The interplay between culling and density-dependence in the great cormorant: a modelling approach

Summary

• 1
   The population of great cormorants Phalacrocorax carbo sinensis breeding in northern Europe has increased from 5000 pairs around 1970 to c. 100 000 pairs in the late 1990s, leading to serious conflicts with fishery and aquaculture interests. Management action, including widespread culling, has been taken in several countries.
• 2
   Since 1990, presumed density-dependent declines in demographic performance have appeared in cormorant populations. We employed an extended Leslie matrix model to study the interaction between culls and density-dependence in regulating breeding and autumn population sizes, with emphasis on evaluating the effects of culling.
• 3
   During 1979–92, the breeding population of great cormorants in northern Europe increased by 18% year⁻¹, in accordance with observed life-cycle parameters before the appearance of density-dependent declines.
• 4
   We modelled six scenarios with varying assumptions about the strength of density-dependence in adult survival and the proportions of breeding cormorants. A series of cull estimates was also included. Scenarios with moderate or strong levels of density-dependence provided predictions that fit the observed numbers of breeding pairs, whereas scenarios without density-dependence in survival overestimated real population growth.
• 5
   The most well-supported scenarios indicated that the effect of culls at the present level (1998–99: 17 000 cormorants shot) was limited (< 10% reduction at equilibrium). Increasing the annual cull to 30 000 still had a limited effect, whereas shooting 50 000 birds year⁻¹ led to population extinction within 20–40 years. Shooting a fixed proportion of the population exceeding a threshold, through density-dependent culling, could eliminate differences among scenarios and stabilize the population.
• 6
   We conclude that culls probably have had a limited effect on cormorant populations, but if carried out in a density-dependent way they could stabilize numbers near a desired level. However, a reduction in the number of cormorants may not lead to a similar reduction in conflicts, and actions to control damage rather than cormorant populations are likely to be more cost-effective. If culling is to be continued, we recommend the adoption of an adaptive and co-ordinated management strategy across Europe. We also advocate the need to account for density-dependent mechanisms in general culling strategies.

Introduction

The history of pest control is full of examples of management actions that did not have the expected effect (examples in Feare 1991). In many cases, failures could be attributed to a lack of understanding of the population dynamics of the species concerned. Prior knowledge is likely to provide a better basis for management, but the most reliable way to avoid some failures is to integrate existing information on life-cycle parameters (survival, reproduction, etc.) and their variation into a formalized population model (Caswell 1989; Tuljapurkar & Caswell 1997), which can then be used in scenarios that project current population trends. Population models have been used with success to predict or evaluate the effects of management (Middleton, Nisbet & Kerr 1993; Bédard, Nadeau & Lepage 1995; Wanless et al. 1996). However, the reliability of population models depends critically on the quality of the information used. In particular, neglecting naturally occurring density-dependent mechanisms in models of pest populations may lead to overly optimistic predictions of the effects of management actions.

Piscivorous birds, such as herons (Ardeidae), pelicans (Pelecanidae), cormorants (Phalacrocoracidae), mergansers Mergus spp. and even kingfishers (Alcedinidae), have long been considered as competitors of human fisheries and aquaculture. They have often been persecuted heavily, and population densities have been kept artificially low. For many species, persecution declined during the 1960s and 1970s, allowing return to former population levels. Increase in some cases was so large that conflicts have been renewed, with pressure from fishery/aquaculture interests to reduce some populations. Two notable cases concern the double-crested cormorant Phalacrocorax auritus in North America and the great cormorant Phalacrocorax carbo L. in Europe. Populations of both have grown spectacularly between 1970 and 1995 (van Eerden & Gregersen 1995; Hatch 1995), and fish farmers (catfish Ictalurus spp. in North America and carp Cyprinus carpio in Europe) in particular claim that predation by cormorants endangers their economic livelihood (Price & Nickum 1995; Adamek, Klinger & Staub 1997). In Europe, most conflicts concern the continental subspecies of the great cormorant P. c. sinensis Blumenbach (‘cormorant’ from here on), which has increased much faster than the Atlantic subspecies P. c. carbo (Debout, Røv & Sellers 1995; Trolliet 1999). Recently, indications of density-dependence in cormorant life-cycle parameters have been identified (Bregnballe 1996a; Frederiksen & Bregnballe 2000a; M. Frederiksen & T. Bregnballe, unpublished data). Here, we used a density-dependent matrix population model to evaluate the effects of management actions on population growth of the population of P. c. sinensis breeding in northern Europe.

