Mateusz Ciechanowski

Weronika Kubic
email: weronikarogalska@wp.pl

Aleksandra Rynkiewicz
email: olarynkiewicz@gmail.com

Adrian Zwolicki

: A Rynkiewicz

Reintroduction of beavers Castor fiber may improve habitat quality for vespertilionid bats foraging in small river valleys

Keywords: Castoridae, Chiroptera, Ecosystem engineer, Habitat use, Keystone species

Beavers strongly modify their environment by not only building dams and creating ponds, which slow the water flow, but also by selective cutting and removing of trees, which change the spatial structure of the forest. We aimed to test the hypothesis that beaver activity promotes new foraging sites for insectivorous bats. The beaver's influence can be especially significant on aerial hawkers that prefer moderate structural clutter, like the Pipistrellus species (by creating new canopy gaps), and on water-surface foragers, like Myotis daubentonii (by creating ponds with smooth water surface). The study was conducted on small streams in forest areas of northern Poland, which were colonized by the European beaver (Castor fiber). Bat activity was recorded with a Pettersson D-980 ultrasound detector on line transects. The number of bat passes was significantly higher in the stream sections modified by beavers (flooded and subjected to intensive tree cutting) than in the unmodified sections (for Pipistrellus nathusii, Pipistrellus pipistrellus, Pipistrellus pygmaeus, Nyctalus noctula, and all species lumped together). Contrary to our expectations, the activity of the Myotis species was significantly lower on the transect with the largest beaver ponds, possibly due to the blanket of duckweed (Lemnaceae), which is known to produce clutter echoes, thereby reducing prey detection by echolocating M. daubentonii.

Introduction

Species that strongly modify the structure of phytocoenoses, topography, geomorphology, and water conditions affect almost all elements of local ecosystems, and thus may be regarded as keystone species [START_REF] Paine | The Pisaster-Tegula interaction: prey patches, predator food preference, and intertidal community structure[END_REF]) and ecosystem engineers (Jones et al. 1994). Canadian beaver Castor canadensis and European beaver Castor fiber may serve as an example. Their ability to modify river valley ecosystems has no equivalent in the animal kingdom; thus serious conflicts associated with both economy and conservation have emerged in several parts of beavers' geographic range [START_REF] Baker | Beaver Castor canadensis[END_REF]. On the other hand, their activity favors regeneration of degraded habitats and increase of biological diversity at a local scale [START_REF] Rosell | Ecological impact of beavers Castor fiber and Castor canadensis and their ability to modify ecosystems[END_REF]. Foraging of woody plants by beavers creates canopy gaps, decreases canopy cover and (if shrubs are also eaten) may decrease density of undergrowth. They not only change the spatial structure of plant communities but also change species composition at the herb layer [START_REF] Zwolicki | European Beaver Castor fiber-a keystone species for the river valley ecosystems[END_REF][START_REF] Hood | A comparison of riparian plant community response to herbivory by beavers (Castor canadensis) and ungulates in Canada's boreal mixed-wood forest[END_REF]. Beavers also build dams, which create extensive water bodies ("beaver ponds") that protect entrances to their lodges or burrows [START_REF] Baker | Beaver Castor canadensis[END_REF]. Flooding caused by beavers changes water conditions by altering hydrochemistry, increasing water storage and sedimentation rates, and facilitating the development of ecotones at the riparian edges [START_REF] Debano | Enhancement of riparian ecosystems with channel structures[END_REF][START_REF] Gurnell | The hydrogeomorphology effects of beaver dambuilding activity[END_REF][START_REF] Butler | The geomorphic influences of beaver dams and failures of beaver dams[END_REF][START_REF] Rosell | Ecological impact of beavers Castor fiber and Castor canadensis and their ability to modify ecosystems[END_REF]. They could also increase the number of standing dead, often hollow, trees.

Modifications of habitat conditions by beavers affect also species diversity of animal assemblages and population sizes of particular species. Damming and consequent flooding of stream valleys by beavers increase species diversity or population density of mustelids [START_REF] Sidorovich | Winter distribution and abundance of mustelids and beavers in the river valleys of Bialowieża Primeval Forest[END_REF], wetland birds, especially waterfowl [START_REF] Nummi | The importance of beaver ponds to waterfowl broods: an experiment and natural tests[END_REF][START_REF] Grover | Bird species richness within beaver ponds in south-central New York[END_REF][START_REF] Nummi | Population and community level responses in Anas-species to patch disturbance caused by an ecosystem engineer, the beaver[END_REF]; amphibians [START_REF] Russell | Amphibian and reptile communities associated with beaver (Castor canadensis) ponds and unimpounded streams in the piedmont of South Carolina[END_REF][START_REF] Dalbeck | Beaver ponds as habitat of amphibian communities in a central European highland[END_REF][START_REF] Stevens | Beaver (Castor canadensis) as a surrogate species for conserving anuran amphibians on boreal streams in Alberta, Canada[END_REF][START_REF] Popescu | Interactions between climate, beaver activity, and pond occupancy by the cold-adapted mink frog in New York State, USA[END_REF], cyprinid fish [START_REF] Collen | The general ecology of beavers (Castor spp.) as related to their influence on stream ecosystems and riparian habitats, and the subsequent effects on fish-a review[END_REF], lenitic insects (e.g., dragonflies and chironomids), bivalves, leeches, oligochaetes and some crustaceans [START_REF] Mcdowell | Structure and function of a benthic invertebrate stream community as influenced by beaver (Castor canadensis)[END_REF][START_REF] Nummi | Simulated effects of the beaver on vegetation, invertebrates and ducks[END_REF][START_REF] Nummi | The importance of beaver ponds to waterfowl broods: an experiment and natural tests[END_REF][START_REF] Collen | The general ecology of beavers (Castor spp.) as related to their influence on stream ecosystems and riparian habitats, and the subsequent effects on fish-a review[END_REF]. However, the response of particular taxa to beaver activities can be diverse and related to species-specific preferences. For example, beaver damming decreases frequency and species diversity of salamanders, but increases these parameters in frogs [START_REF] Metts | Evaluation of herpetofaunal communities on upland streams and beaverimpounded streams in the upper piedmont of South Carolina[END_REF][START_REF] Stevens | Beaver (Castor canadensis) as a surrogate species for conserving anuran amphibians on boreal streams in Alberta, Canada[END_REF]. It may also contribute to the decline of lotic species-mayflies, net-spinning caddisflies, stoneflies, and salmonid fish [START_REF] Mcdowell | Structure and function of a benthic invertebrate stream community as influenced by beaver (Castor canadensis)[END_REF][START_REF] Nummi | Simulated effects of the beaver on vegetation, invertebrates and ducks[END_REF][START_REF] Collen | The general ecology of beavers (Castor spp.) as related to their influence on stream ecosystems and riparian habitats, and the subsequent effects on fish-a review[END_REF][START_REF] Rosell | Ecological impact of beavers Castor fiber and Castor canadensis and their ability to modify ecosystems[END_REF]). In general, most studies focus on the impact of flooding caused by beavers on aquatic or semi-aquatic animal species. Only few studies examine the effect of beaver activities on terrestrial animals, although tree cutting and brush grazing may benefit some phytophagous forest beetles [START_REF] Martinsen | Indirect interactions mediated by changing plant chemistry: beaver browsing benefits beetles[END_REF]) and riparian vegetation developed in beaver ponds attract even large ungulates [START_REF] Rosell | Ecological impact of beavers Castor fiber and Castor canadensis and their ability to modify ecosystems[END_REF][START_REF] Baker | Interaction of beaver and elk herbivory reduces standing crop of willow[END_REF][START_REF] Hood | The effects of high ungulate densities on foraging choices by beaver (Castor canadensis) in the mixedwood boreal forest[END_REF]. In general, the net effect of beaver colonization on biodiversity is considered positive, so reintroduction of beavers is often proposed as a relatively cheap method of wetland restoration in heavily disturbed ecosystems [START_REF] Baker | Beaver Castor canadensis[END_REF]. European beaver-formerly absent or endangered in many countries of its native range-is recently expanding by human reintroduction and natural dispersal, again becoming a common element of local faunas [START_REF] Halley | Population and distribution of European beavers (Castor fiber)[END_REF] and, presumably, increasing its impact on the ecology of riparian habitats.

