The consequences of disrupted dispersal in fragmented red-cockaded woodpecker Picoides borealis populations

Authors


* Present address and correspondence: Karin Schiegg, Institute of Zoology, University of Zurich, Winterthurerstr. 190, CH-8057 Zurich, Switzerland (fax +41 1635 68 21; e-mail kschiegg@zool.unizh.ch ).

Summary

  • 1Habitat fragmentation may adversely affect animal populations through several mechanisms. However, little is known about how the impacts of some of these mechanisms are manifested in altered dynamics of wild populations.
  • 2We used a spatially explicit individual-based simulation model to examine the potential effects of disrupted dispersal due to fragmentation on the population dynamics of the endangered, co-operatively breeding, red-cockaded woodpecker Picoides borealis .
  • 3We simulated population dynamics as a function of population size and spatial aggregation of territories. Dispersal success (but not mortality or fecundity) was an emergent property of model runs. In the model all female and some male fledglings dispersed in straight lines in random directions, and the remaining males stayed on their natal territories as helpers and competed for breeding vacancies in their immediate neighbourhood.
  • 4Population trend was tied to the higher dispersal success of both males and females in larger and less fragmented populations. Helpers were more successful than dispersing males. Male breeder recruitment depended entirely on helpers when populations were small (25 or 100 territories).
  • 5Declining populations were characterized by high emigration rates and both failure and delay in female recruitment. The large numbers of unpaired males resulted in lowered reproductive output at the population level and in the loss of territories. Populations of 25 territories were stable when territories were highly aggregated, despite high emigration rates. These results closely match empirical observations.
  • 6A number of co-operatively breeding species are endangered. The unusual dispersal behaviour of helpers may make such species sensitive to habitat fragmentation but also resilient to reductions in population size when territories are aggregated. Small populations of co-operative breeders may have considerable conservation value as a source of genetic diversity.

Introduction

A large number of studies report adverse effects of habitat fragmentation on avian species. Particularly prominent are increased nest predation or parasitism (Robinson et al. 1995; Faaborg et al. 1998), reduced food abundance (Zanette, Doyle & Tremont 2000) and disrupted dispersal (Stouffer & Bierregaard 1995; Matthysen 1999; Walters, Ford & Cooper 1999). Few investigations, however, have attempted to describe how effects of fragmentation are manifested in altered population dynamics (Harrison & Bruna 1999; Debinski & Holt 2000; Dale 2001). Impacts on population dynamics are not necessarily obvious. For example, in the Mid-western United States, greatly reduced nesting success in highly fragmented forests has not resulted in declines of avian species inhabiting forest fragments, due apparently to regional source–sink dynamics (Robinson et al. 1995; Brawn & Robinson 1996; Faaborg et al. 1998). Although population decline is often attributed to habitat fragmentation, the actual dynamics of populations in fragmented landscapes are largely unexplored. Particularly interesting in this regard is the impact of disrupted dispersal. Disrupted dispersal may lead to population decline because individuals may fail to find mates or even to reach suitable habitat. Reduced dispersal success may cause biased sex ratios or increased emigration rates, further accelerating population decline (Dale 2001; Fahrig 2001).

Obtaining experimental evidence of effects of fragmentation on demographic processes is challenging. Investigations into population- or individual-level responses to landscape structure require long-term data on reproduction, dispersal and survival from control and treatment sites, which are notoriously difficult to obtain. Additionally, landscape structure can hardly be altered experimentally and replication is almost impossible to achieve. One alternative to experimental field studies is to conduct virtual experiments using population models that project population dynamics for several decades in artificial landscapes (Pulliam, Dunning & Liu 1992). Individual-based models (Beissinger & Westphal 1998; Grimm 1999) can be used to explore critical aspects of the dynamics of populations exposed to fragmentation, such as dispersal success of individuals or site occupancy. These models track the fate of individuals and are parameterized at the level at which mechanisms responsible for fragmentation effects operate. Previously, no study has taken advantage of these features of individual-based models to investigate population dynamic processes (Grimm 1999). We employed a spatially explicit individual-based model of population dynamics of the red-cockaded woodpecker Picoides borealis Vieill. (Letcher et al. 1998; Daniels, Priddy & Walters 2000; Walters, Crowder & Priddy 2002) to explore the species’ response to habitat fragmentation.

