Numerical and functional responses in generalist

predators: hen harriers and peregrines on Scottish

grouse moors

STEPHEN M. REDPATH* and SIMON J. THIRGOOD{*Institute of Terrestrial Ecology, Hill of Brathens, Banchory, Kincardineshire, Scotland AB31 4BY; and

{The Game Conservancy, Crubenmore Lodge, Newtonmore, Invernessshire, Scotland PH20 1BE, UK

Summary

1. The functional and numerical responses of two generalist raptors (hen harrier

and peregrine) were studied on one moor for 6 years and on ®ve other moors for

5 years.

2. Neither species showed numerical responses to grouse abundance. Harrier densi-

ties were highest in areas and years where their small prey (meadow pipits and

small mammals) were most abundant. Peregrine densities were highest on southern

study moors, probably in association with high abundance of racing pigeons.

3. For harriers preying on grouse chicks, the available data ®tted a sigmoidal or

type III functional response. Peregrines showed a type II response to adult grouse

densities around eyries.

4. The proportion of grouse chicks taken by harriers was estimated to have been

highest at densities of 67 chicks km±2 (equivalent to a mean of about 12 broods

km±2). The proportion of adult grouse taken by peregrines appeared to be inversely

density dependent, such that an increasing proportion of grouse was taken at

grouse densities below 20 km±2.

5. In the absence of persecution, the impact of harriers on grouse populations is

most likely to be greatest on moors where alternative prey and thus harriers are

abundant. The question of whether harriers may dampen grouse population cycles

at low grouse density is discussed.

Key-words: Circus cyaneus, functional and numerical responses, generalist preda-

tors, Lagopus lagopus scoticus, predation.

Journal of Animal Ecology (1999) 68, 879±892

Introduction

The impact of predation on prey populations

depends largely on whether and how predators

respond to changes in prey density. Predators can

respond either functionally, by changing individual

predation rates, or numerically, by changing their

density (Solomon 1949; Holling 1959). According to

their responses, di�erent predators have been classi-

®ed as specialists or generalists (Andersson &

Erlinge 1977). Specialists respond numerically either

by immigrating (nomadic specialists) or by higher

breeding success and survival (resident specialists),

whereas generalists respond functionally as well as

numerically (Andersson & Erlinge 1977).

Theoretical models suggest that generalist preda-

tors can have a large impact on prey populations in

certain situations (Murdoch & Oaten 1975;

Andersson & Erlinge 1977; Hanski, Hansson &

Henttonen 1991). This generalist predator hypoth-

esis (GPH) states that high densities of generalist

predators are maintained by a wide range of prey

species and that the predators switch between these

as the relative densities of the prey species change.

This density-dependent predation has a stabilizing

in¯uence on prey numbers, and the GPH has been

suggested to explain variation in vole population

dynamics between Scandinavia and Canada (Erlinge

et al. 1983, 1988; Erlinge 1987; Hansson 1987;

Hanski et al. 1991; Reid, Krebs & Kenney 1997).

In Britain, red grouse (Lagopus lagopus scoticus)

typically show cyclic changes in abundance

(Williams 1985; Hudson 1992). Several generalist

predators prey on red grouse, but their impact is

usually small (Jenkins, Watson & Miller 1964; Moss

& Watson 1985; Hudson 1986). However, game-

keepers usually reduce predator numbers vigorously

Journal of Animal

Ecology 1999,

68, 879±892

# 1999 British

Ecological Society

(Newton 1979; Hudson 1992; Etheridge, Summers &

Green 1997). Several grouse-moor owners recently

allowed their main grouse-killing raptors [hen har-

riers (Circus cyaneus) and peregrine falcons (Falco

peregrinus)] to breed freely and increase to more nat-

ural densities. This has enabled us to study the

impact of these raptors on grouse numbers.

In this paper we examine the numerical and func-

tional responses of harriers and peregrines in the

breeding season. According to the GPH, harriers

and peregrines will stabilize red grouse populations

if they exhibit a density-dependent functional

response to grouse and no numerical response to

changes in grouse density. More speci®cally, we ask:

(i) do harriers and peregrines respond numerically

and functionally to changes in grouse density? and

(ii) does the proportion of the grouse population

killed by these raptors vary with grouse density?

ECOLOGY OF RED GROUSE, HARRIERS AND

PEREGRINES

Red grouse are monogamous, territorial birds which

live in heather (Calluna vulgaris)-dominated moor-

lands of Britain and Ireland. Two main hypotheses

have been proposed to explain their population

cycles: one proposes that cycles result from changes

in grouse breeding success caused by the parasite

Trichostrongylus tenuis (e.g. Hudson, Dobson &

Newborn 1985; Hudson & Dobson 1990; Dobson &

Hudson 1992); the other is that cycles are caused by

changes in recruitment because of variation in

grouse social structure and associated territorial

behaviour (e.g. Moss & Watson 1985; Mountford

et al. 1990; Moss, Watson & Parr 1996). Predation

has been rejected as a possible cause of red grouse

cycles (Hudson 1992; Moss et al. 1996).

Female harriers hunt over grouse moors through-

out the year, although males generally winter else-

where (Watson 1977; Marquiss 1980). They make

their nests in heather and pairs can nest in close

proximity. Harriers are sometimes polygynous, with

one male mating with up to several females.

Peregrines are monogamous, territorial and tend to

stay on territory throughout the winter, although

they may leave during periods of bad weather

(Mearns 1982). Nests tend to be on cli� ledges,

fairly evenly spaced over suitable habitat. Both har-

riers and peregrines take a wide variety of prey,

although during the breeding season meadow pipits

(Anthus pratensis) tend to dominate the diet of har-

riers (Watson 1977), and racing/feral pigeons

(Columbia livia) that of peregrines (Ratcli�e 1993).

Study areas

Most data came from 1992 to 1996 on six study

moors in Scotland, and some additional data came

from 1997 on Langholm moor and moor C (Fig. 1).

