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Chapter 7
Estimating Risk
The concept of risk is central to the implementation of the Endangered Species Act. The
committee was asked to review the role of risk in decisions macle under the act, review whether different
levels of risk apply to different types of decisions made under the act, and identify practical methods for
. .
assessing rls (.
Risk is the probability that something (usually a bad outcome) will occur. Risk assessment aims
to estimate the likelihood of a particular (usually bad) outcome occurring. Risk management is an
integrating framework that assesses the likelihood of bact outcomes and analyses ways to minimize the
risk of bad outcomes, or at least to respond appropriately if they occur. Many risk assessments follow
the framework developed by the National Research Council to apply to human health (NRC, 1983~; an
example of a specific risk assessment framework is the one clevelopec! by EPA (Risk Assessment Forum,
1992), which tracks patterns of exposure to harmful substances and responses of ecological systems to
these exposures. The sometimes confusing terminology of risk assessment and some of the issues in
applying risk assessment to ecological systems were described by Policansky (1993~; further examples
were cliscussect by the National Research Council (NRC, 19931.
The main risks involves! in the implementation of the Endangerec! Species Act are the risk of
extinction and the risks associated with unnecessary expenditures or curtailment of land use in the face of
substantial uncertainties about the accuracy of estimated risks of extinction ant! about future events. In
this chapter, we consider the problem of estimating the risk of extinction and the limitations of our
current ability to estimate this risk. Mociels are an important too! for analyzing the consequences of
complex processes, because intuition is often not reliable. In some cases, the predictions of the models
discussed are not precise because information is lacking or because the underlying processes are not fully
unclerstood. They are valuable as guides to research and as tools for analyzing the comparative effects of
various environmental and management scenarios.
ESTIMATING THE RISK OF EXTINCTION
Since the inception of the ESA, there have been enough developments in conservation biology,
population genetics, and ecological theory that substantial scientific input can be used in the listing and
recovery-planning processes.
. . .. . . .
The following synthesizes and evaluates the various approaches and
conclusions that nave emergect from recent attempts to unclerstanc! the vulnerability of small populations
to extinction. The material focuses on random changes in population sizes and in their structure, changes
in genetic variability, environmental fluctuations, and habitat fragmentation. Additional theoretical and
field research are needled to resolve or reduce uncertainties, but existing analyses give insight into the
relative magnitude and possible scaling of various influential factors in the extinction process. More
thorough and technical reviews were provided by Dennis et al. (1991), Thompson (1991), and Burgman
et al. (19921.
SOURCES OF RISK
Habitat loss, effects of introduced species, and in some cases overharvesting are almost always
99
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Science and the Endangered Species Act
the ultimate causes of species extinction. Decline of populations to a low density makes them vulnerable
to chance events and sets into play the extinction risks outlined below. When conditions have
deteriorated to the point that a well population cannot maintain a positive growth rate, no sophisticated
risk analysis is required to tell us that extinction is inevitable without human intervention. Our attention
will be focused instead on cases in which a population with a positive capacity for growth in an average
year is still vulnerable to chance events that cause short-term excursions to low densities. Limitations of
these approaches are cliscusseci at the enc! of the section.
Random Demographic Changes
Demographic features, such as family size, sex, and age at mortality, vary naturally among
individuals. In populations containing more than about 100 indivicluals, individual variation averages
out and has little effect on the (lynamics of population growth. However, in small populations, random
variation in demographic factors can occasionally reach such an extreme state that extinction is certain.
This can arise, for example, if all members of one sex die before reaching maturity or if all progeny are
of the same sex, as was the case in the dusky seaside sparrow (Ammociramus maritime nigrescens) after
loss of habitat led to its population clecline.
Substantial effort has been expended to develop general models for predicting the risk to small
populations of extinction clue to demographic stochasticity. Several assumptions must be macle about the
ways in which populations grow, in particular, about the way population growth rates respond to density.
From the standpoint of an endangered species, the simplest conceivable mode} assumes that the
population has been pushed to its limits resources (habitat and food availability) have become so scarce
that, on average, the expected number of births in an interval is the same as the expected number of
deaths. In this case, with incliviclual births ant} cleaths being random, the mean time to extinction for a
population starting with N individuals is simply N generations (Leigh, 1981), i.e., the time to extinction
increases linearly with the population size. (Box 7-1 contains definitions of terms; Box 7-2 has
definitions of symbols used in analyses.)
A more common situation is one in which resources are sufficient to support an average positive
population growth when the population density is below a threshold. Due to chance, the actual growth
rate in any generation will deviate somewhat from its expected value, and in the rare event that the
cumulative growth rate realizer! over several consecutive generations is sufficiently negative, the
population size will be reclucec! to zero (i.e., extinction will occurs.