Picoides borealis is an endangered species found in the south-eastern United States and occurs today mostly in small, fragmented populations ( Azevedo et al. 2000 ). The species is a co-operative breeder, living in groups consisting of a monogamous breeding pair and between zero and four adult helpers on permanent territories ( Walters 1990 ). Due to the spatially restricted dispersal behaviour of helpers and the reduced number of individuals dispersing long distances ( Zack & Rabenold 1989 ; Emlen 1991 ), co-operative breeders are likely to be particularly affected by isolation of territories. Conner & Rudolph (1991 ) compared fragmented and non-fragmented populations of P. borealis and found that habitat loss was associated with reduced group size in small populations with scattered territories. They concluded that both disrupted dispersal and insufficiency of foraging habitat might explain the observed pattern. Evidence of important effects of disrupted dispersal exists for other co-operatively breeding species such as the brown treecreeper Climacteris picumnus Temm. & Lang ( Walters et al. 1999 ; Cooper & Walters 2002 ) and the Florida scrub-jay Aphelocoma coerulescens Bosc. ( Stith et al. 1996 ; Fitzpatrick, Woolfenden & Bowman 1999 ).

Walters et al. (2002 ) have previously used the same model as we employed in a population viability analysis and found that population dynamics of P. borealis were highly sensitive to the spatial distribution of territories, suggesting vulnerability to habitat fragmentation. Here, we show that the interaction between territory distribution and dispersal behaviour leads to fundamental changes in population dynamics when populations are fragmented, causing the decline of these populations. We focused on two main questions. How does population size and spatial aggregation of territories affect dispersal success? How are population dynamics altered by habitat fragmentation?

Methods

DESCRIPTION OF THE MODEL

The model is based on extensive demographic data collected from a marked population (roughly 220 groups) of P. borealis in south-central North Carolina from 1982 to 1996 (Carter, Stamps & Doerr 1983; Walters, Doerr & Carter 1988a). This is one of the largest remaining populations living in a predominantly non-fragmented forest. Model parameters and their values are given in Appendix 1. Model parameter values were based on empirical data, as described in detail in Letcher et al. (1998).

Simulated landscapes are 32 × 24 km in size and contain breeding territories at fixed locations and non-breeding space that the birds must cross to find territories. Territory locations are fixed, because in P. borealis territories are centred on clusters of cavities constructed in live mature pines. Single cavities take, on average, more than 10 years to construct (Conner & Rudolph 1995; Harding 1997) and can be used for decades (Doerr, Walters & Carter 1989). The number of territories and their arrangement in the landscape can be set prior to each model run. The landscape size was chosen to match the range of territory densities observed among existing populations (Letcher et al. 1998). A territory is removed from the landscape when it is abandoned for more than 5 consecutive years. New territories are formed by budding, i.e. the splitting of an existing territory into two, which occurs with an annual probability of 1%. Budding is commonly found in co-operative breeders and is the most frequent means by which new territories are added to real populations of P. borealis (Hooper 1983; Doerr et al. 1989).

