Habitat Destruction and the Extinction Debt Revisited

Habitat Destruction and the Extinction Debt RevisitedAuthor(s): Craig Loehle and Bai-Lian LiSource: Ecological Applications, Vol. 6, No. 3 (Aug., 1996), pp. 784-789Published by: Ecological Society of AmericaStable URL: http://www.jstor.org/stable/2269483 .

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Ecological Applications, 6(3), 1996, pp. 784-789 ? 1996 by the Ecological Society of America

HABITAT DESTRUCTION AND THE EXTINCTION DEBT REVISITED1

CRAIG LOEHLE Environmental Research Division, Argonne National Laboratory, Argonne, Illinois 60439 USA

BAI-LIAN Li Center for Biosystems Modelling, Department of Industrial Engineering, Texas A&M University,

College Station, Texas 77843-3131 USA

Abstract. A very important published analysis of the problem of habitat destruction (Tilman et al. 1994 [Nature 371:65-66]) concluded that such destruction may lead to an extinction debt, which is the irreversible, preferential loss of competitive species following a prolonged transient or delay after the habitat destruction. We analyzed this model using analytic and simulation techniques. Relating this analytic model to real-world situations shows that it applies to scattered permanent devegetation of small patches and to across- the-board decreases in fecundity such as could be caused by pollution. For repeated spatially random disturbance, we develop a new model that shows an even more severe extinction- debt effect. For larger fragments of remnant vegetation, such as forest woodlots, we argue that the assumptions of the model are violated but that an extinction debt nevertheless occurs due to gradual stochastic elimination of species that are very rare and isolated in these fragments. For habitat destruction on regional scales (reduction in ecosystem area without disturbance in remnant areas), one must, in contrast, apply species-area relations based on the distribution of different habitat types (e.g., elevational and rainfall gradients; physiographic and edaphic variability). Such an analysis predicts rapid, not delayed, loss of all types of species, not just competitive types. We conclude that the extinction-debt effect is real and arises in three different models, but relating the models to real-world conservation problems must be done with care.

Key words: endangered species; extinction-debt model; extinction theory; habitat fragmentation; landscapes; spatial scale, importance of; species-area curve.

INTRODUCTION

Extinction, the irreversible loss of a species, is per- haps the most serious of all of the effects of human population upon the natural world. Models have been central to how ecologists have approached the question of extinction, both in terms of species-area relation- ships (Simberloff 1992, May et al. 1995) and metapopulation dynamics (Levins 1969, 1970, Hanski and Gilpin 1991, Lawton 1995). In particular, Tilman et al. (1994) generalized an earlier study by Nee and May (1992) to examine multispecies metapopulations in which a number of hierarchically competing species can persist together in an environment where there are many habitat patches along with habitat destruction or patch removal. Their analysis made some interesting ecological conclusions that habitat destruction may lead to an extinction debt, which is the delayed extinction of species. Nee and May (1992) also predicted that the species lost will be the most competitive (least ruderal). This model is important because, if valid, it means that observed effects of disturbance and habitat loss may not be reliable indicators of long-term species losses; however, the assumptions behind their approach are not rigorously related to specific ecological conditions.

Dytham (1994) has used a cellular automaton model and Moilanen and Hanski (1995) have used the spatially realistic incidence-function model described by Hanski (1994) to reexamine the effect of habitat destruction on competitive coexistence in Nee and May's (1992) model (which had formed the basis for the model of Tilman et al. [1994]). Both of these studies (Dy- tham 1994, Moilanen and Hanski 1995) argued that the basic assumptions in Nee and May (1992) are gross simplifications of reality because all that matters is patch density, which is assumed to affect colonization rate. Furthermore, Dytham (1995) also argued that the assumptions that Tilman et al. (1994) make are un- realistic, making their model an unsound basis for conservation strategies. Whether colonizers are dispersed purely at random or whether they deliberately search for appropriate sites will also affect the results. Because the prediction of an extinction debt is a very serious one, it is important to clarify the extent to which the rather abstract model of Tilman et al. (1994) applies to real situations. Three issues are addressed here: (1) the relationship of the analytic extinction-debt model to real situations of habitat destruction, including the development of an alternative extinction-debt model; (2) the evaluation of the lag period preceding extinction of doomed species; and (3) the relationship between this model and species-area models.