All the demographic models discussed in this section assume that all members of the population
are functionally identical. There is no variation baser! on age or sex; inctivicluals are assumed to be
iclentical with respect to reproductive and mortality rates. Thus, strictly speaking, the results apply best
to short-lived asexual organisms or to hermaphrodites that synchronously reproduce toward the end of
their life, as cio many annual plants and some invertebrates. Models incorporating age structure, which
are appropriate for vertebrates, require information on the mean and variance of age-specific mortality
and fecundity scheclules (Lance and Orzack, 1988; Tu~japurkar, 1989), information that is limited for
even the best-studiec! species in nature.
iWith this type of model, the mean time to extinction increases exponentially with the product of the expected
population growth rate at low density, r, and the population carrying capacity, K, where K can be viewed as the
number of individuals that a reserve can sustain at stable density (see Example 7-1~.
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Estimating Risk
101
adaptive variation-genetic variation for characters upon which natural selection operates and which may
be favored within the range of environments experienced by a species.
character the overt (phenotypic) expression of a gene or group of genes.
deme a local population of interbreeding organisms.
density dependence the influence of population density on a specific phenomenon, e.g., density-dependent
growth.
effective population size-the number of breeding adults that would give rise to the rate of inbreeding
observed in a population if mating were at random and the sexes were equal in number. The effective
population size is always less than the actual population size.
fitness relative reproductive success or genetic contribution to future generations.
gametic mutation rate- the average total number of new mutations arising de nova in a gamete.
gene pool the total set of genes contained within a population or species.
genetic variance variability in the genomes of individuals within and between populations.
genome the complete set of genetic material carried by an individual.
genotype-the specific set of genes-including the specification of their allelic forms carried by an
individual; may refer to a single genetic locus (e.g., blood genotype of an individual) or to the allelic forms
of the complex of genes influencing the expression of a multifactorial trait.
homozygous most species inherit parallel sets of genes from their parents. For a gene with a particular
function, a homozygous individual is one that inherits identical copies of the gene (i.e., the same allelic
form) from both parents. If the allelic forms are different, the individual is heterozygous.
mutation a heritable change in a gene.
outbreeding depression a reduction in fitness in the hybrid progeny, or later descendants, of crosses
between members of different populations.
population a group of closely related, interbreeding individuals.
population bottleneck a transient and extreme reduction in population size relative to normal population
sizes such that genetic diversity is reduced simply by the reduction in population size.
random genetic drift changes in gene frequencies arising from chance sampling of gametes in small
populations.
stochasticity random variation.
Box 7-l Definitions of terms.
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Science anti the Endangered Species Act
C the rate at which a subpopulation will recolonize an area.
E probability of extinction of a subpopulation.
K population carrying capacity; number of adults the environment can support.
N population size.
Ne effective population size.
Pe the average probability of extinction per generation. Only in the special case that Pe is constant in
time does t e= 1lPe
r the intrinsic rate of population growth; i.e., the expected exponential rate of population increase at
densities less than K.
r the long-run average growth rate; equal to r - Ve/2.
the selection intensity operating against a deleterious mutation in the homozygous state. For example,
if the deleterious gene affects viability to maturity such that s = 0.05, then a homozygote for the
deleterious allele (all other things being equal) has a 5 % reduction in the probability of surviving to
maturity.
t e the mean time to extinction, measured in generations.
Ve between-generation variance of the population growth rate; i.e., the mean squared deviation of r in
any generation from the expected value of r.
the genomic deleterious mutation rate. Almost no data exist on this, except for Drosophila, although
a fair amount of empirical work is now going on to fill this gap in our knowledge. The general
principle of all experiments to estimate ,u is the same start with a genetically uniform stock; create
sublines; maintain the sublines in isolation from each other with a minimum possible population size
(to minimize the efficiency of natural selection against new mutations); and then over time watch the
lines decline and diverge in terms of mean fitness. The details are somewhat complex statistically,
but from this information (on the rate of decline in mean fitness and the rate of divergence of subline
specific fitness), it is possible to get a downwardly biased estimate of ,u (Mukai, 1979; Houle et al.
1992~.
Box 7-2 Definitions of mathematical notation.
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Representative terms from entire chapter:
endangered species
Estimating Risk
103
: ~uPpose ~ he exP ed : a gr th t ~ a: : ag --- 1 t.4 . 1 i n s~ e i:s ~! a :
.:.::::: :r. `:i:i: ::r n .:i: ::~:~: -fi' ~ h th 't ' tlir '' i't'he ' ' 'v'r' ' 'm ' 'f :'t'r' ' '1'' ' a'r'fHm'i' ''' r' ' th' ret ' d' ' ' ' ' ' ' I t' ' ' '''' '
O.~/ye.ar.implies. that,..a.t. 1 den it : the p let n a d
t en iai ~ 03 be a ex i c i n i (in era i ~ is a ei
::::: ~ 4~: ~ : ~ ~ ': : ~ : : : 4 : :: \: :::: ::::: ~ 7:: : :: : :: : : : : :: :: .> : := : : ,:: : :: `: 4 .: :::::::: : : . . ~:: ~:
r)~r ~) where e.- 2:.~2 i he as a ga
|~ ~this~expression~ean~he~wri~tten :a s (( 1~+~ ~r~ i'~2rK)~.~ The~term ~(e7~
104
Science and the Endangered Species Act
extinction risk. Their mocle} is quite flexible in that it allows for any pattern of density-depenclence in
the birth ant! death rates.