Bats of the temperate zone are among animals that might be modified by beaver activity. They are almost exclusively insectivorous [START_REF] Vaughan | The diets of British bats (Chiroptera)[END_REF]) and concentrate their foraging activity in habitats of the highest prey abundance (e.g., in river valleys), where they benefit from emerging aquatic insects [START_REF] Fukui | Effect of emergent aquatic insects on bat foraging in a riparian forest[END_REF]. Riparian zones and water bodies usually hold the highest diversity of bats and the highest density of foraging individuals [START_REF] Rachwald | Habitat preference and activity of the noctule bat Nyctalus noctula in the Białowieża Primeval Forest[END_REF][START_REF] Rydell | Habitat use by bats along rivers in north east Scotland[END_REF][START_REF] Walsh | Foraging habitat preferences of vespertilionid bats in Britain[END_REF]Vaughan et al. 1997a;[START_REF] Grindal | Concentration of bat activity in riparian habitats over an elevational gradient[END_REF][START_REF] Russ | Habitat associations of bats in Northern Ireland: implications for conservation[END_REF][START_REF] Ellison | Examining patterns of bat activity in Bandelier national monument, New Mexico, by using walking point transects[END_REF]Menzel et al. 2005a). In the diet of several species, like Daubenton's bat (Myotis daubentonii), pipistrelles (Pipistrellus spp.) or noctules (Nyctalus spp.), insects whose larvae develop in water may dominate [START_REF] Vaughan | The diets of British bats (Chiroptera)[END_REF][START_REF] Rydell | The diet of the noctule bat Nyctalus noctula in Latvia[END_REF]. However, bats' adaptations to particular hunting tactics bring serious limitations regarding the use of various habitats, even those supporting extremely abundant prey. Aerial hawkers may capture prey only in some distance from obstacles, e.g., tree crowns [START_REF] Baagøe | The Scandinavian bat fauna: adaptive wing morphology, and free flight in the field[END_REF][START_REF] Jones | Flight performance, echolocation and foraging behaviour in noctule bats Nyctalus noctula[END_REF][START_REF] Kalko | Insect pursuit, prey capture and echolocation in pipistrelle bats (Microchiroptera)[END_REF]. Therefore, their foraging might not be effective in dense tree stands and their activity is negatively correlated with stand density [START_REF] Erickson | Association of bats with local structure and landscape features of forested stands in western Oregon and Washington[END_REF]. Some species (e.g., M. daubentonii), adapted to hawking insects just above the water or even gaffing them directly from its surface [START_REF] Jones | Flight performance, foraging tactics and echolocation in free-living Daubenton's Bats Myotis daubentonii (Chiroptera: Vespertilionidae)[END_REF][START_REF] Todd | Strategy-switching in the gaffing bat[END_REF], benefit from an acoustic mirror effect [START_REF] Siemers | Acoustic mirror effect increases prey detection distance in trawling bats[END_REF]. However, they cannot detect prey if water surface is turbulent, as frequently occurs in shallow and narrow streams [START_REF] Mackey | The influence of physical clutter and noise on the activity of bats over water[END_REF][START_REF] Rydell | Echolocation constraints of Daubenton's bat foraging over water[END_REF], or if it is covered by floating vegetation (i.e., pleustophytes) [START_REF] Boonman | Prey detection in trawling insectivorous bats: duckweed affects hunting behaviour in Daubenton's bat, Myotis daubentonii[END_REF][START_REF] Ciechanowski | Spatiotemporal variation in activity of bat species differing in hunting tactics: effects of weather, moonlight, food abundance, and structural clutter[END_REF]. Bats reveal clear microhabitat preferences, dependent on their foraging tactics. In forests, aerial hawkers hunt mostly in canopy gaps, on glades, in ecotones [START_REF] Kusch | Foraging habitat preferences of bats in relation to food supply and spatial vegetation structures in a western European low mountain range forest[END_REF], or in corridors formed by streams and trails, which are apparently used as flyways to avoid high clutter [START_REF] Lloyd | Bat activity on riparian zones and upper slopes in Australian timber production forests and the effectiveness of riparian buffers[END_REF]. Some species prefer calm sections of rivers and avoid those with fast current [START_REF] Warren | The distribution of Daubenton's bats (Myotis daubentonii) and pipistrelle bats (Pipistrellus pipistrellus) (Vespertilionidae) in relation to small-scale variation in riverine habitat[END_REF].

