Ecological Modeling in Risk Assessment - Chapter 5 docx

These include: • Deterministic age- or stage-based matrix models Caswell 2001 • Stochastic age- or stage-based matrix models Caswell 2001 • RAMAS®* Age, Stage, Metapop, or Ecotoxicology

© 2002 by CRC Press LLC

Population Models — Life History Steve Carroll

Life-history models track characteristics of organisms as a function of age or stage Stages can be defined by size, morphological state, or any classifying variable deemed to be demographically important The most common characteristics that are tracked in such models are survival rates and

fecundities, collectively referred to as vital rates The typical endpoints for life-history models are:

• Population abundance

• Abundances of individual age or stage classes

• Population growth rate or related parameters (e.g., sensitivity, elasticity)

Life-history models are important for several reasons In many populations, survival probabil-ities and fecundprobabil-ities vary among age or stage classes, and toxic chemicals may affect the various classes differently The predictions made on the basis of life-history models generally differ from those made on the basis of simple population models in which individuals are assumed to be identical Life-history models allow the exploration of age-specific or stage-specific management options

For the purposes of this review, matrix models were classified into four categories, with the last two representing software implementations of the first two (Table 5.1) These include:

• Deterministic age- or stage-based matrix models (Caswell 2001)

• Stochastic age- or stage-based matrix models (Caswell 2001)

• RAMAS®* Age, Stage, Metapop, or Ecotoxicology (Ferson 1993; Spencer and Ferson 1997b,c; Applied Biomathematics 2000)

• ULM (unified life model) (Legendre and Clobert 1995)

For an in-depth treatment of matrix population models, see Caswell (2001) Density dependence,

or the lack thereof, is not explicit in this classification scheme Thus, within a category, both density-dependent and density-indensity-dependent models are included

DETERMINISTIC MATRIX MODELS (AGE OR STAGE BASED)

These models assume that survival rate and fecundity are functions of the age class or stage to which an organism belongs Age- and stage-structured models have been important tools in natural

* RAMAS is a registered trademark of Applied Biomathematics.

1574CH05.fm Page 55 Tuesday, November 26, 2002 4:55 PM

P

Table 5.1 Internet Web Site Resources for Life-History Models

Model Name Description Reference Internet Web Site

Deterministic age- or

stage-based matrix

models

Life-history matrix models with fixed fecundity and survivorship parameters

Caswell (2001) http://www.ramas.com/ramas1.htm;

http://www.ento.vt.edu/~sharov/PopEcol/lec7/

leslie.html;

http://www.ets.uidaho.edu/wlf448/Leslie1.htm Stochastic age- or

stage-based matrix

models

Life-history matrix models incorporating random variability in fecundity and survivorship parameters

Caswell (2001) http://www.ramas.com/ramas1.htm

RAMAS Age, Stage,

Metapop, or

Ecotoxicology

Software for life-history modeling of age- or stage-structured populations

Ferson (1993); Spencer and Ferson (1997b,c); Applied Biomathematics (2000)

http://www.ramas.com/

ULM (unified life model) Software for life-history modeling of age- or

stage-structured populations

Legendre and Clobert (1995) http://www.snv.jussieu.fr/Bio/ulm/ulm.html

http://eco.wiz.uni-kassel

de/model_db/mdb/ulm.html

© 2002 by CRC Press LLC

resource management, especially for fish, since the 1950s (Barnthouse 1998) The simplest life-history model of this type is the Leslie population projection matrix (Leslie 1945):

N(t) = LN(t – 1) where N(t) and N(t − 1) are vectors of the numbers of organisms in each age class (N0, Nk)

L =

where

sk = age-specific survivorship probability

fk = average fecundity at age k Life stages, when not defined by age, are generally defined by size (height, weight, etc.) or morphological state Individuals within a given age class or stage are assumed to have identical survival probabilities and fecundities It is assumed that the vital rates do not vary as a result of random environmental fluctuations or demographic stochasticity Depending on whether or not density dependence is included, the vital rates may vary (deterministically) as a function of population size The vital rates, which comprise the population matrix, can be obtained either from laboratory experiments or from field observations

Realism — HIGH — These models reflect that vital rates generally change with age In many cases,

they incorporate all available demographic data because measures of variability in vital rates are often unavailable Within this category of models, age- or stage-structured models with density dependence are more realistic than those without it

Relevance — HIGH — Potential endpoints include expected population size (age specific), lambda

