Negative density-distribution relationship in butterflies
© Päivinen et al; licensee BioMed Central Ltd. 2005
Received: 10 January 2005
Accepted: 01 March 2005
Published: 01 March 2005
Because "laws of nature" do not exist in ecology, much of the foundations of community ecology rely on broad statistical generalisations. One of the strongest generalisations is the positive relationship between density and distribution within a given taxonomic assemblage; that is, locally abundant species are more widespread than locally sparse species. Several mechanisms have been proposed to create this positive relationship, and the testing of these mechanisms is attracting increasing attention.
We report a strong, but counterintuitive, negative relationship between density and distribution in the butterfly fauna of Finland. With an exceptionally comprehensive data set (data includes all 95 resident species in Finland and over 1.5 million individuals), we have been able to submit several of the mechanisms to powerful direct empirical testing. Without exception, we failed to find evidence for the proposed mechanisms creating a positive density-distribution relationship. On the contrary, we found that many of the mechanisms are equally able to generate a negative relationship.
We suggest that one important determinant of density-distribution relationships is the geographical location of the study: on the edge of a distribution range, suitable habitat patches are likely to be more isolated than in the core of the range. In such a situation, only the largest and best quality patches are likely to be occupied, and these by definition can support a relatively dense population leading to a negative density-distribution relationship. Finally, we conclude that generalizations about the positive density-distribution relationship should be made more cautiously.
Species that are locally abundant tend to be more widespread than species that are locally rare [1, 2]. This positive relationship between density and distribution of species has been observed in a variety of species assemblages over a spectrum of spatial scales, and it has been suggested that it may be almost an universal pattern in ecology [3–6]. However, a few studies document a negative relationship between density and distribution [7–14] (but see ). Only recently Gaston et al.  encouraged ecologists to pay more attention to the possibility of a negative relationship.
Nine mechanisms have been proposed to explain the positive relationship between density and distribution [2, 3, 14, 16–25]. Of these, two are artefactual (sampling artefact, phylogenetic non-independence) and seven are ecological (pattern of aggregation, range position, niche breadth, resource availability, density dependent habitat selection, dispersal ability and vital rates). Negative relationship between density and distribution can be generated by similar mechanisms that give rise to a positive relationship, but for substantially different circumstances and parameter values [5, 6]. Below we discuss briefly all of the mechanisms that can possibly explain the positive relationship between density and distribution, and evaluate whether they could also generate a negative relationship.
Since low density species are less likely to be detected in surveys, a positive density-distribution relationship may result from systematic under-recording of the distribution of species that occur at low density [2, 3, 20]. It follows logically that sampling artefact is not expected to generate a negative density-distribution relationship . However, there is a possibility that rare species with limited, but known, distribution face proportionally higher sampling effort resulting in inflated estimates of their density. When this is the case, a false negative relationship between density and distribution may be generated.
Both positive and negative density-distribution relationship may result from related species being considered as independent data points [19, 26, 27]. However, phylogenetic non-independence may be the causative factor of a density-distribution relationship only if species density and distribution are determined by species specific life history characteristics affected by the common ancestry, and if there are differences between taxa in their density and distribution. Phylogenetic non-independence has been rejected as an explanation for the positive density-distribution relationship in all previous studies that have controlled its effects [5, 14, 25, 28, 29].
Patterns of aggregation
A positive density-distribution relationship may be generated as a result of an underlying theoretical spatial distribution of individuals. For a given level of aggregation, a species with more individuals in a given area is expected to occur in more locations than a species with fewer individuals in the same area [20, 24]. However, whether this purely statistical mechanism can actually cause a positive density-distribution relationship rather than serves as a restatement of the relationship in another form, is questionable . This mechanism is unable to generate a negative density – distribution relationship .
Empirical observations suggest that habitat occupancy and the density of individuals decline when moving along a gradient from the centre of the species geographical distribution range toward its edge [2, 30–32]. Therefore, a positive density-distribution relationship in any particular region may result when species are at different positions relative to the centre of their geographical range . Gaston et al.  argued that this mechanism cannot generate negative density-distribution relationship. More recently, Hanski  has pointed out that if patches are more isolated toward range edges, only the largest or best quality patches, i.e. those patches that are able to support the most dense populations, will be occupied. We note that this may lead into a negative density-distribution relationship.
Brown  hypothesized that a positive density-distribution relationship arises because species which have an ability to use a broader range of resources are assumed to be widespread and more abundant. However, while some evidence exists that species with greater niche breadth are more widespread [3, 5, 34–40], virtually all published studies fail to document a positive interspecific relationship between niche breadth and abundance (see the reviews in [5, 25]). On the contrary, many species with wide niche breadth are widely distributed but locally rare [5, 25]. However, even if the relationship is commonly and almost predominantly negative, it is not often significantly different from zero. Nevertheless, it seems that the relationship between niche breadth and abundance may in fact generate a negative rather than a positive density-distribution relationship.
On the assumption that density and distribution of resources determine the density and distribution of the species utilizing them, a positive or a negative density-distribution relationship in the resource will generate the same relationship in the consumer [3, 22]. Most of the density-distribution relationships of the resource are reported to be positive [2, 41].