A bird's behaviour depends on its sex and status class. Individuals disperse in random directions and in a straight line. When they cross the boundary of the landscape they are lost to the population. Male fledglings either stay as helpers on their natal territory or disperse, in proportions set by a model parameter (Appendix 1). Dispersing males move at a speed of 2·3 km year−1 and compete for breeding vacancies within their search radius (3 km) each time step (3 months) as they move across the landscape. Helpers attain breeding status by inheriting their natal territory or by competing successfully for a breeding vacancy in their vicinity (i.e. within 3 km). Males can occupy empty territories, but females can only occupy territories that already contain a male. Female fledglings disperse from their natal territory in their first year and breeding females disperse when their son or father replaces their mate. Dispersing females move at a speed of 4·8 km year−1 and, like dispersing males, compete for breeding vacancies within their search radius (3 km) each time step as they traverse the landscape. The oldest resident helper wins the competition for male vacancies. If no resident helpers are present, helpers from nearby territories and dispersing birds compete for the vacancy. When several birds compete for the vacancy, the closest bird wins and, among equidistant competitors, the oldest bird wins. Competition for vacancies among females follows the same rules, but involves only dispersing birds.

Mortality parameter values vary with sex and status class. The number of fledglings produced on a territory each breeding season is a function of the probability of nesting successfully and the probable number of young fledged if successful. Letcher et al. (1998) describe a four-stage fecundity model based on the male's age, the female's age and the number of helpers in the territory. For the current work, however, the fecundity model was simplified to aid the addition of environmental stochasticity. The four-stage model from Letcher et al. (1998) was collapsed into two stages: equation 1, the attempt to breed and probability of nest failure were replaced by one equation to determine the probability of any fledglings at all, and equation 2, the mean number of fledglings and the probability of renesting were combined to determine the total number of fledglings, if any. Both stages used negative exponential functions of the breeder's ages (male age = Agem, female age = Agef) and the number of helpers (Numh), similar to those used in Letcher et al. (1998). The probability of having any fledglings at all was found using logistic regression (n = 1234, P < 0·0008). Function parameters are given in Appendix 1.

image(eqn 1)

If the nest did not fail, the mean number of fledglings (Numfl) was calculated (F3,867 = 37·012, P < 0·00001) as:

image(eqn 2)

To reflect natural variation in the population, Numfl was used as the mean of a normal distribution with a standard deviation estimated from actual data (0·69) to generate the realized number that fledged. If Numfl generated from the normal distribution was less than one, contradicting the success of the nest, one fledgling was used. Such contradiction between stages occurred in only a small number of cases (< 1%) in even the lowest fecundity group arrangement (1-year-old breeders, no helpers).

The model simulates demographic stochasticity by applying annual survival probabilities, annual status transition probabilities of male fledglings, and probabilities of producing different numbers of offspring to each individual. This is accomplished by drawing a deviate from a random uniform distribution and determining whether or not the deviate is less than the appropriate probability value. Mortality probabilities and probabilities of producing different numbers of offspring vary each year to simulate environmental stochasticity. This was achieved by determining the variance in these parameters among 14 years of data from the North Carolina Sandhills and then drawing randomly each year from the resulting distribution to determine that year's probability value.

Although their values vary to simulate demographic and environmental stochasticity, rates of mortality and fecundity are model parameters. They do not change with landscape structure as they might, for example, were food supply reduced or nest predation elevated in fragmented landscapes. In contrast, dispersal patterns and rates of transition between status classes are emergent properties of model simulations that can change as the landscape changes. Thus this exercise is largely an exploration of the consequences of variation in landscape structure, including habitat fragmentation effects, for dispersal patterns and population dynamics, given our current understanding of movement and social behaviour.

MODEL RUNS

Simulations were run in 12 landscapes differing in territory number and aggregation in a 4 × 3 design. Landscapes contained either 25, 100, 250 or 750 territories that were either scattered, moderately clumped or highly clumped spatially (Fig. 1). Based on Letcher et al. (1998) and Walters et al. (2002), we expected 25 moderately clumped groups and 25 and 100 randomly distributed groups to represent declining populations, and the remaining combinations to represent stable or increasing populations. To generate the moderately aggregated territory distributions we used the k parameter of the negative binomial distribution. For each particular number of territories used in the simulations, we determined the k-values when territories were randomly distributed (i.e. maximum k) and maximally clumped (i.e. minimum k) by overlaying a grid, 4 km to a side, over the landscape, counting territory centres in each cell and using a maximum likelihood estimate (Bliss & Fisher 1953). To create the intermediate aggregation level, we selected a k-value 25% of the distance between log kmin and log kmax (Fig. 1).

