Landscape Ecology 16: 161–173, 2001. © 2001 Kluwer Academic Publishers. Printed in the Netherlands.
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Research Article
The effect of breeding-habitat patch size on bird population density Cristi´an F. Estades Depto. Manejo de Recursos Forestales, Universidad de Chile, Chile, and Dept. Wildlife Ecology, University of Wisconsin - Madison, U.S.A.; Present address: Depto. Manejo de Recursos Forestales, Universidad de Chile, Casilla 9206, Santiago, Chile (Phone: 56-2-678-5871; Fax: 56-2-541-4952; e-mail:
[email protected]) Received 19 January 2000; Revised 22 August 2000; Accepted 22 November 2000
Key words: bird density, foraging patterns, habitat patch size, landscape mosaic, resource distribution
Abstract An individual-based simulation model was used to study the effect of the relative location of food and nest sites in the landscape on the relationship between the breeding habitat patch size and bird population density. The model predicted that when both food and nest sites are located exclusively in the breeding habitat patches, larger patches tend to harbor higher population densities. But when food starts to be added to the ‘matrix’ habitat and taken out of the breeding habitat the advantageous effect of larger patches diminishes and eventually the trend reverses, with small patches having higher population densities. This pattern arises from the combined effect of the existence of an extended foraging area around patches and an intrinsic advantage of large habitat patches associated with the concentration of food resources and potential colonizers. The effects of interspecific interactions and the management implications of the model are discussed.
Introduction The distribution of animals in patchy environments has been a central theme in ecology for the last three decades (Fretwell and Lucas 1970; Charnov 1976; Wiens 1976; Simberloff and Abele 1982; Pulliam 1988; Gilpin and Hanski 1991; Robinson et al. 1995; Tilman et al. 1997). The fact that individual animals interact with their environment over a rather limited area (Tilman et al. 1997) and that most resources (e.g., food, cover, nest sites, etc.) are discontinuously distributed in the landscape, can make the spatial arrangement of these resources a crucial factor in the use that animals make of them. The size of habitat patches has usually been regarded as a critical variable in determining their suitability for a given species and several studies on breeding land birds have shown that the population density of many species declines with the average size of the habitat remnants (Ambuel and Temple 1983; Freemark and Merriam 1986; Robbins et al. 1989; Herkert 1994; Robinson et al. 1995). Thus, it
has been suggested that conservation of the so called ‘area-sensitive’ species (Robbins et al. 1989) requires protecting large areas of continuous habitat (Robinson and Wilcove 1994; Robinson et al. 1995). However, many other bird species do not show that trend, and some may even be more abundant in smaller habitat fragments (Martin 1981; Haila et al. 1987; Loman and von Schantz 1991; Andrén 1994; Schieck et al. 1995; Bellamy et al. 1996; Hinsley et al. 1996; Estades and Temple 1999). A potential reason for the discrepancies between the response of different bird species to habitat patch size may have to do with the very definition and delineation of those habitat patches. Most researchers tend to equate the concept of wildlife habitats to vegetation associations (Hall et al. 1997) and they usually derive their spatial definition from aerial photographs or other source of cartographic information where discrete boundaries are defined. Despite the problems inherent to the use of a set of discrete patches to represent a landscape where elements may grade into one another, landscape mosaics constitute a useful ap-
162 proach to understanding spatial processes in ecology (Wiens 1995a). However, most models that explain the effect of the characteristics of landscape mosaics on animal populations have used a single descriptor of habitat quality for different patches (e.g., suitability, Fretwell and Lucas 1970; prey density, Bernstein et al. 1988; fitness, Pulliam 1988; residence time, With and Crist 1995) and a large proportion of them such as metapopulation models (Gilpin and Hanski 1991) and models based on the theory of island biogeography (MacArthur and Wilson 1967), correspond to patchmatrix models where patches of habitat are embedded in an often unusable matrix. An animal’s habitat is defined by the resources and conditions present in an area that determine its use by the species (Hall et al. 1997). However, there is no reason for these resources and conditions to be equally distributed in space and it is likely that some of them may actually extend their presence to areas that are beyond the species ‘habitat’ (i.e., the area where the key resources co-occur). On the other hand, some of these resources may not co-occur at all and the species will meet different needs using different areas (Block and Brennan 1993). One of the implications of these patterns is that the definition of a habitat patch becomes less straightforward, even in a landscape where discrete boundaries exist between vegetation types. The fact that the boundaries of vegetation patches do not necessarily represent boundaries of species’ habitats poses a problem to the use of landscape mosaic models to study animal populations. It is not only a matter of