(the asymptotic population growth rate), or lambda-based measures such as sensitivity and elasticity All of these endpoints are relevant to ecotoxicological assessments Survivorship and fecundity parameters can be adjusted to reflect the effects of toxic chemicals observed in laboratory tests (e.g., Munns et al 1997)

Flexibility — HIGH — All parameters are species-specific The number of age classes, as well as the

vital rates, can vary among populations Therefore, different population structures and life histories can be modeled

Treatment of Uncertainty — LOW — Neither environmental nor demographic stochasticity is

incor-porated in the basic approach However, generalizations are being developed to deal with

environ-mental stochasticity (e.g., see below Stochastic Matrix Models and Caswell 2001).

Degree of Development and Consistency — HIGH — Several software programs implement this

model type, and documentation and technical support are available Understanding the workings of the model is relatively easy

Ease of Estimating Parameters — MEDIUM — Parameters can in principle be obtained relatively

easily, either from laboratory experiments or from field observations Alternatively, fecundity and survivorship values may be approximated from standard survivorship and birth rate curves in the literature However, particularly when laboratory experiments are not appropriate or feasible, assess-ing the magnitude of chemical effects on each vital rate may be very difficult

Regulatory Acceptance — HIGH — The model is being used by several regulatory agencies.

Credibility — HIGH — The model type is well known within academia Many applications of the

model exist

Resource Efficiency — HIGH — Application of the model requires no programming because software

is available In many cases, available data are sufficient However, when available data are not sufficient, considerable effort may be needed to obtain new data

1574CH05.fm Page 57 Tuesday, November 26, 2002 4:55 PM

1 2

k

L L L L L

































© 2002 by CRC Press LLC

STOCHASTIC MATRIX MODELS (AGE OR STAGE BASED)

Like the deterministic age- or stage-based matrix models, these models assume that survival rate and fecundity are functions of the age class or stage in which an organism resides In contrast with their deterministic counterparts, the stochastic models incorporate environmental or demographic stochasticity or both in the estimates of survival probabilities and fecundities (Caswell 2001) Depending on whether density dependence is included, the vital rates may vary as a function of population size The vital rates, which comprise the population matrix, can be obtained either from laboratory experiments or field observations

Realism — HIGH — In addition to reflecting that vital rates generally change with age (or stage),

these models recognize that the rates may also vary as a result of random environmental fluctuations and demographic stochasticity They generally incorporate all available demographic data Within this category of models, age- or stage-structured models with density dependence are more realistic than those without it

Relevance — HIGH — Possible endpoints include expected population size (age- or stage-specific),

risk of decline, risk of extinction, and expected crossing time (the time at which the population is expected to go either above or below a given size) These measures are all relevant to ecotoxicological assessments As the deterministic version of this model, the survivorship and fecundity values can

be adjusted to reflect the effects of toxic chemicals observed in laboratory tests

Flexibility — HIGH — All parameters are species-specific The number of age classes or stages, the

vital rates, and the variation in the vital rates can vary among populations Therefore, different population structures and life histories can be modeled

Treatment of Uncertainty — HIGH — Both environmental and demographic stochasticity can be

incorporated

Degree of Development and Consistency — HIGH — Several software programs implement this

model type, and documentation and technical support are available It is relatively easy to understand the workings of the model

Ease of Estimating Parameters — MEDIUM — Required parameters include average vital rates and

their standard deviations Furthermore, chemical impact on these parameters must be considered (this can be handled, for example, by estimating two matrices — one with toxins and one without toxins) Obtaining estimates of all such parameters can often be quite difficult However, model parameters are intuitive and can be interpreted biologically

Regulatory Acceptance — HIGH — The model is used by several regulatory agencies.

Credibility — HIGH — The model is well known within academia There are many applications of

the model

Resource Efficiency — MEDIUM — Application of the model requires no programming, as software

is available In some cases, data must be collected, but in many cases, available data are sufficient

RAMAS AGE, STAGE, METAPOP, OR ECOTOXICOLOGY

These four computer programs (Spencer and Ferson 1997b; Ferson 1990; Ferson and Akçakaya 1988; Akçakaya 1998b) are collapsed into one category because they share a common source and they receive the same ratings Each program applies matrix models for age- or stage-structured populations to estimate population-level parameters such as growth rate and extinction risk