Damming of water courses by beavers reduces stream velocity and increases flooding outside the original channel [START_REF] Rosell | Ecological impact of beavers Castor fiber and Castor canadensis and their ability to modify ecosystems[END_REF] while selective removal of trees [START_REF] Zwolicki | European Beaver Castor fiber-a keystone species for the river valley ecosystems[END_REF] forms canopy gaps and reduces density of undergrowth (i.e., vertical obstacles). These modifications may increase attractiveness of a beaver-inhabited valley as a foraging site for several bat species. In general, distribution of hunting bats along rivers and streams relates to the spatial structure of riparian vegetation [START_REF] Warren | The distribution of Daubenton's bats (Myotis daubentonii) and pipistrelle bats (Pipistrellus pipistrellus) (Vespertilionidae) in relation to small-scale variation in riverine habitat[END_REF][START_REF] Downs | The use by bats of habitat features in mixed farmland in Scotland[END_REF], physical characteristics of the current [START_REF] Rydell | Echolocation constraints of Daubenton's bat foraging over water[END_REF][START_REF] Warren | The distribution of Daubenton's bats (Myotis daubentonii) and pipistrelle bats (Pipistrellus pipistrellus) (Vespertilionidae) in relation to small-scale variation in riverine habitat[END_REF], and water quality [START_REF] Vaughan | Effects of sewage effluent on the activity of bats (Chiroptera: Vespertilionidae) foraging along rivers[END_REF][START_REF] Biscardi | Foraging requirements of the endangered long-fingered bat: the influence of micro-habitat structure, water quality and prey type[END_REF][START_REF] Mc | Effects of wastewater treatment plant effluent on bat foraging ecology in an urban stream system[END_REF], which are all features known to be modified by beavers [START_REF] Rosell | Ecological impact of beavers Castor fiber and Castor canadensis and their ability to modify ecosystems[END_REF]. Documenting relationships between bats and beavers would support the hypothesis about the keystone function of beavers in such ecosystems that is justified based on data about the impact of beavers on the other groups of fauna and flora [START_REF] Rosell | Ecological impact of beavers Castor fiber and Castor canadensis and their ability to modify ecosystems[END_REF]. However, no such effect on bats has ever been documented, although some publications mention the use of beaver-modified habitats by chiropterans. Among Appalachian wetlands, the highest activity of Myotis lucifugus was recorded at a site containing a permanent, 2-ha beaver pond [START_REF] Francl | Bat activity in Central Appalachian Wetlands[END_REF]). The so-called "beaver meadows" (former ponds filled with sediments and overgrown with herbaceous vegetation) support moderate bat activity among the acoustically surveyed habitats of Massachusetts (Brooks and Fords 2005). Radio-tracking studies revealed that evening bats (Nycticeius humeralis) roost under exfoliating bark on dead snags in beaver ponds [START_REF] Menzel | Tree-roost characteristics of subadult and female evening bats (Nycticeius humeralis) in the upper coastal plain of South Carolina[END_REF].

The recognition of links between the spatial structure of habitat and distribution of foraging sites acts as a base for conservation and management of bat populations in anthropogenically altered landscapes [START_REF] Brinkmann | The role of bats in landscape planning[END_REF]. Assessment of beavers' impact on various elements of local biota supports the hypothesis about their function as keystone species and ecosystem engineer, thus providing arguments for proper management decisions (including that of reintroduction). The objective of this study was to compare the foraging and commuting activity of vespertilionid bats among sections of small, forested river valleys modified and unmodified by European beavers. We hypothesized that (1) both aerial hawking and water-surface foraging (trawling) species would be more active at sections flooded by beaver dams than at the sections with unmodified streams; (2) aerial hawkers would additionally reveal higher levels of activity at sections with extensive cutting of trees by foraging beavers than in uniform, unmodified stands.

Materials and methods

Study area

The study was conducted in the forested valleys of two small watercourses in Bory Tucholskie (vicinity of Osiek), Pomeranian Lakeland, northern Poland. The last beavers in the country of study became extinct by about 1844, and remained so, until a series of successful reintroductions and translocations between 1943-1949and 1975[START_REF] Mcdowell | Structure and function of a benthic invertebrate stream community as influenced by beaver (Castor canadensis)[END_REF][START_REF] Halley | Population and distribution of European beavers (Castor fiber)[END_REF]. Both streams are tributaries of the Wda river, itself belonging to the Vistula river catchment area. Beavers were reintroduced in that area in 1971 and since then have colonized spontaneously almost the whole drainage area of Wda. Both valleys are surrounded by heavily managed, uniform monocultures of Scotch pine (Pinus sylvestris) with poorly developed vertical structure.

Site 1 was located in a valley with a small brook near Stara Rzeka village (53°39′21.72″N, 18°17′6.82″E). The brook itself was about 1-m wide, very shallow (average depth, below 10 cm) and rapid, but with very small discharge. It flows through the wide meadow and dense, mature broadleaf forests. Pedunculate oak Quercus robur, hornbeam Carpinus betulus, aspen Populus tremula, and Norway spruce Picea abies dominate valley slopes, but black alder (Alnus glutinosa) and birch (Betula pendula) dominate closer to the stream. Activity of beavers, including construction of four dams more than 100-m long, led to an extensive flooding, which covered a few hectares of riparian forest and meadow with patches of reed beds. From May to late autumn, these beaver ponds were covered almost completely by duckweed (mostly Lemna minor). Beavers also cut many trees on the slopes and the bottom of the valley, which significantly thinned out the stand at a distance up to a few dozens of meters from the water edge.

Site 2 was located in a valley with a stream near Suchobrzeźnica village (53°42′31.63″N, 18°20′25.37″E). The stream was wider (2-3 m) and had much higher discharge, velocity, and depth up to 50 cm. The stream cuts through dense stands of black alder and Scotch pine forest with mixture of aspen, birch, and Norway spruce. Beavers constructed a series of eight small dams (usually not exceeding 20 m in length) that formed a chain of small ponds (less than 0.1 ha each). They remained free of duckweed during the whole study period, but water levels fell notably during mid-summer because of a decrease in precipitation, so the few largest ponds became overgrown by emergent vegetation, mostly cutleaf water parsnip (Berula erecta). The impact of beavers on trees appears to be lower than in Stara Rzeka (Site 1). The modifications were restricted to flooding and the death of a narrow forest strip in the lower section of the valley and the cutting of some trees, which resulted in the creation of localized canopy gaps.