whether animals perceive a different degree of patchiness than researchers (Wiens 1976), but that they may also have to deal with independent spatial patterns for the different resources they depend on. While the juxtaposition of resources is an ideal situation that reduces the cost of using them by an animal (Patton 1992), this is far from being the norm. This is reflected in the long distances some bird species have to fly from their nest sites to their feeding grounds (Northern Harrier [Circus cyaneus], up to 9.5 km, Martin 1987; Wood Stork [Mycteria americana], up to 63.1 km, Bryan et al. 1995; Light-mantled Sooty Albatross [Phoebetria palpebrata], > 1,000 km, Weimerskirch and Robertson 1994). Therefore, rather than using a single descriptor of quality for habitat patches, a more general understanding of how patchiness affects animal populations may be achieved by modeling the spatial distribution of some key resources a species uses. In a non-spatial scenario, these two alternatives should generate identical results be-
cause the quality of a habitat could be considered a function of these resources (i.e., Habitat Suitability Index Models, Schamberger et al. 1982). However, in a spatial context, the value of one resource may also depend on the relative location of other resources or conditions. Thus, an area that provides no food for a bird species, but has good cover may be used intensively by a population if it is located close to foraging areas or may not be used at all if it is far away from them. In this paper I propose a simple model to describe the effect of breeding-habitat patch size on bird population density, based on the relative spatial location of food and nest sites. While the habitat of a bird species may be difficult to delimit precisely, the areas where the species can potentially carry out different aspects of its life history may be easier to define. For the purpose of this model, a breeding-habitat patch is defined as an area containing the necessary resources and conditions for a bird to build a nest. Using an individual-based simulation program, I first explore the model assumptions and predictions. Secondly, I discuss the effects of factors other than nest sites and food (e.g., predation) on the model.
The model Consider a fragmented landscape where patches of breeding habitat for a bird species are embedded in a matrix of a different kind of environment. The case shown in Figure 1A depicts a situation where both nesting sites (black dots) and food resources (shading) are located within the patches. This scenario might represent the case of an old-growth forest specialist in fragments of forest surrounded by crops or any land bird species in a real archipelago. Figure 1C shows the case where nest sites are located inside the patches but food resources are located in the matrix. This could represent the case of a sea bird species that nests on islands and forages in the ocean. Finally, Figure 1B shows an intermediate case where food is evenly distributed in the landscape while the nest sites are restricted to the patches. For many cases such as the one illustrated in Figure 1A, there exist significant evidence that the density of a bird species is positively correlated with the average breeding-habitat patch size (e.g., Bengtson and Bloch 1983; Robbins et al. 1989; Robinson et al. 1997) whereas in the case of aquatic and sea birds, small patches of breeding habitat usually support very
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Figure 1. Different scenarios for a landscape where patches of breeding habitat are surrounded by a different type of habitat (matrix). A. both nest sites and food resources are located within the patches. B. food is evenly distributed in the landscape. C. food is located in the matrix habitat.
high population densities (Buckley and Buckley 1980; Erwin et al. 1995). These two situations represent the two extremes of a potential series of landscapes where the spatial covariance between food and nest sites varies from positive to negative. Figure 2 shows a general prediction for the relationship between the latter variable and the effect of breeding-habitat patch size on bird population density. Birds in landscapes of type A (e.g., Figure 1A) should have higher densities in larger breeding-habitat patches, whereas for birds in landscapes of type C (e.g., Figure 1C), the opposite should be true. For intermediate cases of spatial covariance of food and nest sites such as, a landscape of type B (e.g., Figure 1B), it seems reasonable to expect that the relationship between bird density and breeding-habitat patch size should also be intermediate, although the shape of the curve is not derived intuitively (Figure 2). However, understanding this relationship over the entire range of possible scenarios may be very important for management purposes such as, determining the conservation value of patches of breeding-habitat for birds in different types of landscapes. I developed an individual-based model to simulate the response of a bird population to different landscape scenarios such as the ones depicted in Figure 1. In a landscape consisting of an array of 80 × 80 grid cells, I randomly allocated square breeding-habitat fragments of four different sizes (1 16 × 16-fragment, 4 × 8-fragments, 16 4 × 4-fragments and 64 2 × 2fragments, in order to have the same total amount of habitat per size class). Fragments were separated from each other by at least one grid-cell width.