Random Environmental Changes
Demographic stochasticity becomes less important as the density of a population increases and
in(livi(lual differences average out; however, this is not the case when temporal variation in an exogenous
factor, such as the weather, influences the reproductive or survival rates of all individuals in a population
simultaneously. Environmental fluctuations influence different individuals to different degrees, but to
this point, the theory has only been developed for the situation in which all individuals respond in an
identical manner to environmental change. The discussion below expands on the preceding section by
incorporating environmental as well as demographic stochasticity.
Most mociels consider the population to be growing with an average growth rate of r per capita
per year, ant! variance in this rate among generations, Ve, is clue to environmental fluctuations.
Typically, it is assumer! that the variance is independent of population size and that there is no
correlation between the state of the environment in one generation and the next. Such assumptions are
probably rarely fulfilled in natural populations, and violations of them would most likely enhance the
risk of extinction, as when generations of poor growth conditions tend to be clustered. These caveats
asicle, a general prediction of models that incorporate environmental stochasticity is that the mean
extinction time is determined by the ratio r/Ve the higher the average growth rate ant! the lower the
variance, the longer the population is likely to survive. Moreover, the rate of increase of population
longevity with increasing K is much slower when environmental stochasticity is present than when
demographic stochasticity operates alone (Example 7-21. Depending on the magnitude of Ve relative to
r, even populations with several hundreds or thousands of indivicluals can be vulnerable to
environmental stochasticity.
The theory just discussed treats environmental variation as a factor that drives variation in the
intrinsic rate of population growth, r . While this is certainly likely to be true in many cases,
environmental factors can also define the carrying capacity of a population. Thus, an alternative
approach to the treatment of environmental stochasticity is to let K, as well as r, vary. Variation in K
alone cannot cause extinction, unless the carrying capacity actually declines below zero. However, K
puts a ceiling on the attainable population size and bottlenecks in K can magnify the effects of
demographic stochasticity by enhancing the variation in the population growth rate due to the smaller
sample of reproductive adults. Only limited work has been done on these issues (see Roughgarclen,
1975; Slatkin, 1978).
Catastrophes
Catastrophes are extreme forms of environmental variation that sullenly anti unpredictably
reduce the population size. To the extent that these events are determined by the weather, lightning fires,
epidemics, etc., human intervention can clo little to influence their frequency. However, because
catastrophes affect most members of a population to snore or less the same extent, it is clear that, on the
basis of chance alone, larger populations will have an increased likelihood of some individuals surviving
this kind of event.
12'"
Estimating Risk
i05
· ln.~.~Qlally.Yaryl g enY O~em the l:~ng-t ng ow-th- te ~- - :Y /2 he Y 1 Fa~iiity
........ pooulatio a i i , 96 9 .
rate of populat~o e si - I nsta ~, f a popula i uld pa ~ ~ ~ ely a~er t n s
its e~pect d size uld b ert: i es i s i..it si e. Bu in a vari e ir e
t~mes~ i a s . a i e a r i e
the imporeance of ~a i -i p la n ro r s i (~ : e p u a io i 1 1i s e
'...'..d,2"t,e'r'~,"2~''n'~s.ti'~al.~.' ''F r'' e' ase'i i h, p io g'o' s' 'ih 'an'
the carry) a i a tim to £ c io is ro rti I t (1 ~ 19 1 . i s t at
~the~s~cal ing~of ~the~time~to~ extinction with ~popula1:ion~s~ze~depends on ~the~ratio~at~the ~mean ~ ta~ the~var~ance~ of ~the;~ rate~|
....... ~.ipopul i graw5, /~: If his ati is .~/2, whi h. implie a lo ru g whr. {e fle , .:hee i ti m is
expe e i s i a I i : as i he as raphi s i i , . e i e i
the rate of ~rowth is at th :2r. th ext~n tio- -ti - -ea.e:s::-l ra idl hen lr 1 i h ~
Unless they inco~orate all aj s r: s f va iabil th m ~ 1 p id 1~1
ti tion . s r ia i ~s r i e~ a i
... . ~- ..
enviro al st ~ ti sid he si i i hichK ~-100,: 0.1, ~ ~O.1. I ~ s s,
Q.~.~- ~ratei slightly posiiv, r Q.~.::In~abs e f vir l ~ ti ~g It
g~= o a i s i£i 3, a e i Gi is pr i : ea il a
the ather hand a~r a ive b 9 3 hi i
e i a ii, i i i i . i i
inc p jai, r i sa a e i I l es
allow ~nsit ~ p d t:~t gi t p p l ti th (t ~gh -1981 ~ 976 li dO
. . . . ... . .. . . . ...
. ........ .
........
..... ..
::::: ::::::
.........
........
::::::::::::::::
........
.........
.
........
:::::::
,.......
