study site and population
A population of 18–53 pairs of long-tailed tits was studied between 1994 and 2002 in the Rivelin Valley, Sheffield, UK. (53°23′N 1°34′W). The study area occupies a 3-km long section of the valley which is approximately 1 km wide and runs West to East. Suitable habitat for long-tailed tits within this part of the valley consists of about 160 ha of interconnected patches of woodland and scrub. The part which is not woodland is almost entirely grassland (agricultural pasture and golf course) that is unsuitable habitat for long-tailed tits. Woodland in the study area is connected at both ends by narrow corridors to poorer-quality habitat.
Long-tailed tits spend most of the year, from June to January, in flocks of 10–30 individuals. These flocks break up when pairs form in late winter. All long-tailed tits attempt initially to breed in pairs, but the rate of nest failure is high because of predation by corvids. As a result some individuals abandon independent breeding, and help a close relative to raise their brood. The major contribution of helpers to nestlings is in the provisioning of food. For further details of the study area, species and social system see Hatchwell et al. (2001, 2004) and MacColl & Hatchwell (2002).
Unringed adults were colour-ringed and weighed before breeding started, or in some cases during the nestling period. Birds ringed as adults in the first year of the study (1994) were not included in our calculations of fitness. Birds ringed as adults in all subsequent years were classed as immigrants, and were assumed to be 1 year of age when first recorded breeding. Helpers from outside the study area were colour-ringed soon after first appearance at a nest. Birds that were caught were weighed (to 0·1 g) and had their right tarsus measured (to 0·1 mm). Nests were located by observation of pairs and checked at least every other day. If a pair failed in a breeding attempt we relocated the birds and any subsequent nest by extensive searching of the study area. Chicks were counted (‘number of fledglings’), weighed to 0·1 g (‘nestling weight’) and ringed with unique colour combinations when 10–13 days old. Ninety per cent (n = 104 broods) were weighed at 11 days. The survival of chicks in nests which were not depredated was very high (97·7% from hatching to day 11; Hatchwell et al. 2004). Chicks were sexed using a molecular technique (Griffiths et al. 1998), using blood taken by brachial venipuncture at the time of ringing.
Chicks that were known to have fledged were counted as recruits to the local breeding population if they were resighted during intensive fieldwork at the beginning of each breeding season. As well as the study area itself we searched the first few hundred metres of the woodland areas adjacent to the study area at its East and West ends in several years of the study as time allowed. Very few marked birds were ever found. To the North the study area is bounded almost entirely by pasture, and we believe that there is little dispersal in that direction. To the South the study area is bounded by residential housing, and most short-distance dispersal out of the study area probably takes place into the gardens of these houses. It is difficult to quantify this dispersal because this land is privately owned. However, neither public appeals for sightings nor the personal observations of the second author (B. J. H.) on adjacent public land have ever provided any records of colour-ringed birds. These facts, coupled with a previous formal survival analysis on this population that indicated a between-year resighting probability of close to one for living adults (McGowan, Hatchwell & Woodburn 2003), suggests that few birds disperse just past the margins of the study area. We were unable to control for longer distance dispersal in our calculations, although we have no reason to believe that this should effect our conclusions.
The complete reproductive histories of birds which hatched between 1994 and 2000 and had died by 2002 were recorded. Long-tailed tits raise a maximum of one brood per year, and always attempt to breed in every year from the age of 1 year. Lifetime reproductive success and individual fitness of birds were estimated from the number of their offspring that recruited to the local breeding population. We believe that recruits are the correct unit of reproductive success in this species because of the extended period of parental care (Brommer et al. 2002). Previous work has shown that helpers do not affect the number of chicks that fledge from the nest where they help because they arrive too late to affect clutch size, while nestling mortality due to causes other than catastrophic predation is generally very low. However, helpers do increase the number of fledglings that recruit locally (Hatchwell et al. 2004).
Extra-pair paternity and intraspecific brood parasitism are rare in long-tailed tits (< 5% of offspring), and unlikely to affect estimates of fitness. However, in calculations all known extra-pair young were assigned to their most likely true parents (Hatchwell et al. 2002).