Recording of bat activity

In each valley, a linear transect was marked parallel to the stream channel to record echolocation calls of commuting and foraging bats. At site 1, the transect was 1,210 m long (walked in 35 min) and divided into 11 sections: three unmodified by beavers (40% of total length-brook flowing freely through a meadow and dense forest) and eight modified (60% transect-flooded meadow, flooded forest with dead snags, dams, tree cuttings, and resulting canopy gaps). At site 2, the transect was 1,660 m long (walked in 30 min) and divided into 16 sections, covering subsequent beaver ponds (i.e., the first 50 m above each dam) and unmodified fragments of the stream with a notably faster current.

The activity of bats in both valleys was studied during spring (April-May), summer (June-July), and early autumn (September). In total, site 1 was visited 22 times and site 2 was visited 21 times from 2005 to 2007. Only one site was visited per evening. Bat echolocation calls were recorded using a Pettersson D-980 (Pettersson Elektronik AB; Uppsala, Sweden) bat detector attached to a Sony WMD-6C stereo tape recorder. The detector worked in real-time (retained amplitude frequency division) mode, and calls of frequency divided by 10 were recorded constantly on the left channel if the original sound fell into range, 10-200 kHz. At any time, when signals of passing bats were heard in the frequency divider, a person that conducted recording triggered the time-expansion mode (range, 10-150 kHz) to preserve all characteristics of the recorded ultrasound. In this mode, the detector sampled at 350 kHz with 8 bits of resolution, storing was selected at 3.0 s of sound in digital memory and played it back, time-expanded by a factor of 10. A full spectrum sample was subsequently recorded on the right channel, parallel to real-time frequency division recording. Every sequence of at least two calls recorded on one of the two channels (either frequency-divided or time-expanded) was considered a bat pass. Each time, the transect was walked twice in the evening. The first walk began half an hour after sunset [START_REF] Rachwald | Habitat preference and activity of the noctule bat Nyctalus noctula in the Białowieża Primeval Forest[END_REF][START_REF] Warren | The distribution of Daubenton's bats (Myotis daubentonii) and pipistrelle bats (Pipistrellus pipistrellus) (Vespertilionidae) in relation to small-scale variation in riverine habitat[END_REF] while the second walk began immediately after the end of the first. Such an approach allowed us to record activity of several species that differ in timing of evening emergence from daily roosts (cf. [START_REF] Jones | Foraging strategy and predation risk as factors influencing emergence time in echolocating bats[END_REF].

Bioacoustic analysis of bat calls

Recorded echolocation calls, attributed to particular sections of the transects were downloaded as audio files into a computer using BatSound 3.3 (Pettersson Elektronik AB; Uppsala, Sweden) at 22.5 kHz with 16 bit resolution. The calls were analyzed using a 1024-point fast Fourier transform, hanning window. We based species recognition on tonal quality (shape) of the calls (based on spectrogram), peak frequency or frequency of maximum energy (measured on power spectrum), pulse duration, and interval length (measured on oscillogram). All extracted parameters and additional diagnostic features were compared with those available in the literature [START_REF] Ahlén | Identification of bats in flight[END_REF][START_REF] Barataud | The world of bats. Acoustic identification of French bats[END_REF]Vaughan et al. 1997b). Echolocation calls of various Myotis species are similar in structure, thus hard to identify reliably, so we classified them into one group (Myotis sp.). However, the identification of recorded individuals as M. daubentonii at site 2 was in several cases, confirmed by observations of a specific hunting style which included circling repeatedly just a few centimeters above the water surface [START_REF] Ahlén | Identification of bats in flight[END_REF]). Congenerics were thereby ruled out based on visual observation. Both Myotis mystacinus and Myotis brandtii are extremely rare species in the region and no breeding has been confirmed there for the latter [START_REF] Sachanowicz | Distribution patterns, species richness and status of bats in Poland[END_REF]. We have never recorded the exceptional broadband signals of Myotis nattereri, which may be considered diagnostic (mean bandwidth, 119 kHz; [START_REF] Siemers | Echolocation signals reflect niche differentiation in five sympatric congeneric bat species[END_REF]. Therefore, it is highly probable that either the only representative of Myotis genus in the study area was M. daubentonii or the occurrence of its congenerics was negligible.

Statistical analysis

Because the assumptions of normality were violated in several subsets of data, we tested all differences in bat activity, using non-parametric statistics: Mann-Whitney U test between sites, Wilcoxon signed-rank test between sections of transects generally classified as modified or unmodified by beavers, and Friedman's ANOVA among sections assigned to different original habitats (meadow, intact forest) as well as different types and levels of beaver impact (tree cuttings-canopy gaps, flooding-beaver ponds, lack of visible modification). In every case, the number of bat passes per 100 m was defined as a response (dependent) variable. Predictor (independent) variable in Friedman's ANOVA was defined as a habitat type (five categories: (1) forest, (2) flooded forest with canopy gaps created by beavers, (3) forest with beaver-created canopy gaps but no flooding, (4) meadow, and (5) flooded meadow). Only nights, when a particular taxon appeared on a transect, were taken for such comparisons. Additionally, species composition (proportion of passes) between sites was compared using Pearson's chi-squared test and species diversity (H' Shannon-Wiener index) between sites was compared using the modified t test [START_REF] Zar | Biostatistical analysis[END_REF]. We performed all the analyses using Statistica 6.0 (StatSoft, Inc.) except the comparison of H' index that was performed using Microsoft Excel 2003. Statistical significance was accepted at P<0.05.