Table 1. Amount of food resources per habitat type in different simulation scenarios. Scenario
Number of food units per grid cell of indicated habitat: Breeding Matrix habitat habitat
Covariance1 of food resources and abundance of nest sites
1 2 3 4 5 6 7 8 9
10 10 10 10 10 10 10 5 0
0.79 0.71 0.63 0.55 0.47 0.39 0.00 −0.39 −0.79
0 1 2 3 4 5 10 10 10
1 the covariance was calculated using the 6400 grid cells as
sample units.
Inside the breeding-habitat fragments, I randomly distributed a total of 600 nest sites. Therefore, some grid cells were assigned more than one nest site whereas some were assigned none. The rest of the landscape (the matrix habitat) contained no nest sites. I represented food resources as a discrete variable that could take values from 0 to 10 (food units) in each grid cell. I simulated nine different scenarios where food resources were differentially assigned to grid cells defined as breeding habitat or as matrix habitat (Table 1). For simplicity purposes I modeled asexual birds, therefore single individuals could produce offspring. At the beginning of each simulation scenario 100
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Figure 2. Hypothetical effect of spatial covariance of food and nest sites on the relationship between breeding-habitat patch size and bird population density. Letters A through C refer to scenarios in Figure 1.
birds were randomly assigned by the program to one of the grid cells containing a nest site and no grid cell received more than one bird (i.e., one grid cell represented the breeding territory of the bird). Birds moved following a modified random walk pattern. The probability of moving diagonally was penalized by dividing it by the squared root of 2 in order to assure an isotropic movement pattern. Initially, birds would start at the grid cell that contained their nest site. During one simulation step birds would either feed or move. If food was available a bird would take one unit and return immediately to the nest to feed its offspring. If food was not available the bird would move to a neighboring cell. To incorporate some realism into the movement pattern I modified the basic rule in three ways. First, birds returning to the nest would do it in a straight line and during one time step, regardless of their location. Second, having fed their offspring birds would return to the last grid cell where they found food, and they would do it in a direct way and in one time step. Finally, birds had a memory that stored the average food intake they had experienced in the two different habitat types. The probability of moving to grid cells of different habitat types was then weighed by this factor so birds would spend, on aver-
age, more time in areas more likely to provide food. A total of 1,000 time steps constituted one season. During that time I recorded the number of times each bird returned to the nest with food and the total distance traveled by that individual. At the beginning of every season, the amount of food in every grid cell was restored to its original value. Reproduction and mortality took place at the end of the season. Within a range of values, the probability of an individual producing a new bird was proportional to the number of times that individual visited its nest with food. For values below and above that range, reproduction happened with 0 and 1 probabilities, respectively. I applied the same procedure to mortality but this time using total distance traveled as the descriptor. Additionally, I included a constant (densityindependent) probability of mortality. I selected the values for all the parameters in the reproduction and mortality functions after having tried several combinations of them, looking for the ones that produced stable populations and a significant effect of breeding-habitat patch size on reproduction and survival for scenario 1 (Table 1). Most of the discarded parameter sets either produced populations that declined to extinction or populations that grew rapidly saturating the simu-
165 lated landscape through dispersal. The latter were not of interest to the present model because their growth was not limited by food resources but by the number of breeding territories available to them. The new individuals added to the population settled randomly in a territory within a radius from the nest in which they were born. If they could not find a suitable territory within that area they would search over areas with increasing radius until they succeeded. When no territories were available the individuals that could not settle were deleted from the population. In other words, the model did not consider the existence of non-territorial ‘floaters’. However, the deletion of individuals was a very rare event as there were almost always available territories for dispersers. Most populations stabilized after 15 seasons. Therefore I ran the simulations for 20 seasons and used the results for the last five seasons as the average density. I conducted seven replicates for each scenario. For each of the latter I divided the bird densities by the maximum density recorded in the scenario to scale the results to values from 0 to 1. Finally, I regressed the average scaled bird density in each one of the four patch-size classes on the logarithm of the patch size. I used the slope of the linear regression function as an expression of the effect of breeding-habitat patch size on bird density.