Gamekeepers managed each moor, killing the mam-

malian and corvid predators, and burning heather in

small patches to provide nutritious young growth

for the grouse. On all moors, gamekeepers allowed

raptors to breed freely and between them the moors

held a wide range of red grouse densities. On ®ve of

the six moors we estimated, from conversations with

grouse-moor managers and local raptor enthusiasts,

the year when illegal raptor control ceased. On the

sixth moor we knew that raptors had bred freely for

at least 5 years before the study began. As it was

unclear at exactly which time of year the illegal con-

trol had stopped, we took year one as the year fol-

lowing the change in management policy.

On each moor we estimated the density of red

grouse, obtained measures of abundance for moor-

land passerines and small mammals, monitored

breeding attempts by harriers and peregrines, and

studied the diet of these predators by watching birds

at nests and by analysing pellets and prey remains.

We undertook intensive studies of grouse on

Langholm moor, which was sampled in more detail

as a consequence. We also obtained information on

peregrines and their prey on two other areas, one in

northern England and one in the eastern highlands

of Scotland.

Methods

COUNTS OF RED GROUSE

Managers divided Langholm moor into six areas, or

beats, where grouse shooting took place. Within

each beat, we chose two 0´5-km2 sites for grouse

counts. The sites were widely spread, typical of habi-

tat within that beat and with terrain suitable for

Fig. 1. Map of Scotland, showing the study moors

Langholm and moors A±E.

880Numerical and

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generalist

predators

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Ecological Society

Journal of Animal

Ecology,

68, 879±892

counting grouse. On each of the other ®ve study

moors, we chose two 1-km2 areas, and on each of

the further two areas used for estimating peregrine

numbers and diet we counted grouse on four 1-km2

areas.

Grouse were counted during the ®rst half of April

and the second half of July using standard counts

with pointing dogs (Jenkins, Watson & Miller 1963).

This involved the observer walking parallel transects

at 170m intervals with the dog quartering approxi-

mately 85m on either side of each transect, pointing

all grouse encountered. The same combination of

dog and observer was used throughout the study.

We estimated grouse brood size and chick abun-

dance during the ®rst week of June on each area

where we were studying harrier diet. The observer

walked a minimum of 12 1-km transects on each

area. Upon encountering a brood, the dog was

worked for 5min in an attempt to ®nd all chicks.

Chick density was the mean brood size in June mul-

tiplied by the density of hens in July. Radio-tracking

had earlier indicated very low rates of adult mortal-

ity during these months (Redpath & Thirgood

1997).

COUNTS OF MEADOW PIPITS

Meadow pipits were counted on line transects

(Bibby, Burgess & Hill 1992) in three 1-km2 squares

selected at random from each of the six Langholm

beats, and six 1-km2 selected from each of the other

®ve study moors. Two parallel transects, 500m

apart, were walked through each square between

06.00 h and 09.00 h during June each year. This was

carried out in the mornings, because previous work

had shown that passerine estimates were in¯uenced

by diurnal variation in detection rates (Thirgood,

Leckie & Redpath 1995). The same observer under-

took all counts in good visibility, light or moderate

winds and no precipitation. He recorded the number

of individuals (by species) within 200m either side

of the transect.

ABUNDANCE OF SMALL MAMMALS

Estimates of small mammal abundance were

obtained by snap-trapping in April. We chose two

trapping sites in representative habitat in each of the

beats at Langholm, and four in each of the other

®ve study moors, again representative of each moor.

In each site, 50 unbaited snap traps were set over

two nights, giving 100 `trap nights' per site. Traps

were checked each morning to record the numbers

of ®eld voles (Microtus agrestis), wood mice

(Apodemus sylvaticus), common shrews (Sorex ara-

neus) and pygmy shrews (Sorex minutus). No other

species of small mammal was caught. Previous work

showed that two nights of snap trapping provided

accurate indices of the abundance of small mammals

(Redpath, Thirgood & Redpath 1995).

NUMBERS OF BREEDING RAPTORS

The number of hen harriers and peregrines attempt-

ing to breed was recorded in early spring by watch-

ing from vantage points for displaying harriers and

by visiting potential peregrine nesting sites for signs

of occupancy. For harriers we also determined

whether males were bigamous by watching how

many females they associated with. Females were

considered either alpha (primary) or beta (second-

ary), depending on which of the two laid her eggs

®rst. No case of males with three or more females

was observed. Harrier densities were expressed as

nkm±2 of grouse moor, as opposed to nearest-neigh-

bour distance, because harriers were not strongly

territorial and occurred in small groups within parts

of the study moors. Peregrines nested at lower den-

sity than harriers (Redpath & Thirgood 1997) and

nests tended to be evenly spaced (Ratcli�e 1993).

For comparison between areas, we therefore used

the spacing pattern of peregrine nests (measured as

the nearest-neighbour distance of eyries used in

1994±96) in a region including the given estate, but

extending beyond that estate's boundaries. As these

peregrine nests were located in a wide area over a

number of estates, some human interference was

suspected in all regions, although its extent was

unknown. For relationships with prey between

areas, we excluded peregrines from moor E and its

surrounds, because this was a coastal area where

birds fed partly on seabirds, and so were not strictly

comparable with the inland peregrines. Each raptor

nest found in spring was monitored through the

breeding season to determine clutch size, and the

number of chicks hatched and ¯edged. Checks were

made regularly in all areas to ensure that no late

breeders or relays were overlooked.

RAPTOR DIET

Harrier diet was recorded from hides during the

nestling period. Each nest was watched for up to

180 h over 6weeks, until the chicks left. We recorded

the start and stop time of each watch, the number

and age of chicks, the time when food was brought

to the nest, the sex of the provider, and the type of

prey. Where possible, prey was identi®ed to species,

but where not, was simply recorded as passerines,

small mammals, nidifugous young (such as grouse

or wader chicks) and lagomorphs (rabbits or hares).