Results

In total, seven species of bats were recorded on both transects: Daubenton's bat M. daubentonii (including those determined as Myotis sp.), serotine Eptesicus serotinus, common pipistrelle Pipistrellus pipistrellus, soprano pipistrelle Pipistrellus pygmaeus, Nathusius' pipistrelle Pipistrellus nathusii, noctule Nyctalus noctula, and brown long-eared bat Plecotus auritus. Species composition differed significantly between sites (χ 2 =103.65, df=6, p<0.0001). At site 1, the most numerous species was P. nathusii, followed by P. pipistrellus and N. noctula while activity of Myotis bats was almost negligible. On the contrary, at site 2, the most numerous were representatives of the Myotis genus, followed by P. pipistrellus and P. nathusii (Table 1). Both sites also differed in species diversity, being slightly lower at site 2 (t=2.18, df=463, p=0.03). The density of bat passes was significantly higher at site 1, regarding all taxa combined (Mann-Whitney U test: U = 75.00, Z = 3.52, p = 0.0004), P. pipistrellus (U=73.50, Z=3.56, p=0.0004), P. pygmaeus (U=93.00, Z = 3.05, p = 0.002), P. nathusii (U = 53.50, Z = 4.08, p=0.00004), and N. noctula (U=68.00, Z=3.70, p=0.0002), but the Myotis species were more active at site 2 (U= 83.00, Z=-3.31, p=0.0009). There were no differences in density at either site for E. serotinus (U=171.00, Z=1.02, p=0.30) or P. auritus (U=178.50, Z=-0.82, p=0.41).

The number of bat passes was significantly higher in sections of valleys modified by beavers than in unmodified sections (Wilcoxon matched pairs test, site 1: n=19, T= 0.00, Z=3.82, p=0.0001, Fig. 1; site 2: n=20, T=52.00, Z= 1.98, p=0.048, Fig. 2). When regarding particular species separately, four species occurred frequently enough at site 1 to perform such comparison and all revealed higher activity in sections modified by beavers (P. pipistrellus: n=18, T=1.00, Z=3.68, p=0.0002; P. pygmaeus: n=13, T=8.00, Z=2.62, p=0.008; P. nathusii: n=18, T=0.00, Z=3.72, p=0.0002; N. noctula: n=16, T=0.00, Z=3.52, p=0.0004, Fig. 1). Only two species were frequent enough to compare modified and unmodified sections at site 2, and none of them revealed a significant difference in activity (Myotis species: n=16, T=48.00, Z=1.03, p=0.30; P. pipistrellus: n=13, T=40.00, Z=0.38, P=0.70, Fig. 2).

Bat activity, in particular habitats at site 1, differed significantly (Friedman's ANOVA: n=20, χ 2 =39.79, df=4, p=0.00001) with the highest number of passes in flooded forest with canopy gaps created by beavers. Significantly fewer passes were recorded in a forest with canopy gaps only and in intact unmodified forest. Meadows flooded by beavers were used more intensively than unflooded meadows (Fig. 3e). The same result was obtained for P. nathusii (n=18, χ 2 =39.72, df=4, p=0.00001), including similar paired comparisons between habitats (Fig. 3c).

Activity of P. pipistrellus differed significantly between habitats (n=18, χ 2 =24.42, df=4, p=0.00007), with more passes being recorded in the flooded forest with cuttings than in the intact forest and more passes over flooded meadows than over the unflooded meadow (Fig. 3a). A variation in activity of P. pygmaeus among habitats was Fig. 3 Differences in bat activity between particular habitats distinguished along the transect at site 1. F, forest; FFG, flooded forest with canopy gaps created by beavers; FG, forest with beaver-created canopy gaps but no flooding; M, meadow; MF, flooded meadow. Arrows indicate significant differences (p<0.05) revealed in post hoc tests also significant (n=13, χ 2 =18.77, df=4, p=0.0009) but only the number of passes over flooded and dry meadows differ significantly in paired comparison (Fig. 3b). The notable exception was N. noctula (n=16, χ 2 =24.29, df=4, p=0.00007) that revealed the highest median activity not in flooded forest with gaps, but over the flooded meadow. Significantly, more passes of N. noctula were recorded in the latter habitat than over the meadow that was not flooded. In addition, increased activity appeared in flooded forests where beavers cut trees than in forests with cut trees but no flooding, or in forests not modified by beavers (Fig. 3d). Although we revealed differences between modified and unmodified sections of the transect at site 2, no similar distinction among habitat types was possible there. All the original habitat appeared to be dense, intact forest, and any visible effect of beaver activity was restricted to flooding of a narrow strip along the stream and dispersed tree cuttings.

Discussion

We found that the nightly activity of vespertilionid bats at the two sites of northern Poland was higher in sections of small river valleys visibly transformed by recently reintroduced European beavers (i.e., flooded and with tree cuttings) than in sections of the same valleys not subjected to such transformations. Our study is the first to document significant effects of beavers' foraging and building activities on spatial distribution of foraging or commuting bats. However, it confirmed our expectations only partially, with respect to aerial hawking species, but not watersurface foragers (i.e., groups that might benefit from the different aspects of beaver activity).

Occurrence of more bats in areas modified by beavers at both sites reduced the possibility that observed differences were due to chance alone. Accurate quantification of a sitespecific magnitude of bat activity at rivers and ponds can be achieved with a sampling intensity of at least 14 nights [START_REF] Broders | Another quantitative measure of bat species activity and sampling intensity considerations for the design of ultrasonic monitoring studies[END_REF], and our sample size exceeded that value by more than one third. It is also highly unlikely that increased activity of bats in some sections of the transect was related to location of daily roosts from which bats emerged during recordings, even if the use of riverine habitats by hunting chiropterans is known to correlate negatively with the distance from nursery colonies [START_REF] Dietz | Small scale distribution patterns of female and males Daubenton's bats (Myotis daubentonii)[END_REF]. Although trees killed by flooding by beavers can be used as roosts by some forest bats [START_REF] Menzel | Tree-roost characteristics of subadult and female evening bats (Nycticeius humeralis) in the upper coastal plain of South Carolina[END_REF], timing of survey largely excluded such possibility. Significant differences in the number of passes between modified and unmodified sections were produced mostly by predominant, aerial hawking taxa (Pipistrellus, Nyctalus and, less importantly, the Eptesicus genus) that are known to emerge 8 to 32 min after sunset, on an average [START_REF] Jones | Foraging strategy and predation risk as factors influencing emergence time in echolocating bats[END_REF]. Thus, when the outward leg of the transect was walked, most bats had already emerged and their presence or absence in particular parts of the studied valleys was related to the attractiveness of the habitat as a foraging site or a flyway.