:st~ll sharter times t ext~nction. :
Example 7-2
Hanson anc! Tuckwell (1981) anc! Lande (1993) have considerec} the time to extinction for
populations exposec! to ranclomly occurring events, each reducing the population size to a constant
fraction of its current size, the former using a logistic, and the latter an exponential growth moclel. In
these models, there is no clemographic or environmental stochasticity of the kinds noted above. Rather.
extinction only occurs when, by chance, a cluster of catastrophes occurs. Proviclec! the long-run growth
rate is positive, the mean extinction time increases exponentially with the carrying capacity under this
model, with the rate of scaling increasing with the frequency of occurrence anct magnitude of
catastrophes. Assuming catastrophes act locally, spatial subdivision of a species provicies a simple
means of protection against extinction cause(i by clevastating events.
Accumulation of Deleterious Genetic Factors
The reduction of a population to a low density has several negative genetic consequences that
can magnify vulnerability to extinction. Most species harbor far more than enough deleterious recessive
genes to kill inclividuals if they were to become completely l~omozygous (Simmons ancl Crow, 1977;
CharIesworth and Chariesworth, 1987; Ralis et al., 1988; Hecirick anc! Miller, 19921. This large genetic
load is essentially unavoicIable because it is maintained by a deleterious mutation rate of approximately
one per indivi~iual per generation (Mukai, 1979; Houle et al., 19921. In large populations, deleterious
genes, particularly lethal genes, have only minor consequences the frequencies of most deleterious
genes are kept low by natura] selection, anc! their expression is minimal because they are usually masked
in the heterozygous state. This situation can change ciramatically in small populations. During
bottIenecks in population size, mildly deleterious genes, previously kept at low frequency by natural
106
Science and the Endangered Species Act
selection, cart rise to high frequency by chance. When these genes become completely iFixecl (reach a
frequency of 100%), a permanent reduction in population fitness results3.
Although some cleleterious genes may be purged from a population early in a population
bottleneck (Templeton and Read, 1984), the continued maintenance of a population at small size can
only magnify the long-term accumulation of mildly cleleterious genes. As notes! above, deleterious
mutations arise at a rate of about one per indiviclual per generation. Provided the individual selective
effects of these penes are small (on the order of 1/4N. ~ or lessee theY w. ill accumulate at the aenomic
~ _ _ ~~ ~ ~ -~ ^ _ ~ _ O _ ~ ~ ~ ~ - - ~ ~ ~ ~ O
~ , ~ · . ~ . · AT ~ ~ ~ ~ A ~
mutation rate (,u)' causing a decline In mean illness ot approximately ,us per generation Lynch, lYY4~.
Thus, if,u = l and s = 0.025 (as described in footnote 3), a small population would be expecteci to
experience a roughly 2.5% decline in fitness per generation due to cleleterious mutations alone, and the
rate of mutation accumulation declines with increasing population size. If the effective population size
(Ne) is greater than 1,000, mutation accumulation is essentially halted for time scales relevant to
endangered species management. However, if the accumulation of deleterious genes reaches the point at
which the net reproductive rate of individuals is less than 1, tile population is incapable of replacing
itself. At this point, the population size begins to decline, and random drift progressively overwhelms
natural selection; consequently, decline in fitness accelerates due to the accumulation of cleleterious
mutations. This synergism, whereby tile rate of decline in fitness increases with the accumulation of
cleleterious genes, has been referred to as a "mutational meltdown" (Lynch ant! Gabriel, 1990; Lynch et
al., 1993) anti, once initiated, can leac! to rapid extinction.
Loss of Adaptive Variation Within Populations
Most populations, even those undisturbed by human activity, are exposed regularly to temporal
anti spatial variation in physical and biotic features of the environment. In principle, some species can
cope with such selective challenges by simply migrating to suitable habitat (Pease et al., 1989~.
However, endangered species often live in highly fragmented! habitats with inhospitable barriers;
migration might not be an option. This leaves adaptive evolutionary change, which requires heritable
genetic variation, as the primary means of responding to selective challenges (habitat degradation, global
climatic change, species introductions, etc.) that threaten species with extinction.
Consider a population that is faced with a gradual change in a critical environmental factor, such
as temperature, humidity, or prey size. If the rate of change is sufficiently slow and the amount of
genetic variance for the relevant characters in the population sufficiently high, then the population will
be able to evolve slowly in response to the environmental change, without a major reduction in
population size. If the rate of environmental change is too high, the selective loact (reduced viability and
fecundity) on the population will exceed the population's capacity to maintain a positive rate of growth,
an(l although the population might respond evolutionarily, it will become extinct in the process. Thus,
3Roughly speaking, if He is the effective number of breeding adults and s is the selection intensity opposing a
deleterious gene in the homozygous state, then selection is ineffective if 4Nes < 1. Typically, because of high
variance in family size, the effective population size is a third to a tenth of the actual number of breeding adults
(Heywood, 1986; Briscoe et al., 19924. Thus, as a first approximation, if the number of breeding adults is less
than 21s, natural selection will be essentially incapable of eliminating a deleterious gene its future frequency will
be governed bY chance. with the probability of fixation being equal to the initial frequency. The current wisdom
~ , , , _
~ ~ ~ in- 1 ~ _ 1 ^~7~7 ~ .1~ ~ ~1 1 nits I:
IS that s for an average mutation is approximately u.uz~ Commons and ~row, lo/ l, noult; c;r ~1., l>~^J. l~u~lll~,
that 2/0.025 = 80, this implies that a substantial number of the rare deleterious genes in a population can drift to
high frequency if the number of breeding adults is reduced to 100 or fewer individuals for a prolonged period.