Figure 1.

Spatial arrangement of territories as a function of territory number and aggregation for each of the simulation scenarios. kmax   =  randomly distributed, k25%   =  moderately clumped, kmin   =  maximally clumped. Dots represent the territories.

Initial conditions were 100% territory occupancy with 90% breeding pairs and 10% solitary males, with a number of helpers equal to half of the number of territories. Helpers were added randomly, so that nearly half the territories had one helper, and a few had more than one. No dispersing birds or fledglings were present initially and there was no immigration. Each simulation was run over 30 years and was replicated 100 times. We used 30 years rather than a longer simulation period (i.e. 100 years) because the fate of a population generally was decided within that interval, and to reduce error accumulation (Power 1993).

ANALYSES OF MODEL OUTPUT

To explore the effects of territory number and aggregation on social structure, we calculated the relative frequencies of adult males and females in the various status classes (i.e. helper males, dispersing males and females, solitary males, breeding males and females) for each simulation. All calculations were averaged over the 30 years of simulation, or until the time at which a population became extinct. To measure dispersal success, we determined how many adult non-breeding males and females obtained a breeding position (i.e. a mate and a territory) after each time step, as well as the mean time the birds spent as non-breeders before they attained a breeding position. Females may disperse a second time after their natal dispersal, namely when leaving their breeding site to avoid incest (Daniels & Walters 2000a). Because these are rare events not influenced by territory number or aggregation, we did not distinguish between natal and breeding dispersal.

The influence of territory number, aggregation and status class (for males only, helpers or dispersers) on the probability of obtaining a breeding position and on the time elapsed until non-breeding birds acquired a breeding position was tested using generalized linear models (GLM; SAS genmod procedure; SAS Institute 1999–2000). When response variables were probabilities we included a logit link to account for binomial data (trial/events structure in SAS terminology: total number of birds in a given status class vs. number of successful birds in that class). The number of observations was the number of replications × number of simulated landscapes × number of status class levels (the latter for males only). No successful dispersal event was recorded in some simulations of small populations, which reduced the number of observations for some analyses. All calculations were done using SAS 8·1 (SAS Institute 1999–2000).

Results

As expected, randomly distributed populations of 25 and 100 groups and moderately clumped populations of 25 groups declined. Maximally clumped populations of 25 groups and moderately clumped populations of 100 groups were stable and the remaining populations increased. In the smallest, most fragmented (i.e. randomly distributed territories) population all of the initial 25 territories were abandoned and lost to the population within the 30 years of simulation in all runs, whereas in the largest population with maximally clumped territories on average only 0·4% (0·1–2·1, n = 100) of the initial 750 territories were lost.

INFLUENCE OF TERRITORY NUMBER AND AGGREGATION ON DISPERSAL SUCCESS OF MALES

Territory number and aggregation as well as status class (helper or disperser) influenced the probability that non-breeding males acquired a breeding position (Table 1). Helpers were much more successful than dispersers in obtaining a breeding position except at the largest population size (Figs 2 and 3). Males were more likely to obtain a mate in larger than in smaller populations, and this effect was stronger among dispersing males (Figs 2 and 3). Males were more successful in obtaining a breeding position when territories were more clumped, except among helper males at the largest population size, where success was relatively high regardless of territory distribution (Fig. 3), and among dispersing males at the two smallest population sizes, where success was negligible regardless of territory arrangement (Fig. 2). In randomly distributed or moderately clumped populations of 25 groups, neither type of male enjoyed much success in obtaining breeding positions.