There are at least two main factors that may explain the higher activity levels of bats in sections subject to habitat modifications caused by beavers. The first, apparently more obvious, is flooding (i.e., increase in water table and creation of beaver ponds, covering former terrestrial habitats). All four species that revealed significant differences between sections of the transect at site 1 (P. pipistrellus, P. pygmaeus, P. nathusii, N. noctula) are known to prefer water bodies or riparian zones [START_REF] Rachwald | Habitat preference and activity of the noctule bat Nyctalus noctula in the Białowieża Primeval Forest[END_REF][START_REF] Rydell | Habitat use by bats along rivers in north east Scotland[END_REF]Vaughan et al. 1997a;[START_REF] Mickevičiené | The importance of various habitat types to bats (Chiroptera: Vespertilionidae) in Lithuania during the summer period[END_REF][START_REF] Russ | Habitat associations of bats in Northern Ireland: implications for conservation[END_REF][START_REF] Downs | The use by bats of habitat features in mixed farmland in Scotland[END_REF][START_REF] Kaňuch | Relating bat species presence to habitat features in natural forests of Slovakia (Central Europe)[END_REF]. As beavers extend riparian habitats, they improve the habitat quality for bats and provide them with large areas where prey is much more abundant than over the shallow and narrow streams. Moreover, biomass of emerging chironomids, an important prey of Pipistrellus and Nyctalus [START_REF] Vaughan | The diets of British bats (Chiroptera)[END_REF], increased in the valley section after construction of a beaver dam, at least during the first few years [START_REF] Nummi | Simulated effects of the beaver on vegetation, invertebrates and ducks[END_REF]. The second factor is related to a significant reduction of forest-associated clutter, being a serious limitation for aerial hawking species. Although woodlands, especially deciduous ones, are among the most preferred habitats by bats, along with riparian zones [START_REF] Walsh | Foraging habitat preferences of vespertilionid bats in Britain[END_REF][START_REF] Russ | Habitat associations of bats in Northern Ireland: implications for conservation[END_REF], closer examination reveals that most aerial hawking bats avoid internal parts of dense, intact stands [START_REF] Rachwald | Habitat preference and activity of the noctule bat Nyctalus noctula in the Białowieża Primeval Forest[END_REF][START_REF] Lloyd | Bat activity on riparian zones and upper slopes in Australian timber production forests and the effectiveness of riparian buffers[END_REF]). Their activity is negatively correlated with the area of closed canopy [START_REF] Kusch | Foraging habitat preferences of bats in relation to food supply and spatial vegetation structures in a western European low mountain range forest[END_REF]) and density of trees [START_REF] Erickson | Association of bats with local structure and landscape features of forested stands in western Oregon and Washington[END_REF]. In managed forests that are subject to commercial logging, aerial hawkers use either stream corridors [START_REF] Lloyd | Bat activity on riparian zones and upper slopes in Australian timber production forests and the effectiveness of riparian buffers[END_REF] or artificial areas of low clutter, which include thinned stands, clear-cuts [START_REF] Patriquin | Foraging by bats in cleared, thinned and unharvested boreal forest[END_REF], and trails [START_REF] Lloyd | Bat activity on riparian zones and upper slopes in Australian timber production forests and the effectiveness of riparian buffers[END_REF]. In unmanaged and unharvested forests, the same group of bats have to use natural canopy gaps that are usually created by the aging of older trees, windthrows, outbreaks of phytophagous insects, and pathogenic fungi [START_REF] Weiskittel | Canopy gap characteristics of an oakbeech-mapple old-growth forest in Northeastern Ohio[END_REF][START_REF] Worrall | Forest dynamics and agents that initiate and expand canopy gaps in Picea-Abies forests of Crawford Notch, New Hampshire, USA[END_REF]. Cutting of trees by beavers may have a similar function in forests adjacent to water bodies and wetlands inhabited by these rodents.

We cannot explicitly indicate which of the two, mentioned above, effects of beavers on the ecosystem of the small river valley has the greater impact on insectivorous bats. Moreover, they appear to act additively. The total activity of bats, as well as specifically that of P. nathusii and N. noctula, was significantly higher in forests with beaver-created canopy gaps than in dense, unmodified forest, which suggests that beaver foraging (and tree cutting) may separately improve habitat quality for hunting bats, thus confirming our first hypothesis. However, the activity of bats was also significantly higher in the flooded forest with gaps than in the non-flooded forest with gaps only. Flooding may also act independently as a factor promoting the use of habitat by bats, as evidenced by higher activity of all four species over the flooded part of the meadow than over the section outside of the beaver pond. This difference is especially important in N. noctula, an open-space forager with low maneuverability that hunts at high altitude, far from any vertical obstacles [START_REF] Baagøe | The Scandinavian bat fauna: adaptive wing morphology, and free flight in the field[END_REF][START_REF] Jones | Flight performance, echolocation and foraging behaviour in noctule bats Nyctalus noctula[END_REF]. The latter species may rely more on wide meadows, subjected solely to flooding than on beavercreated forest gaps, although a difference between the two most important habitats for noctules in our study was not significant. On the contrary, Pipistrellus spp. commute and hunt in quite a maneuverable style and are able to circle around trees at much lower altitude [START_REF] Baagøe | The Scandinavian bat fauna: adaptive wing morphology, and free flight in the field[END_REF][START_REF] Kalko | Insect pursuit, prey capture and echolocation in pipistrelle bats (Microchiroptera)[END_REF], at least, if clutter is moderately reduced. They may prefer a combination of flooding and tree cutting found in beaver ponds with numerous snags, which are remains of the riparian forest, partially immersed in water after damming. The activity of pipistrelles appears to be the highest in close proximity to tree lines and gradually decreases at greater distances from them [START_REF] Downs | The use by bats of habitat features in mixed farmland in Scotland[END_REF]. Thus, the forest habitats altered by beavers may be more frequently used than beaver-transformed open habitats.