Estimating Risk
for TV non'~l~tion there must be a critical rate of environmental chance that allows the population to
107
WE I_ _ l~ ~ ~
Or islet fact e.noll~h to maintain a stahle size. Lvnch and Lande (19931 showed that this critical rate is
~ ~ . 1 ~ , ~ · 1 1 , · · . ~
directly proportional to the genetic variance for the character upon wn~cn selection Is acting.
Several factors influence stancling levels of genetic variation for characters associated with
morphology, physiology, and behavior. Most forms of natural selection cause a reduction in the genetic
variance by eliminating extreme genotypes, the exact amount depending on the intensity of selection.
Small populations also lose an expected 1/2Ne of their genetic variance each generation clue to the chance
loss of some genes by random genetic drift. Mutation adds genetic variation to each generation of a
population. When populations are kept at a constant size and under constant selective pressures, they
ultimately evolve an equilibrium level of genetic variance, at which point the loss due to selection and
drift is balanceci by mutational input.
For large populations, the magnitude of this equilibrium variation is debatable, because it
depends on the gametic mutation rate and the distribution of mutational effects, neither of which are very
well understood (Barton and Turelli, 19891. However, for populations with effective sizes of a few
hundred or fewer inclivicluals, the expected amount of variation for a typical quantitative character is
nearly inclepenclent of the strength of selection and proportional to the product of the effective population
size and the rate of mutational input of variation (Burger et al., 1989; Foley, 1992~. This implies that for
populations containing hundreds or fewer individuals, the rate of environmental change that can be
sustained for a prolonged period of time is directly proportional to the effective population size. In other
words, a cloubling in population size effectively doubles the evolutionary potential of the population.
Some attempts to identify a critical minimum population size for captive populations from a
genetic perspective have focuses! on goals such as the maintenance of 90% of the genetic variation
present in the ancestral (predisturbance) population for 200 years (Franklin, 1980; Soule et al., 19861.
Goals of this nature take into consideration the fact that populations that are c~winciling in size cannot be
in equilibrium. However, these goals are rather arbitrary with respect to choice of acceptable loss and
time span. For long-term planning, an alternative approach is to consider that above a certain effective
population size, the (lynamics of genetic variation are influenced predominantly by selection and
mutation so that any further increase in the effective population size would not significantly influence the
amount of genetic variation maintainer} in the Copulation. Basect on the above arguments ant! because
_ ~ ~ . ~ ~ _
.~ ~ . - ~ . - · · 11 1 ~ 1 1 1 _ _ _ `1_ _ _ `1~ ~ _1 A_ ~ ~ ~ ~1:~ ~1..16~
the effective population size Is generally severaitoict less than the actual number of Dreea~ng augurs
(Heywooci, 1986; Briscoe et al., 1992), populations must have about one thousand individuals to
maintain their genetic variations
Habitat Fragmentation
A major area of uncertainty in conservation biology concerns the (legree to which population
subdivision influences the vulnerability of species to extinction. Even for fairly simple, single-factor
investigations in which demographic or environmental sources of randomness are assumed to dominate
(Quinn and Hastings, 1987, 1988; Gilpin, 1988), the debate about the effectiveness of a single large
reserve as opposed to several small ones is far from being resolvecl. An advantage of a single large
reserve is that it is buffered from demographic stochasticity, but multiple small reserves can buffer an
entire species from extinction clue to local catastrophes ant! environmental stochasticity. On the other
4The actual number depends in part on the biology of the organisms involved, such as sex ratio, breeding
behavior, and so on. It can be greater than one thousand if the effective population size is much smaller than the
actual population size.
108
Science and the Endangered Species Act
hand, small isolatecl populations are precisely the ones that are expecteci to suffer from inbreeding
depression, mutation loacI, ant! loss of adaptive potential. Much of the recent theoretical and empirical
work on the dynamics of populations with a metapopulation structure can be found in recent volumes by
Gilpin and Hanski (1991) anti Burgman et al. (19921.
Population subdivision acicis another dimension to species viability analysis, because questions
are focused not just on the risk of extinction for an indiviclual dome, but for an entire complex of demes.
Levins (1970) called a collection of partially or totally isolated populations of the same species a
metapopulation, and his early models for site occupancy form the conceptual basis of most current
efforts in this area. Levins showed that in an ideal world consisting of an effectively infinite number of
subpopulations, each with a constant probability of extinction E ant' a recolonization rate C, the entire
metapopulation will eventually reach an equilibrium with a fraction 1 - E/C of the total sites occupied.
Because of the randomness of extinction and colonization, tile specific sites that are occupied will vary in
time.
The intuitive notion behind Levins's work is that unless the extinction rate is zero, the total
amount of suitable habitat for a species is unlikely ever to be completely occupied. Elimination of
suitable but unoccupied patches of habitat reduces tile recolonization rate by making it more clifficult for
migrants to find suitable sites. Thus, habitat removal could theoretically have the paradoxical effect of
increasing the fraction of apparently suitable habitat that is unoccupied, but this is only clue to an overall
clecline in metapopulation size.