In several European countries, central or local authorities have now authorized cormorant culls at night roosts or elsewhere, in most cases without subsequent assessment of the effects on populations. Management recommendations about cormorant populations in Europe have recently been drawn up (Anonymous 1997). They do not include measures to reduce the range-wide population size, but mention the option of attempting to reduce numbers of cormorants at a regional level by shooting or intervention in breeding colonies. There is clearly a need to know how such actions might affect population growth, and a predictive population model should be very useful in this situation. A particularly critical question is how culling cormorants will interact with density-dependent regulation.

Two previous attempts have been made to model cormorant population growth in a management context (Lebreton & Gerdeaux 1996; Bregnballe, Goss-Custard & Durell 1997). However, both were limited by data availability (Kortlandt 1942). Nevertheless, some robust conclusions were reached, such as: (i) population growth rate of cormorants is more sensitive to changes in adult survival than in fecundity, indicating that the shooting of adults may be the most efficient way to regulate population size; (ii) if density-dependence is assumed to occur naturally, hunting or culling may reduce the level of stabilization and induce faster stabilization. We took advantage of recent findings on cormorant population dynamics (Frederiksen & Bregnballe 2000a,b; M. Frederiksen & T. Bregnballe, unpublished data) and cull estimates from several European countries in the 1990s to achieve detailed projections of population growth. We modelled the size of both the breeding population and the population present in autumn (before culling), because major conflicts involving cormorants occur during the non-breeding season in areas outside the breeding range.

The aim of this study was first to illustrate how a well-founded predictive population model may be used to evaluate the effects of actual and planned management actions, when these actions interact with naturally occurring density-dependence. Secondly, we also asked the following. (i) Has the cormorant population breeding in northern Europe stabilized, or can further growth in numbers of breeding pairs and/or the autumn population be expected? (ii) To what extent have the culls carried out in several European countries affected the population growth, what is the effect of interactions between culls and density-dependence, and what will be the effect of various culling practices in future years? (iii) Is culling an adequate tool for the management of cormorant conflicts on a regional scale?

The case study

Study population

The cormorant is a large (2500–3000 g) colonial waterbird that feeds almost exclusively on fish (Orta 1992). It is an opportunistic non-territorial feeder, and large numbers of individuals may aggregate to exploit rich food sources, either natural or human-made. Nesting habits are flexible, but in P. c. sinensis the majority of colonies are in trees or on the ground on islands without terrestrial predators.

The breeding population of cormorants in the Baltic–North Sea region of Europe was reduced nearly to extinction by human persecution in the early 20th century. As late as in 1971, only c. 16 colonies with a total of 4749 occupied nests were known in the Netherlands, Germany, Denmark, Sweden and Poland (Bregnballe 1996b). Following protection (partial from 1971, full from 1980), the population in these countries, which we will refer to as the five main countries, increased to 9116 nests in 1979 and 103 204 nests in 1996 (T. Bregnballe, unpublished data). During 1979–92, the annual rate of growth was approximately constant at 18%, but since 1992 population growth in these countries has been much slower. In 1999 there were 114 859 nests, representing a mean growth rate of 3·6% since 1996. Concurrent with the rapid population growth, the range has expanded, and cormorants now breed in England, Belgium, France, Italy, the Czech Republic, Slovakia, Lithuania, Latvia, Estonia, Russia and Belarus, although in much smaller numbers.

Cormorants from the Baltic–North Sea region winter over large parts of Europe, from the Baltic to the Mediterranean coast of North Africa (van Eerden & Munsterman 1986; Yésou 1991; Bregnballe, Frederiksen & Gregersen 1997). Large numbers winter along Mediterranean coastlines, but wintering inland in central Europe is also common, especially in mild winters (van Eerden & Munsterman 1995).

Conflicts and management

Cormorants conflict with human fishery and aquaculture interests in several ways. The strongest interactions between cormorant predation and human exploitation are in areas where fish densities are high as a consequence of fish farming, stocking, spawning activities or entrapment in, for example, pound nets. The most widespread perceived conflicts are listed below.

