Density effects on life-history traits in a wild population of the great tit Parus major: analyses of long-term data with GIS techniques

Authors


Teddy A. Wilkin, Edward Grey Institute of Field Ornithology, Department of Zoology, South Parks Road, Oxford OX1 3PS, UK. E-mail: teddy.wilkin@zoo.ox.ac.uk

Summary

  • 1Population density often has strong effects on the population dynamics and reproductive processes of territorial animals. However, most estimates of density-dependent effects use the number of breeding pairs per unit area in a given season and look for correlations across seasons, a technique that assigns the same density score to each breeding pair, irrespective of local spatial variation.
  • 2In this study, we employed GIS techniques to estimate individual breeding densities for great tits breeding in Wytham Woods UK, between 1965 and 1996. We then used linear mixed modelling to analyse the effect of density on reproductive processes.
  • 3The areas of Thiessen polygons formed around occupied nestboxes were used to approximate territory size (necessarily inverse of breeding density). There were significant, independent and positive relationships between clutch size, fledging mass and the number of offspring recruited to the population, and territory size (all P < 0·001), but no effect of territory size on lay-date or egg mass.
  • 4Thiessen polygons are contiguous and cover all of the available area. Therefore, at low nest densities territory polygons were excessively oversized. Using a novel procedure to address this limitation, territory sizes were systematically capped through a range of maxima, with the greatest effect in the models when territories were capped at 0·9–2·3 ha. This figure approximates to the maximum effective territory size in our population and is in close agreement with several field-based studies. This capping refinement also revealed a significant negative relationship between lay-date and territory size capped at 0·9 ha (P < 0·001).
  • 5These density-dependent effects were also detected when analyses were restricted to changes within individual females, suggesting that density effects do not merely result from either increased proportions of low-quality individuals, or increased occupation of poor sites, when population density is high.
  • 6Overall, these results suggest that, in the current population, great tits with territories smaller than c. 2 ha independently lay smaller and later clutches, have lighter fledglings, and recruit fewer offspring to the breeding population. These analyses thus suggest a pervasive and causal role of local population density in explaining individual reproductive processes.

Introduction

Population density has a strong effect on the population dynamics and the reproductive processes of territorial animals (Newton 1992; Sutherland 1996). In many bird species, including the great tit Parus major, clutch size (Kluijver 1951; Lack 1958; Perrins 1965), fledgling mass (Both 1998a; Garant et al. 2004) and recruitment of offspring (Both & Visser 2000) have been found to decline with increasing population density. High density has also been shown to reduce the chance of a territorial pair starting a second brood, the survival of territorial adults, the growth rate of chicks (Both & Visser 2000), and hatching and fledgling success (McCleery & Perrins 1985). Competition for limited resources is more intense at high density and is often cited as the likely cause of reduced fecundity under such conditions (Both 1998a; Both & Visser 2000). Reduced output at high density can result from several other concurrent processes such as mass starvation, the exclusion of a proportion of the population from reproduction (Newton 1992), or nest predation (Krebs 1971; Julliard et al. 1997; Sasvari & Hegyi 1998).

Most previous studies have analysed the effects of density at the population level, comparing mean reproductive output in a given year with the year-specific population density. However, numerous problems exist in between-year population-level analyses of density effects. For example, the efficiency of reproductive processes may decline with a rise in density due to proportionally more poor-quality sites being occupied during high-density years (Andrewartha & Birch 1954; Dhondt, Kempenaers & Adrianensen 1992). Also, in populations of small passerines, density is often determined by variation in overwinter survival during the previous winter. ‘High-density’ years usually occur after mild, food rich winters and are therefore often characterized by a high proportion of young and low-quality birds that produce few recruits. Between-year analyses do not adequately account for these sources of variation. Problems also arise with within-year analyses of the effects of density; as competition for nest sites is likely to increase with declining nest site availability, density dependence could result from better-quality individuals settling in areas with fewer nest sites and reproducing more successfully (Garant et al. 2005). Analyses of the effects of density should therefore aim to control for the characteristics of individual females as well as within-environment differences in habitat quality.

Density is most often measured as the number of breeding pairs per unit area (e.g. Perrins 1965; Orell & Ojanen 1983; Perrins & McCleery 1989; Both, Tinbergen & Visser 2000). Using this approach, all pairs of breeding birds in a given year are assigned the same breeding density value irrespective of spatial variation at the level of individual breeding events. However, variation in breeding density is likely to occur, usually due to variation in the availability of resources, such as suitable nest sites. For example, Brown, Mehlman & Stevens (1995) found that many bird distributions were characterized by large areas containing a few individuals, interspersed with ‘hot spots’ of high density. An alternative method for measuring breeding density at the level of the individual is based on the distance to the nearest breeding neighbour (e.g. Krebs 1971). Although this method has the advantage of assigning an individual measure of breeding density to each pair, it acknowledges no neighbours other than the nearest, and thus does not account for spatially variable breeding densities. For example, two pairs breeding close to each other, but a considerable distance from others, would be assigned the same nearest neighbour value as another similarly spaced pair in the centre of a densely packed cluster.

