Coastal and Estuarine Risk Assessment - Chapter 11 ppt

Methods for the derivation of these probability density functions can be found in Efron and Tibshirani.2 11.2.1.1 Mercury Concentration in Fish P[C]i|F i distribution of mercury concentr

Structuring Based Ecological

11.2.1.3 Spatial Function11.2.1.4 Toxicity Response Function11.3 Population-Based Risk Characterization11.3.1 Population Modeling for the Great Blue Heron11.3.2 Characterization of Population Dynamics11.4 Discussion

References

11.1 INTRODUCTION

Ecological risk assessment is not a purely scientific endeavor Rather, it is mostcommonly applied as an exercise in regulatory compliance intended to illustrateobjectively demonstrable harm (or lack thereof) as the result of identified humanactivities Legal guidance is limited to very broad directives requiring the protection

con-tentious Risks to individual plants or animals are the easiest types of impacts toidentify However, within the context of providing protection to the environment,the magnitude of individual impacts may very well represent inconsequential11

events Therefore, the characterization of harm may be misrepresented if limitedsolely to the individual Simple and transparent (i.e., easy to understand and repli-cate) methods should be developed for application in a regulatory context to expandthe scope of ecological risk assessments to the level of spatially defined subpopu-lations and populations, in order to determine whether an activity or activities inquestion actually represent an unacceptable risk within the legal context of envi-ronmental protection.

This chapter examines a probabilistic method of population-level ecological riskassessment It is intended for application within the regulatory context of a remedialinvestigation under the Comprehensive Environmental Response, Compensation andLiability Act (CERCLA) It describes a risk assessment in terms of impact on

herodias) exposed to methylmercury from fish taken as prey from an inland lake inthe northeastern United States Although the lake and its surrounding environs wereused to parameterize both the risk model and the later-discussed heron populationdynamics model, it was necessary to assume higher mercury concentrations in fishand other media than those measured in the lake to demonstrate certain attributes

of both models Therefore, the lake and the results of this assessment are ical This being the case, the general approach described herein is relevant to marinesystems as well as freshwater systems

hypothet-To describe the impact of this hypothetical exposure, two separate but nected models were developed The first was a probabilistic risk assessment used toestimate the proportional population impact resulting from methylmercury exposure.The second was a population dynamics model to describe the risk estimates in terms

intercon-of their impacts on the stability intercon-of the exposed heron subpopulation The goal is toprovide an approach that may be applied within a regulatory context to betterillustrate the results of an ecological risk assessment in terms that may be quantita-tively applied to evaluate environmental protection

11.2 ECOLOGICAL RISK ASSESSMENT MODEL

The objective of the assessment component of this analysis was to express the impact

of individual exposures to a toxic contaminant in terms of the risk to receptorpopulations To determine the overall impact of all potential individual responses,

it was necessary to quantify the probability of every possible response occurringwithin the exposed population The paradigm used to characterize risk is the same

where risk (r) is expressed as the ratio of the exposure rate (e) to the expectedexposure-dependent response (T):

(11.1)

In ecological risk assessment, the underlying assumption is that there is no risk

of an adverse impact if the rate of exposure of a receptor is less than a defined

r  T -e

response threshold However, if the exposure exceeds the threshold, as indicated by

an r value greater than 1, then a risk exists that the response ascribed to T will occur

If it is assumed that the risk to be characterized is the result of the exposure of

a receptor to a toxic contaminant (C) that is found in an environmental medium F,then the risk paradigm can be expressed as a model where the risk of a receptor isestimated as the product of its exposure rate (ER) and the contaminant concentration

in the medium of exposure ([C]F), divided by the dose-dependent response thresholdfor C(TC) Hence, a generic risk model can then be expressed as follows:

(11.2)

If the risk is to be characterized for a group or population of individuals, thenneither the exposure rate of the receptor, nor the contaminant concentration of themedium, nor the dose-dependent response of the receptor is an absolute value Eachvariable parameter possesses a distribution of possible values within the exposedpopulation, and from observations of the relative frequency of occurrence, a prob-ability function for risk can be discerned The relation between a parameter valueand its probability of occurring is referred to as a probability density function Torepresent this, the variables must be expressed as probability density functions(generically denoted as D(x), where x represents the independent variable for thefunction), which is the integral of potential occurrences of all possible parametervalues for the exposed population (generically denoted as P(x), where x representsthe parameter for which the probability is expressed) Hence, the generic risk modelcan be expressed as follows:

Solving the probability function for risk (D(r)) can be accomplished either by

techniques When using Monte Carlo techniques, the probability of risk is determinedusing the pooled estimated probabilities associated with the parameters of the model

population, N, as follows:

(11.4)

the probability for all concentrations of contaminant C within medium F, the

simultaneous situations, and the probability of all possible dose-dependent responses

to C by the receptors Hence, the risk function is now defined as a probability densityfunction D(r) for the characterization of risk

11.2.1 R ISK M ODEL P ARAMETERIZATION

The generic risk model derived above was parameterized to predict the risk to a

population of great blue herons exposed to methylmercury in fish from a lake Most

of the eastern and southern shore of the lake has been developed for either urban

or suburban uses The western shore remains largely undeveloped and provides

habitat to numerous avian and mammalian species Its shallow sloping banks and

moderate bank cover make it excellent heron foraging habitat, and herons are

commonly observed during the warm-weather seasons

The exposure received by a population of receptors is not simply related to the

distribution of the contaminant (C) in the entire medium, but rather to the

concen-tration of C in the constituents of medium F that the receptors contact directly In

situations where such distinctions may be made within a medium, the probability

of exposure to a subcomponent of F (F iof known [C]) across the range of all possible

exposures (F i to F i) as follows:

The relationship P([C]i|F i) is the probability of encountering a specific

for further explanation of such conditional probabilities.) This may represent

empirical distributions such as time spent in a specific location, or may be used

to distinguish between the probability of ingesting specific prey items Methods

for the derivation of these probability density functions can be found in Efron

and Tibshirani.2

11.2.1.1 Mercury Concentration in Fish P([C]i|F i)

distribution of mercury concentrations used in the risk model was based on the

likelihood observed for the distribution of mercury concentrations in individual fish

(F i) from the lake, and the likelihood that a fish would be preyed upon by a heron

Likelihood, in this context, is defined as a past probability (i.e., observed) based on

reported distributions

The mercury distribution was determined empirically from data collected from

the lake in 1992 The probability that a sampled fish, containing a known

as the product of the likelihood (L) of the heron selecting that size of fish (prey),

and the likelihood of that species of fish being available from the lake (available)

Therefore, the probability that any individual heron would ingest a fish represented

by size and species by a specific sampled fish can be expressed as follows:

The likelihood that a fish would be prey for the heron was determined from

prey is fish ranging from 3 to 33 cm in length Proportional dietary content based

on fish size was reported from the survey to be 8, 40, and 52% for fish 3 to 7, 7.1

to 14, and 14.1 to 33 cm, respectively The sampled fish were ranked according to

size Sampled fish outside the range of 3 to 33 cm were excluded The remainders

were classed into three cohorts based on the above size ranges and L(prey) for each

sampled fish was then determined as follows:

(11.7)

P c is the proportion that the cohort represents in the heron’s diet, and n c is the number

of sampled fish in that cohort

The likelihood that a sampled fish is available as prey for the great blue heron

is dependent on the abundance of that species in the lake Because the fish samples

were not random with regard to fish species, abundance within the sample cannot

be assumed to be representative However, overall abundance statistics were available

from lake surveys Therefore, the L(available) for any fish in the sampled group was

deemed proportional to the abundance of that species, within each size cohort,

throughout the entire lake (A t) Only fish species typically available to the heron

were considered Deepwater species that are not available for prey were excluded,

as were fish determined to be either too large or too small to constitute heron prey

To control for bias in the sample due to disproportional representations of fish species

defined as follows:

(11.8)

Assuming that size selection by the heron was independent of species abundance

in the lake, the product of these two likelihoods defines the probability of selection

(P(F i)) Therefore, the probability of the heron’s exposure to a given concentration

of mercury could be derived as follows:

(11.9)

The estimate of the probability density function across all potential prey fish

(D([Hg] i |F i)) was determined by bootstrapping (with replacement) the sampled

mer-cury data using the individual P(F i) values as the metric of probability for selection

Each mercury observation was assigned a probability of occurrence based on the

above likelihood The mercury concentrations were then selected with replication

based on the probability assigned to derive a probability distribution of potentialexposures A more detailed discussion of this method is available in Chapter 24 of

the probability density function (D([Hg]i|Fi), illustrated in Figure 11.1

11.2.1.2 Heron Exposure Rate (P(ER))

The dietary intake rate (IR) for the great blue heron may also be described as aprobability density function Unfortunately, there is rarely a sufficient record ofempirical observations to develop an adequate distribution for this parameter directly.However, since the dietary requirements of the heron are related to its energydemands, it is possible to model the dietary requirements based upon a metric for

equa-tion, specifically for wading birds, by regressing a series of observed dietary intakerates against the paired body masses (BW) for the birds An estimation for thedistribution of body masses for the great blue heron population has been developed

herons from the northeastern United States, it was found that the distribution of thisparameter conformed to a normal distribution with an average mass (BW) of 2300 g