We also collated data from two earlier studies on

harrier predation of red grouse chicks (Picozzi 1978;

Redpath 1991).

At 5weeks, harrier chicks started to leave the nest

and spend time in surrounding vegetation. Some

881S.M. Redpath &

S.J. Thirgood

# 1999 British

Ecological Society

Journal of Animal

Ecology,

68, 879±892

prey was dropped away from the nest during this

period, and so fewer items could be identi®ed to

type. In the ®rst 4weeks, 89% or more of items

could be identi®ed to type, but in weeks ®ve and six,

this ®gure dropped to 71% and 60%, respectively.

For comparisons within and between areas, we

therefore used data from nest watches in the ®rst

4weeks only. When using data from Picozzi (1978),

we included only his data collected during the ®rst

3weeks of the nestling period, so as to be roughly

comparable with our data (Picozzi 1978, table 5).

We studied male and female harriers separately,

because the sexes vary in size and diet, and because

some harriers were polygynous. We also collected

harrier pellets through the breeding season, to com-

pare pellet contents during and after the nest-watch

period.

Peregrine pellets and prey remains were collected

during regular visits to nests. The minimum number

of prey individuals was recorded, based on body

parts. For larger prey items, wings, feet or sterna

were counted to give minimum numbers. For small

prey, each pile of body feathers was counted as a

separate individual. Estimates of prey weight came

from Ratcli�e (1993). Watches from hides at three

nests indicated that adult peregrines consumed an

estimated 188 g day±1 of prey and chicks 222 g day±1,

during the 42-day nestling period (Redpath &

Thirgood 1997), similar to estimates by Weir (1978).

Racing pigeons were available mainly during race

days, when they could be superabundant in pere-

grine territories for short periods. This made them

extremely di�cult to count and consequently ana-

lyses of the availability of peregrine prey necessarily

emphasized grouse. In contrast to harriers, which

nested on the heather moorland, some peregrine

eyries were away from moorland. Therefore, when

comparing diet with grouse availability, we esti-

mated the proportion of heather-dominated moor-

land within a 2-km radius of each. This distance was

approximately half the overall nearest-neighbour

distance. The area of heather-dominated moorland

was estimated by marking such habitat onto maps

in the ®eld. Eyries with dovecotes nearby were

excluded from the analyses to prevent the potential

confounding e�ect of increased pigeon abundance.

Prey remains were collected from some eyries in

more than one year. To minimize the problem of

interdependence between data points, we used

annual mean values for these eyries.

Results

NUMERICAL RESPONSE: HARRIERS

Before considering the numerical response of rap-

tors, we had to know whether their numbers chan-

ged after raptor protection began. During the

previous period of suspected illegal control, harrier

numbers were low and birds generally failed in their

attempts to breed (Redpath & Thirgood 1997). At

Langholm, two nests failed for unknown reasons in

1992, although human interference was suspected.

For four of the moors we had data on harrier num-

bers for each year following the start of protection.

There, the mean densities of females increased year-

on-year for 4 years (Fig. 2). In testing for changes in

prey availability in relation to nesting densities of

harriers, we therefore used only data from year four

onwards. As meadow pipits, red grouse and small

mammals formed 83% of identi®ed prey items at

the nests (see below), we restricted analyses to these

three prey types.

Mean harrier densities varied from 0´06 to

0´21 km±2 between moors (Table 1), and densities of

both males and females were positively correlated

with meadow pipit abundance (Fig. 3). To a lesser

extent, female densities were positively correlated

with small mammal abundance (Table 2). Within

moors, variation in harrier densities from year to

year were related to small mammal abundance, but

not to grouse or meadow pipit abundance. At

Langholm, numbers increased from two to 20 breed-

ing females in 1992±97.

NUMERICAL RESPONSE: PEREGRINES

Whilst harrier numbers on particular moors ¯uctu-

ated more than twofold from year to year, peregrine

numbers were generally more stable (Table 1). Only

at Langholm did peregrine numbers attempting to

breed increase from three to six pairs, whilst drop-

ping by one pair on two of the other study moors.

Latitude was positively correlated to nearest-

neighbour distance of peregrines over the seven

Fig. 2. The mean density of female harriers km±2 (2 1 SE)

from four study moors in relation to the number of years

since raptors were protected from persecution. Year 0

represents the year at which protection started.

882Numerical and

functional

responses in

generalist

predators

# 1999 British

Ecological Society

Journal of Animal

Ecology,

68, 879±892

study areas (Fig. 4. rs=0´82, N=7, P=0´024).

The relationship between spring grouse density and

nearest-neighbour distance was not signi®cant

(rs=±0´25, P=0´52), even after accounting for lati-

tude (P=0´97).

FUNCTIONAL RESPONSE: HARRIERS

Harriers took a wide variety of prey, although

mostly passerines (63%), with grouse forming 15%

of items identi®ed to species (Table 3). Of the 263

grouse seen being brought to harrier nests, 96%

were chicks. For male and female harriers, we stu-

died how provisioning rates varied in relation to the

local abundance of grouse, meadow pipits and small

mammals (Fig. 5). Both males and females tended to

have higher delivery rates of speci®c prey when

these prey were more common. When we used log-

transformed provisioning rate, the relationships

were signi®cant between grouse chicks and both

sexes of harriers (males: r=0´67, N=24,

P<0´001; females: r=0´53, N=31, P=0´002),

pipits and male harriers (r=0´45, N=22,

P=0´038), and small mammals and female harriersTable1.Abundance

(21SE)ofthethreemain

preytypes

andofharriers

andperegrines

onsixScottishmoors

(Fig.1).Lrepresents

Langholm

moor

Study

area

Sizeof

moor

(km

2)

Years

Year

control

stopped*

Meanabundance

Grouse{

Meadow

pipit{

Small

mammalx

Meandensity

(range){

Harrier

Peregrine

L48´6

92±97

1990

30´6

21´4

18´3

22´1

2´2

20´6

0´21

20´05(.04-.41)