Table 1.  Effects of territory number, territory aggregation and status class (helper or disperser) on the probability that non-breeding males obtain a breeding position (success, 2400 observations) and on the time elapsed until non-breeding males obtain a breeding position (time, 2332 observations)
SourceSuccessTime
d.f. χ 2Pd.f.F -ratio P
Territory number336·23< 0·0013      98·90< 0·001
Territory aggregation223·20< 0·0012        8·81< 0·001
Status class140·78< 0·001113988·26< 0·001
Number × aggregation616·21    0·0126        3·01< 0·001
Number × status class320·28    0·0013      71·09< 0·001
Aggregation × status class213·16< 0·0012        5·57< 0·001
Figure 2.

Mean percentage of dispersing males finding a breeding vacancy each time step (3 months) in relation to territory number and aggregation. Aggregation levels are randomly distributed (filled bars), moderately clumped (cross-hatched bars) and maximally clumped (open bars). Medians are given (± interquartile ranges) over 30 years of simulation ( n   =  100).

Figure 3.

Mean percentage of helpers finding a breeding vacancy each time step (3 months) in relation to territory number and aggregation. Key as in Fig. 2 .

Territory number, aggregation and status class also affected the time elapsed before non-breeding males acquired a breeding position (Table 1), although differences were not as dramatic as for the probability of obtaining a breeding position. Successful helpers required more time to obtain a breeding position than successful dispersing males (Figs 4 and 5). Dispersing males (Fig. 4), but not helper males (Fig. 5), obtained breeding positions sooner when territories were maximally clumped. Dispersing males (Fig. 4), but not helper males (Fig. 5), obtained breeding positions sooner in small populations. Thus declining populations (i.e. moderately clumped populations of 25 and randomly distributed populations of 25 and 100) were characterized by failure rather than delays in male breeder recruitment.

Figure 4.

Mean time (years) successful dispersing males required to obtain a breeding position in relation to territory number and aggregation. Key as in Fig. 2 .

Figure 5.

Mean time (years) successful helpers required to obtain a breeding position in relation to territory number and aggregation. Key as in Fig. 2 .

INFLUENCE OF TERRITORY NUMBER AND AGGREGATION ON DISPERSAL SUCCESS OF FEMALES

Territory number and arrangement significantly influenced both the success of female dispersers in obtaining a breeding position and the time required to do so (Table 2). Female dispersers were more successful in larger populations and when territories were more clumped, and territory distribution mattered more in smaller populations. The proportion of non-breeders finding a breeding vacancy each time step was almost an order of magnitude greater for females (Fig. 6; maximum value 66%) than for males (Figs 2 and 3; maximum value 15%). Successful female dispersers found a mate faster in larger than in smaller populations, with the exception of the two largest population sizes (250 and 750 territories; Fig. 7). At the two smallest population sizes, the time female dispersers spent searching for a breeding vacancy was shorter when territories were maximally clumped than when they were randomly distributed, but this was not the case at larger population sizes (Fig. 7). Thus declining populations were characterized by both failure and delays in female recruitment.

Table 2.  Effects of territory number and territory aggregation on the probability that dispersing females obtain a breeding position (success, 1200 observations) and on the time required (time, 1189 observations) to obtain a breeding position
SourceSuccessTime
d.f. χ 2Pd.f.F -ratio P
Territory number31168·07< 0·001353·67< 0·001
Territory aggregation2  143·58< 0·001222·31< 0·001
Number × aggregation6    57·25< 0·0016  9·13< 0·001
Figure 6.

Mean percentage of dispersing females finding a breeding vacancy each time step (3 months) in relation to territory number and aggregation. Key as in Fig. 2 .

Figure 7.

Mean time (years) successful dispersing females required to obtain a breeding position in relation to territory number and aggregation. Key as in Fig. 2 .

CONSEQUENCES FOR POPULATION DYNAMICS

Low success of dispersing females in populations of 25 groups with randomly distributed or moderately clumped territories led to high relative frequencies of solitary males (Fig. 8), many of which (52% and 27%, respectively) died before obtaining a mate. Hence the poor success of helper males in obtaining breeding positions in these populations (Fig. 3) was primarily due to inability to obtain mates rather than inability to obtain territories.