Lande (1987) introcluceci a series of habitat-occupancy models showing that if suitable patches
are clisperse(1 to a large enough degree that migrants are unlikely to find them, the local extinction rate
will exceed the colonization rate. Thus, there exists a mini~nu~n fraction of the total landscape
throughout a region that must be suitable for a species to persist. These extinction thresholds, definer! by
the demographic and clispersal properties of the species, cle~nonstrate that locally abundant species can
sometimes be very close to extinction if the proportion of suitable habitat is near the extinction threshoIcl.
This again emphasizes that population size alone is not always a good indicator of vulnerability to
extinction.
Lancle's (1987) models are idealize~i in that they envision a florid consisting of two kinds of
habitat patches hospitable an(l inhospitable, all of equal size. The real worIcl, of course, is more
complex. Patches differ in size and shape, patch quality is usually a continuous variable, and some
patches are connected by corridors, others not at all (see Chapter 5~. More generalized approaches are
cliscusse~i by Ak,cakaya and Ginzburg (19911. A significant feature of their approach is the inclusion of a
correlation between the extinction probabilities of adjacent patches. This correlation, if positive, causes
a reciuction in the expected time to extinction. In other words, if all patches in an area became
inhospitable at the same time, there would be no refuges available.
For many species, the adverse consequences of habitat fragmentation are not caused so much by
a loss of total area as by changes in the quality of habitat due to the (development of edge effects on the
margins of reserves (Lovejoy et al., 19861. Edge effects range from microclimatic changes resulting
from structural changes in the environment to major alterations in the vegetational community to
invasions by exotic species from agricultural and urban settings. The complete impact of edge effects
may require several years to develop and may ultimately extend for several kilometers beyond the edge
of the reserve. Some attempts have been made to capture the key features of edge effects in
mathematical models (Cantrell and Cosner, 1991, 19931. The issues are very complex because they
involve interspecific interactions, such as competition between reserve and invading species. Ultimately,
~, ~ O
4_ A
the practical application of any ot these models requires a deep unclerstanc~lng of the ecology of the
species under consideration.
Estimating Risk
109
Supplementation
An increasingly common strategy for maintaining wild populations of enclangerec! species is
augmentation with stock from breeding facilities, as in the case of hatcheries for Pacific salmonids. An
implicit assumption of such procedures is that recipient populations, when they still exist, actually derive
some benefit from an artificial boost in population size. There are, however, several reasons why
long-term deleterious consequences of supplementation may outweigh the short-term advantage of
increaser! population size.
First, over evolutionary time, successful populations are expected to become morphologically,
physiologically, and behaviorally adapted to their local environments. Thus, the introduction of
nonnative stock has the potential to disrupt adaptations that are specific to the local habitat. This type of
problem takes on addect significance when the population employed in stocking has been maintained in
captivity. Captive environments are often radically different than those in the wilcl, and over a period of
several generations, "domestication selection" can potentially lead to the evolution of rather different
behavioral or morphological phenotypes (Doyle ant! Hunte, 1981; Frankham and Loebel, 1992, NRC,
1995:genotypes that perform well in the captive environment are expected to gradually displace those
that do not. Furthermore, an overly protective captive breeding program may simply result in a
relaxation of natural selection and the gradual accumulation of cleleterious genes. For hatchery
salmoni(ls, egg-to-smolt survivorship is typically 50% or greater, as compared with 10% or less in
natural populations (Waples, 1991; NRC, 19951.
Second, local gene pools can be coadapteci intrinsically (Templeton, 1986~. Just as the external
environment molds the evolution of local adaptations by natural selection, the internal genetic
environment of indivicluals is expecter! to lead to the evolution of local complexes of genes that interact
in a mutually favorable manner. The particular gene combinations that evolve in any local population
will be largely fortuitous, depending in tile long run on the chance variants that mutation provides for
natural selection. The break-up of coaciapted gene complexes by hybridization can lead to the production
of indivicluals that have lower fitness than either parental type (outbreeding clepression) and takes its
extreme form in crosses between true biological species that cannot produce viable progeny. However,
outbreeding depression can even occur between populations that appear to be adapted to identical
extrinsic environments. The most dramatic evidence comes from recluced fitness in crosses of inbred
lines of flies (Templeton et al., 1976) and plants (Parker, 1992), but crosses between outbreeding plants
separated by several tens of meters can exhibit reclucec! fitness (Waser and Price, 1989), as can crosses
between fish (lerive(1 from different sites in the same drainage basin (Leberg, 19931. Outbreeding
depression in response to stock transfer is a major concern in the management of Pacific salmon, which
are subdivided into demes that home to specific breeding grounds (Waples, 1991; Hard et al., 1992,
NRC, 19951.