0´10

20´01(.06-.12)

A29´7

92±96

1990

18´8

20´9

21´7

22´5

2´6

21´0

0´19

20´04(.10-.34)

0´10

20´00(.10-.10)

B25´1

92±96

<1989

6´7

20´9

14´9

21´7

2´4

20´8

0´17

20´04(.12-.28)

0´04

20´00(.04-.04)

C52´8

93±97

1989

48´1

23´9

6´7

21´2

1´7

20´5

0´06

20´01(.00-.09)

0´04

20´01(.02-.06)

D15´0

92±96

1987

22´9

23´3

11´9

21´4

1´5

21´3

0´08

20´01(.07-.13)

0´07

20´00(.07-.07)

E40´1

92±96

1981

0´8

20´4

16´5

24´2

1´6

20´7

0´17

20´01(.15-.20)

0´03

20´00(.02-.05)

*Yearin

whichillegalraptorcontrolwasthoughtto

havestopped

{Springdensities

per

km

2´

{Summer

counts

per

km

transect.

xSpringcapturesper

100trapnights.

{Breedingattem

pts

per

km

2ofgrouse

moor.

Fig. 3. The mean (2SE) harrier density km±2 for (a)

males, and (b) females in relation to mean meadow pipit

abundance (2 SE) on the six study moors. Only data col-

lected after 4 years of raptor protection were included.

883S.M. Redpath &

S.J. Thirgood

# 1999 British

Ecological Society

Journal of Animal

Ecology,

68, 879±892

(r=0´52, N=29, P=0´004). The other relation-

ships were not quite signi®cant (small mammals and

males: r=0´41, N=22, P=0´06; pipits and

females: r=0´26, N=29, P=0´17).

Delivery rates of grouse chicks to nests by male

and female harriers varied between nests. To try to

explain some of this variation, a stepwise multiple

regression model was used, with grouse delivery

rates (log transformed) as the dependent variable.

The independent variables were estimates of prey

density, hatch date, the number of harrier chicks

and harrier breeding status (measured as monoga-

mous, alpha and beta for females, and monogamous

or bigamous for males). Data from Picozzi's study

(Picozzi 1978) were excluded, because he gave no

measure of pipit or small mammal abundance. For

male harriers (N=22) the overall regression model

accounted for 71% of the variation in grouse provi-

sioning (F6,21=6´23, P=0´002), with the density of

grouse chicks accounting for 53% of the variation

and male status a further 9% (Table 4). None of the

other variables contributed signi®cantly to the

model. For females (N=29), the overall model

accounted for 75% of the variation (F6,28=10´92,

P<0´001), with female status accounting for 39%

of the variation, the number of harrier chicks in the

nest another 20%, and the density of grouse chicks

a further 11%. So, the abundance of alternative

prey was not related to the provisioning rate of

grouse chicks by harriers.

A second regression model incorporated the

breeding density of harriers as an independent vari-

able, to test whether interference between harriers at

high density might reduce their provisioning rates of

grouse chicks. Its inclusion reduced the signi®cance

of the overall regression for males (F7,21=3´1,

P<0´05). Harrier density itself was excluded from

Table 2.Male and female harrier densities in relation to the abundance of the three main prey types. For each sex, two

ANCOVA models were used: between moors, controlling for year e�ects; and within moors, controlling for area e�ects. Log-

transformed data were used throughout

Source d.f.

Adjusted

sums

of squares

Coe�cient

for

covariates F P

Between moors

Males

Red grouse 1 0´001 ±0´013 2´01 0´174

Meadow pipits 1 0´001 0´097 13´76 0´002**

Small mammals 1 0´007 0´041 2´73 0´604

Error 18 0´009

Females

Red grouse 1 0´000 ±0´001 0´52 0´478

Meadow pipits 1 0´009 0´113 11´48 0´003**

Small mammals 1 0´004 0´066 4´42 0´050*

Error 18 0´014

Within moors

Males

Red grouse 1 0´000 ±0´002 0´00 0´958

Meadow pipits 1 0´001 0´033 1´83 0´193

Small mammals 1 0´001 0´033 4´19 0´056{Error 18 0´006

Females

Red grouse 1 0´002 ±0´000 0´00 0´994

Meadow pipits 1 0´000 0´023 0´60 0´448

Small mammals 1 0´004 0´042 4´87 0´041*

Error 18 0´008

Fig. 4. The mean nearest-neighbour distance between pere-

grine nests in relation to latitude for seven areas in moor-

land Britain.

884Numerical and

functional

responses in

generalist

predators

# 1999 British

Ecological Society

Journal of Animal

Ecology,

68, 879±892

the stepwise regression model, with only the density

of grouse chicks being left in the model (t=4´01,

R2=45%). The inclusion of harrier density had lit-

tle e�ect on the overall regression model for females

(overall F7,28=10´4, P<0´001), and the same three

variables were selected using the stepwise model. It

appeared therefore that harrier density had little

e�ect on grouse provisioning rates.

To estimate the number of grouse chicks taken by

harriers during the nestling period, we combined the

data for males and females. A type III functional

response curve was ®tted to the data. This

Table 3.Prey taken by hen harriers, during 2614 h of nest watches at 26 nests in three areas (22 at Langholm, 2 at moor B

and 2 at moor E). Percentages are of all prey seen delivered to nests

% of items at

Prey type Langholm Moor B Moor E

Meadow pipit 45 51 23

Skylark 5 5 15

Other identi®ed passerines 1 2 10

Unidenti®ed passerines 12 21 7

Red grouse 12 0 2

Pheasant 0´1 0 15

Identi®ed waders 1 2 5

Unidenti®ed nidifugous young 2 0 8

Field vole 6 4 1

Rabbit/hare 2 2 4

Other identi®ed mammals 0´5 0 0

Unidenti®ed mammals 5 0 0

Other identi®ed prey 0´3 0 0

Other unidenti®ed prey 8 14 9

Total 2101 126 97

Fig. 5. Relationships between (i) rates at which grouse chicks were brought to harrier nests and grouse chick density; (ii)

rates at which meadow pipits were brought to harrier nests and meadow pipit abundance; and (iii) rates at which small

mammals were brought to harrier nests and small mammal abundance. Each point represents a separate nest and the sym-

bols indicate di�erent study areas. &=Glen Dye (Picozzi 1978); ~=a moor in Perthshire in 1988 (Redpath 1991);

*=Langholm 1993±96; ^=moor E 1993; +=moor B 1995; and &=mean values. Data presented for male and

female harriers separately.