Figure 8.

Relative frequencies of adult male status classes in relation to territory number and aggregation. Mean values are given over 30 years of simulation ( n   =  100). Key as in Fig. 2 .

The proportions of helpers and actively dispersing males were remarkably consistent across populations. Thus higher proportions of solitary males were reflected in lower proportions of breeding males (Fig. 8). As a result, populations with many solitary males exhibited lowered productivity. The smallest (25 territories) most fragmented population produced an annual average of 1·09 (median; interquartile range = 0·40–1·61; n = 100 simulations) fledglings per adult male, whereas the largest (750 territories) least fragmented (i.e. maximally clumped territories) population annually fledged 1·84 (1·73–1·96; n = 100) young per adult male. Among those solitary males that acquired a mate, the average time required ranged from 0·42 years (0·29–0·61; n = 100) in the smallest population with randomly distributed territories, to 0·10 years (0·08–0·13; n = 100) in the largest population with maximally clumped territories.

Many of the unsuccessful dispersers moved beyond the boundaries of the landscape. Median male emigration rate (number of male emigrants/number of breeding males) was 12·5% (0·0–66·7; n = 100) in the smallest population with randomly distributed territories, compared with 2·5% (0·8–5·0; n = 100) in the largest population with maximally clumped territories. Interestingly, median emigration was also quite high (18·5%; 1·0–33·4; n = 100) in the smallest stable population (25 territories, maximally clumped).

Discussion

DISPERSAL AND HABITAT FRAGMENTATION

Our results suggest that if populations are sufficiently small, habitat fragmentation can negatively affect the dynamics of P. borealis populations by altering dispersal processes. Success of all classes of non-breeding individuals in obtaining breeding positions was reduced when territories were less aggregated. When dispersal success in real, fragmented, populations is low, whether dispersing individuals suffer increased mortality when crossing gaps (Dawson et al. 1987; Sisk, Haddad & Ehrlich 1997), are selective in site choice (Faaborg et al. 1995; Zanette 2000) or are simply unable to locate territories (Matthysen 1999), is often unclear. Our study reveals that disrupted dispersal alone can cause population decline, provided we have modelled dispersal behaviour accurately. Nor are our results dependent on any tendency to avoid gaps or unsuitable habitat when dispersing. If such effects existed, as they seem to in the co-operatively breeding brown treecreeper, for example (Cooper & Walters 2002), disruption of dispersal by habitat fragmentation would be even more pronounced.

Small populations with randomly distributed territories were dependent on helpers for male breeder recruitment. Because most helpers become breeders by inheriting their natal territory (Walters et al. 1988a), even isolated territories can recruit replacement males. The majority of solitary males that acquire breeding status are found by a dispersing female rather than winning a competition for a breeding vacancy in their vicinity (Walters et al. 1988a). Hence the persistence of P. borealis populations depends critically on how efficiently dispersing females are able to locate solitary males, which in turn is a function of the number and spatial arrangement of the territories. This is a novel finding for P. borealis and may be valid for other species with female-biased dispersal as well. In his review of the causes of extinction in small and isolated bird populations, Dale (2001) suggested that unsuccessful female dispersal was an important, so far mostly overlooked, factor contributing to negative population trends. He concluded that high reproductive success and survival did not guarantee population persistence and more effort should be invested in evaluating dispersal success, especially in females.

POPULATION DYNAMICS

The predominant effect of population size and spatial distribution on population dynamics was the association of high proportions of solitary males with poor dispersal success of females in scenarios in which populations declined. High numbers of unpaired males have been noted in real, fragmented P. borealis populations (Walters et al. 1988b; Conner & Rudolph 1991; Jackson 1994), as well as in other bird species in fragmented landscapes (Porneluzi et al. 1993; Walters et al. 1999; van Lengefelde 2000; for a review see Dale 2001). Large numbers of unpaired males may be a useful indicator of poor population dynamics, which can be assessed for most bird species within one breeding season.