For a territorial species, territory size may provide a more accurate estimate of breeding density at the level of the individual where competition and reproductive decisions are thought to operate. However, the time spent in the field needed to assess territory sizes is considerable and often prohibitive. Furthermore, defensive behaviour does not necessarily relate to intraspecific breeding density or territory size, as the area defended may vary at different stages of the reproductive cycle. For these reasons, and because this method is not suitable for analysing historic, long-term data sets, there is a need to develop geometric territory models that estimate individual breeding density and take into account spatially variable breeding sites (see Adams 2001 for a review).

The aims of the current study were twofold. First, we examined the utility of a geometric tessellation technique for estimating territory size for 5007 pairs of great tits breeding over a 32-year period. We argue that the areas of the resulting territory polygons (necessarily inverse to local breeding density) serve as a simple model of local breeding density that operates at the level of the individual and accounts for spatial variation. Second, we use our measure of local breeding density to examine density dependence at different stages of the reproductive cycle and discuss possible causative processes.

Methods

field data

Data were obtained during the Edward Grey Institute's long-term study of the great tit at Wytham Woods, near Oxford, UK. The data used in the present study were collected between 1965 and 1996, in accordance with methods described previously (e.g. Perrins 1965, 1979; Gosler 1993). Great tits breed almost exclusively in nestboxes in Wytham, the locations of which have remained more or less constant throughout the study, unless a minor move was necessitated by tree fall. Nestboxes were visited at least once a week to ascertain clutch initiation date (lay-date, where 1 April = 1), egg mass (the mean of three to five unincubated eggs) and clutch size, and chicks were weighed and ringed on day 15 after hatching (where hatch day = 1). For the purpose of this study, fledgling mass was averaged for each brood. Parents were trapped at nestboxes after the chicks reached 7 days of age (to reduce desertion risk), aged and sexed (Svensson 1994), and ringed, or their identities were established from (BTO) rings already fitted.

We analysed first clutches (second clutches are very rare in Wytham), and only those in which more than four eggs were laid. Reproductive success was measured by the number of young from each brood that were recruited to the breeding population in subsequent years. This figure does not reflect the total numbers that survive to breed, as many leave Wytham and breed elsewhere (McCleery & Perrins 1985). However, the number of recruits remains an accurate measure of the relative success of nests within the context of this population study. Habitats were classified into the following four categories as in Gibson (1988), Gosler (1990) and Gosler, Higham & Reynolds (2005): (1) Ancient seminatural woodland; (2) eighteenth and nineteenth century plantations; (3) twentieth century plantations; and (4) secondary regenerated wood pasture (544, 223, 141 and 98 nestboxes, respectively). The spring temperature each year was recorded as the sum of the maximum temperatures for each day between 1 March and 20 April (the Warmth sum), as in McCleery & Perrins (1998).

digital mapping

Map Info Professional ver. 7 was used to produce yearly maps detailing the location of nestboxes in Wytham Woods that were occupied by great tits, or by great and blue tits during the breeding seasons of 1965–96. Altitude readings and the strength of the topographic slope for each nestbox were extracted from an Inverse Distance Weighting (IDW) interpolation of a 50-m resolution Land Form profile Digital-Terrain-Model (DTM) data set provided by Ordnance Survey. The GIS software was also used to measure the distance between each nestbox and the woodland perimeter.

territory model

The GIS software was used to generate quantitative predictions about the spacing of nestboxes and the size and shape of territories based on the relative location of nestboxes within the perimeter of the wood (20 km in length). By using a Dirichlet tessellation technique, we formed Thiessen polygons (Rhynsburger 1973; Tanemura & Hasegawa 1980; Stoyan, Kendall & Mecke 1987) around each nestbox at Wytham and used their sizes as a measure of nestbox spacing (Fig. 1a). A tessellated polygon is a geometric construct that contains all points closer to the generating point (in this case a nestbox) than to any other. This is achieved by placing boundaries exactly mid-way between all adjacent neighbours up to and including the woodland perimeter. The polygons are formed on a flat surface and therefore do not account for topographic variations in polygon size. For this reason, in all models we tested for an effect of gradient strength and an interaction with polygon size and found no effects. Polygons, hereafter called tessellated territories, were also formed around nestboxes occupied by great tits in each year (Fig. 1b) and used as a simple model for territory size. The model assumes that territoriality is strongest at the nestbox and declines with distance, as has been observed in many territorial animals (Giraldeau & Ydenberg 1987). The model also assumes that pairs maintain equal spacing, are of equal defensive ability and that territories are contiguous, mutually exclusive and cover all of the available habitat. Territories are assumed to be of equal quality. However, we might expect a negative relationship between habitat quality and territory size to reduce defensive costs and the risk of cuckoldry. Therefore we tested for an interaction between habitat type and territory size; we found no effect in these data. For each tessellated territory, the number of contiguous neighbours was also counted as a measure of crowding pressure (Fig. 1b). Great and blue tits compete for the same nestboxes and for food (Minot 1981; Minot & Perrins 1986). For this reason, Thiessen polygons were also formed around nestboxes occupied by either species (interspecific polygons Fig. 1c), and their areas calculated. In this study we use the difference in size between the tessellated territory (Fig. 1b) and the interspecific polygon (Fig. 1c) to yield an estimate of the local density of blue tits for each pair of great tits. Using this method, a pair of great tits breeding in an area with no blue tits present would have an interspecific polygon equal in size to their tessellated territory, and therefore their local blue tit density would be zero. However, a pair of great tits breeding in close proximity to several blue tits would have an interspecific polygon considerably smaller than their tessellated territory and therefore would be assigned a higher score for local blue tit density.