885S.M. Redpath &

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# 1999 British

Ecological Society

Journal of Animal

Ecology,

68, 879±892

accounted for 43% of the variation in provisioning

of grouse chicks [model ®tted by least squares,

a=0´21 (SE=0´04), b=51 (SE=6), k=5´1

(SE=3)]. The standard error for k was large, but

there was a suggestion that the model was a better

®t than the type II response (R2=36%). Also the

reduction in the percentage variation accounted for

was borderline on statistical signi®cance

(F1,29=3´45, P=0´07). We ®tted a type III curve

to the data (Fig. 6), which was then used to calculate

the rate at which grouse chicks were taken from the

moor. This rate allowed us to estimate the numbers

and proportion of available grouse chicks that were

taken during the breeding season. We estimated the

proportion of grouse chicks taken at various harrier

densities, using this equation:

% grouse chicks taken= [Grouse per hour (from

Fig. 6)� 15 h available (Watson 1977)� harrier nests

km±2 grouse moor)]/Grouse chicks km±2.

This calculation assumed that grouse chicks were

brought to harrier nests at the same rate during

weeks 5 and 6 of the nestling period as in the ®rst

4weeks. For nine of the observed nests, >20 h of

observations were obtained during these last

2weeks. At these nests, the rate at which grouse

were brought in at this time was compared with the

rate during the ®rst 4weeks. We found no evidence

for less provisioning of grouse chicks in the last

2weeks (Wilcoxon signed ranks test T=23, N=9,

P=0´5). The functional response curve suggested

that harriers took the highest proportion of grouse

chicks at densities of 67 chicks km±2 (Fig. 7). At high

harrier densities, the curve suggests that over 60%

of available grouse chicks may be taken over the 6-

week nestling period. In the course of the study, the

mean grouse brood size in early June was approxi-

mately 5´5 chicks per pair (Redpath & Thirgood

1997). A density of 67 chicks km±2 therefore is

equivalent to roughly 12 grouse broods km±2.

Table 4. Outputs from a stepwise multiple regression model, examining variation in the provisioning rate of grouse chicks

by male (N=22) and female (N=29) harriers. The dependent variable was the delivery rate of grouse chicks to the nest

(log). Independent variables were grouse chick density, meadow pipit abundance, small mammal abundance, harrier breed-

ing status (monogamous or bigamous), harrier hatch date and harrier brood size. Only signi®cant relationships are shown

Variable R2 (%) R2 (%) Cumulative Coe�cient t P

Males

Grouse chicks 53´5 53´5 0´016 4´79 ***

Harrier status 9´5 63´0 0´330 2´22 *

Females

Harrier status 39´4 39´4 0´290 4´19 ***

Harrier brood size 19´7 59´1 0´194 3´54 **

Grouse chicks 10´7 69´8 0´007 2´98 **

Fig. 6. Rate at which grouse chicks were brought to harrier

nests by males and females combined in relation to the

density of grouse chicks. Each point represents a mean

(2 SE) for one moor in one year. The ®tted curve was:

Y=0´21x5´1/(515´1+x5´1).

Fig. 7. Estimates of the percentage of grouse chicks

removed by harriers over the 6-week nestling period in

relation to the density of grouse chicks. Lines are derived

from the functional response equation for ®ve di�erent

densities of harriers (km±2), which re¯ect the variation in

observed harrier density.

886Numerical and

functional

responses in

generalist

predators

# 1999 British

Ecological Society

Journal of Animal

Ecology,

68, 879±892

Predation of grouse chicks continues beyond the

nestling stage. We had earlier shown that chick dis-

persal occurred at 60 days (median, range 58±

64 days) after hatching, i.e. 18 days after the nest

watches stopped (Redpath & Thirgood 1997). In the

breeding seasons of 1993±96, we excluded samples

of <10 pellets, and compared the percentage of pel-

lets containing grouse in weeks 1±4 (N=7 nests,

mean=24´9%), weeks 5±6 (N=9 nests,

mean=23´9%) and weeks 7 dispersal (N=7 nests,

mean=28´8%). When the e�ect of year was

removed, the collection period had no signi®cant

e�ect on the proportion of pellets that contained

grouse (F1,18=0´75, P=0´4). These data suggest

that the percentage of grouse in the diet of harriers

stayed broadly the same from hatch to dispersal.

FUNCTIONAL RESPONSE : PEREGRINES

Peregrine pellets were collected from a number of

eyries over the ®ve years (Table 5). Pellet analysis

showed that a higher percentage of pellets in north-

ern England and the Highlands contained remains

of Galliformes than pellets from south-west Scotland

(ANOVA controlling for year and season

F1,88=4´43, P=0´038). Second, a higher percen-

tage of pellets during winter contained remains of

Galliformes than in spring or summer (ANOVA con-

trolling for year and area F1,88=10´7, P=0´002).

During the breeding season, we collected 876 prey

items from 20 peregrine nest sites on six moors. The

bulk of these items consisted of racing and feral

pigeons (48%), with red grouse the second most

abundant (Table 6). Of the grouse collected, most

were adult (92%), but remains of 10 chicks were

noted.