I Manuscript received 12 December 1994; revised 15 Oc- tober 1995; accepted 12 December 1995.

784



August 1996 EXTINCTION DEBT REVISITED 785

ANALYSIS OF THE EXTINCTION-DEBT MODEL

The basic model

The basic model (Tilman et al. 1994) assumes a uniform area gridded into cells of a size that one individual adult can occupy. Sites are linked via dispersal. If species that are competitively superior within sites are poorer dispersers, multispecies coexistence occurs (Til- man 1994). The model is defined in terms of the proportion of sites occupied by species i (pi), species-specific colonization rates (ci), mortality (or local extinction) rates (mi), and habitat destruction (D; proportion of sites permanently destroyed). Species are ranked from the best competitor for a limiting resource ("species 1") to the poorest. Superior competitors instantly outcompete inferior ones on undestroyed sites. The abundance equation for species i is

dt= cPi ( 1-D-PE p - pmiP -2 cjpipj, (1)

where j indexes the other species competing with species i. The terms on the right are, respectively, the reproduction by dispersal to habitable patches, random mortality, and mortality due to competitive displace- ment.

From Eq. 1, the equilibrial (dpldt = 0) abundance is

1- D pi _ Pit i) (2)

which must be solved from species 1 to i, with ci > 0 and Pi ' 0 for all i. This model is analytic and therefore assumes rather restrictive spatial-homogeneity relations.

Because the Tilman et al. (1994) model is an exten- sion of the Levins (1969) model of a metapopulation to multicompeting species, after a model of two competing species by Nee and May (1992), let us go back to look at the original Levins' model:

dpldt = cp(1 - p) - mp,

or

dpldt = immigration (or colonization) rate - extinction rate, (3)

in which p is the fraction of occupied population sites in a homogeneous habitat, and c and m are the probabilities of local immigration and of extinction (mortality), respectively. The immigration (or colonization or propagule production) rate (cp[1 - p] or cpi[1 - D - j=pi] in Eq. 1) is the number (or the proportion) of successfully colonized empty sites per unit of time, and the extinction rate (mp or mipi + 1,i_lc.pjpj in Eq. 1) is the number (or the proportion) of extinctions in occupied sites per unit of time. This type of model is analogous to population models in which the rate of change of abundance is expressed as the difference between birth and death rates (Hutchinson 1978).

In Tilman et al. (1994), D is defined as the proportion of sites permanently destroyed. Let us see what this definition could mean in practice. The model assumes a homogeneous area divided up into patches. All patches are equally accessible from all patches in Nee and May's (1992) model on which Tilman et al. (1994) based their model. This accessibility means that no spatial refuges exist in the system (Dytham 1994); however, real colonization processes may be restricted to adjacent patches. (We note that Tilman et al. [1994] used an explicitly spatial simulation model considering neighbor patches; but Eq. 1 itself does not consider spatial aspects.) Because species repro- duce by dispersal to habitable patches, if D% of these patches are destroyed, then D% of the species reproduction will be unsuccessful. This model seems to apply most closely to a case where the D% destroyed patches are permanently made uninhabitable and are distributed uniformly across the habitat (otherwise, the habitat uniformity condition is violated). We can imagine placing paving stones the size of an adult plant in a uniform grid in a grassland in such a way that D% of the area is covered by stones. It is easy to see that this spatial arrangement meets, as closely as possible, the modeled effect of a reduction in successful reproduction that is more serious for the more competitive species with the lower reproductive rate (smaller ci). This reduction leads to the extinction of the more competitive species following a delay, as in Tilman et al. (1994). Although this scenario matches the model, it is difficult to identify a real-world example of habitat destruction that corresponds to this scenario. Formation of persistent animal (e.g., gopher) mounds in a grassland is the only example that comes to mind. Patchy habitat destruction, such as conver- sion of forest into a patchwork of forest and farms, is at a far larger scale (discussed in next section).