Third, augmentation of wild populations with stock from captive breeding programs can have
negative ecological or behavioral consequences. Unlike genetic effects, which can take several
generations to emerge fully, ecological and behavioral effects can be immecliate. For example,
high-clensity hatchery populations of fish are prone to epicie~nics involving diseases that are uncommon
in the natural environment. Such events provide strong selection for disease-resistant varieties of
hatchery-reerect fish, which subsequently can act as vectors to the wilct population. The Norwegian
Atiantic salmon is now threatened with extinction resulting frown a parasite brought to Atlantic drainages
by resistant stock from the Baltic (Johnsen and. Jensen, 19861.
Fourth, if a wild population is small because of habitat loss or alteration, the increased
population (lensity that results from augmentation can increase competition for foocl, space, or whatever
else the habitat provides. That competition can further reduce the size of the wild population. Harvest of
110
Science and the Endangered Species Act
augmented wild populations (particularly if harvest levels are based on total population) can reduce the
wild segment of the population unless the harvest effort is directed away from the wild population.
A captive breeding and reintroduction program is appropriate only when there is no alternative
means of ensuring short-term population viability or when there is strong evidence of historical gene
flow. Habitat loss and clegraclation are the main reasons species become threatened or endangered;
therefore, the protection of habitat plays a greater role in preserving these species than captive breeding
and reintroduction. For example, as of 1991, the species specialist groups of the International Union for
the Conservation of Nature (IUCN), which are international groups of scientists with expertise on
specific kinds of animals, hac! completed conservation plans for 1,370 mammals. Of the
recommendations in these plans, 517 concern protecting or managing habitat, while only 19 concern
captive breeding ant! reintroduction (Stuart, 19911.
Captive breeding and reintroduction are appropriate when suitable unoccupied habitat exists and
the factors leacling to extirpation of the species from this habitat have been identifier! and reduced or
eliminated. Under these circumstances, captive breeding and reintroduction of threatened ant!
endangered species can be part of a comprehensive strategy that also addresses the problems affecting
species in the wild (Foose, 1989; Povilitis, 1990; Ballou, 1992~. For example, captive breeding and
reintroduction enabled the peregrine falcon (Falco peregrinus) to repopulate much of North America
after the use of DDT was eliminates! (Cede, 19901. Similarly, Arabian oryx (Oryx [eucoryx) were
successfully reintroduceci in several areas of their original range where hunting was prohibited (StanIey-
Price, 19891.
Captive breeding and reintroduction programs should be avoicled when possible; however, once
the need for a captive breeding program has been identified, it is acivisable to initiate it as soon as
possible. Starting the program before the wild population has been recluced to a mere handful of
indivicluals increases a program's chances of success. Starting sooner provides time to solve husbandry
problems, increases the likelihood that enough wile! inclividuals can be captured to give the new captive
population a secure genetic and demographic founclation, and minimizes a(lverse effects of removing
individuals from the wilct population.
Captive breeding and reintroduction programs are the most expensive forms of wildlife
management (Conway, 1986; Kleiman, 1989) and involve research and management actions. Although
genetic and demographic management techniques for captive populations are fairly well developed ant!
can be applied to most species (Ballou, 1992; Ralis and Ballou, 1992), husbandry and reintroduction
techniques tent! to be species specific. Zoos do not know how to breec! many species, such as cheetahs
(Actir~omyx jubatus), reliably in captivity. In such cases, expensive and time-consuming research on
genetics, behavior, nutrition, clisease, or reproduction might be necessary to find the reasons for lack of
breeding success. The reintroduction of captive-brec! individuals also poses substantial technical
challenges. Considerable research, in captivity and in the field, often is necessary during the early stages
of the reintroduction process to clevelop successful techniques (Kleiman, 1989; Staniey-Price, 19914.
Focusing Conservation Efforts
Life-history models can also help to identify the stages of an organism's life history most likely
to be sensitive to conservation efforts. For example, the National Research Council (NRC, 1992)
concluded from life-history data and models that protecting juvenile and sub-adult sea turtles would have
a greater effect on increasing population growth than reducing human-caused deaths of eggs ant!
hatchlings. Similarly, by performing an analysis of the sensitivity of the population growth rate of the
northern spotted owl to various demographic parameters, Lande (1988), based on the data available then,
Estimating Risk
concluded that the most important contributors to the ow1's survival were the adults' annual survival rate,
followed by the survival rate of juveniles cluring their dispersal phase and annual fecundity.
Distribution of Extinction Times
The prececling discussion summarizes the state of our knowlecige of how various factors
contribute to the risk of population extinction. For practical reasons, the existing theory focuses almost
entirely on the expected time to extinction. However, in the listing and management of endangered
species, the primary focus is usually on the likelihood of extinction within a given time frame (Shaffer
1981, 1987; Mace and Lande, 1991~. Risk analysis requires information on the dispersion of the
probability distribution of extinction times about the mean. For the moclels previously cited and many
others (Burgman et al., 1992), the distribution of extinction times typically is strongly skewed to the
right, with the most likely extinction time (the mode) being substantially less than the mean. In general,
it is probably more useful to estimate extinction probabilities as a function of time for different
population sizes than to identify some specific MVP.