In RAMAS Ecotoxicology, a model of population dynamics and toxicant kinetics can be constructed and linked to bioassay data Using this program, a modeler can import data from standard laboratory bioassays, incorporate these data into the parameters of a population model, and perform a risk assessment by analyzing population-level differences between potentially affected and control samples The user specifies the control survivorship and fecundity for each age class or stage Density dependence in the form of ceiling, logistic, Ricker, or Beverton–Holt functions can be added for specific age classes or stages A user simulates toxic effects by selecting

© 2002 by CRC Press LLC

and parameterizing dose–response models (Weibull, probit, or logit) linked to survivorship and fecundity values Parameters can be specified as scalars, intervals, or distributions to account for environmental variability and uncertainty Monte Carlo simulations are then used to predict future population trajectories and calculate the risk of adverse events such as extinctions or algal blooms The software checks the validity of the data input and model structure specified by the user

Realism — HIGH — RAMAS Age models age-structured populations, and RAMAS Stage models

stage-structured populations RAMAS Metapop can model either age-structured or stage-structured populations RAMAS Ecotoxicology can also model either age-structured or stage-structured pop-ulations and can also explicitly model the effects of toxic chemicals All four programs can include density dependence as well as environmental and demographic stochasticity

Relevance — HIGH — Possible endpoints include expected population size (stage-specific), lambda,

lambda-based measures such as sensitivity and elasticity, risk of decline, risk of extinction, and expected crossing time (the time at which the population is expected to exceed or to decrease to less than a given size) These measures are all potentially useful in ecotoxicological assessments Effects of toxic chemicals are not explicitly modeled but can be incorporated by adjusting survivor-ship and fecundity values to reflect toxic effects (e.g., Munns et al 1997)

Flexibility — HIGH — All parameters are species-specific The number of age classes or stages, the

vital rates, and the variation in the vital rates can vary among populations Therefore, different population structures and life histories can be modeled In RAMAS Ecotoxicology, different toxic chemical dynamics and dose–response functions can be modeled

Treatment of Uncertainty — HIGH — Both environmental and demographic stochasticity can be

incorporated

Degree of Development and Consistency — HIGH — These models are easy to use and easy to apply

to different populations Each program has a detailed user’s manual explaining the scientific basis

of the model as well as the capabilities of the program The programs include several internal checks for consistency

Ease of Estimating Parameters — MEDIUM — Required parameters include vital rates at the very

least In some cases, average vital rates and their standard deviations need to be estimated Further-more, the chemical impact on these parameters may need to be considered (e.g., by choosing and parameterizing a dose–response function or by estimating two matrices — one with toxins and one without toxins) Obtaining estimates of all such parameters can often be quite difficult Thus, ease

of parameter estimation varies among cases However, model parameters are intuitive and can be interpreted biologically

Regulatory Acceptance — HIGH — These models are being used by several regulatory agencies Credibility — HIGH — These models are widely used within academia Many applications of the

models exist

Resource Efficiency — HIGH — No programming is necessary to use these programs In some cases,

data must be collected, but in many cases, available data are sufficient

UNIFIED LIFE MODEL (ULM)

ULM (Legendre and Clobert 1995) is a computer program that implements deterministic or stochastic matrix models for analysis of population dynamics ULM is somewhat similar to RAMAS, except for its interface and varied capabilities ULM accommodates a wide range of populations with variable life-history characteristics ULM can model any species life history as

a matrix model with or without density dependence, environmental stochasticity, demographic stochasticity (as branching processes), inter- or intra-specific competition, parasitism, and metap-opulations Results are expressed as population trajectories, distributions, growth rate, population stage- or age-structure, generation times, sensitivities to changes in parameters, probability of extinction, and extinction times The stochastic models within ULM are implemented as Monte Carlo simulations

1574CH05.fm Page 59 Tuesday, November 26, 2002 4:55 PM

© 2002 by CRC Press LLC

Realism — HIGH — ULM models age-structured and stage-structured populations The number of

age classes or stages is variable Environmental stochasticity is included

Relevance — HIGH — Possible endpoints include expected population size (age- or stage-specific),

lambda, lambda-based measures such as sensitivity and elasticity, and risk of extinction These measures are all used in ecotoxicological assessments

Flexibility — HIGH — All parameters are species-specific The number of age classes or stages, the

vital rates, and the variation in the vital rates can vary among populations Therefore, different population structures and life histories can be modeled

Treatment of Uncertainty — HIGH — Environmental stochasticity can be incorporated.

