, multispecies modeling allowed managers observed distributions was satisfactory. Less to better understand the potential tradeoffs in satisfactory results were obtained by match- responses of species. ing observed versus predicted distributions of Attempts to validate SEPMs are rare in dispersing individuals in an unusual landscape the literature (Conroy et al. 1995, Schiegg et that developed later (Dunning et al. 2000). The al. 2005). Unfortunately, as with stochastic latter result suggested that the dispersal sub- single-population and metapopulation models routines could be improved. discussed above, many SEPMs used in con- As with metapopulation models, sensitiv- servation applications are designed to predict ity analyses have been conducted primarily as population patterns that operate at too great a simulation exercises to identify key parameters, spatial or temporal scale to permit direct vali- ratherthan to gain insights into management.In dation (e.g. extinction rates predicted in 50 or more sophisticated analyses, several parameter 100 years). One common approach to model values are varied in a factorial experimental validation is to parameterize the model with design, allowing the detection of interaction data from one region of interest and then apply effects among parameters(Pulliam et al. 1995). the model to anotherarea to determine if model Sensitivity analyses have been done with the predictions are robust (Ak^akayaand Atwood SpottedOwl, Bachman'sSparrow, Red-cockaded 1997, Akcakaya 2000a, Schiegg et al. 2005). Woodpecker,and CaliforniaGnatcatcher mod- McCarthyet al. (2000)built a model to see how els. The lattermodel proved to be most sensitive fragmentationaffects two species of Australian to density-dependent effects, weather-related treecreeper using data from outside the main catastrophes,and adult survival and fecundity study area and then determined the model's (Akgakayaand Atwood 1997).In the Bachman's ability to predict extinction and colonization Sparrow model, demographic parameters, events within the region. The model tended to such as adult survivorship and habitat-specific underestimate the observed number of extinc- reproductivesuccess, were identified as having tions and colonizations, perhaps because of a greater influence on model results than land- imperfect detection probabilities derived from scape characteristicsor dispersal (Pulliam et al. field surveys. The validation attempt for the 1992). The Red-cockaded Woodpecker model treecreeper model improved model develop- was also more sensitive to mortalityparameters ment by highlighting the model components than to dispersal parameters, except under that may have contributed to errors in model conditions of extremely low population density predictions (McCarthyet al. 2000).Schiegg et al. (Letcheret al. 1998).

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The appeal of spatially explicit models lies in residual variationin population dynamics. This their ability to capture the actual variabilityof is an effectof landscapecomposition (Dunning et specific landscapes,but this also representsone al. 1992)and can be modeled with a simpler ana- of their greatest weaknesses. If a model is built lytical approach (e.g. Olson et al. 2004). Urban to test the response of a specific population in a (2005) has recently proposed a graph analysis particularlandscape, it is not clear whether the technique that produces results that are similar results can be generalized to other species in to spatially explicit metapopulationmodels but the same landscape, or to the same species in a does not requirethe same level of detail. different location. Different species move over An example of how to determine the proper landscapes in different ways (Belisle 2005). A degree of model complexity is provided by mappingof landscapechange at a particularspa- McGarigal and McComb's (1995) excellent tial and temporalscale for sparrows may not be landscape study of breeding birds in mature relevant for modeling Red-tailed Hawks (Buteo forest of the Oregon coastal range. Most bird jamaicensis).Research to determinethe flexibility species showed strong landscape-composition of spatially explicit modeling across different effects, such as increasing their numbers in landscapes and different species is urgently areas with more old forest, but few species were needed; one published example is the applica- affected strongly by the spatial arrangementof tion of the Red-cockadedWoodpecker model to habitat patches. A landscape model for most an Australianspecies with a similar life history species would not need to be spatially explicit, (Cooper et al. 2002). This need is compounded because the model would need only track the by the large amounts of natural-historydata area of late-seral habitat in a given region and required to parameterizemodels accuratelyfor not the location. Species that responded to edge, multiple species on various landscapes. patch size, or other aspects of spatial arrange- Simulatinghypothetical populations on artifi- ment might be more profitably modeled in a cially generatedlandscapes can provide general spatially explicit manner. resultsthat test landscapeecology theory (Fahrig Several theoretical studies have suggested and Merriam 1994, With 2005). For instance, that the effects of placement of objects in the With and King (2001)modeled songbirdpopula- landscape are most apparent when the criti- tions on artificiallandscapes to test the relative cal habitat resources constitute 5-30% of the Lambersonet al. importance of edge effects and area sensitiv- landscape (Fahrig 1992, 1992, the critical habitat ity. They determined that the effect of habitat Andren 1994). When type the fragmentation could be reduced by retaining makes up <5%of the landscape, patches may some large habitat patches within a landscape. be too isolated to be found easily by dispersers. of the Although the results of models of hypothetical When the habitat exceeds 30% landscape, move the populations can produce managementinsights, dispersers may easily throughout struc- resourcemanagers are reluctantto acceptthe rel- landscape and few effects of landscape evance of theoreticalresults. With any complex ture are significant. Overall habitat loss has a model, the tradeoffbetween realismand general- greater effect on population loss than fragmen- which that ity is disproportionate.Loss of generalityis a cost tation alone (Fahrig 1997), suggests be exam- that users of spatiallyexplicit models sometimes landscape composition effects should a model for accept in generating results needed for specific ined before developing fully spatial conservationsettings. a specific conservationsituation. Not all landscape models need to be spatially If one accepts the accuracyof a given model, allow the of explicit. The data-demanding nature of these spatially explicit models study models and the computer expertise required population dynamics at the spatial and tempo- decisions are made. to design them suggest that simpler model- ral scales at which land-use the habitat- ing approaches should be adopted whenever Because they directly incorporate that affect the possible. For instance, an important landscape change processes may popula- SEPMs should variable affecting some bird populations is the tion dynamics of many species, amount of suitable habitat within a reasonable be able to provide important insights. But we well distance of current populations (Pearson 1993, must understand key biological processes McGrathet al. 2003).The specific location of the to incorporatethem correctly.Spatially explicit models we suitable habitat may not explain much of the population models, like the other