Another interesting result was that emigration rate was higher in small populations than in larger ones. In fact, movements from small P. borealis populations into large ones are regularly reported, whereas migration from large into small populations has not been observed (Walters et al. 1988b; Conner et al. 1997; Ferral & Edwards 1997). Our study suggests that the gradual loss of birds emigrating from the study area may have contributed to declines of small populations. Even though it is obvious that emigration rates will have profound effects on population viability, surprisingly few studies have addressed this issue (Dale 2001; but see Hill, Thomas & Lewis 1996; Kindvall 1999; Fahrig 2001). While it is well-known that too short dispersal distances can lead to isolation in fragmented populations, the fact that too long dispersal distances may cause high emigration rates and ultimately population decline (Lande 1987) is hardly considered. Although emigration is hard to distinguish from mortality and thus to measure empirically, we suggest that at least modelling studies should address causes and consequences of emigration more often.

CO-OPERATIVE BREEDING AND POPULATION PERSISTENCE

Helpers were clearly more successful in filling breeding vacancies than dispersing males in small populations (≤ 100 territories). Even when the population encompassed as few as 25 territories, the transition rate of helpers to breeders seemed to be sufficient to stabilize the population, if territory arrangement was sufficiently clumped to facilitate female dispersal. Hence, helpers can buffer the effects of environmental and demographic stochasticity, as suggested in both empirical and modelling studies (Conner & Rudolph 1991; Walters 1991; Walters et al. 2002). In fact, some real populations of P. borealis containing only 25, or even 10, breeding pairs are remarkably persistent (James 1995). The buffering effect of helpers is likely to be even more important in other co-operative breeding species in which female helpers, as well as male helpers, are common. Small aggregated populations of such species might be even more stable, and aggregation even more important, than our simulations suggest for P. borealis.

Buffering effects of helpers will occur only if the frequency of helping is unaffected by changes in the landscape, however. Helping is facultative in many co-operative breeders, for example in the Seychelles warbler Acrocephalus sechellensis Oustalet (Komdeur et al. 1995). In some such species changes in the factors that predispose individuals to become helpers may accompany habitat fragmentation. Habitat quality, which is linked to helping in many species (Emlen 1991; Stacey & Ligon 1991; Koenig et al. 1992), may be especially important in this regard, because habitat fragments are often degraded. Where helping declines as habitat degrades, the population dynamics of co-operative breeders species will converge on those of non-co-operative species.

Due to the short dispersal distances (Zack & Rabenold 1989; Emlen 1991), populations of co-operatively breeding species are more likely to be isolated from one another in fragmented landscapes than populations of more vagile species (Stith et al. 1996). However, our results suggest that such populations, provided the spatial configuration of territories is favourable, might not only be persistent, but also might serve as sources of emigrants to other populations. This is an important finding for the conservation of small populations of co-operatively breeding species. We suggest that preserving small populations of co-operatively breeding species may, through migration, promote genetic diversity within larger populations. We did not include the demonstrated effects of inbreeding depression (Daniels & Walters 2000b) in our simulations, however, and these could potentially significantly reduce the viability of small populations (Daniels et al. 2000).

EMPIRICAL SUPPORT OF MODELLING OF DISPERSAL BEHAVIOUR

The outcome of the simulations is in many ways a test of the validity of assumptions about dispersal included in the model. One result that seems counterintuitive is that dispersing males took longer to find breeding vacancies in large than in small populations. This result can be linked to high emigration rates: in small populations a dispersing male finds a breeding vacancy within a short time or it emigrates from the area. In a landscape with many territories, in contrast, a dispersing male that has not found a breeding vacancy within a few time steps still has a chance to find one later, which increases the average time spent dispersing.