Applications of the basic model

The spatially explicit simulation of this process in Tilman et al. (1994) illustrates this interpretation. The authors created a hexagonal grid of 50 x 49 sites, with D% of randomly located sites being permanently destroyed and with reproduction dispersing randomly to neighbors. (Imagine D% of a grassland being covered by large stones.) In this case, reproduction falling on destroyed sites is not successful. This situation again corresponds to a D% reduction in fecundity across all species, although the closest correspon- dence with the analytic model is obtained with uniform, not random, placement of destroyed sites; however, this result depends on the placement of destroyed sites at the scale of the dispersal of individuals (as in the Tilman et al. [1994] simulation). Consider, by contrast, a case where destroyed sites are concentrated, rather than scattered. For a 100 x 100 grid, with a central square block 30 cells on a side destroyed (D = 0.09 or 9%), only the cells next to the edge of the



786 CRAIG LOEHLE AND BAI-LIAN LI Ecological Applications Vol. 6, No. 3

destroyed area (4 x 30 cells) have their fecundity reduced by 50%, giving an overall reduction of 120 X 0.5/9100 = 0.0066 or 0.66% effective D, not the nominal 9%. (Only the percentages in the remnant area are evaluated by Pi; thus the 9100 cells.) This analysis shows that the results of Tilman et al. (1994) are strongly dependent on the spatial configuration of destroyed sites and overestimate the extinction risk when destroyed sites are clustered. Thus, the model of Tilman et al. (1994) does not apply generally to reduction in habitat area, but only to the limiting case of uniformly distributed habitat destruction on scales comparable to the patch-occupancy size and dispersal distance of individuals. In the case of larger patches, the destruction D does not uniformly reduce reproductive success across all individuals, because only seed leaving the remnant area fails to produce off- spring. Interior individuals experience no change in reproductive success.

For habitat destruction at larger scales (patches larger than that occupied by an adult individual), other considerations come into play. The spatial configuration of suitable habitat (occupied and unoccupied) and the ecology of dispersal of species act as key factors in governing the extinction or persistence of species (Thomas and Jones 1993). On the basis of metapopulation-dynamics theory, fragmentation and isolation of populations pose a greater threat of extinction for species with poor dispersal abilities than for good dispersers, and the most isolated populations go first (Quinn et al. 1994, Lawton 1995). Habitat destruction may have very different consequences de- pending on whether there is an overall decrease in patch density or an uneven removal of patches from restricted areas (e.g., the largest patches with the low- est local extinction probabilities are among the ones removed). Results of simulations by Turner et al. (1989) showed that the spread of disturbance is a function of the proportion of the landscape occupied by the disturbance-prone habitat and the frequency and intensity of the habitat-specific disturbance. Analyses of a cellular automata-based multispecies vegetation model indicated that the rate of species lost from the system depends on disturbance grain, extent, and frequency (Li and Forsythe 1992; B-L. Li unpublished manuscript), and the response of habitat patches of different sizes to disturbance are also different (Li and Archer, unpublished data). We believe that considering the spread of disturbance and habitat response to disturbance in the coexistence of multicompeting species is more realistic, especially in a situation like correlated environments (Harrison and Quinn 1989). The result of Moilanen and Hanski (1995) showed that the minimum patch density for metapopulation persistence as estimated from the Levins model (as in Nee and May 1992) is an underestimate. We believe the same is true for the Tilman et al. (1994) model. Instead of the extinction debt falling on the most com-

petitive species, in the case of large patches it will fall on the rare species (whether competitive or not) because they will be subject to stochastic extinction (locally). Thus, in the case of native remnants there is also an extinction debt effect, but due to gradual stochastic elimination of rare species populations, not due to delayed competitive dynamics. Such stochastic local extinction in habitat remnants is, in fact, well documented in the conservation literature.

There is another case where Eq. 1 would apply, when fecundity is, in fact, reduced directly. In this case, D would not represent "destroyed sites" but rather a direct reduction in fecundity. For example, chemical pollutants could reduce fecundity of plants or animals across-the-board. If pesticides reduced pol- linator abundance, then fecundity could again be reduced (more or less) across-the-board for plants, as in Eq. 1. For these cases, all of the results of Tilman et al. (1994) about the extinction debt and the non- linear effect of D hold. This argument suggests that heavily polluted areas could, in fact, be accruing sub- stantial extinction debts that current assessment meth- ods do not detect.