Degree of Development and Consistency — MEDIUM — Some programming is required to use the

model This programming must use a language defined by the authors of the program Legendre and Clobert (1995) explain the use of the model and provide examples

Ease of Estimating Parameters — HIGH — Parameters can be obtained relatively easily, either from

laboratory experiments or field observations

Regulatory Acceptance — LOW — No information on the model’s regulatory acceptance is available

The model is not likely to be used by a regulatory agency at present because programming is required

to use the model

Credibility — MEDIUM — Several (approximately 20) publications apply the model to different cases Resource Efficiency — MEDIUM — Some programming is necessary to use this program In some

cases, data must be collected, but in many cases available data are sufficient

DISCUSSION AND RECOMMENDATIONS

Life-history models (Table 5.2) are well developed and are already being used for ecotoxicological assessment (Levin et al 1996; Munns et al 1997; Crutchfield and Ferson 2000) (Table 5.3; also see Barnthouse [1993] for a review of other applications) These models have already been gener-alized to be spatially explicit within a metapopulation framework (RAMAS Metapop) and to explicitly include the dynamics and effects of toxic chemicals (RAMAS Ecotoxicology) Deter-ministic and stochastic matrix models and RAMAS Age, Stage, Metapop, or Ecotoxicology are therefore recommended for further evaluation and use in chemical risk assessment Suggested future developments include development of software that includes both spatially explicit effects and the dynamics/effects of toxic chemicals Software should be developed for calculating risk-based

(probabilistic) sensitivities with respect to vital rates to answer questions such as How does the probability of decline change as a result of changes in the vital rates? This method would be an

adaptation of the results of Uryasev (1995) This development would allow the conversion of sensitivity-based methods, such as decomposition of the change in lambda, into the language of risk Such sensitivity-based applications are used to identify age-specific or stage-specific manage-ment strategies The new methods will generalize widely used methods of lambda decomposition (Caswell 2001)

© 2

Table 5.2 Evaluation of Population Models — Life History Models

Evaluation Criteria

Model Reference Realism Relevance Flexibility

Treatment

of Uncertainty

Degree of Development

Ease of Estimating Parameters

Regulatory Acceptance Credibility

Resource Efficiency

Deterministic age- or

stage-based matrix

Stochastic age- or

stage-based matrix

RAMAS Age, Stage,

Metapop, or

Ecotoxicology

Ferson (1993);

Spencer and Ferson (1997c); Applied Biomathematics (2000)

Unified life model

Note: ◆◆◆ - high

◆◆ - medium

◆ - low

© 2002 by CRC Press LLC

Model Species Location/Population Reference

Deterministic age-based matrix Burrowing mayflies,

Hexagenia spp.

(H limbata and

H rigida)

Western Lake Erie Madenjian et al

(1998)

Subtidal snail

(Umbonium costatum)

Hakodate Bay, northern Japan

Noda and Nakao (1996)

Mysid (Americamysis

bahia)

Laboratory Kuhn et al (2000) Pea aphid

(Acyrthosiphon pisum)

Laboratory Walthall and Stark

(1997) Northern sea lions

(Eumetopias jubatus)

Marmot Island, Alaska

York (1994) Deterministic age-based matrix and

deterministic stage-based matrix

Polychaetes (Capitella

benedicti)

Estuaries and littoral wetlands throughout much of the United States

Levin et al (1996)

Deterministic stage-based matrix Pea aphid

(Aeyrthosiphon pisum)

Laboratory Stark and

Wennergren (1995)

Soil mite (Platynothrus

(Porcellio scaber), and nematode (Plectus

acuminatus)

Laboratory Kammenga et al

(2001)

Bluegill sunfish

(Lepomis

macrochirus)

Generic lake in central Florida

Bartell et al (2000)

Brook trout (Salvelinus

fontinalis)

Southern Appalachian mountain streams

Marschall and Crowder (1996) Estuarine fish

(Fundulus

heteroclitus)

New Bedford Harbor, Massachusetts

Munns et al (1997)

Loggerhead sea turtles

(Caretta caretta)

Trawl fisheries of the southeastern United States

Crowder et al (1994)

Yellow mud turtles

(Kinosternon

flavescens) and

Kemp's ridley sea

turtles (Lepidochelys

kempi)

Texas Heppell et al (1996)

Killer whales (Orcinus

orca)

Pacific Northwest Brault and Caswell

(1993) Savannah grass

(Andropogon

brevifolius Schwarz)