Results and discussion The effect of the size of the breeding-habitat patch on bird density (which was defined as significantly positive for scenario 1) reversed when one unit of food was added to the matrix and became more negative as the covariance between nest sites and food decreased (Figure 3, black dots). Because the total amount of food in the landscape varied among scenarios, so did the total number of birds at equilibrium. To see whether the shape of the curve was due to the effect of the total food abundance, I modified the rule for assigning food to the different habitats so that the total amount of this resource in the landscape would be the same for all scenarios (using the level of scenario 1, Table 1). The open squares in Figure 3 represent the latter case. Although the scale in the x axis differed between the two curves because of the different amounts of food per grid cell (which affects the covariance with nest sites) the main trend remained the same, that is, the effect of breeding-habitat patch size on bird density reversed
when the matrix grid cell contained 10% of the food in a breeding-habitat patch grid cell. The model predicts that, when the only resources and conditions that determine habitat selection by breeding birds are nest sites and food, larger breedinghabitat patches will support higher population densities than the smaller patches if these two resources are located exclusively in the breeding habitat. If part of the food resources are located in the matrix the relative advantage of larger fragments drops and, as a higher proportion of food is added to the matrix the smaller patches start to harbor higher numbers of individuals per unit area. There seem to be two major components to this pattern. First, the existence of food resources outside the breeding-habitat patch provides an extended foraging area for the individuals using that patch and, if there is a positive relationship between food abundance and population density, this additional foraging resource will increase population density in that patch. If there exists a maximum distance for a foraging trip, then this distance is the maximum potential extension of the foraging area beyond the limits of the breeding-habitat patch. And if the width of the extended foraging area is independent of the size of the breeding-habitat patch, then its positive effect on population density should be relatively higher in smaller patches. For the simple case of a square fragment used in the simulation, the density (D) of individuals is approximately D(s, d) = a ∗ (s ∗ f bh + ((s 1/2 + 2∗ d)2 − s)∗ f m)/s ; where s is the size of the fragment, d is the average maximum distance of a foraging trip, fbh is the food density in the breeding habitat, fm is the food density in the matrix habitat and a is the term that transforms food density into population density. Figure 4A shows the behavior of D(s, d) for different values of d. Again, the y axis represents the slope of the linear regression line between D(s, d) and the logarithm of s. Clearly, as the distance to which birds can travel beyond the limits of the fragments diminishes, the effect of having an extended foraging area becomes less important for population density. From Figure 4A it is also evident that the effect of the extended foraging area does not account for the positive effect of breeding-habitat patch size on bird density when the amount of food in the matrix is insignificant. Therefore, another component of the pattern in Figure 3 has to account for some ‘intrinsic’ advantage of large over small habitat patches for population density.
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Figure 3. Effect of spatial covariance of food and nest sites on the relationship between breeding-habitat patch size and the simulated bird population density. The y-axis represents the slope of the linear regression between the logarithm of habitat patch size and the scaled density of birds. The numbers along the line represent the scenarios described in Table 1. The original model is represented by the dark line and black circles and the modified model where total food is set to be the same for all scenarios by the empty squares.