Figure 1.

Definitions of polygons and territories for breeding great tit density. An area of Wytham (Bean Wood) showing (a) all nest boxes with their tessellated polygons the areas of which provide an estimate of nest box spacing, (b) nest boxes occupied by great tits in 1972 and their tessellated polygons which provide a simple model for territory size, and (c) nest boxes occupied by great tit (solid circles) and blue tits (half solid circles) in the same year with their tessellated interspecific polygons. The nest box in the shaded area has a spacing polygon size of 0·4 ha. The great tit using the same nest box in 1972 had a tessellated territory size of 1·8 ha with five contiguous neighbours (b), and an interspecific polygon of 0·7 ha (c). The difference between the sizes of polygons (b) and (c), 1·1 ha, is used in the present study as a measure of local blue tit density for the focal pair of great tits.

To compensate for excessively large tessellated polygons in areas of low nestbox density, we systematically imposed a range of ceilings upon the size of territory polygons, and tested the effect of imposing a particular ceiling on the explanatory power of territory size in each model. For example, at a ceiling level of 1 ha, all polygons above this size were replaced with a value of 1 ha while polygons below 1 ha in size remained unaffected. This procedure was repeated with ceilings from 0·2 to 4·6 ha in increments of 0·1 ha (affecting 99% of the territory polygons at the 0·2 ha level and 4% at the 4·6 ha level). We hypothesized that ceilings at the high end of the range would reduce excessively large polygons to a more biologically reasonable level, with the result that using the capped territory data ought to explain more variation in reproductive traits than uncapped data. At the lower end of the range, the ceilings will reduce the area of realistically sized polygons, such that the capped data will explain less variation in reproductive traits. This combination of effects should be detected as a maximum in the effect size (test statistic) for the effect of territory size in the models. It was our aim to establish the ceiling level (i.e. maximum size) at which tessellated territory size explains the maximum amount of variation in reproductive traits. This method was employed rather than testing for a quadratic term because it yields more information regarding the scale at which the signals are maximized in the models.

statistical analyses

Linear mixed models (LMM) with normal errors were performed with genstat ver. 7·2 (VSN Intl 2003) to assess the effect of our measure of territory size on lay-date, clutch size, egg mass and fledgling mass. A Generalized Linear Mixed Model with a Poisson error structure was used to analyse the number of recruits to the breeding population with respect to territory size. In each model, year of reproduction and female identity were included as random effects and territory size was always included as a fixed effect. We also included terms for life-history stages occurring before the subject of analysis in each case (for example, clutch size in the case of number of recruited offspring). By including year as a random effect we control for between-year differences due to overall population density, and by including female as a random effect we control for systematic differences between females (due, for example, to differences in biometrics and condition). Our analyses, therefore, specifically and effectively consider variation within annual environments. The significance of factors in explaining variation was assessed from the Wald statistic, which is distributed asymptotically as χ2 (VSN Intl 2003), and the amount of variation explained by each model was estimated as a percentage of the difference between the residual variance when only random effects were included and the residual variance of the final model. Five models were built using backward stepwise removal of nonsignificant factors depending on their Wald statistic: (1) the lay-date model controlled for the age of the female, spring temperature (warmth sum), altitude, female status (resident or immigrant, defined as whether hatched in a Wytham nestbox or not, respectively) and habitat type; (2) the resulting clutch size LMM included lay-date and the age of the female as fixed effects (as in Perrins 1965); (3) the egg mass model controlled for the age of the female, distance to the edge of the woodland and lay-date; (4) the fledging mass model controlled for clutch size, mean egg mass and lay-date as fixed effects (as in Garant et al. 2004) but also altitude (earlier phenology at lower altitudes; see Hopkins 1938); and finally (5) the number of recruits model controlled for lay-date, fledging mass and clutch size as fixed effects (as in Perrins & McCleery 1989). The models explain variation in a sequence of reproductive stages. Therefore, by including the previous stages as covariates, our analyses investigated the independent effect of density upon each stage. For ease of presentation, data are displayed graphically as residuals estimated by removing the polygon data from the model and rerunning the analysis.

To explore the effect of interspecific density on reproduction in great tits, models were also run using, as an alternative predictor, our measure of local blue tit density capped through a similar range of maxima to that used for the tessellated territories, and the results plotted in the same way. In this way we aimed to determine the level at which inter- and/or intraspecific density explained most variation in the dependent traits.

All subset regressions (genstat, VSN Intl 2003) were used to select the combination of polygon data that explained most variation in the reproductive traits. Explanatory variables other than polygon data were forced in each model, while territory data and local blue tit density data capped at each level were included as possible explanatory variables. The combination of polygon data that returned the lowest Akaike value (see Burnham & Anderson 1998) was deemed to be the most suitable model. Thus, this is a formal statistical analysis of the graphical approach described above.