We were unable to confirm our hypothesis that damming of the stream increase habitat use by water-surface foragers (e.g., M. daubentonii) due to the formation of large areas of smooth water, which serve as an acoustic mirror for prey detection. The activity of the Myotis species was almost negligible at site 1, with no difference between flooded and non-flooded sections. However, all beaver ponds at that site were completely covered by a dense, floating layer of pleustophytic vegetation, mostly formed by duckweed (Lemnaceae). A much lower discharge and stream velocity excluded the effective removal of these plants, which were absent on the ponds' surface only during April, when no bats forage there probably due to low air temperatures. Duckweed is known to produce significant acoustic clutter that suppresses foraging of M. daubentonii by producing complicated background echoes that interfere with a bat's prey detection [START_REF] Boonman | Prey detection in trawling insectivorous bats: duckweed affects hunting behaviour in Daubenton's bat, Myotis daubentonii[END_REF], thus it may also negate any benefits to trawling bat species from the creation of ponds by beavers in some areas. The same reasoning also applies to other kinds of floating vegetation [START_REF] Ciechanowski | Spatiotemporal variation in activity of bat species differing in hunting tactics: effects of weather, moonlight, food abundance, and structural clutter[END_REF]. The effect of pleustophytes on bat activity over beaver impoundments may not be obligatory, and streams with a higher velocity of current and stronger flow probably remove floating vegetation, thus keep the surface of beaver ponds free of duckweed. A notable example of such a situation appeared to be in site 2, where the activity of Myotis species was significantly higher than at site 1, and this taxon dominated in local bat assemblage. Moreover, we directly observed the individuals of M. daubentonii hunting over the surface of small, duckweed-free beaver ponds just above the dams. Although we were unable to obtain a significant difference between dammed and untransformed sections of the stream for these species, this may be a result of generally low bat activity at site 2, thereby reducing samples often to just few passes each night, which makes differences between data points sensitive to stochastic variation. Future comparative studies repeated at more sites might document preference of dammed valley sections by any water-surface bat species. This phenomenon may especially apply to the older ponds. Duckweed achieves the greatest surface coverage in youngest impoundments (less than 10 years after damming), but declines afterwards, replaced by larger macrophytes (lily pads) and finally, after about 40 years, some ponds establish vegetation that lack significant floating cover [START_REF] Ray | Macrophyte succession in Minnesota beaver ponds[END_REF]. The latter may become available foraging habitat for trawling bat species.

Confirmation of our first hypothesis provided a strong argument that reintroduction of the beaver to the small river valleys may improve habitat quality for aerial hawking insectivorous bats, thus reintroduction might be recommended with respect to bat conservation. Bats are known to benefit from restoration of formerly drained wetlands, as indicated by an increase in activity on areas subjected to such treatment (Menzel et al. 2005b). Usually, active riparian restoration is applied to obtain such results, including vegetation plantings, creation of small clearings to mimic natural disturbances and development of canopy gaps, placement of coarse woody debris on floodplain and in stream corridors, reconfiguring channelized riches to increase their sinuosity and floodplain connectivity [START_REF] Kauffman | An ecological perspective of riparian and stream restoration in the Western United States[END_REF][START_REF] Roni | A review of stream restoration techniques and a hierarchical strategy for prioritizing restoration in Pacific Northwest watersheds[END_REF], and closing drainage ditches with earthen plugs (Menzel et al. 2005b). These methods are often costly and time-consuming; thus, reintroduction of a keystone species, such as the beaver, appears to be a reasonable option, which is cost-effective and leads to the restoration of a whole ecosystem of a small river valley. They not only create new foraging sites for bats, but also increase the influx of emerging aquatic insects to surrounding forests, as usually observed in situations where any water body contact with the woodland [START_REF] Nakano | Reciprocal subsidies: dynamic interdependence between terrestrial and aquatic food webs[END_REF], thus they may benefit even bat species that prefer to hunt under a canopy rather than over a riparian strip. Finally, maternal colonies of bats are known to aggregate in close vicinity of proper foraging sites [START_REF] Dietz | Small scale distribution patterns of female and males Daubenton's bats (Myotis daubentonii)[END_REF], so beaver activities may increase suitability of surrounding roosting habitats as well. The expected effect may appear in a short time after colonization by beavers because bats often start to exploit new sources of food in an astonishingly short time [START_REF] Fenton | Opportunistic feeding by desert bats (Myotis spp.)[END_REF].

It has to be noted, however, that beavers might benefit bats regarding foraging habitats only in valleys of small streams because larger rivers intersecting forest areas provide corridors and act as linear canopy gaps with smooth water surfaces at the bottom, wide enough to support hunting by both aerial hawkers and trawling bats. In such situations, further reduction of clutter, associated with tree cutting on valley slopes, would be of negligible importance. Locally, some negative effects of beaver reintroduction on local bat assemblages might also be expected, as beavers select trees mostly at closest distance from the water [START_REF] Haarberg | Selective foraging on woody plant species by the Eurasian beaver (Castor fiber) Telemark, Norway[END_REF], whereas in open agricultural landscapes, bats forage mostly along river sections lined with trees from both sides [START_REF] Warren | The distribution of Daubenton's bats (Myotis daubentonii) and pipistrelle bats (Pipistrellus pipistrellus) (Vespertilionidae) in relation to small-scale variation in riverine habitat[END_REF][START_REF] Downs | The use by bats of habitat features in mixed farmland in Scotland[END_REF]. Extensive removal of such tree lines would lead, in fact, to degradation of bat foraging habitats. Although this is not the case of forest landscapes, where bats react positively on moderate tree removal due to reduction of clutter, there are notable exceptions. Some clutter-adapted, gleaning species require high coverage of stand canopy [START_REF] Ford | Relating bat species presence to simple habitat measures in a central Appalachian forest[END_REF]. However, even if beaver reintroduction is regarded as beneficial for bat populations at a particular site, it must be weighed against other natural values of the particular area.

In formerly drained, degraded valleys, colonization by beavers is considered to enhance strongly their biodiversity; however, when the valley holds the last remnants of natural forest among large blocks of heavily managed plantation, foraging beavers may cause their final degradation [START_REF] Zwolicki | European Beaver Castor fiber-a keystone species for the river valley ecosystems[END_REF]. Moreover, some of the most sensitive, strictly rheoand oxybiontic species of freshwater invertebrates might even be threatened by beaver dams and the resulting silt deposition [START_REF] Rosell | Ecological impact of beavers Castor fiber and Castor canadensis and their ability to modify ecosystems[END_REF]. Despite these arguments, the presence of beavers should be included in any assessments of bat habitat potential in small river valleys, bearing in mind that, until recently, links between beavers' ecosystem engineering and distribution of bats have been neglected both in North America and in Europe.