There are several reasons why some bird species might be less abundant in small habitat patches (Newton 1998). Many of these factors, however, have to do with interactions with other species (e.g., predation) or some changes in the physical environment (e.g., solar radiation), none of which plays a role in the present model (although they will be considered later). There are two mechanisms by which a large breeding habitat patch may represent an advantage over a small one in the present model: a reduced concentration of food resources around nests in small patches and a reduced rescue effect (sensu Brown and Kodric-Brown 1977) for populations breeding in small patches. It is a trivial fact that individual organisms need a minimum amount of food to survive or to perform some specific functions (e.g., reproduction). Consequently, the abundance of food may influence the use of space by animals and it has been shown that in many cases the area occupied by an individual bird (or pair) may be inversely related to the density of food (Newton 1998). The maximum amount of food present in one of the smallest fragments in the simulated landscapes (10 units × 4 grid cells = 40 units) was, in fact, not enough to allow an individual to reproduce (because of the parameters used in the model). Among the individuals nesting in small patches, the only ones that
had some chance to produce offspring were those that could use additional resources such as, food in the matrix (if there was any) or food in neighboring patches. Hinsley et al. (1995b) observed that the woodpecker Dendrocopos major would breed in forest fragments as small as 0.26 ha if it could access other fragments to obtain food for its nestlings. However, the simulation program penalized these long distance foraging trips by increasing mortality probability as a linear function of total distance traveled (i.e., a combined effect of energy costs and predation risk). Therefore, the low availability of food resources around the nest reduced significantly the reproductive success and increased the mortality of individuals nesting in small patches. All other things being equal, small populations have a higher probability of extinction than large populations (Shaffer 1987). Accordingly, several studies have shown that the extinction probability of bird populations in real and ‘habitat’ islands decreases with population size (Pimm et al. 1988; Opdam 1991; Hinsley et al. 1995a; Bellamy et al. 1996). In the simulated landscape, the maximum possible number of birds breeding in a patch was equal to the size of that patch in grid cells (provided that each grid cell had a nest site, which was rarely true). Therefore, the smallest patches (four grid cells) had a relatively
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Figure 4. A. Comparison of the simulation model (dark line with black circles) with an analytical model based on the presence of an extended foraging area around breeding habitat patches (gray lines). See explanation in text. The parameter d is the maximum distance (in terms of grid cell widths) that a bird will fly during a foraging trip. As in Figure 3, the y-axis represents the slope of the linear regression between the logarithm of habitat patch size and the scaled density of birds. B. Comparison of the simulation model (dark line with black circles) with a modified version of the analytical model (gray lines) that, along with the effect of an extended foraging area, incorporates the combined effect of food and colonizers concentration around the nest site. See explanation in text.
168 high probability of losing all their occupants in one season only due to chance events (there was a 20% density-independent mortality probability per season). However, because the probability of a 4-grid cell patch of losing its occupants at a given time due to simple chance is the same probability of a 4-grid cell subset of a larger patch of losing its occupants during the same time period, random mortality alone cannot account for differences in population density in patches of different sizes (although it can for differences expressed in terms of presence and absence). On the other hand, the probability of a 4-grid cell being recolonized by dispersing individuals is smaller than the probability of a 4-grid cell subset of a larger patch being re-colonized because the latter has, on average, more potential sources of dispersers around. Therefore, on average, smaller habitat patches are less likely to benefit from by the rescue effect. Both the effect of concentration of food resources and of potential colonizers combine to reduce the average bird population density D(s, d) in small habitat patches. Thus, D(s, d) is multiplied by a term f (s) to represent the ‘total’ effect of the size of the patch on the population density, D(s, d)∗ = D(s, d) × f (s). Figure 4B shows the behavior of D(s, d)∗ for different values of d, for the case when f (s), the combined effect of food availability and rescue effect on population density, is arbitrarily defined as log(s). The predictions of the analytical model and the simulation model are qualitatively similar. The effect of breedinghabitat patch size on population density is positive when all the food resources are located inside the patch. This effect starts to become less pronounced as food is added to the matrix and eventually reverses making smaller patches hold higher population densities as the proportion of food in the matrix increases. From the analytical model it is apparent that the rate at which that shift in effect direction takes place is governed by the maximum distance at which individual birds will travel into the matrix (d), being more rapid when birds can travel long distances to forage. Although food and nest sites may play an important role in determining the use of patches of habitat by birds, there is strong evidence that other factors, such as nest predation (Andrén et al. 1985; Small and Hunter 1988; Hoover et al. 1995; Arango-Vélez and Kattan 1997), brood parasitism (Brittingham and Temple 1983; Robinson et al. 1995) and competition (Ambuel and Temple 1983; Wilcove and Robinson 1990) may affect the quality of breeding habitat patches of different sizes. Due to their high edge-