This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions 26 ORNITHOLOGICALMONOGRAPHS NO. 59 review, cannot substitute for carefully designed to conduct pedigree analyses on a verified pedi- field studies. Their construction,parameteriza- gree, or to identify species or stocks (Haig et al. tion, reliability, and validation are critically 1994a, 1995, 1997, 2003; Daniels and Walters dependent on field studies. On the other hand, 2000; Jones 2002; Blouin 2003; Gautschi et al. SEPMs can benefit field studies by identify- 2003; Ballou and Rails 2004). A great challenge ing what parameters most affect population to these efforts is the common problem of how dynamics and what data may be most valuable to construct pedigrees in the absence of infor- for conservation(Dunning et al. 1995). mation pertaining to the relatedness of known individuals (Gautschi et al. 2003, Russello and Genetic Models Amato 2004). Often, people choose assignment tests on the basis of extrapolations of related- All models discussed to this point represent ness from known individuals to unknown. descriptions of population dynamics. The However, Wang (2004) proposed a model that current and future dynamics of populations used information about groups, instead of are a major concern in conservation, but they individuals, to manage populations. Molecular are not the only concerns. Below, we discuss genetic applications to conservation have been models used to investigate two related ques- well reviewed (Avise and Hamrick 1996, Haig tions, genetic variation and geographic distri- 1998),so we concentrateon understandinghow bution. We begin with genetics. models are used to evaluate genetic goals. The chief conservation concerns regarding Genetic goals related to preserving genetic genetic variation are preservation of genetic variability and avoiding effects of inbreed- variabilityand avoidance of inbreeding depres- ing can be used to define population viability. sion. Describing genetic variation is useful, not Genetic goals have been much discussed over only in this context,but also in assessing various the past 10-15 years in relationto the importance aspects of population structurecritical to popu- of genetic, as opposed to demographic, goals lation models. Therefore, the word "genetics" in population recovery efforts (Lande 1988a, is used in several distinct ways in discussions Schemske et al. 1994). Briefly,one view is that of modeling in conservation:molecular genetic populations should be managed to maximize techniques are used to describe genetic varia- genetic variability, because this may increase tion and to diagnose population structure,tax- the likelihood of long-term population persis- onomy, and other biological features; whereas tence. The opposing view is that habitatis being genetic models are used to diagnose popula- destroyed and populations are declining too tion status and viability and to test hypotheses quickly for managersto be concernedwith long- regarding recovery actions. term genetic goals, and that demographicpopu- Molecular genetic techniques have been lation goals should thereforebe paramount.Both widely applied to conservation problems genetic and demographicfactors are important (Hedrick and Miller 1992, Avise and Hamrick in assessing population viability,but their rela- 1996, Haig 1998, Websteret al. 2002). For exam- tive importancevaries depending on the situa- ple, mitochondrial DNA, amplified fragment tion (Haig 1998). For example, when the last of length polymorphisms (AFLPs),single nucleo- the Guam Rails (Rallusowstoni) and Micronesian tide polymorphisms (SNPs), random amplified Kingfishers (Todiramphuscinnamomina cinnamo- polymorphic DNA (RAPDs), and microsatel- mina)were brought into captivity,it was critical lites have all been used in conservation studies to identify close relatives prior to establishing to identify metapopulation structure so that a captive breeding program (Haig et al. 1994a, appropriatepopulation viability analyses could 1995). Once this was determined, it was then be done. Molecular techniques have also been important to expand the populations as fast as used to identify mating systems so that social possible to reduce the risk of extinctionbrought structure and other features could be param- about by stochasticdemographic events. eterized appropriately in demographic PVA models (Haig et al. 1993b, 1994b). Similarly, Structure of Genetic Models moleculardata can be used to identify individuals in a pedigree to properly incorporatepopu- Effective population size.- Critical to avian lation structurein population viability analysis, population biology and conservation is the

This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions MODELSIN AVIANCONSERVATION 27 theoreticalmodel posed by Wright(1931) when Franklinand Frankham(1998) have argued that he defined "effectivepopulation size" (Ne)as the an Ne of 500-1,000 is appropriate. Thus, the number of individuals in a population that con- debate continues. tribute genes to the next generation. Useful for Unfortunately,choosing impossible or unre- estimating the magnitude of genetic loss over alistic goals has weakened the popularity of time in a small population, Neis a descriptionof using Ne as a concept in management. Many the effect of genetic drift on a naturalpopulation avian populations could never practicallyattain when conditions are not ideal. Characteristicsof an Ne of 500, and many have never realized an an ideal population are both genetic and demo- Ne of 5,000. A more appropriateuse of the con- graphic,and include large and stable size, equal cept is that proposed by Mace and Lande (1991) genetic contributionof both sexes, no inbreed- when they revised the criteriafor listing species ing, equal family size, and non-overlapping for the InternationalUnion for the Conservation generations. Most organisms violate some or of Nature (IUCN)Red List. They proposed vari- all of these characteristics. Deviations from ous categories for listing based on estimates of the ideal population size, or the relationship Ne and other factors, such as amount of habitat between Ne and the censused population size alterationand chance of catastrophe.Thus, fac- (N), are compared to evaluate the status of an tors affecting Ne estimates are considered, but actual population (Waples 2002). Ne is gener- managersare not held to specific numeric goals. ally substantiallyless than N, often constituting Below, we discuss how managing for improved only 10-25%of total population size (Frankham Ne can be carried out through pedigree and 1995, Waples 2002). Comparison of Ne with N viability models. and changes of Neover time provide a useful Pedigree analyses.- Perhaps some of the least yardstick with which to measure progress of known, most poorly understood, but helpful a population toward recovery. Furthermore, genetic models for small populations are pedi- managers can examine the specific parameters gree analyses (Fig. 4), which are based on the that are affecting changes in Ne as a means of gene-drop model (MacClueret al. 1986, Mace diagnosing factorsinhibiting recovery. 1986, Haig and Ballou 2002). Pedigree analy- The usefulness of Neas a means of measuring ses were developed for assessing management population status, more specifically its relative strategiesfor captive populations, but they have vulnerabilityto inbreeding depression and loss proved helpful for understanding processes in of genetic variabilitythrough genetic drift, was natural populations as well. They are a way recognized early in the history of conservation of assessing genetic variability so that adverse biology. Franklin (1980) and Soule (1980) sug- effects of inbreeding can be avoided. gested that small populations ideally should Gene-drop pedigree analyses are Monte attain an Ne of 50 individuals over the short Carlo simulations in which 10,000 iterations of term and of 500 individuals over the long term. the model representsampling of an individual's This "50/500 rule" was quickly incorporated entire genome. Each founder is assigned two into recovery planning efforts, such as that unique alleles at the beginning of a simulation directed at Red-cockaded Woodpeckers (U.S. (Fig. 4). Using SPARKSsoftware (Lacy 2004), Fish and Wildlife Service 1985).This merging of the model "drops" each of the two alleles for genetic and demographic informationwas well each founder through an established pedigree, intended, but choosing specific numeric goals generation by generation, assuming Mendelian has not served the purpose, because some man- inheritance. Model iterations generate a distri- agers have adopted the specific numeric goals bution of probabilities that individuals in the (e.g. 50 or 500) without regard to the structure living population share founder alleles in a of their populations. For the Red-cockaded proportion related to genetic events encoun- Woodpecker,a genetically effective size of 500 tered over generations. Thus, events such as may requireat least 509 breeding pairs or a total inbreeding or over-representation (referred population size of 1,322 individuals, includ- to as "over-breeding")of certain individuals ing nonbreeding helpers (Reed et al. 1988). will result in a disproportionate number of Later, Lande (1995) elaborated on the 50/500 some founders' genes in the living population. rule by proposing that a minimum effective Overall, the gene drop provides an estimate size of 5,000 should be attained. More recently, of genetic diversity in the living population.

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Fig. 4. Gene-droppedigree model and analysis for a small population. (I) In this example pedigree, each of the three founders (birdsA, B, C) has been given differentalleles (nos. 1-6). (II)The gene-drop model operates by randomlypassing founder alleles through the pedigree from parents to offspringwith a 50%chance of each allele's passing to the offspring.After one iterationof the simulation,birds H and J are homozygous, whereas others in the living population (birds G and I) are heterozygous. Thus, 50%of the heterozygosity is retained (two of four living individuals).In the living population,three unique alleles (1, 4, 6) have survived and all three founders are represented.Because some alleles have been lost (2, 3, 5), founder contributionis variable:four of eight alleles in the living population are contributedby founder A, one of eight from founder B, and three of eight from founder C. llie simulation would continue by returningto the original startingpedigree (I) and beginning a new iterationof the gene-drop process. This process would be repeateduntil 10,000iterations had been completed to produce probabilitydistributions of the model outputs (see text for details).