One conceptually simple way of relating risk to the mean extinction time is to assume that if the
current ecological conditions remain stable, the probability of extinction per generation also remains
stables. That cannot be strictly true, even in a constant environment, because demographic and genetic
sources of stochasticity will ensure that the probability of extinction is not constant in time. For
example, if by chance the population size dwindles, the risk of extinction will be elevated above the
average risk until the population has recovered to its average size.
LIMITATIONS OF OUR ABILITY TO ESTIMATE RISK
We close this section by again emphasizing that the practical utility of any extinction model
depends on the validity of its underlying assumptions. Virtually all work on the vulnerability to
extinction has taken a single-factor approach, under the assumption that this will at least yield an
understanding of how the expected extinction time scales with population size when a single factor is
operating. Other than analytical and computational simplicity, there seems to be little justification for
this approach to population viability analysis. Chapter 5 gives some examples of population viability
analyses that have been useful and points out the neec! to recognize the uncertainties discussed here. In
nature, populations are exposed to multiple sources of risk simultaneously. Synergism between different
risk factors is not reiRected in many models, and therefore the risk of extinction can be underestimated, as
shown in Example 7-2 (see also Gabriel and Burger, 19921. A field example of such synergism was
described by Woolfenden and Fitzpatrick (19911; epizootic infections of the Florida scrub jay, which
sIn this case, the conditional probability of extinction in any generation (given that the population has survived
to that point) is simply the reciprocal of the mean extinction time, i.e., Pe = 1/t e where t e is the mean time to
extinction measured in generations. Because the probability that extinction does not occur in (x - 1) consecutive
generations is (1 pox-, and the probability that those (x - 1) generations are immediately followed by extinction
is Pe, the probability of extinction in generation x is pe(l pe)X~~. With this approach, the cumulative probability
that the population will be extinct by generation t can be computed by solving the preceding expression for x = 1
to x = t, and summing these probabilities. Results in Gabriel and Burger (1992) and Tier and Hanson (1981)
suggest that this approach may provide a good first-order approximation to the distribution of extinction times due
to demographic and environmental stochasticity under a broad range of conditions.
112
Science and the Endangered Species Act
reduced local populations by 50%, also lowered reproductive success in the following seasons even after
the death rates nau returnee! to normal.
Although analytical results are valuable as guides to research ant! as methods of comparing the
effects of various environmental and management scenarios, they are probabilistic in nature, so they
often ignore the underlying mechanisms. Perhaps their greatest potential is in combination with
empirical evidence on extinction times, both in the laboratory and in the field! (see for example Pimm et
al., 19931. It remains to be seen how relevant such results are to natural populations. Most of the work
on vulnerability of species has also focused on nonfragmented populations anal, except in the case of
asexual populations (Lynch et al., 1993), few formal attempts have been macle to incorporate genetics
into extinction moclels. There is a clear need for mociels that predict distributions of extinction times as a
function of population density, demographic rates, mating system, environmental variation, etc. These
models, which can only be evaluatecl by computer simulation (Shaffer and Samson, 1985; Caswell, 1989;
Menges, 1992), can be expected to advance substantially in the next few years because computational
power is now widely available.
CONCLUSIONS AND RECOMMENDATIONS
· Since the implementation of the Endangerec! Species Act, numerous models have been
cievelopec! for estimating the risk of extinction for small populations. Although most of these moclels
have shortcomings, they do provide valuable insights into the potential impacts of various management
(or other) activities and of recovery plans. With only a few exceptions, biologically explicit, quantitative
models for risk assessment have player! only a minor role in decisions associated with the ESA. They
should play a more central role, especially as guides to research and as tools for comparing the probable
effects of various environmental ant! management scenarios.
· Despite the major advances that have been made in ~nodels for predicting mean extinction
times, the existing treatments still have substantial limitations. Most of the models are unifactorial in
nature and fad! to incorporate the negative synergistic effects that multiple risk factors have on the time
to extinction. Efforts to jointly integrate genetic, demographic, and environmental stochasticity into
spatially explicit frameworks are badly needled.
· Most extinction models primarily address the mean extinction time. Because decisions
associated with endangered species usually are couched in fairly short time frames less than 100
years- models that predict the cumulative probability of extinction through various time horizons would
have greater practical utility.
· Results from population-genetic theory provicle the basis for one fairly rigorous conclusion.
Small population sizes usually leac! to the loss of genetic variation, especially if the populations remain
small for long periods. If the members of the population do not mate with each other at random (the case
for most natural populations), then the effect of small size on loss of genetic variation is made more
severe; the population is said to have a smaller effective size than its true size. Populations with
long-term mean sizes greater than approximately 1,000 breeding adults can be viewer} as genetically
secure; any further increase in size would be unlikely to increase the amount of adaptive variation in a
population. If the effective population size is substantially smaller than actual population size, this
conclusion can translate into a goal for many species after survival of maintaining populations with more
than a thousand mature individuals per generation, perhaps several thousand in some cases. An
appropriate, specific estimate of the number of individuals needec! for long-term survival of any
particular population must be based on knowledge of the biology of the organisms involvecl, such as sex
ratios, breeding behavior, and so on. If information on the breeding structure of that species is lacking,
information about a related species might be useful.
Estimating Risk
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