• 1
  Reduction of natural fish populations may lead to decreases in fishery yields. Several studies indicate that this problem is of minor importance, at least in lakes and coastal areas (Dirksen et al. 1995; Keller 1995; Zuna-Kratky & Mann 1995).
• 2
  Predation affects standing fishing gear. Cormorants are attracted to pound nets and gill nets, consuming or injuring fish when attempting to catch them (Bildsøe, Jensen & Vestergaard 1998). This problem may affect the economic viability of this type of fishery, which is widespread in the Baltic area, particularly in Denmark and Sweden.
• 3
  They feed at fish farms. Cormorants are attracted to fish farms, mainly carp ponds, which are too big to be adequately protected by netting or other passive means. Here, they may reduce the yield and injure some of the remaining fish (Glahn & Brugger 1995; Lebreton & Gerdeaux 1996). Carp farming is a widespread traditional activity in central Europe, for example in France, southern Germany, Poland and the Czech Republic.

In management recommendations for cormorants in Europe (Anonymous 1997), it is suggested that each country or regional authority attempts to reduce conflicts through local solutions, which may include lethal means. Measures for reducing the population at a regional level (culling, destruction of eggs or young in the colonies) are mentioned as options, and permission to shoot fairly large numbers of birds has been given in several countries, for example France, Germany and Switzerland. Members of the European Union are not allowed to introduce an open hunting season because the cormorant is not a quarry species in the EU Bird Directive (Directive 79/409).

Cormorant population biology

Most information on life-cycle parameters comes from recent analyses of a long-term study at the Danish colony Vorsø (Bregnballe 1996a; Bregnballe & Gregersen 1997; Frederiksen & Bregnballe 2000a,b; M. Frederiksen & T. Bregnballe, unpublished data). The colony expanded rapidly until 1991, and decreases in adult survival, fecundity and breeding propensity became apparent after 1990 when the colony stabilized and later declined. During colony growth, annual adult survival was approximately 0·89 (range 0·86–0·93) and first-year survival varied around 0·60 (0·50–0·75). Fecundity increased with age until 5 years, when 2·3 chicks were fledged per breeding female. Cormorants started to breed at ages 2–8 years, females earlier than males; c. 45% of 2-year-old females bred. Analyses also indicated that most life-cycle parameters of cormorants breeding at Vorsø were negatively affected by the rapid increase in colony and/or total population size, the exception being first-year survival.

Methods

Model type

We used an extended Leslie matrix model (Leslie 1945; Caswell 1989; McDonald & Caswell 1993) with a pre-breeding census, i.e. the model basically tracks population size at the beginning of the breeding season. The number of age classes in the model was eight, corresponding to the age of full breeding; preliminary analyses showed that extending the model to 20 age classes to allow for senescent declines in survival had no appreciable effect on growth rate. Only the female population was modelled explicitly, and we assumed a balanced sex ratio when calculating total population size. Simulation models were set up and run in ulm 2.1 (Legendre & Clobert 1995) and matlab 4.0 (The MathWorks Inc. Natick MA, USA), where parameters can easily be defined as constant, density-dependent or stochastic (with random variation around a fixed mean). These models were used in a series of steps to answer our basic questions.

Basic input parameters

In order to model population growth in the absence of density-dependent effects, we used mean parameters estimated from Vorsø data in the period prior to 1990, i.e. before obvious declines (Table 1). However, the available data from Dutch colonies (van Eerden & Gregersen 1995; Bregnballe 1996b; Bregnballe, Goss-Custard & Durell 1997) suggested that the breeding output at Vorsø and other Danish colonies was higher than in the Netherlands, and we therefore adjusted all fecundities downwards by 0·3 chicks female⁻¹ to achieve values presumably more typical of the species. No data were available to evaluate whether the values we used for survival and proportions of breeders could be considered typical for Europe in the 1980s and 1990s.