Density dependent habitat selection
If a species tends to inhabit more habitats when density is high and fewer when density is low, then locally abundant species will tend to occupy more habitats and have wider distributions . At present, there is little evidence for positive density-dependent habitat selection [5, 25]. Instead, some evidence exists for negative density-dependent habitat selection [42–44]. A negative density-distribution relationship arises when a species has a wider distribution, i.e. inhabits more habitats, when the density is low.
Metapopulation theory may explain both positive and negative density-distribution relationships . A positive relationship may arise where a species that has high density is less likely to go extinct in a given patch than a species that has lower density, or where dispersal increases with density, thereby promoting colonization of empty patches [3, 18]. Conversely, a negative relationship may emerge when the species differ in dispersal ability, since dispersal can reduce density but increase distribution [21, 33].
If a set of species differs only in respect to its mortality rate, then species with higher mortality will have a lower density. Moreover, the species will inhabit fewer patches than a species with low mortality, leading to a positive density-distribution . Under rather restricted conditions, the vital rates mechanism could also generate a negative density-distribution relationship ; however, to test this mechanism, population level data on density-dependent birth and death rates are necessary .
Here, we will examine the relationship between density and distribution of Finnish butterflies (Hesperioidea and Papilionoidea), and test the possible mechanisms affecting this relationship. The density-distribution patterns of butterflies have been examined in many previous studies, and if a relationship was found, it was generally positive [3, 14, 25, 38, 45–47]. However, most of the studies were conducted in the British Isles, thus representing a sort of pseudoreplication in terms of range of environments and selection of butterfly species studied. Using density and distribution data from two extensive butterfly censuses, we will assess which of the four mechanisms – phylogenetic non-independence, range position, niche breadth and dispersal ability – are best at explaining the density-distribution relationship of Finnish butterflies. We will also discuss the effects of sampling artefact on the density-distribution relationship.
Distribution of butterflies
Simple linear regressions for the distribution of butterflies.
Multiple linear regression for the distribution of butterflies.
Density of butterflies
Simple linear regressions for the density of butterflies.
Multiple linear regression for the density of butterflies.
Linear regression results between all variables after controlling for the phylogenetic non-independence. N is the number of independent contrasts.
Density and distribution of butterflies
A positive relationship between the density and distribution of species is expected to be an almost universal pattern in ecology [3–6]. In contrast to this, we found a strong negative relationship between density and distribution in Finnish butterflies. Here we will discuss three mechanisms-range position, niche breadth and dispersal ability – that could be responsible for generating this negative relationship.
We conclude that many of the ecological mechanisms proposed to create a positive density-distribution relationship are also able to generate a negative relationship. Indeed, it is intriguing that many studies, which have found a positive density – distribution relationship have failed to find an ecological mechanism that would explain the observed pattern. This may not be surprising if the ecological mechanisms are more likely to generate a negative rather than positive density – distribution relationship. In support of this view we found a strong negative density-distribution relationship but what is more important also empirical support for ecological mechanisms that are able to explain the observed pattern.
Our study area (Finland) is a long, northern country extending more than 1100 km from south to north. Many of the studied butterfly species meet the edge of their distributional range in Finland. On the edge of a distribution range suitable habitat patches are likely to be more isolated than in the core of the range. In such a case, only the largest and best quality patches are likely to be occupied, but because these are the best quality patches, they may support a relatively dense population , leading into a negative density – distribution relationship. We suggest that one important determinant of the density-distribution relationships is the geographical position of the study area and, therefore, future studies should place greater emphasis on the comparison of the relationship in different geographical areas.
Our data is predominantly based on published literature [49, 50] and the results of The National Butterfly Scheme in Finland (NAFI). We included all 95 butterfly species that are classified as resident or fluctuating in Finland  and excluded 21 species classified as migratory, irruptive or extinct .
Distribution of butterflies
The distribution of butterfly species is based on the "Atlas of Finnish Macrolepidoptera" . This atlas contains extensive and detailed distribution data of butterflies in Finland, covering all reliable records and observations of butterflies from 1747 to 1997 . The data are compiled from many different sources including c. 1500 literature references and information extracted from several large museum and private collections . The distribution data in the atlas are divided into old observations (before 1988) and new observations (1988 – 1997). We chose to describe the distribution of butterflies by the new observations, which represent the current distribution more accurately and also correspond more favourably with our density data. Moreover, there was a very strong positive correlation between distribution of butterflies based on old and new observations (Pearson correlation: r = 0.966, n = 95, P < 0.001). We describe the distribution for a given species as the number of 10 km × 10 km grid squares on the Finnish national coordinate system from which the species was recorded during the period 1988 – 1997 .
Density of butterflies
The National Butterfly Scheme in Finland (NAFI) is a formal study that was established in 1991 for the purpose of monitoring the population trends of the butterflies across the country [51, 52]. Monitoring studies may be liable to sampling biases , therefore explicit instructions were drafted in order to avoid any bias in sampling or reporting the abundance of butterflies . NAFI provides quantitative abundance data including the 10 km × 10 km grid square of the Finnish national coordinate system in which the observation was made, the year, the number of individuals of each species observed and the number of observation days . During the first ten-year period (1991–2000) of NAFI, 432 lepidopterologists participated in the study, providing data on 1 523 989 individuals, representing a total of 106 butterfly species.
