Henk van der Jeugd, Edward Grey Institute of Field Ornithology, Department of Zoology, South Parks Road, Oxford OX1 3PS, UK. Tel.: 0044-1865-271277; e-mail: email@example.com
We investigated the effect of spatial autocorrelation on heritability (h2) estimates of laying date and clutch size in a population of great tits Parus major. We found that h2 of laying date, but not clutch size, declined significantly with increasing distance between the nestbox of mothers and daughters. This decline was caused by a decreasing effect of spatial autocorrelation in laying date, rather than by the existence of genotype–environment interactions (GEI). After correcting for the effect of spatial autocorrelation, h2 of laying date was low (0.16 ± 0.07), but significant, and surprisingly consistent with increasing distance between parental and offspring environments. The h2 of clutch size was not much affected by spatial autocorrelation.
Most previously published estimates of the heritability of laying date include various degrees of common environment effects, which can bias estimates both upwards and downwards. We suggest that using techniques that take spatial autocorrelation into account might be a fruitful approach to estimate h2 of traits that show a high degree of plasticity.
Measurements of heritabilities (h2) and selection can be used to predict microevolutionary changes of quantitative traits in natural populations. However, observed phenotypic changes rarely correspond to predicted responses to selection (for example Larsson et al., 1998; Meriläet al., 2001a; but see Grant & Grant, 1995; see van Tienderen & de Jong, 1994 and Meriläet al., 2001b for reviews). Timing of reproduction in birds has frequently been used as an example to demonstrate that heritable traits that are under strong (directional) selection do not necessarily evolve in the predicted direction, or indeed often do not evolve at all. At least six different hypotheses have been proposed to explain the discrepancy between predicted and observed changes in breeding date (van Noordwijk et al., 1995). One explanation for the lack of evolution of breeding date towards the ecological optimum is the model by Price et al. (1988), that shows that when a nonheritable trait, such as female nutritional status, influences both breeding date and fecundity through different pathways, breeding date is not expected to evolve, despite the presence of additive genetic variance for the trait. This model assumes that there is no causal link between breeding date and fitness, an assumption that has recently been challenged by several studies showing experimentally that such a link exists (Brinkhof et al., 1993; Verhulst et al., 1995). Another explanation is offered by the `constraint hypothesis' (Lack, 1966; Perrins, 1970; Nager et al., 2000), which states that only a limited number of females reaches a certain threshold nutritional state that is needed for egg production sufficiently early in the season, whereas most females are constrained and are forced to delay their breeding until after the best time for offspring rearing. Although superficially similar to the model by Price et al. (1988), the constraint hypothesis does not refute a causal link between breeding date and fitness.
Most of the evidence for the existence of a genetic component of timing of reproduction stems from parent–offspring regressions in natural populations that did not take confounding nongenetic factors into account (Findlay & Cooke, 1982; Wiggins, 1991; Merilä & Sheldon, 2000; but see van Noordwijk et al., 1981). Many other studies failed to demonstrate h2 of breeding date altogether (Jones, 1973; van Noordwijk et al., 1981; Newton & Marquiss, 1984; Hochachka, 1990; Perdeck & Cavé, 1992; Svensson, 1997; Phillips & Furness, 1998), although this is likely to be the result of small sample sizes in the majority of these studies. Heritability estimates obtained from parent–offspring regressions in natural populations are generally inflated when mothers and daughters share the same environment (Falconer, 1989). The magnitude of the shared environment effect on h2 estimates is likely to differ between traits and species. Plastic traits with a large component of environmental variation, as for example laying date in birds, are likely to show considerable spatial autocorrelation in heterogeneous habitats. When birds are philopatric, i.e. tend to breed close to their natal site, the effect of this spatial autocorrelation on estimates of h2 might be quite large. One way to get around the problem of shared environments is to perform cross-fostering experiments. However, when spatial autocorrelation is strong and cross fostering is carried out over relatively small distances (as will usually be the case for logistic reasons), the problem persists. Quite surprisingly, the effect of spatial autocorrelation on estimates of h2 of laying date has been ignored in the avian literature. In this paper we address this issue by showing that: (1) h2 estimates based on mother–daughter regressions in field studies are environment dependent estimates; in the case of laying date they gradually decline to zero with increasing distance between mothers' and daughters' breeding environment, (2) that this is caused by laying date in birds showing strong spatial autocorrelation and (3) that spatial autocorrelation, in combination with nonrandom sampling, potentially can bias h2 estimates both upwards and downwards.