Table 1.  Age-specific parameter values used in the density-independent model, based on results from Vorsø. Fecundities have been adjusted downwards by 0·3, and proportions breeding were derived from a function approximating observed values (see text for details). Survival indicates the probability of surviving from age i − 1 to age i

Age class	Survival	Fecundity	Proportion breeding
1	0·601	0	0
2	0·873	1·3	0·404
3	0·882	1·5	0·620
4	0·889	1·8	0·797
5	0·893	2·0	0·905
6	0·896	2·0	0·958
7	0·897	2·0	0·983
8 +	0·896	2·0	0·993

To facilitate modelling changes in age-specific breeding proportions, we did not use the actual estimates derived from data, but rather a smoothed model of the form:

where a = age (2–8 years). This model provided a close approximation to the observed proportions breeding (Fig. 1).

Figure 1. Age-specific breeding proportions of female cormorants, as estimated from resightings at Vorsø, Denmark (mean of 1980–89 birth cohorts; M. Frederiksen & T. Bregnballe, unpublished data), and as modelled by the equation y = 1/(1 + e^{(2·15−0·88a)}), where a = age.

Inclusion of density-dependence

We simulated the growth of the breeding and autumn population in the five main countries. We started these models at the beginning of the exponential phase of population growth in 1979, with a known number of breeding pairs (9116) and an age distribution predicted from the density-independent model. The density-dependent relationships included were mainly based on the results from Vorsø (Bregnballe 1996a; Frederiksen & Bregnballe 2000a; M. Frederiksen & T. Bregnballe, unpublished data). All parameters except first-year survival were affected by the increasing density, and the effects only became apparent after 1990, i.e. at a time when both local and total population size were already very high. Therefore, we included thresholds for density-dependence in the model so that parameter values only began to decline when population size exceeded a certain value. Below the thresholds, the values in Table 1 were used. Because the extent of density-dependence on the whole-population scale was uncertain, and because the observed decline in adult survival might have been caused directly by the culls rather than by density-dependent mechanisms, we modelled a set of scenarios with varying assumptions about the strength of density-dependence (see below).

We modelled variation in a generic parameter y above a threshold population size as:

where y₀ = the parameter value at low density (Table 1), b = the population size (see below), b_t = the threshold, and g = the slope of the density-dependent relationship. Age-specific breeding proportions above the threshold were modelled as:

We modelled fecundity depending on the number of breeding pairs (females), whereas adult survival and breeding proportions depended on the total number of adult females (2 years or older). Slopes and thresholds of the density-dependent relationships were chosen to mimic observed changes in life-cycle parameters (Table 2 and Fig. 2). Because there was some uncertainty about the strength of the various density-dependent relationships, we modelled six different scenarios with either strong, weak or no density-dependence in adult survival, and either strong or weak density-dependence in breeding proportions (Table 2). The effect of varying the strength of density-dependence in fecundity was so small (at least on breeding numbers) that we present no scenarios including such variation, but briefly mention the effect of varying this assumption.

Table 2.  (a) Characteristics of the six scenarios modelled, in terms of assumptions about density-dependence. (b) Thresholds (b_t) and slopes (g) for density-dependent relationships in the scenarios. Threshold values are the number of potentially breeding females for adult survival and proportions breeding, and number of breeding pairs for fecundity. See also Fig. 2

	Density-dependence in adult survival
(a) Density-dependence in breeding proportions	Strong	Weak	None
Strong	Scenario 1	Scenario 3	Scenario 5
Weak	Scenario 2	Scenario 4	Scenario 6

(b)	Adult survival	Fecundity	Proportion breeding
Threshold	120 000	50 000	100 000
Slope ‘strong’ scenarios	0·000005	0·000005	0·00001
Slope ‘weak’ scenarios	0·0000025		0·000005

Figure 2. Density-dependent relationships used in modelling scenarios (see Table 2 for definitions). The three panels show (from the top) the relationship of fecundity of 5Y+ females (5 years or older) to number of breeding pairs, of survival of 8Y+ females to number of females 2 years or older, and of percentage breeding among 2Y females to number of females 2 years or older.

We ran each scenario with and without the culls in order to evaluate whether management has affected population growth or is likely to do so in the future. Scenarios were run for 50 years, starting in 1979, and predictions compared with observed numbers of breeding pairs 1979–99.