to-area ratio, small patches are proportionally more affected by negative ‘edge effects’ and, therefore, they become less suitable for many breeding birds (Yahner 1988; Paton 1994). I modified the basic model to include some edge effect on the probability of mortality. Figure 5A shows the effect of increasing the density independent mortality at the edge (defined as 1-grid cell width) of a breeding-habitat patch by 100 and 200%. Clearly, when there is a strong mortality associated with edges, larger patches present an advantage over the small ones counteracting to some extent the beneficial effects of an extended foraging area in the matrix. Not all interactions with other species make smaller habitat patches less suitable for breeding birds. In fact, the very factors that reduce the quality of small habitat patches for some species (and eventually reduce their population densities) may, indirectly, benefit their competitors or prey. Density compensation, the process by which populations increase their densities in the absence (or at low densities) of their competitors, is believed to be the cause of the high densities of some land birds on small islands (MacArthur et al. 1972; Nilsson et al. 1985; Terborgh et al. 1997). Also, the absence or low densities of predators may increase the survival and reproductive success of birds breeding in small habitat patches (Buckley and Buckley 1980; Greer et al. 1988; Erwin et al. 1995; Tewksbury et al. 1998). Figure 5B shows the result of reducing mortality in smaller patches, as an hypothetical combined effect of both predator and competitor release. The latter was carried out by weighting mortality rates in each patch by the logarithm of the patch’s size (which shows a significant linear relationship with the density of the simulated population). From all the discussed mechanisms, predator and competitor release appear to be the only ones that can make smaller habitat patches harbor higher bird population densities in all types of landscape scenarios. Although the simulation model assigned the same amount of food to patches of different sizes, patch size itself may affect the density and the quality of the foraging resources (Burke and Nol 1998; Robinson 1998). Additionally, small habitat patches may be more exposed to extreme weather conditions which can affect their suitability as habitat for breeding birds (Nilsson et al. 1985; McCollin 1998). The present model attempts to provide a general account of the mechanisms that govern breeding bird abundance in a landscape where nest sites are
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Figure 5. A. Effect of increasing the density independent mortality at the edge (defined as 1-grid cell width) of a breeding-habitat patch by 100 and 200% (dark and light gray circles, respectively) on the original model (dark line and black circles). B. Effect of reducing mortality on smaller patches due a combined effect of predator and competitor release (gray diamonds).
patchily distributed. More specifically, it describes the effects of the breeding-habitat patch size on population density in relation to the relative location of food resources and nest sites. This resource-based model predicts that, when the spatial covariance of food resources and nest sites is high and positive, larger breeding-habitat patches should harbor higher
bird population densities. In this type of landscape, the effects of food concentration, local extinction and re-colonization generate the positive relationship between habitat patch size and bird population density, without the need to invoke any ‘edge effects’. This prediction agrees with the findings of several studies on birds in islands or forest fragments where random ex-
170 tinction associated to small populations is considered the main cause of low population densities in small habitat patches (Newton 1998). The other important prediction of the model is that, when food resources are available in the matrix habitat, the effect of the size of the breeding-habitat patch on bird population density will depend on the relative amount of food in each habitat type and on the capacity of the birds to use the food in the matrix habitat. Specifically, the more food is located in the matrix and the longer the distance that birds can travel into the matrix, the higher the bird densities in small patches (in relation to large patches) will be. Factors such as energetic costs and predation risk determine the distance at which a central place forager will travel to obtain food (Stephens and Krebs 1986). Many passerine birds nesting in forest fragments travel short distances into the matrix to forage (Newton 1967; Martin 1981; Loman and von Schantz 1991; Hinsley et al. 1996; Berg 1997; Estades and Temple 1999; Estades and Temple, unpublished data) and their densities tend to be higher in smaller fragments. Seabirds usually make very long foraging trips (e.g., see Weimerskirch and Robertson 1994) and all their food resources are located in the ‘matrix’ habitat. Although, to my knowledge, there are no studies that relate the area of an island to the density of breeding seabirds, the fact that hundreds to thousands of individuals may nest on islets of no more than a few hectares (Buckley and Buckley 1980) is an indication that, as predicted by the model, breeding seabird densities are significantly much higher on small islands. The predictions of the resource-based model are then modified by the interaction of the breedinghabitat patch size, the matrix characteristics and the effects of predators, competitors and the physical environment. In a sense, the resource-based model could act a as conceptual null model to test for species interaction factors leading to ‘area sensitivity’. Figure 6 summarizes the effect of the mentioned factors on the relationship between breeding-habitat patch size and the population density of a given bird species. The model also shows the usefulness of using the spatial distribution of some key resources as an approach to modeling the effects of habitat patchiness on bird populations.