Materials and methods
The analyses are based on data from the great tit population study in Wytham Wood, Oxford, UK (Perrins, 1965, 1979), and are restricted to the years 1959–2000. Before analyses, second clutches and repeat clutches laid after failure of the first clutch were removed from the data set. Where no indication of previous nesting existed, we assumed that clutches that were started more than 30 days after the day by which the first 5% of clutches were laid in that year were second clutches, and such clutches were therefore also removed from the data set. This method deviates slightly from the one used in van Noordwijk et al. (1995) for the same population, in which all clutches that were started more than 30 days after the first clutch in that year were removed. However, it was necessary to make this adjustment because extremely early clutches were more frequent in recent years, leading to the exclusion of late, but genuine, clutches in those years.
Because of significant differences in mean clutch size and laying date among years and age classes, all values were standardized for year and age of the female using the residuals from general linear models with year and female age as explanatory factors. To investigate the consistency of reproductive traits in individual birds we calculated repeatabilities (Lessells & Boag, 1987) for clutch size and laying date for individual males and females that bred at least twice (range 2–7 and 2–10, respectively). These repeatability estimates set an upper limit to the h2 of reproductive traits in males and females (Falconer, 1989). As a first crude measure of the contribution of the common environment to these estimates we also calculated repeatabilities for individual nestboxes that were occupied at least twice (range 2–19).
To investigate the effect of the environment in which the reproductive traits were expressed in relation to the contribution of parents' genes, the data set was partitioned into three groups with approximately equal sample sizes according to the mean distance between parents' and offspring's nestbox: (1) Offspring breeding within 500 m from their parents (mean 300 m), (2) offspring breeding 500–1000 m away from their parents (mean 731 m) and (3) offspring breeding more that 1000 m away from their parents (mean 1586 m). Females that returned to the study area to breed `dispersed' farther than males, and on average, bred 911 m from their mothers (median 771 m), whereas returning males on average bred 674 m from their fathers (median 532 m) (Fig. 1). This is in close agreement with dispersal distances reported earlier for this population (Greenwood et al., 1979).
There were small, but significant differences in clutch size of mothers and daughters among the three groups (mothers clutch size: 8.8, 9.0, 8.8, respectively, F2,1335=2.83, P=0.06; daughters clutch size: 8.8, 8.8, 8.5 respectively, F2,1334=6.52, P < 0.01). Laying date did not differ significantly among the three groups (P > 0.1).
Heritabilities (h2) were obtained from regressions of mean values of all daughters on mean values of their mother, and mean values of all sons on mean values of their father, respectively. This was first performed for the complete data set, then for each of the three groups separately. Heritability was calculated as twice the slope of these regressions (Falconer, 1989). The interaction between distance class and mean parental values in ANCOVAs including distance class as a factor can be used to investigate whether h2 estimates for the three distance classes differ significantly from each other (Falconer, 1989). However, even when sample sizes are very large, statistical power is usually too weak to detect significant interactions among moderate slopes with the same direction. As we had predicted h2 to decrease with increasing distance, we therefore applied ordered heterogeneity tests to evaluate the effect of distance on h2 by the rsPc statistic, where rs is the Spearman's Rank correlation coefficient between distance group and h2, and Pc equals 1 minus the P-value of the interaction among the three slopes in Rice & Gaines (1994).