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Assumptions of the gene-drop model include is achieved by attempting to equalize founder independence among model runs, no linkage, contribution.The gene-drop approachmeasures and no selection. The consequences of violat- heterozygosityby counting the numberof living ing these assumptions depend on the extent to heterozygous individuals after each run and which linkage and selection occur in the natural averaging across runs. Use of founder genome situation.In a differentapproach, the model can equivalents (FGE) combines maximizing the use a specific pedigree structure, rather than a numberof unique alleles and equalizing founder simulated structure, which adds reality to the contribution.If 21 founders start a population, exercise. The standard data set required for there are 42 unique alleles, and FGEis 21 when gene-drop analysis is simple (Table1), and the all founders are equally representedin the living model can be applied to either captive or wild population and the 42 unique alleles are present populations (Haig and Ballou 2002). as well. Previously,population managersstrove An example of one iteration of the gene- to maximize FGE.In recentyears, the concept of drop model is depicted in Figure 4. In a typical mean kinship has been incorporatedinto these analysis, 10,000 iterations are performed and considerations. Mean kinship is the average the results are summarized as the frequency kinship between an individual and all others in with which neither,one, or both of two alternate the pedigree and is used as a measure of genetic founder alleles survive in the living popula- importanceof an individual in a pedigree. The tion. From this, the following parametersof the relationship between FGE and average mean = * current population can be calculated: founder kinship (AMK)is: AMK 1/2 FGE(Ballou and contribution,the number of unique alleles sur- Lacy 1995). The manager's goal is to minimize viving (allelic diversity), heterozygosity, mean mean kinship or maximize founder genome kinship, inbreeding coefficients, and founder equivalents so that relatednessamong individu- genome equivalents. Founder contributionis a als is kept low and inbreeding does not become measurementof the "presence"of founders in a problem.Inbreeding is consideredby calculat- the living population. A founder is counted as ing an inbreeding coefficient,which is the prob- present in the living population if either or both ability that two individuals carryalleles that are of its alleles are present. The gene-drop simula- identical by descent, a measure of the extent of tion summarizesthe numberof times this occurs mating of close relatives that managers try to in relation to other founders. To maximize minimize. com- genetic diversity, all founders must be equally The gene-drop model can be verified by cal- represented in the living population; thus, paring simulated values to actual values under- or over-represented founders reduce culated by hand from the pedigree. However, be genetic diversity. The number of unique (i.e. variables such as heterozygosity cannot founder) alleles at the end of a gene-drop simu- verified using molecular data, because assump- lation estimates the representationof founder tions of the model are not met by measurements alleles present in the living population. It differs of molecular markers. The model begins by from founder contribution,in that founder con- assuming 100% heterozygosity among found- tributionis made if either or both founder alleles ers (i.e. each founder has two unique alleles), are present, whereas number of unique alleles whereas molecular measures take into account is a direct count of alleles. From a conservation the effects of previous genetic events. perspective,the goal is to maximize the number The informationderived from the gene-drop and of unique alleles in the living population. This model describes population structure Table 1. Structureof the standard input file ("Me, Ma, Pa" file) used to keep studbooks, to constructpedigrees, and for gene-drop analyses. Dead Studbooknumber Sex Dam Sire Alive (A) or (D) 1 M WILD WILD A 2 F WILD WILD A 3 F WILD WILD D 4 M 2 1 A 5 F 2 1 A 6 F 3 4 A

This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions 30 ORNITHOLOGICALMONOGRAPHS NO. 59 indicates the importance of different individu- the potential for improving population viability als to the living population. The technique can through better breeding practices(i.e. introduc- also be used to evaluate various breeding strate- ing individuals of specific age or sex; Haig et al. gies. The consequences of differentpairings can 1993b). Subsequent PVAs merged this genetic be compared by adding hypothetical offspring information with demographic information from selected pairs to the bottom of the pedi- to provide a more comprehensive plan for gree and running the model to see how genetic recovery. diversity or population structureis altered.This exercise is particularlyuseful when setting up Use of Genetic Models in Conservation programs to introduce or translocateindividu- als. For example, when Guam Rails were to be Population viability analysis models usually introduced on the island of Rota, the gene-drop take one of the forms of demographic models was used to determine the best pairings to pro- reviewed above. However, an examination of duce chicks for the release (Haig et al. 1990). popular, commercially available population or One of the most positive aspects of pedi- metapopulation viability software programs gree analyses is that, compared with other indicated that genetic factors, such as reduced approaches, the data sets required are rela- fecundity or survival caused by inbreeding tively easy to construct,particularly for captive depression, were not well incorporatedin any of populations, and the programs are easy to run. them (Table2). Among the programsreviewed, Furthermore, because the gene-drop model VORTEXincorporates genetic factors to the takes into account the exact structure of the greatest extent, but even with it the genetic data pedigree, it is quite realistic. Nevertheless, the entered can be fairly generic. VORTEXuses the greatest obstacle to its use with wild bird popu- gene-drop model to simulate occurrences of lations is the requirement of a deep pedigree inbreeding and lethal homozygotes, and calcu- derived from markedindividuals of molecularly lates mean expected heterozygosity and mean confirmed parentage. For field biologists con- inbreeding coefficient at different intervals ducting long-term studies of marked birds, the (Haig and Ballou 2002). Inbreeding depression insight gained into population structure from is incorporatedin terms of reducedjuvenile sur- gene-drop pedigree analysis is a worthwhile vival, and effects of lethal recessives are incor- dimension that few have explored. For exam- porated through heterozygote advantage. Few ple, when a tiny population of Red-cockaded studies have calculatedlethal equivalents (Rails Woodpeckershad nearly been extirpated from et al. 1988),so exact values for lethal equivalents the SavannahRiver Site in South Carolina,DNA are difficult to find, and the effect of mildly del- fingerprintinghelped prepare a pedigree (Haig eterious mutations may not pose a threat to et al. 1993a). The gene-drop analysis was then populations with Ne > 25 (Gilligan et al. 1997). used to measure heterozygosity and compare However, the latest edition of VORTEX(ver- its loss with the heterozygosity of the original sion 9.5) allows users to determine the type of population; to evaluate inbreeding; to deter- mating for the population (e.g. mating by mean mine which founding birds were over- and kinship). Thus, it uses the pedigrees it createsto under-represented in the living population; make management decisions. A new program and, perhaps most importantly, to determine called ZOORISKmodels captive populations

Table 2. Consideration of genetic factors in common population viability models used in conservation planning.

Potentialto model genetic factors Software Model Hetero- Genetic program input3 Inbreeding zygosity distance Ne Reference VORTEX Individual Yes Yes No No Lacyet al. (2005) GAPPS Individual Yes No No No Downer (1993) RAMAS Matrix Yes No No No Akc.akaya(2004) INMAT Matrix Yes No No No Mills and Smouse (1994) = "Individual identifiesand trackseach individualthroughout the simulation;matrix = based on stages or ages in a population.

This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions MODELS IN AVIAN CONSERVATION 31 using PVA simulations and gives them IUCN- translatetheir results into a formateasily under- like categoriesfor risk, depending on the results stood by those involved in conservation.Second, (Earnhardtet al. 2004). moleculartools should be morewidely employed Incorporatingadditional genetic information to parameterizepopulation structurein models into PVAmodels will provide a more complete used for population-viabilityor metapopulation- and realistic evaluation of population persis- viability analyses. To accomplish this, models tence, but it will not be simple. Population with appropriatestructure are needed. Finally, viability analysis models are demographic because the concept of effective population size models. Thus, genetic factors must be linked is importantand helpful to managers, we need to demography. We could begin by trying to to consider it more carefully and more often in incorporateinbreeding into a model. However, populationrecovery efforts. one can never tell where or how inbreeding will strike in a population. It could affect life Species Distribution Models span, fecundity, sperm count, juvenile mortality, or other attributes.Therefore, it would be The final category of models we will discuss, difficult to attributethe effects of inbreeding to species distributionmodels (SDM),are powerful a specific demographicfactor. Conversely, there tools for converting individual point-locality are some generic rules that could be incorpo- data (e.g. museum collection records) into the rated into models so that they would start to hypothetical distributional range of a species consider genetic factors. For example, a model (Corsiet al. 2000, da Fonsecaet al. 2000) or pre- could assume that for every 20%loss of fitness dicted ranges following environmental change there would be a 20% increase in inbreeding (Polanskyet al. 2000,Peterson et al. 2002a).Thus, depression. Another approach would be to use SDMs have great potential utility for avian con- measuressuch as genetic distanceand gene flow servation,especially because avian biologists are to define the relationshipamong populationsin a often pressed to make recommendationsabout metapopulation.Currently, some models assume conservingbiodiversity in partsof the world with equal distanceamong populations,whereas oth- limited data on species distributions(da Fonseca ers require stating a migration rate, which is et al. 2000, Petersonet al. 2000). Comparedwith often based on an unreliable estimate. Finally, other vertebrate groups, however, the large PVA models could evaluate genetic factors amounts of data available on bird distributions independently of demographic factors, such as and natural history make them one of the best changes over time in heterozygosityor inbreed- groups for SDMs (e.g. Edwardset al. 1996). ing that were estimatedby moleculardata; they Over the past 50 years, a wide variety of could reporta separateprobability of persistence techniques have been used to link animal based on genetic factors.This probabilitycould distributions to habitat features (reviewed in be monitoredover time or tested against various Stauffer2002). Species distributionmodels vary management options. As in PVAs (Beissinger from simple sets of rules based on overlays of and Westphal1998, Reed et al. 2002),the specific environmental and species-occurrence data probabilitiesreported will not be as informative (e.g. BIOCLIMand simple overlay; Nix 1986, as comparisonsof changes in persistencevalues. Busby 1991, Loiselle et al. 2003) to sophisticated The most comprehensive applications of multivariate analyses (Pereira and Itami 1991, genetic considerations in conservation should Carpenter et al. 1993), or artificial-intelligence use all the analysesdescribed above with the goal techniques using rule-based sets of algorithms of improvingNe (i.e. use moleculartools to deter- (e.g. GARP;Stockwell and Peters 1999, Godown mine population structure, perform pedigree and Peterson 2000, Anderson et al. 2003). analysis,and incorporategenetic factorsin PVA). Predicted species distributionmaps are also an Such an approachhas rarelybeen undertaken. integralpart of gap analysis, which is concerned A more prominentrole for genetic models and with locating concentrationsof high biodiver- genetics in conservationdepends on resolution sity and identifying species, usually terrestrial of several issues. First,resistance to considering vertebrates,that are poorly represented by the genetic factors needs to be overcome. Toward current set of protected and managed areas this end, workers involved in moleculargenetic (Scottet al. 1993, 1996).The goals of using these analyses and modeling have a responsibilityto models are (1) to establishrelationships between