A final application of Eq. 1 concerns a type of habitat destruction that we often observe, which is patchy but temporary and repeated. Examples include diver damage to reefs, slash-and-burn agriculture, storm damage, wave damage on rocky shores, fuelwood cuttings, se- lective logging, and groundhog burrows. Random, patchy mortality, as in slash-and-burn agriculture, is equivalent to fixing D = 0 and increasing mi, the random mortality rate, by a fixed amount k (all species are affected equally; the disturbed patch is denuded). This gives a population-dynamics equation differing from the original:

dp1 ( \ -

d cpi I - E pj - (mi + k)pi - cp pip. (4)

Here, equilibrium abundance for species i is given by

(mi +k) t-J ( ?( ci j=I \\ Ci

which must be solved from species 1 to i, with ci > 0 and Pi j5 0 for all i. The effect of this model is similar to that of varying D, except that increasing m across-the-board has less effect on species with higher per capita fecundity, ci, because of the term (mi + k)l ci. The best competitor, for example, has , - 1 - (ml + k)1cl and undergoes extinction when ml + k = cl is passed. In this case, as one moves toward species that are less competitive but more fecund (ci is larger), the effect of random mortality becomes less and less severe. This is particularly so, because the longer life span of competitively superior species typically makes the nominal mi lower than for more ruderal species. The net result favors poor competitors (good dispersers or weeds). In this case, the extent of extinctions as k increases is even more severe among




the good competitors, and more species are at risk, than in the case studied by Tilman et al. (1994); that is, for random disturbances that produce patchy mortality, the extinction debt is even more severe than the original analysis projected, although it may occur more quickly.

Time-lag considerations

An important prediction of the model concerns the time lag following habitat destruction before doomed species go extinct. Tilman et al. (1994) estimate this lag at 50 to 400 yr or more. Note that this result is highly dependent on m, the individual mortality rate. In the report by Tilman et al. (1994), m for all species was set at 0.02, which gives (on average) a complete turnover by natural mortality in 50 yr. Because, in the model, more competitive species instantly replace (i.e., kill) less competitive ones when they invade a patch, the actual turnover time is considerably shorter than this. This kind of turnover rate (or higher) could apply to grasslands. In contrast, it is not unusual to find old-growth forests where the average tree age exceeds several hundred years and where more shade- tolerant species must wait for extant overstory trees to die. In this case, the transient before species are lost could exceed hundreds to thousands of years. Data in Loehle and LeBlanc (1996) suggest that such long transients may be common in forests; for example, in spite of almost complete loss of reproductive ability in the American chestnut, this species has persisted as stump sprouts for >70 yr. When we approach an extinction lag of thousands of years for forests of long-lived trees, it is not entirely clear that this is a problem one could classify as urgent, since not only will our land use practices change over this period, but even climate may change.

Comparison with species-area model

Tilman et al. (1994) compared their results to those of the species-area model S = cAz, where S is the number of species, A is the area, and c and z are constants. However, much of the increase in the observed number of species with area that is predicted by the species-area model results from the progressive inclusion of more habitat types (due to gradations in elevation, soil, rainfall, etc.) in larger areas (Huston 1994). In very uniform habitats, the change in species number with area can be very gradual. In remnant forest patches, patch area and species number may be unrelated if remnants represent uniform topographic sites (Dunn and Loehle 1988). The extinction-debt model, in contrast, is specifically based on a model that seeks to explain multispecies coexistence within a uniform habitat. To relate this model to regional- scale habitat destruction and compare it with the species-area curve, one would have to create a model of multiple uniform habitats with relations within each habitat being governed by Eq. 1 (or maybe Eq. 4). To

do this, one would have to remember that many species occur in more than one habitat. In fact, some species are weeds (high ci and high mi, low competitive ability) in some habitats but are good competitors in others. Thus, direct comparison of Eq. 1 and the species-area curve model (as in Tilman et al. 1994, Fig. ld) is not possible without a version of Eq. 1 with much more explicit spatial structure. It has been shown that emerging properties from dynamics of explicit spatial structure could not be simply predicted by mean-field approximation (Harada and Iwasa 1994). Tree species-area curves derived from isolated forest blocks in Ghana suggest that ecological processes are active, but their effect is very much over- shadowed by that of sampling: larger reserves contain more plots that sample more of the community (Hill et al. 1994). When the sampling effect is removed from the data, the correlation coefficients between species and area are reduced from 0.9 to as low as 0.4. Their study indicated that inferences made about the importance of ecological processes may prove in- accurate, leading to further caution in the use of species-area curves for conservation biology and- in link- ing them to metapopulation dynamics.