To examine spatial autocorrelation in clutch size and laying date we measured the correlation between mean trait values for pairs of nestboxes k metres apart, where k increases from the nearest possible to the farthest possible distance between nestboxes of parents and offspring. This was performed by calculating the distance between all nestboxes in Wytham, sorting the resulting data set according to increasing distance, and then calculating the moving correlation coefficient between 500 pairs of nestboxes, moving through the data set from smallest to largest distance. Approximate 95% confidence limits for the values of the autocorrelation function are –2/√n and 2/√n, where n is the number of samples in the correlation (Dunstan, 1993). As we used 500 pairs of nestboxes for each correlation these confidence limits were –0.089 and 0.089.
We investigated the effect of spatial autocorrelation on the h2 estimates obtained for the three distance groups by randomly choosing 500 pairs of nestboxes that were situated either within 500 m from each other, between 500 and 1000 m, and over 1000 m apart, as in the analyses outlined above. Mean trait values for these nestboxes were then treated as values of parents and offspring and h2 was estimated using regression as described above. Values of first-order relatives were excluded from these analyses. For each group, this procedure was repeated 5000 times, and mean h2 obtained from it was taken as the best estimate of h2 that would have been found solely due to spatial autocorrelation of the trait. Standard errors for these estimates were also calculated as the mean standard error of the 5000 regressions. Significance of the h2 estimates obtained from the randomization procedure was based on the proportion of regressions that was significant.
To obtain h2 estimates controlling for the effect of spatial autocorrelation, we calculated the difference between the h2 estimates obtained from mother–daughter regressions and father–son regressions, respectively, and the h2 estimates obtained using randomly chosen nestboxes as described above. Significance of these differences was evaluated using a t-test. The standard errors of the differences equals √(Va/Nb + Vb/Na), where Va and Vb are the variances associated with the two h2 estimates a and b, and Nb and Na the sample sizes.
Repeatabilities of clutch size and laying date were significantly greater than zero for individual females, males and nestboxes. Repeatability of both traits was about 0.1 for nestboxes, indicating that there are effects of shared environment that potentially can inflate h2 estimates (Table 1).
Table 1. Repeatability estimates for clutch size, laying date and hatch date for great tit males and females, and individual nestboxes in Wytham Woods. All values were standardized for year and age.
Using the complete data set, h2 estimates for clutch size and laying date were moderately high, and highly significantly different from zero for both mother–daughter and father–son regressions (Table 2). However, when the data set was partitioned into three groups, we found that h2 of laying date declined significantly with increasing distance between mother's and daughter's nestbox. For mothers and daughters breeding more than 1000 m away from each other, h2 of laying date was not significantly greater than zero. A similar trend was observed for fathers and sons, although h2 estimates were generally lower and only significantly greater than zero for birds breeding within 500 m from each other. For clutch size, no significant decline in h2 was found, and h2 estimates were significantly greater than zero for all three distance groups when mother–daughter regressions were used (Table 3).
Table 2. Heritability estimates for clutch size, laying date and hatch date for great tits breeding in Wytham Woods. Estimates are obtained from regressions of offspring lifetime mean values on parents' lifetime mean values. All values were standardized for year and age before calculating means.
Table 3. Heritability estimates for clutch size, laying date and hatch date for great tits breeding in Wytham Woods. Estimates are obtained from regressions of offspring lifetime mean values on parents' lifetime mean values. All values were standardized for year and age before calculating means. Data are split into three categories according to the mean distance between the parent's and offspring's nestbox.
There existed significant spatial autocorrelation for laying date, as indicated by the correlogram in Fig. 2: correlations between laying dates of nestboxes that were close together were significantly positive. This effect can be expected to inflate h2 estimates for laying date. Instead of slowly fading out, the autocorrelation function behaved rather erratically at larger distances, increasing first, and then becoming predominantly negative (Fig. 2). For clutch size, very little spatial autocorrelation could be detected, as virtually all points fell within the 95% confidence limits. Nevertheless, although not statistically significant, the consistent positive correlations between clutch sizes in nestboxes less than 1000 m apart should introduce some upward bias in h2 estimates for clutch size (Fig. 2).