This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions 32 ORNITHOLOGICALMONOGRAPHS NO. 59 habitats and biodiversity; and (2) to establish and testing data sets (Petersonand Kluza 2003), links between habitat conditions and the viabil- though Anderson et al. (2003) suggested a pro- ity of one or severalspecies, allowing predictions tocol for model selection based on omission abouthabitat changes (Van Horn 2002). Typically, and commission rates that allows all data to be the focus in most ornithologicalstudies has been used in an analysis. The genetic algorithm for on modeling terrestrialspecies. rule-set prediction works in an iterativeprocess Traditionally,range maps depicting the distri- of rule selection, evaluation, testing, and incor- bution of a particularspecies were either a dot poration or rejection;a method is chosen from map of specific locations where a species had a set of possibilities (e.g. logistic regression or been recorded or a solidly colored range map bioclimatic rules) and then applied to the train- enclosing all know sightings (Butterfieldet al. ing data until a rule is developed or evolved. 1994).The boundariesof the species range were Predictive accuracyis evaluated on the basis of defined either by connecting specimen or sight- points resampled from the test data and points ings locations (e.g. minimum convex polygons) sampled randomly from the study region as a or, more commonly,by drawing arbitrarylines whole, which are summarized in a rule-signifi- to encompassthe suspected range of the species, cance measure. Rules may evolve by a number like range maps that one might find in a field of means that mimic DNA evolution (e.g. point guide. However, most species do not occupy all mutations,deletions, crossing over). The change areas within their range;rather, the distribution in predictive accuracyfrom one iteration to the is patchy.Species distributionmodels attemptto next is used to evaluate whether a particular increasethe accuracyof range maps by eliminat- rule should be incorporatedinto the model, and ing those areas within the known range where the algorithm runs either for 1,000 iterations or the species does not actuallyoccur. until convergence. A second "top-down" approach is to Structure of Species Distribution Models start with the known distribution of a species and attempt to eliminate those parts of Two distinct approaches are commonly used the distribution where the species does not to model species distributions.One "bottom-up" occur. O'Connor (2002) called this approach approach is to start with known locations, or "exploratorymodels." Gap analysis uses such point-location data, and then extrapolate that an approach (Scott et al. 1993, 1996; Jennings information to the entire range of the spe- 2000). Landcovermaps of actual vegetation are cies or to an area of interest. O'Connor (2002) used as surrogates to predict distributions of called these "forecastingmodels." For example, organisms on the basis of habitat-relationship the program DOMAIN (Carpenteret al. 1993) models. Species distributions are then overlaid takes known distributionpoints for species and on maps of management, ownership, or both, uses map layers of environmental factors, such using a geographic information system (GIS). as climate, soil, and land use, to construct an Species with significantamounts of habitatout- environmental habitat envelope or "domain" side the protective envelope of managed lands for those points. The envelope is then compared are defined as "gap species," and unmanaged with environmental data for the region under habitats supporting those species are potential study and a map is produced of similarity "gaps" in need of conservationplanning (Scott ranges of the species' primarydomain. et al. 1993). Although gap analysis can be con- Similarly, genetic algorithm for rule-set ducted on smaller scales (Whiteet al. 1997,Karl prediction (GARP) models include sev- et al. 2000), it is generally considered a "coarse- eral algorithms in an iterative, artificial- filter" approach to conserving biodiversity, intelligence-based approach (Stockwell and because it works best at large scales and with Noble 1992, Stockwell 1999, Stockwell and common species. For example, Brooks et al. Peters 1999) using point-source data (e.g. (2004) and Rodrigues et al. (2004) present the museum specimens). As such, these models use beginnings of a global gap analysis. Becauseit is only data on known occurrence, even if data enacted at such large spatial scales and analyzes exist on areas of nonoccurrence (Anderson et many species, gap analysis is the antithesis of al. 2003). Usually, occurrencepoints are divided endangered species programs that focus on randomlyand evenly within GARPinto training single species that are rare.

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As originally proposed by Scott et al. (1993), inputs, such as digital elevation data, location of the basic components associated with a com- aquatic habitats (e.g. lakes, streams, wetlands), pleted gap analysis include (1) a hierarchically presence of caves, and size of habitat polygons, based map of actual vegetation; (2) predicted have been used in several states to refine the distribution maps for each breeding terrestrial predicted distributions of gap species. Using vertebrate species and, in some cases, other data from the Washington Gap Analysis proj- taxa (e.g. wintering birds, butterflies); (3) a land ect, Smith et al. (1997) demonstrated how avian ownership-management status map depicting habitat-relationship models can be successfully current stewardship; and, most importantly, combined with landcover information. (4) a spatially explicit representation of areas of As in any predictive model, there are four potentially high biodiversity and their relation- possible outcomes of an SDM linking species to ship to current stewardship. habitats: (1) presence of a species is predicted Habitats used by species of interest are accurately; (2) absence is predicted accurately; defined by the landcover map. Each species (3) presence is predicted, but the species is actu- is linked to landcover types using habitat- ally absent (error of commission, false positive, relationship models (Scott et al. 1993, 1996; or type I error); and (4) absence is predicted, but Butterneld et al. 1994). Briefly, habitat- the species is actually present (error of omis- relationship models are developed by identify- sion, false negative, or type II error). Statistically ing those cover types in which a species might valid methods for assessing the accuracy of pre- occur (Morrison et al. 1992). In rare cases, a dicted distributions of animals exist, if those species might be restricted to only one habitat four rates can be estimated. An overall index of (i.e. one landcover category). More commonly, the performance of a species distribution model species occur in several habitat types and may is encapsulated by its kappa value (Fielding and even occur in all habitat types within a given Bell 1997), given by the formula: area. The sum of all habitats in which a species might occur becomes the potential distribution [(a + d)- (((a + c)(a + b) + (b + d)(c + d))/N] of that species. Incorporating the known dis- - tribution of a species within a given area, the [N (((a + c)(a + b) + (b + d)(c + d))/N)] predicted distribution of a species then becomes = all habitats the species might occupy within its where a number of times when both model and = known distribution (Fig. 5). Additional model observations predict occurrence, b number of

Fig. 5. Example of a gap modeling process for the Ovenbird (Seiurusaurocapilla) in Arkansas (see text for details). The known distribution (currentrange) by county within the state was determined from James and Neal (1986)and a committeeof bird experts.The distributionof potentialhabitats within the state was based on habitatsthe species is known to occur in based on input from the committee.The predicted distributionis the combinationof those two maps, showing the potential habitatswithin the known distribution.