Density-dependent effects may occur partially because poor-quality birds are excluded from high-quality areas or those with low nest site availability (Dhondt et al. 1992). This could be termed an indirect effect of density upon the efficacy of reproduction. To investigate whether breeding density has a direct effect on great tit reproduction, we repeated the models with a subset of repeat breeders. In this way, we were able to investigate the effect of territory size on reproductive parameters within individual females; this analysis thus assumes that ‘quality’ is relatively fixed for individuals, and thus it would not detect an effect due to individuals occupying poorer-quality territories in years in which their quality is reduced. However, as breeding-site fidelity is very high in this population (a mean of 112 m between successive breeding attempts in the current data, and see Harvey, Greenwood & Perrins 1979) we judge this process to be unlikely.

We also used Generalized Linear Models with Poisson errors to determine which factor(s) affected the lifetime reproductive success of a female, by testing for significance of the following parameters averaged over a female's lifetime: clutch size, lay-date, fledgling mass and territory size. By not controlling for the number of times she reproduced in her lifetime, this analysis contains an element of survival from one reproductive attempt to another.

Results

territory model

Tessellated territory polygons were formed for 5007 occupied nestboxes over the 32 years of the study. The territories ranged from 0·06 to 14 ha in size with a mean of 1·6 ha (SD = 1·368). Clutch size, mean fledgling mass and the number of recruits from a breeding attempt were independently related both significantly and positively to territory size as estimated by the Thiessen tessellations (all P < 0·001; see Table 1). There was no suggestion of an effect of territory size on lay-date (inline image = 1·65, P = 0·199) or egg mass (inline image = 2·35, P = 0·126; Table 1). Mean residuals from the territory models were plotted against the area of the tessellated territories, expressed in increments of 0·2 ha (Fig. 2). Each significant variable shows an asymptotic function associated with territory size, with the asymptote about 2–3 ha, reflecting the minimum territory size unaffected by negative density effects. A negative relationship between territory size and lay-date is also apparent with a similar asymptote at 2–3 ha, but not significant in the model. Our measure of local blue tit density also explained significant variation in clutch size (inline image = 5·01, P = 0·025), mean fledgling mass (inline image = 7·13, P = 0·008) and the number of recruits (inline image = 7·63, P = 0·006) when included in the models in place of territory size. Thus local breeding density, as measured by tessellated territories, strongly affected three of the five reproductive traits examined and a negative, but nonsignificant relationship was apparent between tessellated territory size and lay-date. Local blue tit density affected the same traits as intraspecific density but effects were weaker.

Table 1.  Results of mixed models assessing reproductive traits of great tits. Data used were from Wytham woods during 1965–96 (n = 4550). General linear models were used in each case, with the exception of the recruitment analysis where a generalized model with a Poisson error structure was used. Year of reproduction (n = 28) and female identity (n = 3484) were included as random effects. Percentages in parentheses indicate the amount of variation explained by the fixed component of each model
Dependent/independent factorWald χ2d.f.Effect/(SE) P
Lay-date (8%)
 Age133·641−0·8412/(0·07312)< 0·001
 Warmth sum 52·951−0·09073/(0·012438)< 0·001
 Altitude 23·931 0·01807/(0·003580)< 0·001
 Female status (immigrant or resident) 16·71 R < I< 0·001
 Habitat type 14·8232 < 3 < 1 < 4< 0·001
 Territory size (ha)  1·651−0·08589/(0·068620)0·199
Clutch size (13%)
 Lay-date374·421−0·06878/(0·003453)< 0·001
 Age of female 42·261 0·1167/(0·01781)< 0·001
 Territory size (ha) 14·681 0·05594/(0·015376)< 0·001
Mean egg mass (1%)
 Age 40·191−0·01060/(0·001673)< 0·001
 Distance from woodland edge (m) 17·371−0·00008172/(0·000019608)< 0·001
 Altitude (m)  8·351 0·0002575/(0·00008912)0·004
 Lay-date  3·791 0·0006508/(0·00033437)0·052
 Clutch size  4·241−0·002752/(0·0013360)0·039
 Territory size (ha)  2·351−0·002373/(0·0015492)0·126
Mean fledgling mass (4%)
 Clutch size 92·311−1·253/(0·1306)< 0·001
 Mean egg mass 51·31110·14/(1·437)< 0·001
 Altitude 28·821−0·04152/(0·007686)< 0·001
 Lay-date 19·751−0·1510/(0·03461)< 0·001
 Territory size (ha) 11·731 0·5331/(0·15619)< 0·001
Number of recruits (10%)
 Lay-date109·521−0·03655/(0·003493)< 0·001
 Mean fledgling mass102·201 0·01769/(0·001750)< 0·001
 Clutch size 29·691 0·07020/(0·012883)< 0·001
 Territory size (ha) 12·331 0·04803/(0·013678)< 0·001
Figure 2.

