Technical Comments

Comment on "On the Regulation of Populations of Mammals, Birds, Fish, and Insects" IV

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Science  07 Jul 2006:
Vol. 313, Issue 5783, pp. 45
DOI: 10.1126/science.1127705


Sibly et al.'s (Reports, 22 July 2005, p. 607) contention that density dependence acts strongly on low-density animal populations irrespective of body size contradicts many long-term studies of large mammals. Their findings were distorted by harvest records, which may poorly reflect population trend. Omitting unreliable data, their massive data set is reduced to only one case for large mammals.

Sibly et al. (1) used a massive collection of data on wild vertebrates and invertebrates [Global Population Dynamics Database (GPDD)] to assess density-related changes in population growth rates (pgr). In the simple logistic population growth model, pgr declines linearly with density, under the assumption that each additional animal's resource use has the same negative effect on the survival and reproduction of others in the population. Sibly et al. found, however, that from insects to mammals, pgr versus population size generally showed a concave relationship, indicating that additional individuals have a more depressing effect at low density. This result, while not novel for short-lived animals, was contrary to expectation for large, long-lived (“K-selected”) mammals, which were thought to exhibit weak density dependence until very near carrying capacity, K (i.e., a convex curve) (2, 3). A chief implication is that overharvested populations of large mammals (well below K) may take much longer to recover than expected. We show that this contention is unfounded.

Many time series in the GPDD are harvest data, not population data. Harvests mirror population size only when hunter numbers or success rates directly respond to changes in animal abundance, as may be the case for steadily growing or declining populations, or predictably cyclic populations (46). Even so, harvests may overestimate variation in population size by several orders of magnitude (7) or may underestimate variation if hunter numbers are restricted by management agencies.

Harvest trends may reflect changing demand for the hunted species. Although this relationship is well known from several centuries of commercial harvests of furbearing mammals (8), Sibly et al.'s analysis included numerous fur harvest records (Fig. 1). Harvests also may vary with economic and social conditions (affecting numbers of hunters, their effort, and their motivation) (Fig. 2) and with hunting methods (efficiency). Wildlife managers are as likely to be alarmed that rising harvests are causing a population decline as they are to take comfort that such harvests are tracking an increasing population. Treatises on the subject of population monitoring do not even address the use of raw harvest numbers to assess population trend (9, 10). Even adjusted for hunter effort, harvests may poorly reflect changes in population size because of other confounding variables (11).

Fig. 1.

Northern fur seal (Callorhinus ursinus) harvests in Alaska, considered by Sibly et al. to be reflective of population size and a case of a concave growth curve for a large mammal (GPDD number 3804, θ = –3.98). The sudden increase in harvest in 1868 reflected the purchase of Alaska by the United States the previous year (indicated by line). During previous Russian ownership, low harvests were a result of a ban on killing female seals and limits on the killing of males, yielding high populations. These restrictions were lifted after the U.S. purchase, promoting more interest in sealing, including the commencement of pelagic sealing, leading to near extermination of the species (21). Hence, these harvest data reflect the inverse of population size. Long-term data on living populations of this species consistently show density effects only near K (15, 22).

Fig. 2.

Bear (Ursus spp.) harvests in North America, taken to be reflective of changes in population size. Sibly et al. considered this a case of a concave growth curve for a large mammal (GPDD number 3769, θ = –12.6). Increasing bear harvests during this period reflected increased European settlement of western North America, and commensurate increased killing and widespread extirpation of bears (23). Hence, these harvest data reflect the inverse of population size, up to the point where bear numbers collapsed to the extent that kills began to decline.

Explanatory information provided with the GPDD indicates that harvest data are regarded as “highly unreliable” as population data. Sibly et al. asserted that their conclusions remained unchanged when certain categories of unreliable data (including harvest data) were omitted; however, they did not indicate the taxonomic breadth or number of remaining cases. We scrutinized the 977 records of GPDD mammal data and found that 65% were harvest data. We eliminated these and other data regarded as low quality, as Sibly et al. had done, and then continued filtering data using their procedures (table S1). This left 14 time series where θ, the parameter describing curvature of the pgr function, was specified and within the ascribed confidence limits. Only three of these valid data sets were large mammals, only one of which exhibited density dependence (with a slightly convex pgr curve). Two had concave pgr functions, but in both of these, pgr related more to rainfall than to density (12, 13); strong environmental variation needs to be accounted for before assessing density-dependent relationships (14).

Large, amalgamated databases like the GPDD may be a potential source for new insights; alternatively, as in this case, interpretations of second-hand data may lead to erroneous inferences. Careful, long-term studies of population change in large mammals, difficult as they are, have consistently concluded that these species exhibit strong density dependence only near K; thus, maximum net increase in population size occurs between K and K/2 (1417). That principle is inherent in national legislation governing exploitation of marine mammals (Marine Mammal Protection Act) (18) and is relevant in projecting population growth and recovery of other previously overharvested, K-selected species, such as grizzly bears (19).

Sibly et al.'s analysis provides little reason to challenge this paradigm of population growth for large mammals. Their regression, indicating that large mammals have a more concave θ than smaller mammals, is not meaningful given that θ was not obtained from reliable population data. Harvest data may yield the perception of a concave relationship even if pgr versus population size is convex. Accordingly, Sibly et al.'s warnings of “dangerous consequences” related to slower-than-expected recovery of large mammal populations seems unwarranted. Nevertheless, because large mammals have low pgr, managers should err on the side of caution and treat local circumstances on a case-by-case basis, because there are likely to be some situations where growth rates are depressed at low density (20).

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Table S1

References and Notes

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