This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions 34 ORNITHOLOGICALMONOGRAPHS NO. 59 times when observations indicate absence and of commission more than it increased errors of model predicts occurrence,c = number of times omission, leading to better overall model accu- when observations predict occurrence and racy.Thus, it would appearthat improvementof model absence, and d = number of times when avian predictivemodels should focus on factors both model and observations predict absence. that decreaseerrors of commission. These kinds of statistical tests typically require Evaluating the accuracy of GARP models an independent data set that was not used in presents an interesting challenge, because the model development, a requirement that may results vary each time a model is run. This is not be met with most SDMs. caused by the way the starting point is selected, Loiselle et al. (2003) compared the accuracy typically at random. One approach is to run of 11 modeling approaches to the actual dis- a model a certain number of times and select tribution of 11 cotingids of conservation con- areas of habitats on the basis of how often they cern in the highly fragmented Atlantic forest appearin the model. Loiselle et al. (2003)ran five of southeastern Brazil using the kappa value. GARPmodels and selected a model at random The models they tested included BIOCLIM, (GARP1),a model based on areas that occurred simple overlay, three versions each of logistic in four of five models (GARP4), or a model regression (50%, 85%, and 95% probability), based on areas that occurred in all five models DOMAIN (85%, 90%, and 95% cut-off), and (GARP5). Running GARP models repeatedly GARP (of five runs, one randomly chosen run and only incorporating those areas that are [GARP1],cells that were selected in four of five consistently identified by the models tends to runs [GARP4],and cells that were selected in decrease the total area of the final model (K. G. five of five runs [GARP5]).Results varied dra- Smith pers. obs.). Anderson et al. (2003) outline matically among the various models, with the a five-step protocol based on accepted levels DOMAIN90and DOMAIN95having the high- of omission and commission, rerunning GARP est kappa values. models until a suitable number of models (e.g. Loiselle et al. (2003) further cautioned that n = 20) fit that criteria, and superimposing conservationplanners need to evaluate the con- those models to create a composite prediction. servation implications of errors of commission Peterson and Holt (2003) demonstrate how and omission before they start the modeling GARP models can be combined using GIS to process. In the case of 11 cotingas,Loiselle et al. examine variationin niche characteristicsacross (2003)found that models that minimized errors the range of a species. of commissionlead to a betterselection of reserve Guisan and Zimmerman(2000) characterized networks. In contrast, because animals rarely many of the modeling approaches currently in occupy all suitable habitats within their range, use as static and probabilistic,meaning that the gap analysis models will generally overpredict models relate distributions of species to cur- species occurrence,leading to a higher rate of rent environmental conditions without regard errorsof commissionthan of omission(Smith and to future environmental change. Typically, Catanzaro1996). The best GARPmodels seem to only one data set is available to construct the have low rates of omission and medium to high model, so that statistical techniques such as rates of commission (Anderson et al. 2003). In jack-knifing,cross-validation, or boot-strapping a direct comparison, gap analysis models had are used to evaluate it. Ideally,one would like to fewer omissions and GARP models had fewer have two independent data sets- one to build overestimations(Peterson and Kluza2003). the model and one to evaluate it (Guisan and Individual bird species differ in how accu- Zimmermann2000). ratelythey can be modeled, which in many cases Suggestions made more than 30 years ago can be determined a priori (Boone and Krohn that modeling approaches should be tested 1999).In general,Boone and Krohn(1999) found using data sets of known structure (Alldredge that sites largerthan 1,000ha with checkliststhat and Ratti 1986) have largely been ignored were based on >10 years of recordshad the low- (O'Connor 2002). Most often, different mod- est commission errors. In building bird-habitat els are compared using a single data set (e.g. relationship (BHR) models for 60 species in Loiselle et al. 2003);only occasionally are mod- northern Idaho, Karl et al. (2000) found that els tested with two or more independent data increasing model complexity decreased errors sets (e.g. Mitchell et al. 2001, O'Connor and

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Wagner 2004). Mitchell et al. (2001) found that A variant of SDM has been used to predict microhabitat and landscape models worked the behavior of invasive species and the loca- equally as well in a managed forest in South tions of future invasions. Using an approach Carolina, and combining the two models did called "climate-matching" (Peterson 2003b), little to improve the results. Models were species are assumed to be able to invade and refined by using other information on species establish populations only in areas that match distributions and analyzing a second inde- the "niche" or ecological conditions where they pendent data set. Models for Neotropical and occur in their native range. Species distribution short-distance migrants were better than mod- models are first constructed and tested in the els for permanent resident species, and models native range of the species, and then applied to performed better for habitat specialists than for other regions to forecast locations favorable for habitat generalists. In her study of birds asso- invasions (Peterson and Vieglais 2001, Peterson ciated with cottonwood (Populus angustifolia) et al. 2002b). Peterson (2003b) provides an excel- riparian forests, Saab (1999) also concluded lent review of this emerging approach. that landscape variables were better predictors Gap analyses are being conducted in each than microhabitat (variation within cottonwood state as part of the Gap Analysis Program of the stands) and macrohabitat (variation between U.S. Geological Survey Gap Analysis Program cottonwood stands) variables. (Jennings 2000). Regional analyses that merge multiple states are underway for several west- Use of Species Distribution Models in ern states whose base maps are complete. This Conservation process will eventually produce a seamless map of biodiversity for most portions of the United There are two main applications of SDMs States. The true value and power of gap analy- to conservation problems: forecasting future sis will then be realized, as ecoregions replace Dietz and ranges of species in relation to environmental states as the units of analysis (e.g. change and gap analyses. We first discuss each Czech 2005). in turn, and then conclude this section by dis- The source of available animal data typically chosen for cussing several issues that apply specifically to dictates the scale that is gap-analysis the usefulness of these models with birds. maps. For example, the Arkansas Gap Analysis A common use of SDMs has been to evaluate project (Smith et al. 1998) used counties as the area to distributions the potential effects of future climate change. smallest geographic map Arkansas has 75 counties Species distribution models are used to create of vertebrates (Fig. 5). Audubon a climate envelope that relates recent species of about equal size, and the Arkansas locations to current climates (e.g. temperature, Society has collected bird distribution data for each for >40 On the precipitation, and seasonality) to estimate cur- portions of county years. rent distributional areas where populations basis of county records and suitable habitat, is to persist in the face of competition, predation, the Ovenbird (Seiurus aurocapilla) predicted and other challenges. Future distributions are breed in the hardwoods of the Interior Highlands then derived by applying the climate envelop to and on Crowley's Ridge in northeastern Arkansas, scenarios for future climate under the assump- but not in the southern Gulf Coastal Plain, which the known tions of different dispersal abilities. Such work has suitable hardwoods but is outside has been conducted with Mexican birds, with breeding range of the species in the state (Fig. 5). never uses birds of the U.S. Rocky Mountains and Great Eliminating habitats that the species Plains, and with endemic Australian vertebrates makes the predicted distribution more detailed data. This (Peterson et al. 2002a, Peterson 2003a, Williams than the original county-occurrence et al. 2003). Thomas et al. (2004) recently used technique can be extrapolated to the entire range a useful tool for this approach to explore the effects of different of a species, providing refining the basis of use or non- climate warming scenarios on future ranges range maps of species on and extinction for a variety of taxa. The ability use of habitat types. of these models to accurately predict distribu- The strengths and weaknesses of species dis- been reviewed tions 50 or more years into the future remains tribution models have recently in untested, and the validity of their predictions is thoroughly by Scott et al. (2002), especially unknown. the chapters by O'Connor (2002) and Van Horn