Venezuelan savannas Canales et al (1994)

Deterministic stage-based matrix and

stochastic stage-based matrix

Snail kite (Rostrhamus

sociabilis)

Everglades Beissinger (1995)

House sparrow (Passer

domesticus)

India, Pakistan Slade (1994) Steller sea lion

(Eumetopias jubatus)

Northeast Pacific Pascual and Adkinson

(1994) American ginseng

(Panax quinquefolium) and wild leek (Allium

tricoccum)

Canada Nantel et al (1996)

Mountain golden

heather (Hudsonia

montana)

North Carolina Gross et al (1998)

Stochastic age-based matrix Brook trout (Salvelinus

fontinalis)

Montmorency County, Michigan

McFadden et al (1967)

Striped bass (Morone

saxatilis)

Potomac River Cohen et al (1983)

© 2002 by CRC Press LLC

Hawaiian stilt

(Himantopus

mexicanus knudseni)

Hawaii Reed et al (1998)

Mediterranean monk

seal (Monachus

monachus)

Atlantic Ocean (North Africa) and eastern Mediterranean

Durant and Harwood (1992)

Roan antelope

(Hippotragus equinus)

Parc National de l'Akagera in Rwanda

Beudels et al (1992)

Asiatic wild ass (Equus

hemionus)

Negev Desert of southern Israel

Solbreck (1991); Saltz and Rubenstein (1995)

African elephant

(Loxodonta africana)

Tsavo National Park, Kenya

Armbruster and Lande (1993) Stochastic stage-based matrix Algae (Ascophyllum

nodosum)

Swedish coast Aberg (1992)

Marine bivalve (Yoldia

notabilis)

Otsuchi Bay, northeastern Japan

Nakaoka (1997) Sea whip coral

(Leptogorgia virgulata)

Northeastern Gulf of Mexico

Gotelli (1991)

Grey seal (Halichoerus

grypus) and ringed

seal (Phoca hispida)

Baltic Sea Kokko et al (1997)

Desert tortoise

(Gopherus agassiz)

Western Mojave Desert

Doak et al (1994)

Red deer (Cervus

elaphus)

Rum, Western Isles, Scotland

Benton et al (1995)

Redwood (Sequoia

sempervirens)

California, Oregon Namkoong and

Roberds (1974)

machrochirus)

Hyco Reservoir, North Carolina

Crutchfield and Ferson (2000)

Striped bass (Morone

saxatilis)

Santee-Cooper system, South Carolina

Bulak et al (1995)

Marbled murrelet

(Brachyramphus

marmoratus)

of Fish and Wildlife (1995)

RAMAS Ecotoxicology Brook trout (Salvelinus

fontinalis)

Montmorency County, Michigan

Spencer and Ferson (1997b)

Lesser kestrel (Falco

naumanni)

Southern Spain Spencer and Ferson

(1997b)

Moose (Alces alces

gigas)

Northeastern Alberta Spencer and Ferson

(1997b) RAMAS Stage Giant kelp (Macrocystis

pyrifera)

Southern California coastal waters

Burgman and Gerard (1989)

Bluegill sunfish

(Lepomis

macrochirus)

North Carolina Crutchfield and

Ferson (2000) Threadfin shad

(Dorosoma

petenense)

South Carolina Barwick et al (1994)

Red-cockaded

woodpecker (Picoides

borealis)

Georgia Piedmont Maguire et al (1995)

Bradshaw’s lomatinum

(Lomatium

bradshawii)

Western Oregon Kaye et al (1994)

Sentry milk-vetch

(Astragalus

cremnophylax)

Grand Canyon National Park, Arizona

Maschinsky et al (1997)

ULM — stochastic stage-based

matrix

Grey partridge (Perdix

perdix)

Northwest and southeast France

Bro et al (2000)

1574CH05.fm Page 63 Tuesday, November 26, 2002 4:55 PM

© 2002 by CRC Press LLC

ULM — deterministic stage-based

matrix

Yellow-legged gull

(Larus cachinnans)

Medes Islands, northwestern Mediterranean

Bosch et al (2000)

ULM — stochastic stage-based

matrix

Passerine songbirds User defined Legendre (1999) ULM — deterministic stage-based

matrix and stochastic stage-based

matrix

Snake (Vipera ursinii

ursinii) and raptor

(Gyps fulvus fulvus)

User defined Ferriere et al (1996)