Nests containing nestlings were watched every other day from hatching (day 0) to fledging (day 16 or 17), usually for a period of 1 h (mean total observation time per nest ± SE = 523 ± 30 min). In this way the rates at which individual carers brought food to nestlings were recorded. For each individual parent a simple linear regression line was then fitted to the relationship between hourly feeding rate and age of nestlings, and ‘provisioning effort’ was estimated as the area under the regression line between 0 and 16 days (MacColl & Hatchwell 2003a). The effort of individuals is repeatable across years (MacColl & Hatchwell 2003a), so the mean of all estimates of provisioning effort over an individual's lifetime was used to calculate ‘mean provisioning effort’. Provisioning effort is related only weakly to the size of the brood that was provisioned (R2 = 0·05) (MacColl & Hatchwell 2003b). However, in analyses where mean provisioning effort was used as a predictor variable, the analyses were repeated using the residuals of provisoning effort from brood size instead. This did not alter the conclusions. Only the results from analyses using mean provisioning effort itself are presented, as these are more easily understandable.
measurement of fitness
Lifetime reproductive success
Lifetime reproductive success is the sum of all local recruits produced by an individual in its lifetime. Following Brown (1988), in the partition of variance in LRS among components (see below) only those birds that succeeded in fledging at least one offspring were considered. It was then necessary to calculate the contribution of these individuals to overall variance in LRS, compared with that of the ‘invisible fraction’ that fledge no young (Grafen 1988). For nt total birds, of which nb succeeded in fledging at least one offspring, the overall variance in LRS for all birds is given by: p · V(LRS) +p · (1 − p) · LRS2, where p=nb/nt, and V(LRS) is the variance in LRS of birds that fledged at least one offspring (Brown 1988). The first term in this equation gives the proportion of the variance accounted for by those that fledged young, the second term gives the proportion accounted for by all other birds that attempted to breed.
Data on the annual reproductive success and survival of each bird were used to construct individual projection matrices according to the method of McGraw & Caswell (1996). The individual fitness of each bird was then calculated as the dominant eigenvalue of its matrix (using mathcad 5·0 (Fausett 2002)). In this way the fitness of each bird was calculated using three different methods to estimate their annual reproductive success. First, half the number of local recruits from each year was used to calculate ‘recruit fitness’λr, under the assumption that the relatedness of parents and offspring was 0·5. The direct fitness (λd) of individuals was then calculated by stripping from each the component of its annual reproductive success that was due to having been helped (see below). This indirect fitness component was divided among the helpers at each nest in accordance with their relatedness, and these fractions were added to their annual reproductive success values (λd) to calculate inclusive, or individual fitness (λi) for all birds (Hamilton 1964; Oli 2003).
To calculate the component of an individual's annual reproductive success that was attributable to having been helped a logistic regression model was constructed of the relationship between the proportion of fledglings that recruited locally and the number of helpers at a nest (Hatchwell et al. 2004). The model controlled for year effects, lay date and the sex ratio of the brood at fledging. This model was used to find the predicted proportion of fledglings that would have recruited locally from nests with helpers if they had had either no helpers or their observed number of helpers. Following Fitzpatrick & Woolfenden (1989), these two quantities were used to calculate the proportion of observed local recruitment from these nests that was due to the effect of helping.
To understand better the usefulness of LRS and individual fitness as measures of fitness, their ability to predict the number of grand-offspring (fledglings) produced by individuals was examined. The number of grand-offspring produced by a sample of individuals whose offspring had all completed their reproductive life spans were counted.
Partition of variance in LRS
A ‘Brownian’ partition of variance (Brown 1988) was used to assess the relative importance of three component terms: breeding life span (L), fecundity (F) and offspring local survival (S) and their products to overall variation in LRS. Breeding life span was the number of breeding seasons in which an individual attempted to breed. Fecundity was the average number of fledglings produced by an individual per season over its breeding life span, and offspring local survival was the total number of local recruits produced by an individual divided by the total number of fledglings. The product of L, F and S was therefore lifetime reproductive success.
Correlates of variation in components of fitness
A series of statistical models was used to examine how individual fitness and LRS and its components were related to cohort effects and to the provisioning effort of parents, their sex, body size and their ‘dispersal status’ (philopatric or immigrant). There were many pairs of males and females in the data set which had the same LRS and/or individual fitness because all their successful nesting attempts (in most cases only a single attempt) were with each other. In analyses where we judged that there was a problem of pseudoreplication the data for males and females were split and analysed separately. Generalized linear models (GLMs) were used to examine relationships. These were performed using proc genmod in SAS (SAS Institute 1999; Der & Everitt 2002). The significance of terms and relevant two-way interactions was assessed from analysis of deviance when terms were fitted last in models. Error distributions and link functions were chosen to be appropriate for each dependent variable, and residuals were checked for normality by visual inspection of residual and normal probability plots (Der & Everitt 2002).