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(2002). Here, we discuss two aspects that apply of the gap-analysis approach is that models specifically to avian models and their useful- only link species distributions to patches at ness in conservation of birds- scale and alter- a specific time in a specific region (O'Connor native analyticalapproaches. 2002). Gap models, therefore,become outdated Two aspects of scale need to be addressed in rather quickly and should be updated on some any SDM: (1) the scale at which various data regular basis (e.g. redone every 10-20 years). sets were collected and analyzed (Holland et al. A third criticism is that using vegetation as a 2004) and (2) the extent to which data collected surrogate for predicted distributions decreases at a smaller scale are extrapolated to some resolution so that additional informationneeds larger scale (Miller et al. 2004). Selecting the to be gathered through more sampling of the wrong scale can lead to misleading or erroneous species distributions (Stockwell and Peterson conclusions concerning how bird species are 2003). associated with various habitat characteristics O'Connor (2002) has suggested that a totally (Mitchell et al. 2001). Birds, particularlymigra- new approach is needed for the modeling of tory species, present a real challenge, because animal-habitat relationships, different from they may perceive the landscape on a scale the current emphasis on correlations (see also from less than a hectare to thousands of square Van Horn 2002). No doubt, the next decade kilometers (Wiens et al. 2002). It is unlikely that will see the development of many other tech- one scale would be appropriate for assessing niques as instrumentation and computer landscape patterns for all bird species within a analyses increase in sophistication. Guisan and region or even within groups of birds with simi- Zimmerman (2000) present a review of many lar ecologies (Mitchell et al. 2001). Conversely, new techniques for development of predictive Savignac et al. (2000) concluded that Pileated species-habitat models that are an improve- Woodpeckers (Dryocopuspileatus) in Quebec ment over existing static models, and Ferrier simultaneously requiredhabitat features at two et al. (2004) present a new global biodiversity differentscales. modeling approach based on richness, faunal The patch of habitat used in any avian turnover, and species-area relationships.Here, landscape study is related to scale. Important we highlight three of those new approaches. aspects of patch dynamics are patch quality; Classification and regression trees (CART) characteristicsof patch boundaries, particularly are an alternativeto many statisticaltechniques as they relate to species movements between now commonly used to model species relation- adjacentpatches; landscape connectivity, or how ships. As discussed in De'ath and Fabricus easily organismscan move across the landscape; (2000) and O'Connor and Wagner (2004), trees and patch context, the characteristicsof land- explain variation of a single response variable scape (or adjacentpatches) surrounding a partic- by repeatedly splitting data into more homoge- ular patch (Wienset al. 2002,Holland et al. 2004). neous groups, using combinations of explana- Forexample, Kilgo et al. (1998)found differences tory variables that can be either categorical or in bird communitystructure in bottomlandhard- numeric. Each group is characterizedby a typi- woods in South Carolinadepending on whether cal value of the response variable, the number the forest patch was enclosed by pine (Pinus of observations in the group, and the values of taeda,P palustris)or by field-scrubhabitats. the exploratory variables that define it. Results One potential problem in gap analysis that are presented graphically,which aids in under- relates to patch size and scale is defining a real- standing the relationships.De'ath and Fabricus istic minimum mapping unit (MMU).Although (2000) list the advantages of this approach:(1) the vegetation maps are typically derived from different types of response variables can be satellite imagery at a resolution of 30 m, the used; (2) it can be used for interactiveexplora- analysis of animals to the vegetation map is tion, description, and prediction;(3) it is invari- done at some larger scale (e.g. MMU of 40 ha or ant to transformationsof explanatoryvariables; 100 ha). Classifying a patch of 100 ha or greater (4) the graphical results allow easy interpre- as a single vegetation type obscures all the veg- tation of complex ecological data, including etation heterogeneity within that patch. Choice interactions; (5) models can be selected by of patch size potentially changes the results of a cross-validation;and (6) missing data values are gap analysis (Karlet al. 2000).Another criticism not a problem.

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Classification and regression trees have centered on the patch or site locations. Each many applications in avian studies (reviewed patch then becomes a single data point in the in O'Connor and Wagner 2004). For example, analysis, and the influence of habitat variables O'Connor and Jones (1997) used CART to measured at a large scale can be used to exam- examine long-term trends in species occurrence ine species abundance or richness. See Holland on Breeding Bird Surveys (BBS)in the conter- et al. (2004) for an example of this approach minous United States. Their analysis suggested and the Landscape Ecology Laboratory web- that 15%of the BBS had lost an average of 17 site (see Acknowledgments) for downloadable species. Using CARTanalysis on Breeding Bird programs to conduct this analysis. Important Census data from the United States, O'Connor issues in this approach are (1) determining the and Wagner (2004) were able to generally con- appropriatelandscape scale, (2) using multiple firm the results of O'Connor and Jones (1997). landscapes at multiple scales, (3) patch- and Beckerand Beissinger (2003)found CARTto be landscape-scale factors, and (4) tradeoffs of an excellent way to analyze the marine habitat intensive sampling versus obtaining adequate characteristicsthat affected the at-sea distribu- sample sizes (see Brennanet al. 2002).Although tion of MarbledMurrelets. it has not been used in any avian studies (J. Use of generalized linear models (GLMs) Holland pers. comm.), Holland et al. (2004) and generalized additive models (GAMs) was estimate that many existing data sets could be the focus of a recent symposium (Guisan et al. re-analyzedusing focal patch analysis. 2002).Generalized linear models are mathemati- What species distribution models lack in cal extensions of linear models that do not force precision, they make up in generality.Products data into unnatural scales, allowing for non- of SDMs can be considered working hypotheses linearity and nonconstant variance structures and should be treated as such. The models are, in the data. Data can be assumed to be from in essence, a structured way to visualize those several families of probability distributions, hypotheses, and should be viewed as starting including normal, binomial, Poisson, and nega- points for discussion of the current and future tive binomial.Generalized additive models have spatial distribution of terrestrial vertebrates. the underlying assumption that functions are The temporal dynamics of the landscape, additive and that the components are smooth. coupled with the dynamics of real populations, The advantage of GAMs is the ability to deal may limit the usefulness of SDMs as a conser- with highly nonlinear and nonmonotonic rela- vation planning tool for specific landscapes tionships between the response and the set (Conroy and Noon 1996, Scott et al. 2002). They efforts of explanatory variables. Guisan et al. (2002) can be more useful in regional planning not be sub- present a brief overview of the mathematical (e.g. White et al. 1997), but should relations among linear regression, GLMs, and stituted for site-specific studies and field work GAMs. Problems that may occur with these (Scottet al. 1993, 2002;Peterson 2005). approachesinclude multicollinearity,limitations in using stepwise regression, and spatial auto- Intelligent Use of Models to Make correlation(O'Connor 2002). Also, both CART Conservation Decisions and GAMmodels tend to be "data-hungry,"pre- cluding their use on relatively small data sets. Attributes of Useful Models Guisan et al. (2002) suggest that CARTmodels use may prove useful in identifying interactions To aid conservationdecisions, intelligent an under- among predictorsused in GLMsand GAMs. of the models discussed here requires Another emerging approach is focal patch standing of their unique attributes.Fortunately, can be used to analysis (Brennan et al. 2002, Holland et al. some generalities emerge that 2004), which takes into account not only the evaluate these models, as well as other model discussed. Certain attri- patch in which a species occurs, but also the types that we have not characteristics of the landscape surrounding butes will make models, regardless of type, decisions. the patch (i.e. patch context; Saab 1999). Data more useful for making conservation are collected on species abundance or richness These attributesare not easily incorporatedinto in a number of patches or sites, and landscape existing models, but they represent goals that to so that field predictor variables are measured in areas modelers should strive reach,