Because the model simulates dispersal in a straight line, time spent dispersing is proportional to distance moved. Dispersing birds, then, moved longer distances when territories were less aggregated. Increased dispersal distances in fragmented landscapes have been reported from P. borealis (Daniels 1997) and other species with generally short dispersal distances, e.g. Florida scrub-jays (Breininger 1999) and nuthatches Sitta europaea L. (Matthysen 1999).

Our finding that success of dispersing females was higher than success of dispersing males also has empirical support. In our model, greater success of females was caused both by the higher availability of breeding vacancies for females, and by females moving faster than males (see Appendix 1), allowing females to assess a larger area per unit time than males. The observation that female breeder mortality is higher than male breeder mortality, leading to higher breeder turnover in females, is well documented (Walters et al. 1988a; Walters 1990; Conner, Rudolph & Walters 2001), but differences in dispersal speed are not.

CONCLUSIONS

We took a novel approach in investigating the effects of habitat fragmentation on dispersal and population dynamics by conducting virtual experiments with a spatially explicit individual-based model. Our method led to new insights into the dynamics of fragmented populations and provided testable predictions for validation. Although individual-based models require extensive long-term empirical data, several such models exist that could be used beyond the level of population viability analysis to identify processes critical for species persistence. Our major finding with respect to conservation of this endangered species is that the co-operative breeding system may stabilize small aggregated populations, which may even act as population sources. We therefore suggest that small populations of P. borealis, and perhaps other co-operatively breeding species, may have considerable conservation value.

Acknowledgements

We thank the Swiss National Science Foundation for financial support (Grant 81EZ-57341 to K. Schiegg) of this study, and two anonymous referees for their suggestions. We also acknowledge Jay Carter and Phillip Doerr, whose continuing efforts contribute greatly to the extension of our data set, and Benjamin Letcher and Larry Crowder for their work on the model.

Appendix

Appendix 1

MODEL PARAMETERS

Parameters were estimated from empirical data in Walters et al. (1988a), Walters (1990) and Letcher et al. (1998). For consistency with Letcher et al. (1998), dispersing adults of either sex are denoted as ‘floaters’.

Mortality
Male fledgling annual mortality =      0·50
Male floater annual mortality =      0·38
Male helper annual mortality =      0·20
Male solitary annual mortality =      0·34
Male breeder annual mortality =      0·23
Female fledgling annual mortality =      0·58
Female breeder annual mortality =      0·29
Dispersal
Proportion of male fledglings dispersing =      0·19
Chance leaving in season 2 =    33%
Chance leaving in season 3 =    33%
Chance leaving in season 4 =    33%
Chance of solitary male leaving =      0%
Male fledgling disperser speed =      5·1 km year−1
Male floater disperser speed =      2·3 km year−1
Female fledgling disperser speed =      4·8 km year−1
Female floater disperser speed =      4·8 km year−1
Male dispersing search range =      3·0 km
Replace breeder search range =      3·0 km
Female dispersing search range =      3·0 km
Male takes empty when no vacancy =  100%
Dispersal direction = random
Fecundity
Nest failure model intercept (b0) =      2·62142
Nest failure model male's effect (b1) =     −1·70424
Nest failure model female's effect (b2) =     −3·91284
Nest failure model helper effect (b3) =     −1·20486
Mean fledgling model intercept (b4) =      2·52997
Mean fledglings male effect (b5) =     −0·45233
Mean fledglings female effect (b6) =     −1·17622
Mean fledglings helper effect (b7) =     −0·45395
Initial conditions
% male occupancy =  100%
% solitary males =    10%
% territories with helpers =    50%
% breeding pair occupancy =    90%
Age distribution = 1990 data
Landscape
Scale =    20 pixels km−1
Size =    32 × 24 km
Maximum territory radius =      0·5 km
Minimum territory radius =      0·3 km
Miscellaneous
Maximum bird age =    15 years
Disuse time before territory removal =      5 years
Emigration test forward angle =  180°
Emigration test forward distance =  100 km
Radial search resolution =    10 per 3 km
Angular bird search resolution =    21 per 360°

Ancillary