Relationships between mean territory size classes and life history traits. Mean residual clutch sizeData used were from Wytham woods during 1965–96 (n= 4550). Year of reproduction and female identity were included as random effects, mean residual fledgling mass and mean residual number of recruits plotted against the area of the tessellated polygon containing the generating nest box. Data are displayed as residuals, estimated from full models without territory size (see text). Vertical bars are standard errors.

capped territory size

To explore the influence of variable ceilings on territory size, the models were rerun many times, on each occasion using territory data capped at a different level. The significance of the territory size measure in explaining reproductive traits was then plotted against the level at which it was capped (Fig. 3). All subset regressions showed that variation in lay-date was best explained by territory polygons capped at 0·9 ha (inline image = 24·64, P < 0·001), and variation in clutch size by polygons capped at 1·8 ha (inline image = 28·69, P < 0·001) (Table 2). The greatest amount of variation in mean fledgling mass was explained by territory polygons capped at 2·3 ha (inline image = 17·15, P = < 0·001), while in the number of recruits model territory polygons capped at 1·9 ha were selected (inline image= 24·14, P < 0·001) (Table 2). The lay-date and recruitment models explained more variation when capped, than when uncapped territory size was used, while the clutch size model explained less total variation. Ceilings of about 2 ha in size affected about 30% of the polygons, while the ceiling of 0·9 ha affected 59% of the polygons. It is striking that several of these analyses gave a consistent estimate of the territory size at which the effect is maximized (i.e. about 2 ha), and that in each case there is a clear maximum in the effect size. The exception is that of lay-date, which is maximized at 0·9 ha, suggesting that the commencement of breeding is affected by density on a smaller scale than are other traits. The maximum effect-size from the interspecific density analysis was lower than the average for intraspecific analyses (1–1·2 ha) and the overall effect size was smaller. This suggests that the scale over which blue tits affect great tits is smaller than the scale of intraspecific density.

Figure 3.

Graphical estimation of the appropriate size at which to cap estimated territory size to account for over-estimation of size in low density areas. Figures show the Wald statistic (distributed as χ2), from Linear mixed models analysing variation in lay-date, clutch size, fledgling mass and the number of offspring recruited to the breeding population, for a range of artificially imposed territory sizes (see text). All models include year of reproduction and female identity as random effects. Clutch size model controls for lay date and age of female; fledgling mass model controls for altitude, mean egg mass within the brood, lay date and clutch size; and the reproductive success model controls for lay date, clutch size and the mean fledgling mass within the brood. Open circles are data for great tits alone; solid circles represent the significance of ceilings imposed upon data indicative of local blue tit density (see text). Squares show the significance of the territory size (open) and blue tit density (solid) when no ceiling was imposed. In each model, territory size capped at between 0·9–2·3 ha was selected by all subsets regressions to explain the most amount of variation in the dependent variable, as indicated by the Akaike value (vertical lines).

Table 2.  Refined mixed models using capped territory size as a measure of local density (see Table 1)
Dependent/independent factorWald χ2d.f.Effect/(SE) P
Lay-date (9%)
 Age135·991−0·8504/(0·07292)< 0·001
 Warmth sum 52·971−0·09077/(0·012472)< 0·001
 Altitude 29·961 0·01935/(0·003536)< 0·001
 Female status (immigrant or resident) 16·71 R < I< 0·001
 Habitat type 12·613 2 < 3 < 1 < 4< 0·001
 Territory size (ha) capped at 0·9 ha 24·641−2·272/(0·4577)< 0·001
Clutch Size (13%)
 Lay-date368·531−0·06835/(0·003448)< 0·001
 Age of female 43·631 0·1185/(0·01782)< 0·001
 Territory size (ha) capped at 1·8 ha 28·691 0·1794/(0·03526)< 0·001
Fledgling mass (4%)
 Clutch size 94·181−1·271/(0·1307)< 0·001
 Mean egg mass 52·21110·24/(1·436)< 0·001
 Altitude 32·191−0·04437/(0·007778)< 0·001
 Lay-date 19·251−0·1479/(0·03458)< 0·001
 Territory size (ha) capped at 2·3 ha 17·151 1·425/(0·3474)< 0·001
Number of recruits (11%)
 Lay-date109·801−0·03656/(0·003489)< 0·001
 Mean fledgling mass 99·461 0·01746/(0·001751)< 0·001
 Clutch size 27·311 0·06731/(0·012879)< 0·001
 Territory size (ha) capped at 1·9 ha 24·621 0·1582/(0·03188)< 0·001

within-female analysis

Within repeat breeding females, territory size capped at 0·9 ha was a significant predictor of lay-date (inline image = 7·92, P = 0·005), while territory size capped at 1·8 ha was a significant predictor of clutch size (inline image = 7·06, P = 0·008; Table 3). Also within females, territory size capped at 2·3 ha was a significant predictor of fledgling mass (inline image = 20·89, P < 0·001) and territory size capped at 1·9 ha was significant in explaining variation of the number of recruits (inline image = 9·63, P = 0·002). Effects were weaker and models explained less variation than the between-female analyses, with the exception of the fledgling mass model. These results are important in suggesting a causal role of population density on reproductive output, as the output of an individual female can clearly be predicted by her territory size in different years.