In the breeding season there was no signi®cant

linear relationship between grouse density and the

percentage of grouse in the diet (log) by biomass

(t18=1´22, P=0´24), although a quadratic function

suggested some curvilinearity in the data (t17=±2´9,

P=0´01). Unlike harrier nests, peregrine nests were

not restricted to heather moorland, but occurred on

ledges. Therefore the area of available grouse habi-

tat varied considerably between eyries. In fact, the

area of heather moorland within a 2-km radius of

each eyrie explained 31% of the residual variation

in the quadratic function (F1,18=9´04, P=0´008).

We therefore combined the area of heather moor-

land around each eyrie with the grouse density on

that moor to estimate the number of grouse avail-

able to each peregrine pair. There was a signi®cant

linear relationship between this measure of grouse

availability and the proportion of grouse in the diet

(t18=2´17, P=0´04), and again there was evidence

of curvilinearity (Fig. 8, t17=±5´5, P<0´001).

For peregrines, a Type II functional response was

®tted using grouse density expressed as numbers per

area of heather habitat. The model accounted for

46% of the total variation in percentage biomass.

There was one unusual observation with low grouse

density and a percentage biomass of 42%. The resi-

Table 5. Prey items in peregrine pellets, from the four main prey groups: gamebirds (Galliformes), pigeons (Columbiformes),

waders (Charadriiformes) and passerines (Passeriformes). Data from all eyries and years pooled. Some pellets contained

more than one item, so percentages add up to >100%

Season Area

Number

of pellets

% Pellets containing

Galliformes Columbiformes Charadriiformes Passeriformes

Spring N England 123 49 53 15 18

SW Scotland 166 17 61 9 23

Highlands 131 40 46 12 30

Total 420 34 54 12 24

Summer N England 233 30 85 22 51

SW Scotland 487 16 73 18 41

Highlands 401 36 48 10 15

Total 1133 26 67 16 34

Winter N England 569 54 44 22 36

SW Scotland 404 46 31 11 33

Total 973 51 40 17 35

Table 6. Peregrine prey items (%) in summer at 20 eyries

in three regions

South-west

Scotland

North

England Highlands

Number of eyries 13 2 5

Racing/feral pigeon 55 46 31

Red grouse 10 27 26

Other gamebird spp. 0´3 2 1

Wader spp. 7 4 5

Passerine spp. 27 21 34

Other spp. 0´3 0 3

Total prey items 611 52 205

887S.M. Redpath &

S.J. Thirgood

# 1999 British

Ecological Society

Journal of Animal

Ecology,

68, 879±892

dual for this value (40´5) accounted for about 50%

of the residual variation. When this was excluded,

the ®tted model accounted for 74% of the total var-

iation, but we had no a priori reason to exclude this

point.

Because habitat around eyries accounted for

much of the variation in predation rate on grouse,

we limit analysis to how peregrine predation would

vary around eyries. For this we assumed that hunt-

ing range did not vary with grouse density, which

seemed reasonable as peregrine density was appar-

ently set by other factors such as pigeon availability.

Most prey remains were collected during the nestling

period, so we restricted our estimates of numbers of

grouse taken to this time. For a brood of three, the

number and percentage of grouse taken was calcu-

lated from the equation:

Grouse removed

(n)={[(2adults� 188 g)+ (3chicks� 222 g)]� 42}/

607 g� proportion grouse in diet,

where: 188 g=daily food intake by adults, 222

=daily food intake by chicks, and 607 g=average

wt. of grouse. % grouse taken=number of grouse

taken/grouse density per km2 of moorland.

The relationship between the percentage of grouse

taken and grouse density indicated inverse density

dependence, with low predation at grouse densities

>20 km2, but increasing predation as density

declined (Fig. 9).

Discussion

Theoretical studies suggest that generalist predators

may be able to stabilize ¯uctuations in their prey if

predator densities are unrelated to prey densities

and if their functional response shows some density-

dependent predation (Hanski et al. 1991). By these

criteria, the ®ndings in our study suggest that har-

riers, but not peregrines, may have the potential to

dampen ¯uctuations in grouse numbers.

NUMERICAL RESPONSES

We found no evidence that breeding densities of

either harriers or peregrines were related to grouse

density. Variation in harrier density within and

between study moors suggested that harriers were

more abundant on moors with more small prey, and

that they responded di�erently to meadow pipits

and small mammals. Their mean density on a given

moor appeared to be set by the abundance of mea-

dow pipits, but between years the number ¯uctuated

around that mean density in accordance with the

availability of small mammals. Peregrine density

was higher on the southern moors, as found by

Ratcli�e (1993), who suggested that this pattern

may be caused by greater availability of racing

pigeons further south.

Harrier densities have been found to ¯uctuate in

line with the abundance of small mammals in

Scandinavia (Hagen 1969; Korpimaki 1985) and

North America (Hamerstrom 1986). In such situa-

tions, the alternative prey hypothesis (APH) states

that the diet of generalist predators changes accord-

ing to the cyclic phase of the main prey, causing an

e�ect on the alternative prey that varies between

years (Keith et al. 1977; Angelstam, LindstroÈ m &

Wide n 1984, 1985; Korpimaki, Huhtala & Sulkava

1990; Kurki et al. 1997). Where vole populations are

cyclic, this hypothesis predicts that generalist preda-

tors should tend to synchronize cycles in popula-

Fig. 8. The percentage of grouse in peregrine prey (by bio-

mass) in relation to estimates of grouse abundance within

a 2-km radius of each eyrie. Line represents ®tted type II

functional response Y=53´4x/(8´4+x).

Fig. 9. Estimates of the percentage of grouse removed by a

pair of peregrines with three chicks in relation to grouse

density within a 2-km radius of their nest sites. Line

derived from the functional response equation.