It is particularly important to note that the consequences of a similar level of habitat destruction are not comparable between a metapopulation model and those predicted from a species-area model. For the same number of species S and initial area, the metapopulation model assumes coexistence of these S species within a uniform habitat. Reduction in area by D% causes a loss of a certain number of the more competitive species (ignoring the issue of patch size of disturbances for the moment). In contrast, the S species coexisting in a region that yields the species- area curve coexist because many of them are spe- cialists in different habitats. Regional reductions in undestroyed areas usually occur at the particular ex- pense of certain habitat types. When this reduction occurs, all species within the destroyed habitats are lost across the entire spectrum of competitiveness or dispersal ability. Furthermore, these species are lost immediately, and not after a lag period as in the extinction-debt model. Thus the types of species lost and the time scale over which they are lost differ radically between the two types of models.

We may further illustrate the incompatibility of the metapopulation and species-area approaches as fol- lows. It has empirically been found that a good de- scription of the species number on an island is given by the equation S = cAZ, where A is the area of the island. If we assume that the number of species lost is SL(SL ? S) because of habitat destruction, the cor- responding area of habitat lost is AL(AL ? A). Follow- ing the Tilman et al. (1994) approach, the conditions SL n (S - SL) = 0 and AL n (A - AL) = o have to hold if



788 CRAIG LOEHLE AND BAI-LIAN LI Ecological Applications Vol. 6, No. 3

SL S - SL ( - AL

PI 1=~ _ 5 c(A ) S - SL cS -AL)z,

and

S= 1 -C(l -D)Z S

because

D= AL- (6) A

These required conditions create a paradox with Tilman et al.'s (1994) metapopulation approach of competitive coexistence of multispecies because they need a bal- ance between the immigration and extinction of species for isolates of different sizes and distances from the source of colonization. Each habitat in a metapopulation model is isolated and does not share common species like weeds, as discussed previously. In contrast to the island-biogeographic case, all species could theo- retically occupy every site, and immigration is related to species richness in metapopulation dynamics (Col- lins and Glenn 1991) because a uniform (or similar) habitat is modeled. Total isolation is extreme in metapopulations (Lawton 1995). Because the Levins (1969) model (and the Tilman et al. [1994] model also) does not incorporate the rescue effect, it does not predict a correlation between geographic distribution and abundance (Gotelli 1991, Lawton 1995). The linkage of metapopulation models and the species-area curve in Tilman et al. (1994) may not be logically sound and is difficult to relate to cases in the real world.

CONCLUSIONS

The extinction debt model makes a significant set of predictions, but it must be related with care to real- world situations. For disturbed landscapes where permanently destroyed sites are uniformly distributed and are at the scale of species' use of space, and also for general reductions in fecundity, the original extinction- debt model applies directly. For habitat destruction that leaves large patches undisturbed, the model overesti- mates likely extinctions, but delayed extinctions due to stochastic loss of small populations should still occur, so the extinction-debt concept still applies, although via a different mechanism. For random, patchy mortality, such as slash-and-burn agriculture, the prop- er analysis modifies m (mortality, or local-extinction rates), not D (proportion of habitat permanently destroyed), and the result is even more severe delayed extinctions of superior competitors than in the original analysis. Thus a variety of models that more closely relate to real-world conservation situations nevertheless produce an extinction-debt effect, affecting either the most competitive or the rarer species. The predic-

tions of species loss by the species-area effect result from different mechanisms, affect species across all competitive classes, and are not delayed, and thus are not directly comparable to losses within a habitat predicted by the extinction-debt model.

ACKNOWLEDGMENTS

This paper was prepared in connection with work per- formed under contract W-31-109-ENG-38 with the U.S. De- partment of Energy, Office of Energy Research, Office of Health and Environmental Research. R. M. Miller, M. Hous- ton, and H. Wu provided helpful reviews.

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Habitat Destruction and the Extinction Debt Revisited