Table 3.  Results of mixed models used to assess significance of determinants of reproductive traits, using capped territory data and constructed within female using repeat breeders; 1094 individuals and 2761 breeding attempts (see Table 1)
Dependent/independent factorWald χ2d.f.Effect/(SE) P
Lay-date (8%)
 Age 64·031−0·7015/(0·08766)< 0·001
 Warmth sum 56·531−0·09117/(0·012127)< 0·001
 Altitude 12·221 0·01799/(0·005146)< 0·001
 Female status (immigrant or resident)  7·001 R < I0·008
 Habitat type  4·763 2 < 3 < 1 < 4< 0·001
 Territory size (ha) capped at 0·9 ha  7·921−1·609/(0·5720)0·005
Clutch size (12%)
 Lay-date147·961−0·05801/(0·004764)< 0·001
 Age of female 21·951 0·1021/(0·02181)< 0·001
 Territory size (ha) capped at 1·8 ha  7·061 0·1276/(0·04952)0·008
Fledgling mass (4%)
 Clutch size 48·821−1·227/(0·1749)< 0·001
 Mean egg mass 23·371 9·228/(1·9031)< 0·001
 Altitude 13·811−0·03929/(0·010571)0·001
 Lay-date 14·921−0·1732/(0·04517)< 0·001
 Territory size (ha) capped at 2·3 ha 20·891 2·151/(0·4613)< 0·001
Number of recruits (8%)
 Lay-date 42·401−0·03044/(0·004675)< 0·001
 Mean fledgling mass 57·051 0·01782/(0·002359)< 0·001
 Clutch size 14·901 0·06628/(0·0171730< 0·001
 Territory size (ha) capped at 1·9 ha  9·631 0·05543/(0·017864)0·002

lifetime reproductive success and survival

For 2935 females, we found significant independent effects of mean lifetime clutch size (t = 8·62, P < 0·001), mean fledgling mass (t = 7·85, P < 0·001) and mean lay-date (t = −12·64, P < 0·001) on the lifetime number of offspring recruited to the breeding population. Our results also show an independent effect of mean lifetime territory size on the total number of lifetime recruits (t = 3·28, P < 0·001) (Table 4). We made no attempt to control for the number of times that a female in the data set reproduced and so these results contain an element of variance due to survival from one reproductive attempt to another. Residuals from the model were plotted against mean lifetime territory size (Fig. 4) showing a clear rise in lifetime reproductive success with mean territory size, until an asymptote at c.2·5 ha. In this case it seems that this relationship may be driven largely by the effect of very small territory sizes; above c. 1 ha the relationship appears flat.

Table 4.  The results of a log-linear model (Generalized Linear Model) with a Poisson error structure assessing the determinants of lifetime reproductive success (total number of offspring recruited to the breeding population) of 2935 female great tits, with respect to mean life-history traits and tessellated territory size
Dependent/independent factorEstimateSE t (2925) P
Lifetime reproductive success
 Constant−2·4590·367 −6·7< 0·001
 Mean lay-date−0·031870·00252−12·64< 0·001
 Mean clutch size 0·10350·012  8·62< 0·001
 Mean fledgling mass 0·013340·0017  7·85< 0·001
 Mean territory size (ha) 0·04360·0133  3·280·001
Figure 4.

Residual lifetime reproductive success as function of mean lifetime territory size. Model controls for clutch size, lay date and mean fledgling mass.

Discussion

Our results demonstrate that Thiessen polygons represent a suitable model for estimating the territory size of great tits in historic data sets. Moreover, the model yields an individual measure of breeding density for each pair and accounts for variation in breeding density within environments. In the current study, territory sizes estimated by Thiessen polygons were highly significant independent predictors of clutch size, fledging mass and reproductive success. Further, we demonstrated a new capping method for refining the territory model by imitating interstices, which subsequently revealed a significant density effect on lay-date. This capping method also yielded an estimation of maximum territory size at different stages of the breeding season. All effects were apparent between and within females. No effect was found on egg mass, and we discuss some explanation for, and implications of, these results below.

territory model testing

To test the territory model we compared the characteristics of the tessellated territories with those measured in the field in previous studies. In agreement with Krebs (1970), we found territories that included the edge of the woodland were larger than interior territories (t = 2·59, d.f. = 6474·27, P = 0·01) and that they had fewer contiguous neighbours (t = 52·24, d.f. = 6476, P < 0·001), although the latter is expected for simple geometric reasons. Note that the difference in size between edge and internal territories was not due to differences in nestbox spacing, as polygons based on this (Fig. 1a) showed no difference between those at the edge and those in the interior (t = 0·67, P = 0·504), suggesting that nestboxes were occupied less frequently at woodland edges. With regard to mean territory sizes, our mean uncapped territory size was 1·6 ha, which is somewhat larger than other field-based studies have found. For example, Krebs (1971) found a mean of 1·26 ha by drawing a perimeter around mapped observations and responses to song playback, and Both & Visser (2000) found a mean of 1·1 ha by enclosing observations with maximum convex polygons. Using an alternative measure, if we calculate density as the numbers of pairs per hectare, then our territory model gives an overall mean of 0·6 pairs per hectare. Perrins (1965) calculated 1·3 and 0·6 pairs per hectare in high- and low-density areas of Wytham (Marley and Great Wood, respectively) while Both et al. (2000) found between 0·3 and 1·1 pairs per hectare in another population. Our underestimate of density is probably due to our territory model using all of the available habitat, which leads to an overestimation of territory size in areas or years of low density. To account for this we capped territories systematically through a range of maxima and found that imposing a maximum territory size of 0·9–2·3 ha maximized the significance of the territory size effect in our models. This value probably represents the maximum territory size in our population, achieved by birds breeding in areas or years of low density. We consider it significant that, following a limitation of 2 ha, our mean territory size was reduced to 1·25 ha, a figure more in line with field-based studies (Krebs 1971; Both & Visser 2000). This is, to the best of our knowledge, the first time that this systematic capping method has been applied to refine a territory model, and we believe that there are many other applications of this technique with respect to spatial analyses where scale is uncertain.

