First, Hudson et al. based their interpretation on large reductions in the amplitude of the 1989 and 1993 declines in grouse numbers in response to treatment, but their measure of grouse numbers was the number of birds shot, not the population size. Indices of population size such as sequential hunting or trapping statistics invariably overestimate the variance in population size when compared to direct counts (3). Hudson et al. compared numbers of grouse shot with numbers actually counted in one control area and showed that variance in the former was at least tenfold larger than in the latter. No attempt was made to shoot birds in 1989 and 1993 in five out of six untreated control populations (4). If the increased variance caused by the sampling process (shooting) is taken into account, it can be inferred that at least 100 birds per square kilometer were present on the control areas in 1989 and 1993. Further, gamekeepers knew the treatment allocations because they were the people treating grouse with anthelmintics, and this could have significantly biased the shooting effort. Thus, there are insufficient data to accurately estimate differences in cycle amplitude between control and treated areas.

Second, despite Hudson et al.'s claim that cycles were stopped, cyclic fluctuations took place on treated areas where parasitism was reduced. Cycle amplitude varies greatly in red grouse populations (as in other species) with cyclic dynamics (5). Parasite dynamics is thought to be dominated by rainfall--which affects the survival of free-living parasite larvae (6)--in drier parts of Scotland, where low amplitude cycles with periods of up to 10 years take place and where parasites are thought not to cause cycles (6, 7). Thus, observing a reduction in cycle amplitude in response to anthelmintics while retaining cyclic dynamics is entirely consistent with hypotheses relating cyclic dynamics to processes other than parasitism (7). Hudson et al. have provided evidence for reduced fluctuations as a consequence of anthelmintic treatment, but the evidence for a change in fluctuation pattern is equivocal.

Xavier Lambin
Department of Zoology
University of Aberdeen
Tillydrone Avenue
Aberdeen AB24 2TZ, Scotland, U.K.
E-mail: x.lambin{at}abdn.ac.uk
Charles J. Krebs
Department of Zoology
University of British Columbia
Vancouver V6T 2A9, Canada
E-mail: c.krebs{at}zoology.ubc.ca
Robert Moss
Institute of Terrestrial Ecology
Hill of Brathens, Glassel
Banchory AB31 4BY, Scotland, U.K.
E-mail: rmoss{at}ite.ac.uk
Nils Chr. Stenseth
Division of Zoology, Department of Biology
University of Oslo
P.O. Box 1050
Blindern N-0316 Oslo, Norway
E-mail: n.c.stenseth{at}bio.uio.no
Nigel G. Yoccoz
Norwegian Institute for Nature Research
Polar Environmental Centre
9005 Tromso, Norway
E-mail: nigel.yoccoz{at}ninatos.ninaniku.no

REFERENCES AND NOTES

1. P. J. Hudson, A. P. Dobson, D. Newbon, Science 282, 2256 (1998) [Abstract/Free Full Text] .
2. D. M. Tompkin, M. Begon, Parasitol. Today, in press.
3. The amplitude of snowshoe hare in Kluane is approximately 14-fold, whereas fur return statistics suggest amplitudes in excess of 1000-fold. Counts of the number of hens in spring in Northern England show an amplitude of 6-fold [ P. J. Hudson, D. Newborn, A. P. Dobson, J. Anim. Ecol. 61, 477 (1992) [CrossRef]], whereas shooting bag statistics suggest amplitude in excess of 1000-fold.
4. Numbers in (1), figures 1A and 2, A and C, are actually number shot +1 as data were plotted on a logarithmic scale. This was not specified in the report.
5. I. Hanski, L. Hansson, H. Henttonen, J. Anim. Ecol. 60, 353 (1991) [CrossRef].
6. R. Moss, A. Watson, I. B. Trenholm, R. Parr, Parasitology 107, 199 (1993) .
7. R. Moss, A. Watson, R. Parr, Ecology 77, 1512 (1996) [CrossRef] [ISI]; J. Matthiopoulos, R. Moss, X. Lambin, Oikos 82, 574 (1998) [CrossRef] [ISI].

Response: Lambin et al. state that we should have used sample counts, not bag records, for our analysis. Their main concern is that the variance in bag records is large at low grouse densities. However, our data show that a decrease in variance only occurred when grouse densities were relatively high, greater than 110 birds per square kilometer (1). Underlying this result is a strong relation between bag records and sample counts that is only slightly confounded by the variance in bag records. In detail, the count data from our main study population show that the variance of the counts fell with the mean grouse density. In other words, at low density there was more variation between counts than at high density because grouse were not evenly distributed across the habitat, but aggregated. At high density, the grouse used all the available habitat and are more evenly distributed.

While we agree that total counts of the whole population would have been useful, this approach would not have been practical. Sample counts would have been less representative than bag records. Moreover, because our description of the population cycles in red grouse (like other cyclic species) is based on indirect estimates of density, we needed to show that our manipulations influenced these indices.

Their second point is that while our manipulations reduced the amplitude of the cyclic fluctuations, there was a residual cycle that could have been caused by some other mechanism. This was predicted from our original model, so the application of Occam's Razor tells us that there is no reason to invoke another mechanism. Based on the preponderance of experimental and monitoring evidence currently available, it is clear that parasites play a dominant role in causing red grouse population cycles (2). In an earlier review of our report, May (3) said of our large-scale experiments that "important ecological questions simply have to be addressed on the right scale--which often means an uncomfortable large scale--even if that means a certain degree of imprecision." We believe that this is a fair appraisal and helps to address the concerns of Lambin et al.

Peter J. Hudson
Institute of Biology
University of Stirling
Stirling FK9 4LA, Scotland, U.K.
E-mail: p.j.hudson{at}stir.ac.uk
Andy P. Dobson
Department of Ecology
and Evolutionary Biology
Eno Hall, Princeton University
Princeton, NJ 08544-1003, U.S.A.
E-mail: andy{at}eno.princeton.edu
Dave Newborn
Game Conservancy Trust
Swale Farm, Gunnerside, Richmond
North Yorkshire, DL8 3HG, U.K.
E-mail: dave.newborn{at}ukonline.co.uk

REFERENCES AND NOTES

1. P. J. Hudson, et al., Science 282, 2256 (1999) ; P. J. Hudson, Grouse in Space and Time (Game Conservancy Trust, Fordingbridge, UK, 1992), figure 4.2, Levenes test for homogeneity, F = 1.91, P = 0.045. Decrease in variance with mean sample count: r = 0.69, P < 0.05.
2. G. R. Wilson and L. P. Wilson, Res. Vet. Sci. 25, 331 (1978) [ISI] [Medline] ; J. L. Shaw and R. Moss, Res. Vet. Sci. 48, 253 (1990) ; P. J. Hudson, J. Anim. Ecol. 55, 85 (1986) [CrossRef]; ___, D. Newborn, A. P. Dobson, J. Anim. Ecol. 61, 477 (1992) ; A. P. Dobson and P. J. Hudson, J. Anim. Ecol. 61, 487 (1992) [CrossRef]; P. J. Hudson and A. P. Dobson, J. Parsitol. 83, 194 (1996) [CrossRef]; P. J. Hudson, D. Newborn, P. A. Robertson, Wildl. Biol. 2, 79 (1997) .
3. R. M. May, Nature 398, 371 (1999) [CrossRef] ; see also D. M. Tompkins and M. Begon, Parasitol. Today 15, 311 (1999) [CrossRef] [ISI] [Medline].