1600 and 3000 g, respectively The model was truncated to disallow values greaterthan or less than the minimum and maximum parameters The variance used remainedunchanged By substituting the allometric relationship, the exposure rate functionwas parameterized based on the distribution in the heron’s body mass as follows:

(11.10)

FIGURE 11.1 Reverse cumulative probability density function for mercury exposure

con-centrations for the great blue heron from lake fish.

11.2.1.3 Spatial Function

The great blue herons found in this area are migratory Although they do nest in thisregion, they winter in the lower Mississippi Valley, the Gulf Coast, and the SouthernAtlantic seaboard.6 Therefore, herons are not present on the lake for a large part of

a year Within its breeding range, the great blue heron may be either colonial orsolitary, depending on its location and situation Herons in this area tend to be solitarynesters, and will establish and defend a nesting territory.6 Great blue herons are mostlikely to be found hunting near their nesting sites, but may range as far as 24 kmduring daily feeding forays.7,8

Because there are two considerations affecting the foraging behavior of theexposed heron population, one for migration and one for local foraging use, twospatial functions had to be developed to control for the heron’s feed locations The

first function was modeled as a temporal parameter (D(t)) that was used to describe the heron’s location in its migratory cycle where P(t) = 1 represents 100% residence around the lake, and P(t) = 0 represents 100% residence somewhere else along the migration route The second distribution was a spatially explicit parameter (D(a))

that was used to describe the probable foraging patterns for the great blue heronsubpopulation that relies on the lake as part of its food source while in residence

around it This also was parameterized in a similar manner where P(a) = 1 sented complete dietary reliance on the lake and P(a) = 0 represented complete

repre-dietary reliance on other locations within the defined foraging range The genericrisk model was therefore structured as follows:

(11.11)

The temporal probability, P(t), was parameterized based upon regional

observa-tions Observations indicate that herons arrive in the area around the lake betweendays 46 and 90, and depart on winter migration between days 258 and 273 Withlack of data to the contrary, it was assumed that the dates of arrival and departure

of any given individual were independent For illustration purposes, the distributionsfor both arrival and departure dates were assumed to be represented by a skewedtriangular distribution with the mode defined at the earliest and latest 10th and90th percentiles for arrival and departure, respectively By solving for the residencytime (departure date minus arrival date) using Monte Carlo techniques, the resultingresidence time was found best to fit a beta distribution of alpha 38.72, beta 3.93,scaled to 227 days and truncated at 168 days (Figure 11.2)

The habitat use function, D(a), was modeled based on the great blue heron’s

bioenergetics Flight to and from any location within the foraging area would require

an energy output proportional to its distance from the nest or colonial roost ciated with this expenditure is also a loss in potential foraging time equivalent tothe time en route This relationship can be expressed as follows:

E (x, y) = (W (x, y) – W(0, 0)) × (t(0, 0) – tFlight) – (WFlight × tFlight) (11.12)The net benefit to the heron by foraging at any given location (denoted as (x, y))

is expressed as the net energy availability at (x, y), (E (x, y)), and is proportional tothe total power (i.e., energy per unit time foraging) that may be derived at the location

(W (x, y)) relative to the power derived if the heron had not traveled, but foraged in

the immediate vicinity of the roost or nest (W(0, 0)) The amount of time available tothe heron to forage at location (x, y) is equal to the amount of foraging time available

at location (0, 0), minus the time necessary to commute to and from (x, y) (tFlight)

It is also necessary to consider the energy expended in commuting between (0, 0)

FIGURE 11.2 Temporal estimate of heron residence in the vicinity of the lake.

and (x, y) This is determined as the product of the power requirement for flight (WFlight) and the duration of the commute, tFlight This is subtracted from the net energy

difference between (0, 0) and (x, y) to derive the net energy available.