lay-date

As for many birds breeding in temperate climates, the timing of breeding is critical for great tits. Early fledglings have higher recruitment probabilities (Lack 1958; Perrins & McCleery 1989; Verboven & Visser 1998; Cresswell & McCleery 2003) probably due to a competitive advantage during the crucial 2 weeks after fledging. At the population level, we might expect mean lay-date to be delayed in high-density years due to a higher proportion of both poor-quality sites being occupied and young or poorer-quality birds being present, but we found no association between lay-date and the number of birds breeding in Wytham at the level of the population when controlling for spring temperature (t28 = 1·41, P = 0·169). Laying date is a highly plastic character, varying with respect to individual age, preceding spring temperature, altitude and habitat type in our analyses (Table 1). Earlier-breeding birds had larger clutches and independently produced heavier fledglings that were more likely to recruit to the breeding population but our analysis showed no effect of uncapped territory size on lay-date at the level of the individual despite a visible relationship between average residual lay-date and territory size (Fig. 2). However, our analyses show a clear density effect on laying date at the level of the individual subsequent to a territory size cap of 0·9 ha to control for oversized polygons. Explaining the maintenance of variation in laying date, despite it being subject to strong natural selection, has long been a challenge, and this trait is illustrative of many other characters that are under directional selection yet show substantial variation within populations (see Price, Kirkpatrick & Arnold 1988; Merilä, Sheldon & Kruuk 2001; Sheldon, Kruuk & Merilä 2003). One popular explanation for the maintenance of variation in this character is that a large component of the variation in timing of breeding represents individual condition, and that selection acts on this component of variation (Price et al. 1988). Our results support this explanation, as we might reasonably expect local density to influence local condition, and hence timing of breeding. The capping of territory sizes also showed that territory size was smallest at the time of egg laying (0·9 ha). The number of tessellated territories affected by this ceiling level was 59%, which is also an approximation of the number of birds that are unaffected by density at the time of egg laying. This could be possibly explain why in the current data set no effect of density on lay-date is found at the level of the population; most birds are unconstrained by density at the time of egg laying. Møller (1990) concluded that territory sizes of many species were largest during the period of fertility, probably to reduce the likelihood of extra pair copulations and cuckoldry. However, Rodrigues (1998) conducted a field-based study on chaffinches Fringilla coelebs and reported a minimal territory size during the fertile period. Our analyses suggest that territory sizes increase through the breeding season, possibly because more resources are required when provisioning chicks later in the season. However, we believe this subject warrants further investigation.

clutch size

Density-dependent clutch size has often been demonstrated in great tits, both in correlational studies (Lack 1958; Perrins 1965; Orell, & Ojanen 1983), in which the mean number of eggs laid in a given year was negatively associated with the number of breeding pairs present, and in experimental studies (Both 1998b) in which changes in density resulted in changes in clutch size in the expected direction (but see Both & Visser 2000). When controlling for lay-date and clutch size, as earlier and older birds independently have larger clutches, we found a positive relationship between clutch size and territory size at the level of the individual. This result is in accordance with previous correlational studies. By examining the relationship between the clutch and territory sizes of repeat breeders, we found density-dependent clutch sizes within females, although this effect was weaker than between females. A similar analysis was performed by Both (1998b), who found that females breeding on the same territory in different years showed a negative correlation between the change in clutch size between years and the change in density. These within-female analyses imply a causal effect of density on clutch size, rather than a greater proportion of poor-quality sites being occupied, or poor-quality birds being present in high-density years. Whether the relationship between clutch size and density results from adaptive adjustment by females, or is instead caused by direct food limitation is unknown; distinguishing between these two explanations would require concurrent experimental manipulations of clutch size and breeding density. We are unaware of any such experimental work.

egg mass

When controlling for potentially confounding factors, our analyses showed no effect of territory size on egg mass at the level of the individual. This is contrary to the findings of Perrins & McCleery (1994) who, at the level of the population, found generally lighter eggs in years of high density. However, their analysis did not control for confounding factors such as age. For example, in our analysis the age of the female had a strong negative effect on the mass of the eggs (inline image = 40·19, P < 0·001). It is intriguing that birds breeding close to the woodland edge had heavier eggs than did birds within the wood, as did birds breeding at higher altitudes; these effects are currently under investigation. These last results, in addition to the age effect, suggest that egg size may be adjusted by individuals in relation to their breeding conditions: the larger eggs laid by younger birds, breeding closer to woodland edge and at higher altitudes suggest that larger eggs may be a response to poorer environmental conditions. If so, the lack of response to density is puzzling. It is also unexpected because clutch size and egg size show strong negative covariance at both phenotypic and genotypic levels in this population (D. Garant & B.C. Sheldon, unpublished analyses). Hence, an increased egg size in response to higher density would be expected as a correlated response to the change in clutch size. It is possible that one influence of increased density is to suppress the covariance between clutch size and egg size, although no interaction was found in these data.