This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions 38 ORNITHOLOGICALMONOGRAPHS NO. 59 biologists will be encouraged to make greater for costly conservation decisions. In addition, use of, and provide data for, their models. mechanisticmodels may provide useful predic- First, there is a necessary tradeoff between tions for application to situations outside the the generality and the realism of models (Levins range of conditions on which the model was 1969). Models that are general in structurelead based. to useful "rules of thumb" but often lack the Third, models should be forward-looking realism needed for application to specific (con- rather than predictive. The limited ability of servation) issues. The compromise is between models to accuratelypredict future events must simple models with minimal data requirements be clearly stated. What actually occurs in the but limited specificity and complex models with future is, at best, one of the many possible simu- extensive data requirementbut high specificity. lated trajectoriesof stochastic model output. As The challenge is in building simple, feasible, the time horizon of a model becomes longer, the and understandable models that nevertheless uncertainty in its predictions becomes greater. are detailed enough to address real problems. Outputs from these models are better treated as In conservation, there is often the percep- heuristic expectations that presumably bound tion that increased realism is needed to apply the range of possible outcomes. models to particularsituations. This can result Fourth, models should contain relevant in the construction of highly complex models variables, and their assumptions and results that may be unreliable because of uncertainties must be biologically realistic. Variablesused as in parameter values (e.g. dispersal behavior model input and the form of model output must and unknown temporal and spatial variation be understandableand relevantto the conserva- in vital rates). A reasonable approach is to tion action. Presenting model results in techni- develop models of intermediatecomplexity that cal and complex terms is certain to diminish have enough realism to be applied to particular their attractivenessto field biologists and their conservation problems but avoid unnecessary value to decision-makers. Unnecessary com- complexity- that is, apply the principle of par- plexity increases the likelihood that data needs simony (Burnhamand Anderson 1992, 2002). and model insights will be ignored. In the case of the Northern Spotted Owl, for Fifth, models should be testable. Their example, an IBM was developed to evaluate hypotheses about how a system operates must competing plans for management of public make predictions that can be tested by experi- lands in the Pacific Northwest of the United ment or observation over both the short and States. Because each plan could be expressed as the long term. For conservation purposes, this a map showing the state of the landscape 100 requires model output in the form of variables years in the future, a spatiallyexplicit model was whose values can be measured in the field. used to rank the two alternatives. This model Given a model-based projection of population was quite complex, including age-structure, response to managementaction, is that response spatial subdivision, and individual variation observed? If not, the model and the decision in vital rates (McKelvey et al. 1993; Noon and must be revisited and revised accordingly. McKelvey 1996a, b). Other researchers have Sixth, models should fully explore system suggested that simpler models excluding age- uncertainty (Possingham et al. 2001, Burgman structure and spatial information (Wennergren et al. 2005).For the foreseeablefuture, conserva- et al. 1995) or using spatially explicit optimization decisions will be made with an incomplete tion procedures (Hof and Raphael 1997) would understanding of system dynamics. It is the have provided similar insights. responsibility of the modeler to fully explore Second, models should be mechanistic.Those the model's uncertainty and make this known used to support conservation decisions should to decision-makers and field biologists. In the be based on current understanding of the key case of population models, the risks of specific processes contributing to a system's dynamics. managementdecisions must be made explicit to Mechanistic models allow decision-makers to the public. see how those processes are influenced by man- Seventh, modeling efforts benefit from agement options. The ability to provide a causal constructing multiple models, because often explanation will increase public understand- there is limited agreement among researchers ing and make it easier to gain public support and decision-makers on how and at what rate

This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions MODELSIN AVIANCONSERVATION 39 nature works. Developing and testing compet- Several publications outline a process for making models offers the opportunity to examine ing decisions about the management of dynamic different mechanistic explanations of how pop- systems that are poorly understood or for which ulations respond to external factors. Ideally, the there is little agreement on the factors that affect models should be structured differently so that the state of the system (Hilborn and Mangel they have the potential to produce qualitatively 1997, Burnham and Anderson 2002, Williams et different projections. Each model's validity is al. 2002). The process, applicable to the conser- evaluated relative to the existing data, and the vation of imperiled bird species, for example, one that is most aligned with existing data gains makes full use of available information and in credibility. Discriminating among competing current understanding to select a single "best models in terms of their relative concordance model" or a set of models with similar support between prediction and observation is the from a data set (Burnham and Anderson 2002, essence of adaptive management. Johnson and Omland 2004). The decision-making It is difficult to develop models that have all process requires the development of two or more these properties. For example, the more com- competing models that bound the breadth of plex types of population models, SEPMs, often uncertainty and describe and project the dynam- meet the last six of the above criteria, but fail on ics of the population. Competing models share the first criterion of generality. A key point is to a common objective: supplying the information make models no more complex than they need needed for making the management decision to be for the problem under consideration or that maximizes the likelihood of realizing a goal than the existing data allow, while retaining the within some set of constraints. Data relevant to mechanistic elements that make them useful in the state of the system (e.g. population size and conservation. Finally, it is useful to consider the reproductive rates) are collected, and a measure results of even the most mechanistic models not of the probability of the data, given that the as precise predictions for the future but instead model is true, is computed. Through application as heuristic expectations that provide a guide to of Bayes's Theorem (Hilborn and Mangel 1997, the effects of management options. Johnson and Omland 2004), this measure is then turned on its head and interpreted as a measure Working with Multiple Models in a Decision- of the chance that the model is the appropriate theoretic Framework description of the system, given the data. To determine which is the best descriptor of the So far, the discussion of model types has population's dynamics, models are compared not explicitly addressed how models can aid in terms of their posterior likelihoods, given the decision-making. Often, there is no obviously data. That is, quantitative predictions of the mod- "correct" model of a population's or system's els are compared with observations provided by dynamics, and decisions about an appropriate an ongoing monitoring program. Insights from model are often made in the context of incom- the current best model are then used to inform plete information. In fact, multiple plausible the conservation decision process. models about how a system works may be The process of model comparison is itera- in competition, each predicting a range of tive, depending on a regular assessment of possible outcomes with different likelihoods. the state of the population. After each period There may, however, be a "best" model in the of data collection, model predictions are again sense of being most consistent with the avail- compared, and the current state of the system able data. When competing scientific models and the posterior probabilities of being the are compared in the context of observable correct model are recomputed for each model. as the basis quantities or data, we move into the realm of The current best model is then used statistical modeling (Nichols 2001). Decision for decision-making until the next assessment theory, in the context of statistical model com- occurs. Management of hunted waterfowl the use of parison, provides a step-down process to aid provides an excellent example of decision-making when there is uncertainty decision-theoretic models for conservation. about the "true" structure and dynamics of the The U.S. Fish and Wildlife Service uses the system being modeled (Possingham et al. 2001, competing model procedure to make manage- of Burgman 2005). ment decisions regarding optimal harvest