888Numerical and

functional

responses in

generalist

predators

# 1999 British

Ecological Society

Journal of Animal

Ecology,

68, 879±892

tions of alternative prey species. In these examples,

mammals (hares in North America and voles in

Scandinavia) formed the main prey, with predators

switching to alternative prey when mammals became

scarce. Our few data from Langholm suggested that

small mammals underwent a 3-year ¯uctuation.

However, we found little evidence of a functional

response to small mammals, so the main e�ect of

the small mammal cycle might be to alter harrier

density. Thus, in contrast to the APH, the impact

on grouse may be greatest in years when small

mammals are most abundant.

FUNCTIONAL RESPONSES

A range of functional response types has been

observed in avian predators. Korpimaki & Norrdahl

(1989, 1991) recorded type I (linear functional

responses) in some species of specialist raptors prey-

ing on voles in Finland. More commonly for general-

ist predators, type II functional responses have been

observed (e.g. Keith et al. 1977; Wikman & Linde n

1981). Type III responses have been suggested for

goshawks preying on grouse (Linde n & Wikman

1983) and have been recorded in some mammalian

predators (e.g. Keith et al. 1977; Pech et al. 1992).

Clearly, the shape of the functional response is criti-

cal in assessing the impact of these di�erent preda-

tors on prey populations. For predators such as

harriers and peregrines which show no numerical

response, a sigmoidal functional response would pro-

vide a mechanism for density-dependent predation.

The two functional response curves that we

recorded depended on data from several moors with

a spread in grouse densities. It is better if such data

can come from within moors over time, to prevent

inherent site di�erences in¯uencing the shape of the

response. It is possible, for example, that habitat dif-

ferences between moors may in¯uence the vulner-

ability of grouse to raptors, so that raptors in

di�erent areas with the same density of grouse may

take these prey at di�ering rates. However, in situa-

tions where prey numbers are limited by their preda-

tors, it may not be possible to measure predation

rates over a wide range of prey densities, as high

densities will not be attained. In such situations,

insights into the pattern of predation may be

obtained by studying predators on di�erent areas.

For harriers preying on grouse chicks, the evidence

suggested that the functional response was sigmoidal

(Type III). In this case, the upper part of the curve

depended on data from Picozzi (1978) and we do not

know how harriers at Langholm would have

responded to similar grouse densities. However, the

data from Langholm were in the critical part of the

curve and, as provisioning rates must level out at

some stage, the assertion that the curve is sigmoidal

seems reasonable. It would be useful to ®nd, if possi-

ble, the grouse chick density at which the curve

would level out within the Langholm study area and

how the curves would vary between areas.

The functional response of harriers to grouse

chick density indicated that relatively small changes

in grouse chick density between 40 and 70 km±2 were

related to marked changes in predation rates. This

suggests that harriers may switch their hunting pat-

terns to search for grouse chicks as grouse densities

increase. This idea ®ts earlier observations of hunt-

ing harriers, where birds selected habitats used by

meadow pipits when grouse were scarce, but habi-

tats used by grouse when grouse were abundant

(Redpath 1992). The relationship between the preda-

tion rates of harriers and the density of grouse

chicks di�ered slightly from that described by

Redpath (1991) using earlier data from other areas.

However, the two relationships pertained to di�er-

ent aspects of harrier predation on grouse, with the

earlier work emphasizing the percentage of grouse

in the diet rather than provisioning rate, so the two

are not directly comparable.

For any given density of grouse chicks, individual

harriers varied considerably in the rate at which

they brought grouse chicks to their nests. Much of

this variation was explained by breeding system and

brood size, such that bigamous birds with large

broods caught grouse at the highest rate. Rates of

polygyny in harriers are known to be related to food

abundance (Hamerstrom, Hamerstrom & Burke

1985; Simmons et al. 1986). In both these studies,

the frequency of polygyny was higher in years when

voles were more abundant. Whether or not the same

applied in the current study is unclear. There was

some evidence that polygyny may have been more

frequent on moors where large prey, such as grouse,

were more abundant (Redpath & Thirgood 1997).

We are currently manipulating food availability in

the spring to establish whether polygyny ratios can

be altered. An understanding of what in¯uences the

breeding system of harriers on grouse moors would

help predict the impact on grouse populations.

Estimates of predation rates derived from func-

tional response curves assumed that harriers did not

interfere with one another and that depletion of

food supply as a result of predation had no e�ect.

Our analyses suggested that the breeding density of

harriers had little e�ect on the provisioning rates of

grouse chicks to harrier nests. There was also no

seasonal reduction in the proportion of harrier pel-

lets containing grouse, suggesting a lack of any clear

e�ect of depletion of grouse chick on provisioning

rates. Redpath (1991) observed a minimum of ®ve

individual males hunting the same 400 ha area of

moorland over the same time period, suggesting that

harriers are relatively tolerant of each other away

from the immediate nest site. Grouse chicks are

available to harriers in broods which are guarded by

889S.M. Redpath &

S.J. Thirgood

# 1999 British

Ecological Society

Journal of Animal

Ecology,

68, 879±892

the adult grouse, and the e�ects of possible deple-

tion might be lessened if harriers used adult grouse

as a cue to the availability of grouse chick.

Although we found no e�ects of depletion when 30±

40% of the grouse chicks were taken, it is likely that

the e�ects may be more apparent towards the maxi-

mum potential predation rates of 60±70% of grouse

chicks being taken.

Why should harriers respond numerically to small

prey, but functionally to grouse? The answer pre-

sumably lies in the seasonal availability of grouse

chicks. Male harriers start displaying to females in

early spring, and females appear to choose males

principally on their provisioning performance

(Simmons 1988). Thus the availability of food to

males is likely to be critical in setting harrier density

on a given moor. Males kill adult grouse very rarely

(one observation in 9 years of study of harriers on

grouse moors) and they provision females with

small prey during courtship and incubation.

However, grouse chicks are readily caught by male

harriers and when they emerge they presumably

represent more pro®table prey items for the male to

feed to his female and brood.