Management implications The practical importance of understanding the relationship between breeding-habitat patch size and bird population density rests on the still unresolved debate over the conservation value of small reserves for birds (e.g., Blake and Karr 1984; Andersen and Mahato 1995; Erwin et al. 1995; Turner and Corlett 1996; Robinson et al. 1997). There is an increasing consensus on the fact that bird habitat fragments cannot be considered as isolated from the surrounding matrix and that the characteristics of the latter may affect their suitability for birds (Wiens 1995b; Kilgo et al. 1997; Sisk et al. 1997; Estades and Temple 1999; Mazerolle and Villard 1999; Norton et al. 2000). The model presented in this article provides a mechanistic framework to account for such influences. While restoration of fragmented habitats may be difficult, the model makes explicit the fact that by managing the matrix in order to provide additional food resources, the detrimental effects of habitat fragmentation on breeding bird populations may be reduced. The model also predicts that the response of bird populations to such management will depend on the species capacity to use those extra resources. Because the distance at which the birds will move into the matrix can significantly affect the ‘advantage’ of having an extended foraging area, it is clear that the species that can make longer foraging trips would benefited more from that management. Consequently, it could be expected that, on average, larger species would respond proportionally better to the addition of supplemental food resources in the matrix because they usually travel longer distances. If this hypothesis is true, this type of management could have special conservation relevance due to the fact that large species are commonly more affected by habitat loss (Turner 1996; Newton 1998). The willingness of a bird to travel into the matrix to forage may depend on the relative quality and abundance of the food resources provided in this habitat and the risk involved in such an activity. Therefore, along with providing additional foraging resources, management should strive to create a less hostile matrix to encourage its use by birds breeding in habitat fragments. Thus, landscapes where the matrix is structurally similar to the breeding habitat fragments may be easier to manage to create an extended foraging areas for birds. In Western United States, Spotted Owls (Strix occidentalis) often forage in secondary forests adjacent to the old-growth forests in which they nest
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Figure 6. General prediction for the interaction between resources (food and nest sites) and interspecific interactions and environmental factors on the effect of breeding-habitat patch size on bird population density.
(Carey and Peeler 1995). In Central Chile, most cavity nesting bird species include in their home ranges the exotic pine plantations that surround the forest fragments where they breed (Estades and Temple 1999; Estades and Temple, unpublished information). The ability of a species to use the food resources in a managed matrix may vary according to its capacity to adapt to new food items. While specialist species may never try new food resources, more generalist species may learn to exploit them very quickly. Newton (1967) hypothesized that a behavioral change had allowed Bullfinches (Pyrrhula pyrrhula) to exploit foraging resources outside the forest patches in which they bred in some areas in Britain. The author (unpublished information) observed that several individuals of the cavity nester Thorn-tailed Rayadito (Aphrastura spinicauda) were feeding their young on the larvae of an exotic moth (Rhyacionia buoliana) that, three years earlier, had invaded the pine plantations that surround the broad-leaved forests in which they nest. Finally, although this factor was not explicitly included in the model, having a matrix that provides some resources to the birds breeding in habitat fragments may enhance the dispersal movements of birds (Andersen and Mahato 1995; Estades and Temple
1999) and increase the colonization rate of patches, reducing the differences in densities between patches of different sizes.
Acknowledgements During the development of this study the author was financially supported by Fondecyt (Chile) grant number 1990786 and a ‘Presidente de la República’ scholarship. S.A. Temple, C.A. Ribic, A.R. Ives, N.E. Mathews, T.C. Moermond, L. Fahrig and two anonymous reviewers made very valuable comments on different versions of this manuscript.
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