Modelling of culls

An analysis of summary data from 17 French departments (made available by the Conseil Supérieur de la Pêche) showed that first-year birds made up approximately 40% of the culled cormorants (n = 648; M. Frederiksen & J.-D. Lebreton, unpublished data). We assumed an extra mortality in addition to the reported numbers killed (crippling loss) of 30%, i.e. the reported culls were multiplied by 1·3, and we distributed the culls among age classes, with 40% to first-year birds and the remainder proportional to the number of birds in each age class. The autumn population size was calculated immediately before the application of the culls. Because some mortality of juveniles would already have taken place at that date, we arbitrarily considered that survival of first-year birds (S₁) could be partitioned so that survival up to the application of the cull was √S₁, and that consequently survival after the cull was also √S₁. All natural mortality of older age classes was assumed to occur after the cull.

We used estimated numbers culled up to 1998–99 (Table 3) and made three different sets of assumptions about the future cull: (i) that the cull of 17 143 cormorants in 1998–99 would continue indefinitely; (ii) that the cull would increase to 20 000, 30 000, 40 000 or 50 000 birds per year; or (iii) that the cull would be density-dependent, removing a fixed proportion (20%, 30% or 40%) of the autumn population minus 300 000 (e.g. 0·2(N_autumn − 300 000). The value 300 000 was chosen as an example, representing a population size smaller than that which the scenarios predicted at equilibrium.

Table 3.  Approximate numbers of cormorants culled in Europe in the winters 1992–99. Numbers are official figures and do not include illegal shooting

Country	1992–93	1993–94	1994–95	1995–96	1996–97	1997–98	1998–99
Sources: France: DNP, Ministry of Environment; Switzerland: D. Gerdeaux (personal communication); Italy: N. Baccetti (personal communication); Bavaria: T. Keller (personal communication); Germany (rest): W. Knief (personal communication).
France	1000	1500	2500	3572	4 480	7 145	10 000
Switzerland	910	1289	824	1026	1 474	1 236	851
Italy			1000	1000	1 000	1 000	1 000
Bavaria				657	6 259	3 285	3 577
Germany (rest)	189	225	245	218	1 263	531	1 715
Total	2099	3014	4569	6473	14 476	13 197	17 143

Results

Density-independent model

Without density-dependence and using the values in Table 1, the estimated population multiplication rate λ was 1·185, close to the true growth rate of the breeding population 1979–92. Using fecundities estimated from Vorsø resulted in a λ of 1·224, so the lower fecundities, which we assumed to reflect mean values for the population, seemed realistic. This model provided a ratio of total female population at the beginning of the breeding season to number of breeding pairs (1·81) and a stable age distribution (Table 4), which we used in setting up the subsequent simulation scenarios. A scenario without density-dependence, but including known culls, predicted a breeding population in 1999 of 247 000 pairs, more than twice the actual population of c. 115 000 nests.

Table 4.  Density-independent population structure, derived from a model using parameter values in Table 1 and a known number of breeding pairs in 1979 (9116, corresponding to 16 499 females), and used as starting point in scenario modelling

Age class	Age structure in percentage	Numbers in spring 1979 (females)
1	25·18	4 155
2	18·56	3 062
3	13·81	2 279
4	10·37	1 711
5	7·81	1 289
6	5·91	975
7	4·47	738
8 +	13·88	2 290
Total	100	16 499

Scenarios with density-dependence and culling

For the initial scenarios, we used the estimated numbers culled (Table 3) and assumed that the culls would continue at the 1998–99 level. Scenarios 1–5, with different assumptions about the strength of density-dependence in adult survival and breeding proportions, all provided simulated numbers of breeding pairs that were close to those observed (Fig. 3 and Table 5), although scenario 1 underestimated the breeding population. Scenarios 4 and 5 provided the best fit, as measured by squared deviations from the observed values (Table 5). In the first four scenarios, both breeding and autumn populations were predicted to stabilize at approximately the numbers occurring in the late 1990s (91 000–107 000 breeding pairs; autumn population 460 000–512 000). Scenario 5, with no density-dependence in adult survival and strong density-dependence in breeding proportions, predicted that breeding numbers would stabilize at 104 000, whereas the autumn population would continue to increase until 2030 and stabilize at more than 800 000. According to scenario 6, the population should not stabilize until at least 2030 (203 000 breeding pairs and 984 000 in autumn). This scenario was less well supported by the observed numbers of breeding pairs (Fig. 3 and Table 5).