Having established that spatial autocorrelation existed, especially for laying date, we then proceeded to investigate the effect of this spatial autocorrelation on the h2 estimates obtained for the three distance groups. The h2 estimates of clutch size and laying date obtained from randomly selected nest boxes within the three distance groups were significantly greater than zero only for the group of birds breeding within 500 m from each other, as was expected from the spatial autocorrelation function (Fig. 2). The h2 estimates of laying date derived from the randomizations declined significantly across the three distance groups (Table 3). The effect of spatial autocorrelation on h2 was particularly large for laying date, with more than 60% of the heritability of laying date being caused by nearby nestboxes tending to have similar laying dates, regardless of the females that were breeding in them. The difference between the h2 estimates obtained from parent-offspring regression and those based on randomly chosen pairs of nestboxes yields a measure of h2 with the effect of this aspect of shared environment removed. For both clutch size and laying date these differences were surprisingly consistent across distance groups, significantly greater than zero for clutch size, and almost significantly greater than zero for laying date (Table 3). Combining the three h2 estimates obtained for each distance group into one estimate for clutch size and laying date, respectively, yielded h2 of 0.34 for clutch size (SE=0.07, P < 0.0001) and 0.16 for laying date (SE=0.07, P < 0.05). In the case of laying date, h2 estimates were substantially lower than the uncorrected h2 estimates (Table 3). The combined h2 estimates for clutch size and laying date are also lower than the estimates obtained for the whole data set without controlling for the effect of autocorrelation (Table 2), although not significantly so (both P > 0.2). The difference between the h2 estimates based on father-son regressions and the ones based on randomly chosen pairs of nestboxes were not significantly greater than zero in any case, and, hence, are not shown in Table 3.
We found that h2 of laying date declined significantly with increasing distance between the nestbox of mothers and daughters, that is, with a presumed decreasing similarity between parental and offspring environments, showing that heritability is an environment-dependent estimate. This result can be explained in two ways. First, when genotype–environment interaction (GEI) exists for a given trait, and the same genotype is being expressed in different environments in parents and offspring, h2 of that trait is decreased. In fact, in the presence of GEI, h2 of a quantitative trait gradually declines to zero with decreasing similarity between the parental and offspring environment (Lewontin, 1974; Pigliucci, 2001). Although this is exactly what we found, the argument works only in one direction, and a decline in h2 cannot be taken as evidence that GEI exist. In this study, we have limited scope to test for the existence of GEI for laying date, because doing so requires analysing trait values of closely related individuals across different environments, which can usually only be performed through partial cross-fostering of large numbers of individuals (Merilä & Fry, 1998; Merilä & Sheldon, 2001). Furthermore, it is usually not possible to define distinct, homogeneous environments in a natural field study. Consequently, there is considerable variation within environments, and such microenvironmental variability tends to overestimate the occurrence of GEI (Kearsey & Pooni, 1996).