Since the ultimate goal is to develop a probability density function based on the

that relates the net energy benefit at any given point (x, y) relative to that at (0, 0) (E(0, 0)) The probability density function may now be expressed as a proportional

function of the relative energy availability at any point (x, y) with its differential

radial distance from (0, 0) (dr) as follows:

(11.13)

The distribution of this function is illustrated in Figure 11.3

The probability density function D(EH) is now a spatially explicit metric that describes the probability of a heron being present at any point (x, y), based solely

on the bioenergetic advantage relative to location (0, 0) This may now be applied

to a measure of habitat quality at (x, y) relative to (0, 0) to predict the likelihood of

a heron’s presence based on the overall advantage that a heron would derive byforaging at that location

Habitat quality is a site-specific parameter and dependent upon estimates of thequantity of available forage fish and the quality of the local environment as adequateforaging habitat The great blue heron is a wading bird that can utilize a variety offreshwater and marine habitats It is found in areas of shallow water that have firmsubstrates and high concentrations of small fish.6 Great blue herons forage in lakes,rivers, brackish marshes, lagoons, coastal wetlands, tidal flats, and sandbars, as well

as wet meadows and pastures.4,6 For the purposes of this assessment, potential heronhabitat was defined as any shoreline or riverbank within 24 km of the lake, with a

FIGURE 11.3 The function of the relative energetic benefit EH(x, y) with distance from the

origin (0, 0) E(0, 0) and E (x, y) are assessed as uniform within the radius of 24 km.

wading depth less than 50 cm for any water body whose minimum dimension wasgreater than 2 m Habitat quality was also assumed to be proportional to relativehabitat density Habitat within urban areas was deemed unsuitable Prey availabilitywas determined from available state surveys For habitats where survey results wereunavailable, prey abundance was estimated based on comparisons with similar sur-veyed water bodies based on size and location

To determine the relative habitat quality, all potential foraging locations wereidentified and mapped relative to location (0, 0) to a radius of 24 km These werethen grouped into octants and segmented into 1/20ths of the total foraging radius(Figure 11.4) Habitat quality (H (x, y)) was expressed as the product of the density of

appropriate habitat (d H (x, y) ) within the segment and the average prey abundance (a (x, y))

relative to the prey abundance at point (0, 0) (a(0, 0)) as follows:

(11.14)

The distribution of habitat density relative to the requirements of the great blue heron

is provided in Figure 11.5

The bioenergetics model describes the probability of a heron being at location

(x, y) based on the potential advantage of commuting from (0, 0) to (x, y) The spatial

habitat quality model describes the potential advantage of a heron being at location

(x, y) based on the availability of prey and the quality of the habitat When these

two are combined as follows, the product is a measure of probability that describesthe likelihood of a heron foraging at any location within the prescribed foraging

range (P(q (x, y))):

FIGURE 11.4 Spatial distribution of great blue heron habitat in the vicinity of the lake Circle

represents the 24-km radius assumed for potential habitat use Shaded areas represent urban regions excluded as potential habitat Segments represent octants segmented radially in 1 / 20 th

of the total radius.





The estimation of overall area use based on habitat quality for the foraging area,centered on the lake, is illustrated in Figure 11.6

The final step in the parameterization of habitat use, D(a), required the expression

of the heron’s foraging behavior relative to the lake To accomplish this, the ability density function for habitat utilization, illustrated in Figure 11.6, was applied

prob-to determine the probability of any heron foraging on the lake (P(a) = 1) vs foraging

at any other location (P(a) = 0) by first quantifying the proportion of the lake shoreline within each of the sections defined in the habitat map (A site(x, y)) First, the

three-dimensional distribution of P(q (x, y)) was then collapsed to a two-dimensional

probability P(q) by grouping all locations relative to the proportional area of the

lake contained within each segment Then the relative area of the lake was thenbootstrapped (with replacement) and the results tracked to develop the probabilitydensity function for area use by the heron subpopulation relative to the proportion

of the lake to which they will be exposed The algorithm used was as follows:

(11.16)

The probability density function for this relation is illustrated in Figure 11.7 and

was used as the distribution for P(a) in the risk model

Insufficient data were available to model mercury exposures outside of the lake

using the P([Hg]|Fi) method detailed above Therefore, mercury concentrations for

exposures that occurred outside of the lake, but within the state, were generalized

FIGURE 11.5 Habitat density, expressed as meters of usable shoreline per meter square of

area, for the environment surrounding the lake to a distance of 24 km.

P q( (x y, )) H(x y, )

H( 0 0 , ) -

FIGURE 11.6 Relative probability of area use based on available habitat and bioenergetic necessity of the great blue heron.

©2002 CRC Press LLC