Figure 3. The fit of predictions from the six modelled scenarios to the observed numbers of breeding pairs (occupied nests) in Denmark, the Netherlands, Germany, Sweden and Poland 1979–99 (T. Bregnballe, unpublished data).

Table 5.  Evaluation of the fit between modelled and observed numbers of breeding pairs for each scenario 1979–99. The r² presented here was calculated as , whereN^pred is the predicted number of breeding pairs for each scenario, and N^obs is the observed size of the breeding population

Scenario	r^2
1	0·955
2	0·985
3	0·974
4	0·992
5	0·992
6	0·927

None of the first four scenarios indicated that the culls had been very important in the stabilization of the population, or that they would be in the future if continued at present levels (examples in Fig. 4); natural density-dependence in adult survival was enough to stabilize the population at the late-1990s level. The reduction in equilibrium population size caused by the culls was 1·2–5·6% on the breeding population and 5·6–7·9% on the autumn population (Fig. 5). Under scenarios 5 and 6, the culls had a slightly stronger effect on equilibrium autumn population size (7·2% and 15·5% reduction, respectively), whereas the two scenarios differed strongly in the cull effect on breeding population (27·0% increase and 2·8% reduction, respectively; Fig. 5). The aberrant results from scenario 5 (increase in breeding population following culls, unusually high ratio of autumn to breeding population), despite the good fit to observed values up to 1999, indicated that the modelled density-dependence in breeding proportions was too strong in this scenario.

Figure 4. The effect of sustained culls at 1998–99 levels on autumn population (top set of lines) and number of breeding pairs (bottom set of lines) under scenarios 2, 3 and 6 (as examples). Note varying abscissa scales.

Figure 5. The effect of sustained culls at 1998–99 levels on equilibrium breeding (top) and autumn (bottom) populations for the six scenarios.

Doubling the intensity of density-dependence in fecundity had a very limited effect on breeding population size in scenarios 1–4, whereas total populations at equilibrium decreased by c. 15%. The effect was much more marked in scenarios 5 and 6, where breeding populations stabilized at 124 000 and 139 000, respectively.

Varying assumptions about future culls

Increasing the future culls had almost identical effects under scenarios 1–4 (examples in Fig. 6). In all cases, a cull of 30 000 or 40 000 would have a small effect (decreasing the autumn population by 5·2–8·0% or 10·0–16·1% relative to unchanged culling, respectively) whereas a sustained cull of 50 000 would drive the population to extinction by around 2020. Under scenarios 5 and 6, the effect of a cull of 30 000 or 40 000 was a reduction in the autumn population of 11·4–14·8% or 26·8–29·2%, respectively; a sustained cull of 50 000 would lead to extinction around 2042 or later (Fig. 6).

Figure 6. The effect of increasing culls starting in 1999–2000 to, respectively, 20 000, 30 000, 40 000 and 50 000 (before crippling loss) on autumn population (top set of lines) and number of breeding pairs (bottom set of lines) under scenarios 2, 3 and 6 (as examples). Note varying abscissa scales.

Density-dependent culls (removing a fixed proportion of the autumn population minus 300 000) at low levels had effects difficult to distinguish from those of continuing the present culls for scenarios 1–4. At higher levels, the density-dependent culls eliminated differences among scenarios, and removing 40% of the autumn population above the threshold of 300 000 in all six cases led to predicted breeding populations of 88 000–97 000 and autumn populations of 419 000–443 000 (Fig. 7).

Figure 7. The effect of density-dependent culls starting in 1999–2000 and removing 40% of the autumn population minus 300 000 (incl. crippling loss) on equilibrium breeding (top) and autumn (bottom) populations for the six scenarios.

Including stochastic variation in parameters

In order to assess the effects of random year-to-year variation in life-cycle parameters, we introduced stochastic variation in survival and fecundity corresponding to the levels of variation observed in these parameters. Under such models, year-to-year fluctuations were more pronounced in autumn population size than in breeding numbers, for example in one run of scenario 4 the autumn population varied between 480 000 and 544 000 during the period when the corresponding deterministic model was stable, whereas the number of breeding pairs varied between 102 000 and 112 000 in the same period. However, the mean population size was unchanged, probably because of the strong density-dependence built into the model. The stochastic model predicted slightly earlier extinction with a cull of 50 000 than the deterministic model.