The second possibility is that a decrease in h2 is brought about by a decreasing effect of shared environments between parents and offspring because of an increasing difference between the environments in which parental and offspring genes are expressed, but without GEI (i.e. there exists plasticity, but all genotypes respond in the same way to different environments). We showed that there exists considerable spatial autocorrelation for laying date in our study site, such that there is a significant and positive correlation between laying dates for nestboxes that are situated close together. The average effect of this spatial autocorrelation decreased across distance groups (Fig. 2). As expected, the h2 estimate based on randomly selected nestboxes decreased accordingly, and in a similar way as the h2 estimate based on mother–daughter regressions across the three distance groups. When the observed h2 estimates are corrected for spatial autocorrelation, a low, but surprisingly consistent h2 for laying date remains. We take the consistency of the corrected h2 estimates as evidence for the absence of GEI. Combining the three estimates into one, we found a significant h2 estimate for laying date of 0.16. This is considerably lower than some estimates published for other populations or species, although this cannot be wholly contributed to the effect of spatial autocorrelation alone as most previously published estimates are also higher than our uncorrected heritabilities [snow goose: 0.44, Findlay & Cooke, 1982; tree swallow: 1.44, Wiggins, 1991; blue tit: 0.44, Svensson, 1997 (not significant); great tit: 0.45, van Noordwijk et al. (1981) (only in 1 of 4 populations); Collared flycatcher: 0.41, Merilä & Sheldon, 2000]. All except one of these studies (van Noordwijk et al., 1981) have not attempted to control for the effect of shared environments. Even more studies failed to find any h2 of laying date altogether (Sparrowhawk: Newton & Marquiss, 1984; Coot: Perdeck & Cavé, 1992; Arctic Skua: Philips & Furness, 1998; Great tit: Jones, 1973; van Noordwijk et al., 1981; Song sparrow: Hochachka, 1990), but most of these studies lacked statistical power to detect or reject the existence of significant h2 because of low sample size. More recently, McCleery et al. (unpublished results) arrived at an estimate of 0.22 for the same population using an `animal model approach', which estimates components of additive genetic and environmental variance using all available information in pedigrees. This estimate, which included a correction for habitat type, is not significantly higher than the one obtained in the present study (t3461=0.63, NS), but the reduction by almost 30% when taking spatial autocorrelation into account shows that the extent to which the inclusion of, for example, area-specific and nestbox-specific effects in animal models is going to eliminate parent–offspring environmental covariation is limited. This is because it is often impossible to identify all major environmental factors that influence the trait that is under study, and because models quickly become over-parameterized when too many factors are included. For hole-nesting birds, inclusion of the nestbox identity is not a powerful tool either because individual females regularly switch to adjacent nestboxes between years. Adjacent nestboxes have a similar `environmental value', but including nestbox identity as a factor in the model cannot capture this shared environment effect. For similar reasons, cross fostering over small or moderate distances is not going to eliminate the problem of shared environments when considerable spatial autocorrelation exists for the trait under study.
The genetic determination of timing of reproduction, and especially the apparent lack of its evolution (Price et al., 1988; Przybylo et al., 2000), has received considerable attention in the literature. It has frequently been used as an example to demonstrate that heritable traits that are under strong (directional) selection do not necessarily evolve in the predicted direction, or indeed often do not evolve at all. We have shown that the heritability of laying date obtained from parent–offspring regression in natural field studies is environment dependent, and without taking such spatial structure into account, heritability estimates might be misleading in the sense that the expected response to selection might be both over- or underestimated. The degree to which timing of reproduction is genetically controlled is important, as it affects the rate with which populations can respond to changes in spring temperatures because of global warming (Crick et al., 1997; McCleery & Perrins, 1998).
The low heritability of laying date might not be surprising, as it a very complex quantitative trait involving many decision rules individuals use when responding to abiotic (e.g. photoperiod, temperature), and biotic (e.g. oak bud burst or emergence of the first winter moth larvae) cues to achieve fine-tuning to the local environment (Nager & van Noordwijk, 1995; Svensson & Nilsson, 1995; Nager et al., 1997, 2000; Visser & Holleman, 2001). Each of these decision rules is likely to have some genetic basis. But even when individuals from different populations breed under identical circumstances, i.e. have to rely on the same cues, differences in laying date between populations can be maintained, as illustrated by a common garden experiment on blue tits (Blondel et al., 1990). It has also frequently been suggested that only a limited number of female birds reach a certain threshold nutritional state that is needed for egg production sufficiently early in the season to be able to breed at the optimal time, whereas most females are constrained and forced to delay breeding until after the best time for offspring rearing (the `constraint hypothesis', Lack, 1966; Perrins, 1970; Nager et al., 2000).