To obtain density for each butterfly species per 10 km × 10 km grid square, we divided the total number of individuals of each butterfly species by the number of 10 km × 10 km squares occupied by the species. Some rare butterfly species with known occurrence sites may face proportionally higher sampling effort than common species . To remove the effect of sampling effort on density, we divided the density by the number of observation days. Note that observation days are the days when the observer was observing at a given square, and thus include also days when a given species was not observed. The number of observation days for each species averaged 20 815, varying between 53 and 50 595 days.
It is possible that size confounds the density and distribution data if larger species are more visible and thus reported more often than smaller species. We analysed the possibility that the size of the butterfly species is a confounding factor. There is practically no dimorphism between the sizes of male and female butterflies. Therefore, as a size measure we used only the female wing span reported in Marttila et al. , in which the mean of a sample of 20 females was reported with an exception of some rare species with fewer individuals measured. We found no evidence of any size bias: there was no relationship between the female wing span and the density or distribution of the species (linear regression F 1,93 = 0.04; P = 0.835, r2 = 0.00 and F 1,93 = 0.99; P = 0.987, r2 = 0.00, respectively).
To determine the range position, we measured the distance (km) between the northernmost distribution record and the southernmost point (Hankoniemi) of Finland from the maps in Huldén et al. (2000). Note that the longest possible range was 1155 km. In analysis including range position, we only included species, the distribution range of which begins from southern Finland . Thus, we excluded the species which occur only in Northern Finland (n = 14, ), and two species (Lycaena helle and Clossiana thore) which do not range to southern Finland.
We describe the niche breadth for each butterfly species using two different measures: 1) larval host plant specificity, and 2) the number of habitat types occupied by the adults. We excluded from this analysis the species which occur only in Northern Finland (n = 14, ). This was done because their larval host plants are unknown or are not confirmed and because the habitat types of Northern Finland are unique compared to other Finnish habitat types.
The data on larval host plant specificity in Finland are based on Huldén et al.  and Wahlberg . We classified the larval host plant specificity into three classes: (1) monophages, i.e. species that feed on a single plant species; (2) oligophages, i.e. species that are restricted to one genus of food plants; and (3) polyphages, i.e., species that feed on one or more than one family of food plants.
The main habitats that Finnish butterflies occupy have been categorised into four types : (1) uncultivable lands (e.g. edge zones beside industrial area, harbour and storage areas, loading places, uncropped fields, and other unbuilt areas which have been exposed to human impact), (2) meadows (many kinds of non-cultivated open grasslands), (3) forest edges (e.g. road sides), and (4) bogs. Adult niche breadth is the number of habitat types in which the adults typically are found. As there were only two species (Pieris napi and Gonepteryx rhamni) that occupied all four main habitat types, habitat types three and four were combined. Value one represents specialist species that are limited to one habitat type, value two represents intermediate species that occur in two habitat types, and value three represents generalist species that occur in three or four habitat types.
Metapopulation theory predicts that species with greater dispersal ability are likely to occupy more habitat patches than species with lower dispersal ability . To describe the relative dispersal ability of butterfly species, we adopted the method described in Cowley et al. . We sent a questionnaire to experienced lepidopterists in Finland and asked them to give a "dispersal ability index" (0–10) for each butterfly species. In the questionnaire, a zero value indicates that a given butterfly species is extremely sedentary and a value of ten means that it is extremely mobile. To obtain a relative dispersal ability for each butterfly species, we calculated the average dispersal ability from returned questionnaires (n = 13).
To ensure our measure of dispersal ability is reliable, we compared our measure with the dispersal ability estimated previously by Bink  (nine dispersal ability classes), Pollard and Yates  (three dispersal ability classes based on mark-release-recapture studies), Cowley et al.  (continuous variable based on questionnaires) and Cook, Dennis & Hardy  (continuous variable based on vagrancy in grids). The correlations between our measure and those of Bink , Pollard and Yates , Cowley et al.  and Cook et al.  were all strongly positive and significant (Pearson correlation; r = 0.672, n = 73, P < 0.001, ANOVA; F3,27 = 8.74, r = 0.567, P < 0.001, Pearson correlation; r = 0.703, n = 31, P < 0.001 and Pearson correlation r = 0.602, n = 11, P = 0.050, respectively), indicating that our dispersal ability is in line with other independent estimates and thus reliable (see also ).
We thank Andrew Warren for discussing the systematics of Hesperiidae with us. We also thank all of the lepidopterologists who lent us their expertise by replying to our dispersal ability questionnaire. We are grateful to Jari Niemelä, Marko Nieminen, Stuart Pimm, Tomas Roslin and Teija Virola for comments on the manuscript. We thank Tapani Lahti for help in compiling the data. The study was supported by Ella and Georg Ehrnrooth Foundation and the Centre of Excellence Programme in Evolutionary Ecology to J.P., and Academy of Finland to V.K and J.S.K.
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