fledgling mass

Density-dependent fledgling mass in the great tit has been shown previously at the level of the population (Garant et al. 2004). In an experimental study, Both & Visser (2000) found that an increase in territory size was followed by an increase in fledgling mass, independently of parent quality. Further, Both (1998a) found that an experimental increase in nestbox density was associated with a decline in nestling mass. The current study also found a strong positive effect of tessellated territory size on fledgling mass at the pair level, when controlling for differences in egg mass, lay-date and clutch size, showing that birds breeding in larger territories have heavier chicks than predicted by these factors alone. A territory effect on fledgling mass independent of clutch size may reflect an incomplete optimization of clutch size or may result from lower density birds being able to both lay more eggs and have heavier chicks. We also found an altitude effect such that birds at lower altitudes had heavier chicks independently of their earlier lay-date. A likely explanation of density-dependent fledgling mass is that nestling provisioning may be reduced in high-density areas, in terms of food quality and/or quantity, particularly if parents also suffer from increased interference from other pairs.

recruitment and lifetime reproductive success

In the great tit breeding success declines seasonally (Perrins 1970; Perrins & McCleery 1989). This relationship is thought to be causal in both blue tits (Norris 1993) and great tits (Verhulst, van Balen & Tinbergen 1995); however, there is some evidence to suggest that differences in quality between early and late breeders also contribute to the seasonal decline (Verhulst et al. 1995). The current analyses also show a significant negative lay-date effect on the number of recruits to the breeding population. Furthermore, the lay-date effect on recruitment was also apparent within females, supporting the causal role of lay-date on reproductive success. Previous studies have shown that heavier fledglings are more likely to recruit to the breeding population (Both, Visser & Verboven 1999; Monros, Belda, & Barba 2002; Garant et al. 2004). The current analysis supports this result as, independent of their earlier lay-date, heavier chicks at Wytham were more likely to recruit. We also found a positive clutch-size effect on recruitment, which suggests that there may be an independent benefit of coming from a large brood. This effect has been shown before and may arise either from a genetic effect whereby fitter parents lay larger clutches (Both, Tinbergen, & van Nordwijk 1998), or from environmental covariance between parent and offspring characters.

In addition to the relationships described above, we found a strong positive effect of territory size on recruitment, independent of earlier lay-dates, larger clutches and heavier chicks. The same was true when we analysed the effect of mean lifetime territory size on lifetime reproductive success without controlling for the number of times an individual reproduced, indicating higher survival in larger territories. This suggests that there are additional fitness benefits of having a larger territory beyond that predicted by those factors controlled for above. For example, females are thought to adjust their clutch sizes to fit the number of offspring that they are able to raise in a given environment (Tinbergen & Daan 1990). If this adjustment were complete then we would not expect to see a strong environmental effect on reproductive success when controlling for clutch size. However, as our results show a strong effect of territory size on reproductive success independent of clutch size, we can conclude either that, in the current population, clutch size adjustment to population density is incomplete or that birds at low density are beyond some threshold in resource abundance and are thus able to produce both large clutches and have heavier chicks, which are more likely to recruit.

What causes this additional effect of territory size on lifetime reproductive output? There are several possibilities, among which are: (1) food limitation between fledging and independence from the parents; (2) increased predator activity during the same period due to attraction to higher density prey breeding areas; (3) an increased tendency for offspring to disperse further (i.e. outside Wytham) from high-density areas, which would appear as reduced recruitment in our data.

Conclusions

Thiessen polygons represent a suitable geometric model for estimating breeding density in great tits. The tessellation model provides an individual measure of breeding density for each pair and accounts for variations in breeding density within environments; estimated territory sizes agreed well with those estimated previously by more intensive methods. In the current study, lay-date, clutch size, fledging mass and reproductive success were strongly predicted by territory size, both between and within females, suggesting a pervasive role of local population density in explaining individual reproductive fitness. However, we found no effect of breeding density on egg mass, suggesting that resource limitation may not be an important determinant of this trait. We have also shown that capping territories imitated interstices effectively to overcome the problem of oversized polygons at low density. Our analyses suggest that mean maximum territory size increases from 0·9 during clutch initiation to 2·3 ha during nestling provisioning. We suggest that the model can be applied to other living systems at any scale in which conspecific environments are both spatially variable and influential.

Acknowledgements

We are grateful to the many people who collected data during the long-term tit study in Wytham, and to C. Both, C.M. Perrins, J.L. Quinn, M.J. Wood and an anonymous referee for their helpful comments on the manuscript. T.A.W. was funded by a studentship from the Biotechnology and Biological Sciences Research Council (BBSRC), D.G. was financially supported by a Natural Sciences and Engineering Research Council of Canada (NSERC) Postdoctoral Research Fellowship, and by a (BBSRC) grant to B.C.S; B.C.S. was funded by a Royal Society University Research Fellowship.

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