Discussion

Validity of the model

The major weakness of our model is that it is based mainly on results from one colony, Vorsø. Because of this, we had to tailor the model (by adjusting fecundity) to fit the observed population growth rate by using lower values for fecundity than observed in the study colony. Likewise, our knowledge about the strength of density-dependent mechanisms on the whole-population scale is very limited. In order to accommodate this uncertainty, we modelled a series of scenarios with varying assumptions about the strength of density-dependence. The ‘true’ values for density-dependent declines in life-cycle parameters probably lie somewhere in the range defined by our six scenarios. In the interest of caution, we therefore base most of our conclusions here on considerations of results from all six scenarios. Data from other cormorant studies within the Baltic–North Sea region are required either to confirm or to invalidate the conclusions presented here.

The value for crippling loss we have assumed here (30%) may seem high, but it is intended as a correction factor that includes both actual crippling loss, unreported culls and illegal shooting. For most, if not all, countries, the values in Table 3 are underestimates of the actual number of cormorants killed (for example in Italy, the true number killed may more realistically be around 3000; N. Baccetti, personal communication). Uncertainty in both population size, the strength of natural regulating mechanisms, and the extent of planned or unplanned human interventions is a general phenomenon in the management of wildlife and natural resources, and this is one of the most compelling arguments for the use of adaptive management strategies (Walters 1986).

Has the population stabilized?

Scenarios 1–5, which all provided a reasonable fit to the observed numbers of breeding pairs (Fig. 3), indicated that the breeding population of cormorants in Denmark, Sweden, the Netherlands, Germany and Poland has stabilized and would only increase slightly over the late-1990s numbers if culls were discontinued (Figs 4 and 5). Stabilization of breeding and autumn populations occurred simultaneously in scenarios 1–4, and, contrary to the findings of Bregnballe, Goss-Custard & Durell (1997), we only found indication that a large pool of non-breeding birds would build up after breeding populations had stabilized in scenario 5. Geographical expansion within the five main countries, for example through relaxation of the measures currently in force in several countries to limit establishment of new colonies (Bregnballe & Asbirk 1995), could conceivably lead to a relaxation of density-dependence and thus further population growth. However, most areas not currently used for breeding by cormorants seem to have rather low carrying capacities and could probably only support a limited growth (Bregnballe, Goss-Custard & Durell 1997).

Under scenario 6, with no density-dependence in adult survival, the autumn population also stabilized at the same time as the number of breeding pairs (Fig. 4); however, this scenario predicted continued population growth until 2030 and was less well supported by the observed changes in breeding numbers in the five main countries (Fig. 3). If the less well-known and faster-growing populations in other countries, for example in the eastern Baltic region, are included the fit may well be better. We have no data that can conclusively show which of our scenarios is closest to reality. All scenarios agreed that the ratio between autumn population size and the number of breeding pairs at stabilization was between 4·7 and 5·2 (7·8 in scenario 5), and that the total number of cormorants of the study population in autumn 1999, i.e. around 1 September, was between 460 000 and 660 000.

Data from the second half of the 1990s indicate that population growth has varied substantially among the five main countries (T. Bregnballe, unpublished data); eastern populations grew faster than western ones. The inclusion of spatial effects in the model might lead to more reliable predictions.

The effect of the culls

In scenarios 1–4 with natural density-dependence in adult survival, culls at present levels had a minor effect on population growth and levels of stabilization (Figs 4 and 5). A constant cull appeared either to be ineffective, if too small, or too effective (leading to extinction), if too large (Fig. 6); the change in behaviour of the model was quite abrupt. This change occurred when the number removed, including the 30% crippling loss, exceeded the maximum absolute growth that the population was capable of. Real culls would not continue unabated when the population declined strongly; increasing expenses and decreasing motivation would reduce numbers being killed, so that the culls would in effect be density-dependent.

In scenarios 5 and 6 without density-dependence in adult survival, the culls had a larger effect on equilibrium autumn population size. A constant cull, if too high, could still lead to population extinction (Fig. 6).