In contrast to harriers, prey remains at peregrine

eyries indicated that in terms of biomass, the pro-

portion of grouse as prey levelled o� at 20±40% at

grouse densities >20km±2. The data for high

grouse densities came from moors other than

Langholm. However, as for the harriers' functional

response, the peregrine data from Langholm were

again in the critical part of the relationship. The fact

that the curve which passes through the Langholm

data must inevitably level out suggests that our

assertion of the curve being asymptotic is reasonable

for peregrines. So, predation by peregrines appeared

to be inversely density-dependent, such that the pro-

portion of available grouse taken was highest at

densities <20 km±2. This implies that peregrine pre-

dation may have a destabilizing e�ect on grouse

numbers. This calculation assumes that food con-

sumption was constant between territories, whereas

consumption may vary according to food availabil-

ity. Such e�ects have not been investigated, and

may alter the slope of the functional response curve.

Further data on the rate of grouse predation by per-

egrines at di�erent prey densities are required to test

this assumption.

IMPACT OF RAPTORS ON RED GROUSE

In addition to the numerical and functional

responses, the potential for harriers to limit grouse

populations at low density is further increased by

three other factors. First, harriers in Britain selec-

tively nest in heather (Redpath et al. 1998), which is

also the main food plant of grouse. Reasons for this

nest choice are unclear, but one inevitable result is

that the encounter rate between the two species

must rise. Second, male harriers, unlike most other

British raptors, are not strongly territorial and can

breed at high density (Newton 1979). Third, harriers

are unusual in that they are frequently polygynous

(Newton 1979), so that high densities of males can

attract even higher densities of females. Hence, the

ratio of harriers to grouse can be high compared

with other territorial, monogamous predators such

as peregrines, which are not restricted to the same

habitat as grouse.

We studied predation during the nestling period

of breeding harriers and peregrines, when food

requirements were highest and when the most accu-

rate data could be obtained. Even over such a short

period, we estimated that predation on grouse

chicks could be over 60% at maximum-recorded

harrier densities. This excluded predation before the

nestling period and that between ¯edging and dis-

persal, when the same number of adult raptors was

present. Breeding birds returned to Langholm in

late February/early March, when we had little infor-

mation on harrier prey. However, Picozzi (1978)

suggested that females may take many adult grouse

before egg-laying commences and our radio-tracking

data showed that mortality because of raptors was

high at this time of year (Redpath & Thirgood

1997). Data from pellets indicated that the fre-

quency of grouse in the harrier diet did not vary sig-

ni®cantly from hatching to ¯edging, so estimated

predation on grouse chicks represents minimum

values. Some female harriers remain on the moor

throughout the year, although males leave as pipit

numbers fall (Watson 1977; Redpath 1989) and

females eat larger prey than males (Marquiss 1980).

Territorial peregrines were present on the moor

throughout the year. The proportion of their pellets

containing grouse in winter and spring, when alter-

native prey species were relatively scarce, exceeded

that in summer (Redpath & Thirgood 1997). It

appears, therefore, that although we studied preda-

tion during a relatively short period, predation rates

are also likely to be high at other times of year.

The impact of predation on grouse numbers

depends, to a certain extent, on whether or not there

is selection for certain individuals. Hudson, Dobson

& Newborn (1992) found that foxes sometimes took

heavily parasitized individuals and Watson (1985)

that predators killed nonterritorial grouse. Our data

from Langholm showed low parasite burdens and

few nonterritorial birds (Redpath & Thirgood 1997).

To summarize, the evidence indicated that there

was density dependence in harrier predation on

grouse chicks but not in peregrine predation on

adult grouse. The breeding densities of these gener-

alist predators were related to the abundance of

alternative prey, so their impact on grouse numbers

varied between moors. On moors with abundant

890Numerical and

functional

responses in

generalist

predators

# 1999 British

Ecological Society

Journal of Animal

Ecology,

68, 879±892

small prey and no raptor persecution, such as

Langholm, breeding densities of harriers were likely

to be high. If these grouse populations were to fall

to densities <12pairs km±2, during cyclic troughs,

our data suggest that harrier predation might hold

them there during the breeding season. This pattern

is reminiscent of the suggested impact of generalist

predators on voles at southern latitudes. In other

words, where alternative prey are abundant, preda-

tors are also abundant and vole populations do not

cycle (Angelstam et al. 1984, 1985; Andre n et al.

1985; Hanski et al. 1991). Our data suggested that

predation by peregrines hunting in the absence of

other predators would not limit grouse numbers.

However, peregrine predation in addition to harrier

predation is likely to reduce the ability of low-den-

sity grouse populations to increase.

Acknowledgements

We thank the landowners, especially Buccleuch

Estates for allowing the work. We are especially

grateful to I. Newton for help and support, and to

M. Avery, I. Bainbridge, C. Galbraith, R. Green, P.

Hudson, I. Newton, G.R. Potts, P. Robertson and

D. Thompson for useful comments, P. Rothery for

statistical support and M. Harris, S. Albon,

A.Watson and two anonymous referees for com-

ments on earlier drafts. Many assistants, students

and raptor observers helped with ®eld data, particu-

larly B. Anderson, G. Buchanen, S. Campbell, D.

Calder, C. Cronin, E. Donnelly, B. Etheridge, C.

Hill, F. Leckie, P. Lindley, M. Madders, J.

Martinez, R. May, B. Mitchell, D. Parish, A. Smith

and A. Tharme. R. Clarke kindly did most of the

pellet analysis. The study was funded by Buccleuch

Estates, Peter Buckley of Westerhall Estates, Game

Conservancy Trust and Scottish Research Trust,

Institute of Terrestrial Ecology, Joint Nature

Conservation Committee, Royal Society for the

Protection of Birds and Scottish Natural Heritage.

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1998

892Numerical and

functional

responses in

generalist

predators

# 1999 British

Ecological Society

Journal of Animal

Ecology,

68, 879±892