The presence of paternal effects on laying date is a theoretical possibility. For example, `high quality' fathers might attract early laying females, or enable their females to lay early by supplying them with a high quality territory or provisioning them with more food. Simultaneously, such fathers might produce `high quality' sons, which in turn will obtain early laying female partners. However, we did not find any firm evidence for the presence of paternal effects on laying date, as the difference between h2 estimates based on father–son regressions and the ones based on randomly chosen pairs of nestboxes were not significantly greater than zero.
Although we removed all known mothers and daughters from the data set that was used to analyse the effect of spatial autocorrelation, it is potentially possible that part of the autocorrelation is caused by more distantly related birds breeding close together. However, we think it very unlikely that the great tit population in Wytham Woods is genetically structured because, on average, 47% of females and 40% of males breeding in any year within Wytham are immigrants that are not born in the wood (McCleery et al. unpublished results). Genetic structuring within populations does occur in other species (for example Piertney et al., 1999), and therefore care has to be taken when analysing the effects of spatial autocorrelation on the heritability of traits in such species.
Our results indicate that clutch size appears to be under much stronger genetic control than laying date. Although some spatial autocorrelation was detected also for this trait, this alone does not explain the high h2 we found. The combined, corrected, h2 estimate for clutch size was 0.34, which is exactly similar to a previously published estimate for this population (McCleery et al. unpublished results). The spatial autocorrelation we observed in clutch size is likely to originate from the generally observed seasonal decline in clutch size (Klomp, 1970; Verhulst et al., 1995), so that nestboxes with similar laying dates tend to produce similar clutch sizes.
Nonrandom distribution of environmental effects among relatives is one of the main problems in the estimation of quantitative genetic parameters. Although our methods are crude, the aim of this paper is to draw attention to the problem of spatial autocorrelation, and to demonstrate its effect on h2 estimates of plastic traits in philopatric species. The problem has received little attention in the avian literature, although its effect has been investigated and simulated in theoretical papers (for example Rausher, 1992; Magnussen, 1993). In the present study, the spatial autocorrelation function for laying date quickly faded out with increasing distance, but then increased again, and eventually became negative at larger distances. This happens because nestboxes that are far apart are no longer a random sample from all the nestboxes in the study area, but instead increasingly tend to be situated in certain areas within the study area, leading to positive or even negative correlations. Thus, because of nonrandom sampling in relatively small study areas, heritabilities of spatially structured traits can actually be under- instead of overestimated (see Fig. 3c). Our results are somewhat analogous to the situation described by Horak & Tammaru (1996), who pointed out that between-cohort variation in growth conditions could bias h2 estimates of morphological traits downwards when data from several years of differing quality are pooled. Instead of 2 years, one bad and one good as in the example given by Horak & Tammaru (1996), we show that pooling data from two discrete areas, one early and one late, similarly underestimates h2 estimates (Fig. 3c).
One could argue that it is wrong to correct h2 for spatial autocorrelation effects in the way we did, but instead view each estimate as the `true' heritability for that particular spatial scale. However, in our view, what one wants to obtain is a measure that can be used to predict an evolutionary response. Using the estimates as they are, and arguing that the expected response is going to be different for different spatial scales might be misleading when, and this is especially true for the smallest scale, estimates include some common environment effect that creates a resemblance between parents and offspring that is of nongenetic origin. It is theoretically possible to incorporate measures of spatial autocorrelation into an animal model, thus controlling for its effect while estimating components of additive genetic and environmental variance. The great advantage of such a method is that confounding environmental effects on estimates of h2 can be taken into account without the need to identify all relevant environmental factors and successfully include them in the model.
We want to thank the many observers that helped collecting the field data over so many years. Arie van Noordwijk assisted with some statistical matters. Mariusz Cichoñ, Chris Perrins, Ben Sheldon, and an anonymous referee commented on an earlier version of the manuscript. Discussions with Ben Sheldon, Juha Merilä and Rick Miller on the concept of heritability were very helpful. HJ was supported by a grant from the Swedish Foundation for International Cooperation in Research and Higher Education (STINT) while in Oxford.