This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions 40 ORNITHOLOGICALMONOGRAPHS NO. 59 waterfowl populations (Nichols et al. 1995, biological details may be more appealing to Johnsonet al. 1997,Johnson and Williams 1999). field biologists, but they increase the burden on In this case, the competing models bracket the field biologists to collect more kinds of data and range of uncertainty associated with random to verify that the biological processes incorpo- environmental variation, incomplete control rated in models are correct.Does survival vary over harvest, and uncertaintyabout the biologi- with density in the manner depicted? Are the cal mechanisms that control population size. movement rules in the model correct?Are the A full discussion of the decision-theoretic measuresand correlatesused to estimateannual approach and its uses in the adaptive manage- variation in fecundity sufficient?Indeed, some ment process is beyond the scope of this review. models are too appealing.Increasingly, modelers However, it is apparentthat these methods will must caution field biologists about their reliance be more commonly used in the future (Clark on complex models that incorporategreat bio- 2005). Hilborn and Mangel (1997), Burnham logical detail, whereas field biologists previously and Anderson (2002),and particularlyWilliams cautionedmodelers about their relianceon mod- et al. (2002) provide a good introduction to els that were too simple biologically. these methods. Collaboration between field biologists and modelers is often a necessity for effective How Field Biologists Can Interact with conservation. Field biologists need modelers Modelers to ImproveConservation Decisions to depict what they know about a system in an appropriate way within a formal framework. Ecology has been described as a science of Modelers need field biologists to provide data case studies and rough generalizations rather necessary for parameterization,to test whether than of general theory and exceptionless processes incorporatedin the model are correct, empirical laws (Shrader-Frechetteand McCoy and to perform model validation. A model can 1993).Despite the heuristic power of an ecologi- guide collection of data and testing of mecha- cal perspective, there is little general theory to nisms. Data can guide selection of the most provide policy-related predictions. Given the appropriatemodel and determine the appropri- imprecisionof ecological theory,it offers limited ate level of complexity (Burnhamand Anderson guidance to adjudicate public conflicts over 2002). Facilitating the link between modelers conservation decisions. Conflict will remain and field biologists are the statisticians. They part of conservation practice as long as divi- play an essential role in designing methods of sions continue in society over the importance data collection and analyses needed to estimate of biological diversity,our ethical responsibility parametersand comparemodel predictionswith to future human generations, and the severity observed outcomes. Field biologists can remind of the conservation crisis. In an arena where modelers, statisticians,and policy makersof the consensus is difficult, any tools that allow us weaknesses of particularmodels. Modelers and to project the possible consequences of pres- statisticians can indicate to field biologists the ent decisions should be fully exploited. The deficiencies in existing data. Productive col- diversity and complexity of models employed laborationsof this sort involving one or more of in avian conservationis increasing rapidly, and the authors have promoted conservationefforts their applicationis becoming more widespread. with Northern Spotted Owls, Red-cockaded Use of models in avian conservationmay not Woodpeckers, Marbled Murrelets, Snail Kites, be a panacea, but neither is it a passing fancy. and Florida Scrub-Jays. Field biologists can Thus, modelers and field biologists are becom- make great contributions to conservation by ing increasingly dependent on one another to participatingin such collaborations. achieve effective conservation. A frequent theme of this monograph has The evolution of models during the era of been the onerous data requirements of new, the personal computer- from limited ability to complex types of models. The constructionand incorporatecomplex biological details to spatial application of population models for inform- and mechanistic models that assume detailed ing conservation decisions has been greatly knowledge of an animal's behavior- promotes hindered by the paucity of species that have synergy between modelers and field biologists. received long-term field studies of population Mechanistic models that incorporate more dynamics (Shafferet al. 2002), and by the lack

This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions MODELS IN AVIAN CONSERVATION 41 of standards and a repository for demographic from presence-absence data collected in field databases. In the case of population models surveys. Validation of population models and (e.g. spatially explicit models, metapopula- genetic models is more problematic.Population tion models, and stochastic single-population projections resulting from stochastic single- models), the information required consists population, metapopulation, and spatially largely of typical demographic and behavioral explicit population models are difficult to vali- data collected by field biologists. However, the date directly,but one can test various secondary specificity of informationrequired (e.g. age- or predictions of the models to evaluate their gen- stage-specificdemographic rates estimated with eral performance.For example, an SEPMmight respect to landscape characteristics),the dura- predict the proportion of young produced on tion of time needed to produce accurate vari- a territory that are recruited into the breeding ance estimatesfor vital rates, and the difficulties population to be a function of territory isola- inherent in accuratelyestimating survival rates tion, a prediction that could readily be tested. If make large sample sizes and long-term field such a prediction proved false, it might indicate studies a necessity. Furthermore,some types that a simpler (i.e. not spatially explicit) model of data required by new population models is sufficient to capture the dynamics of the pop- have rarely been collected, notably information ulation. Applying the models to real landscapes about dispersal and movement behavior.When to compare simulated and observed population incorporatedinto models, estimates of dispersal dynamics may be especially instructive in this parameters are typically based on little or no regard (e.g. Lindenmayer et al. 2003, Schiegg data. Again, the burden is on field biologists to et al. 2005). Sensitivity analysis is also useful in produce these data if the predictive ability of directing attentionto the parametersthat matter models is to be improved.Finally, use of increas- most to model performance.For complex mod- ingly more mechanisticmodels results in further els, identifying important variables to improve demands on field biologists to provide new model accuracyand to guide field studies is the kinds of data and experimentallyconfirm pos- most significantuse of sensitivity analysis. tulated mechanisms. Particularlyimportant is Models can be useful tools for field biolo- informationabout variationin vital rates, espe- gists, as well as managers, if employed wisely. cially as it relates to annual variation,variation Parameter estimates for complex models are with habitat type, and variationwith landscape typically too poor, and our understanding of features(e.g. proximityto edge). Field biologists nature too incomplete, to permit one to have need to keep potentially important sources of much faith in specific predictions, such as variation in mind when designing their sam- the number of years it will take a population pling scheme and analyzing their data. to become extinct, or the size of a population All models have key assumptions. Complex 50 or 100 years into the future. But models models may often make fewer simplifying can be used to ask whether, given our current assumptions than simple models, but they understanding of the system as depicted in demand more data. The validity of basic sim- the model, a population will persist longer, or plifying assumptions is an importantissue with be larger, under one management approach species distribution models and deterministic than under another (Beissinger and Westphal matrix population models. Key assumptions 1998, McCarthy et al. 2003, Lotts et al. 2004). about dispersal patterns and mortality associ- Ideally,these assessments would then be tested ated with movement plague metapopulation through an adaptive management process and spatially explicit models. In these cases, (Walters 1986, Ludwig and Walters 2002). The field biologists can make majorcontributions by best conservation decisions will occur where collecting data to test key model assumptions. cooperative interactionenables field biologists, Validation is a major issue for most of the modelers, statisticians, and managers to con- models discussed. Models can be validated by tribute effectively. testing primary (e.g. population projections)or secondary (e.g. dispersal distributions) predic- Acknowledgments tions, or by evaluating the ability of the model to replicate past system behavior (Bart 1995). We are greatly indebted to C. Thompson and Species distribution models can be validated V. Nolan, Jr., for encouragement and numerous

This content downloaded on Thu, 10 Jan 2013 15:46:37 PM All use subject to JSTOR Terms and Conditions 42 ORNITHOLOGICALMONOGRAPHS NO. 59 editorial improvements of the work leading to environment: A theory and an example. this publication. S.R.B. acknowledges the National Ecology 56:1281-1297. Science Foundation for grant support; the American Anderson, R. P., D. Lew, and A. T. Peterson. 2003. Ornithologists' Union for providing the venue for Evaluating predictive models of species' distri- the symposium that catalyzed this monograph; and butions: Criteria for selecting optimal models. G. White, B. Noon, and the Department of Fishery Ecological Modelling 162:211-232. and Wildlife Biology at ColoradoState University for Andren, J. 1994. Effects of habitat fragmentation hospitality and office space during the final revisions on birds and mammals in landscapes with of this work. K.G.S.and D.G.C. thank the hundreds different proportions of suitable habitat: A of people involved with the Arkansas Gap Analysis review. Oikos 70:355-366. project (www.cast.uark.edu/gap). Their research Arino, A., and S. L. Pimm. 1995. On the nature of was conducted at the Center for Advanced Spatial population extremes. Evolutionary Ecology 9: Technologiesat the University of Arkansas,which is 429-443. directedby W. F.Limp. R. Dzur was especially helpful Avise, J. C, and J. L. Hamrick. 1996. Conservation with that project.Funding for this research and par- Genetics: Case Histories from Nature. ticipation in the symposium was provided through Columbia University Press, New York. the ArkansasCooperative Fish and Wildlife Research Ballou, J. D., and R. C. Lacy. 1995. Identifying Unit by U.S. Fish and Wildlife Service award number genetically important individuals for manage- 14-16-0009-1567,W013 to K.G.S.and W F. Limp. 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