The effect of density-dependent culls depended on the level of the threshold chosen in relation to the ‘natural’ level of stabilization. If the threshold was much lower, as in scenarios 5 and 6, such culls could reduce the population size substantially, without risk of extinction, as also found by Middleton, Nisbet & Kerr (1993) for barnacle geese Branta leucopsis. Furthermore, at the highest level modelled, such culls could become the dominant density-dependent mechanism affecting the population and thus eliminate the differences among the scenarios (Fig. 7). However, density-dependent culls would require good annual estimates of the autumn population size, something that would not be easy to achieve on a broad geographical scale. Alternatively, an adaptive management strategy (Walters 1986; Walters & Holling 1990; Williams & Johnson 1995) could be followed: annual censuses of breeding populations could be compared with the predictions of one or more models, the model(s) could then be adjusted to provide a better fit to the new observations, and a predicted autumn population size derived. Culls could then be based on this prediction, and the process repeated in the following years. For improved efficiency, this process should be carried out at a pan-European level rather than by individual management authorities.

Is culling an appropriate management tool?

Culls could regulate or even eliminate cormorant populations and, if carried out in a density-dependent fashion, it is possible to avoid endangering the survival of the cormorant as a widespread bird in Europe. However, before deciding on such a strategy, it is our opinion that management authorities should consider whether to control cormorants, or the damage that they cause.

Even though population control through culling is feasible, it may not be the most efficient, economical or indeed ethical way of limiting cormorant damage. If killing a large number of cormorants is the primary aim, culls should take place at night in the roosts (as practised, for example in Switzerland; E. Staub, personal communication). Such culls are inevitably expensive to carry out, and experience shows that they will not necessarily discourage cormorants from continuing to use the roost and the associated foraging areas (McKay et al. 1999). Another problem is that the number of cormorants foraging at fish farms might decline less than the total number (or not at all) because these farms are high-quality foraging sites. Culls in high-quality areas may thus even reduce populations primarily in low-quality habitat where economic interests are less important (Bregnballe, Goss-Custard & Durell 1997). Evidence that culling is inefficient in situations with high individual turnover comes from Keller, von Lindeiner & Lanz (1998), who showed that numbers only declined temporarily even though more than 6000 cormorants were shot in Bavaria in winter 1996–97.

At present, culls are decided and carried out at a national or regional scale, depending on the country involved. In addition to features of cormorant demography, as treated above, the effect of regional culls will depend on winter site fidelity; if immigration from other wintering areas is strong, local culling effects will be limited. Frederiksen & Lebreton (2000) used a simple two-compartment model to study the effect of culls in France and concluded that more information about winter site fidelity was needed.

An alternative to culling is to aim for maximum scaring efficiency at centres of conflict. This is best achieved by shooting birds as they arrive, i.e. in the morning at foraging sites and in the evening at roosts, and early in the season. Cormorants may then learn that some foraging sites are dangerous, and may feed elsewhere (McKay et al. 1999).

General management implications

It is not unusual that pests are regulated by density-dependence at levels high enough to cause management conflicts (herring gulls Larus argentatus, Coulson, Duncan & Thomas 1982; Coulson 1991; yellow-legged gulls Larus cachinnans, Bosch et al. 2000; other species, Feare 1991). When this occurs, culls may have less effect than expected, because reductions in population size are compensated for by increases in one or more life-cycle parameters (Coulson 1991). As demonstrated in this study, increasing the culled number is risky, because once the compensatory power of the population is overcome, it will inevitably decline towards extinction if the cull is unchecked; there is no stable equilibrium (cf. Middleton, Nisbet & Kerr 1993). One general inference is that culls should be planned so that they become the most powerful density-dependent mechanism affecting the target population; it is then in theory possible to regulate the pest population at any desired level. As illustrated here, this strategy requires a well parameterized population model, and should also be accompanied by monitoring programmes.

Acknowledgements

This study would not have been possible without the conscientious efforts through more than 20 years of banders and observers at Vorsø, particularly Jens Gregersen. Funding was provided by the French Ministry of Environment (Direction de la Nature et des Paysages, Sous-direction de la Chasse, de la Faune et de la Flore Sauvage) through a grant to J.D. Lebreton and M. Frederiksen. Nadav Nur and an anonymous referee provided useful comments on an earlier version of this manuscript.

Received 22 March 2000; revision received 24 January 2001