Fig. 1 Fig. 2

 12 Fig.1Differences in bat activity between sections of the valley modified and unmodified by beaver's flooding and cutting activities at site 1. Pin, P. nathusii; Pip, P. pipistrellus; Pyg, P. pygmaeus; Nyn, Nyctalus noctula; Tot, the total number of all bat passes, including indeterminate calls

Eur J Wildl Res (2011) 57:737-747

Eur J Wildl Res (2011) 57:737-747

Acknowledgements The study was supported by an internal grant of the University of Gdańsk BW/1440-5-0230-5.

Open Access This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


Simon G Thompson
email: simon.thompson@mrc-bsu.cam.ac.uk

Ulf Ekelund

S Jebb

Anna Karin Lindroos

Stephen Sharp

R Turner

Desiree Wilks

Simon ; Thompson

S ; <none> Lindroos

Anna Karin

Thompson Sg

Jebb Sa

Lindroos Ak

Mander Ap

Sharp Sj

Turner Rm

Wilks Dc

Prof Simon G Thompson

A proposed method of bias adjustment for meta-analyses of published observational studies

Keywords: meta-analysis, study quality, bias adjustment, observational studies, physical activity, obesity Meta-analysis, study quality, bias adjustment, observational studies, physical activity, obesity

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Key messages

We present novel methods for undertaking a quantitative meta-analysis, when the component studies are observational and thus prone to many biases.

We describe how the process can be broken down into small manageable steps, and how to incorporate opinion elicited in a formal manner about the size and uncertainty of the biases in each study.

Bias checklists, elicitation scales and computer code are made available so that others can carry out similar analyses. These methods, or ones similar to them, will increasingly need to be adopted when formulating guidance on public health issues for which randomised trial evidence is not available.

Introduction

Many issues of public health importance cannot be investigated in intervention studies or randomised trials, for either ethical or practical reasons [START_REF] Black | Why we need observational studies to evaluate the effectiveness of health care[END_REF][START_REF] Eccles | Research designs for studies evaluating the effectiveness of change and improvement strategies[END_REF] . Observational studies then provide the only source, or a large component, of relevant evidence. Such studies are notoriously prone to biases, caused for example through selection of participants, confounding and loss to follow-up. Especially when only published information is available, the potential impact of biases on the reported results and their interpretation is often unclear [START_REF] Von Elm | The Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) statement: guidelines for reporting observational studies[END_REF] . This issue comes to the fore when undertaking a systematic review [START_REF] Egger | Spurious precision? Meta-analysis of observational studies[END_REF] , for then the objective is to collate and synthesize all the available evidence in a rigorous way. Systematic reviews have in the main focused on intervention studies, and especially randomised trials [START_REF]Cochrane Handbook for Systematic Reviews of Interventions Version 5.0.2. The Cochrane Collaboration[END_REF] . In these situations, although potential biases still have to be considered, there is an appreciation of their major sources and potential impact [START_REF] Lundh | Recommendations by Cochrane Review Groups for assessment of the risk of bias in studies[END_REF] . Reviews of observational studies commonly reach rather qualitative conclusions, for example based on a tabulation of study-specific results together with a commentary on their idiosyncrasies and potential biases. An overall quantitative conclusion using metaanalysis is often avoided because of the intangible nature of some of the biases, the incompatibility of methods of presenting results in different papers [START_REF] Chene | Methods for summarizing the risk associations of quantitative variables in epidemiologic studies in a consistent form[END_REF] , and the fact that relevant information is often missing in publications. Alternatively, a rather arbitrary dichotomy is introduced to separate the 'better' from the 'poorer' quality studies, and a quantitative meta-analysis of the former presented. This simplistic approach essentially disregards any biases in the 'better' studies, and assumes that the 'worse' studies are totally non-informative. Similarly, simple scoring of studies according to some measure of quality does not directly address their biases [START_REF] Ioannidis | Reasons or excuses for avoiding meta-analysis in forest plots[END_REF] .

In the context of systematic reviews of intervention studies, both randomised and nonrandomised, work has recently been developed to quantify the potential biases using subjective opinion elicited from experts so that meta-analysis can be undertaken [START_REF] Turner | Bias modelling in evidence synthesis[END_REF] . Using elicited opinion is necessary, because there is rarely sufficient empirical evidence about

Methods

Our aim is to make a quantitative conclusion, on the basis of observational studies, about a particular association of public health importance. As an example, we consider the relationship between physical activity and subsequent change in adiposity in children.

Relevant studies were undertaken in different contexts (populations, methods, lengths of follow-up), but we aim to make a conclusion relevant to a specific target setting. The studies then suffer from two forms of bias: first internal bias (or lack of rigour) and second external bias (or lack of relevance to the target setting). In the following explanation of our proposed approach, the focus is on the methods; more details of the example and its interpretation are provided elsewhere [START_REF] Wilks | Objectively measured physical activity and fat mass in children: a bias-adjusted meta-analysis of prospective studies[END_REF] .

Physical activity and obesity example

Obesity is a major global health issue [START_REF]Global health risks: Mortality and burden of disease attributable to selected major risks[END_REF] , and the increase in obesity of children is of particular concern [START_REF] Deckelbaum | Childhood obesity: the health issue[END_REF] . It is proposed that increasing physical activity, which raises energy expenditure, may protect against excess weight gain. But the evidence underpinning this assertion is incomplete. Most cross-sectional studies of physical activity and body weight indeed show an inverse association [START_REF] Jimenez-Pavon | Associations between objectively measured habitual physical activity and adiposity in children and adolescents: Systematic review[END_REF] . However their interpretation is problematic, because the direction of any causal link is unclear (does physical activity lead to lower weight, or does obesity lead to lower levels of physical activity?). In addition, studies not using objective measures may be distorted by reporting biases for physical activity [START_REF] Westerterp | Assessment of physical activity level in relation to obesity: current evidence and research issues[END_REF] .

Thus we focus on longitudinal observational studies in children, which relate objective measures of baseline physical activity to objective measures of subsequent change in adiposity, found in a thorough literature search from January 2000 up to September 2008 [START_REF] Wilks | Objectively measured physical activity and fat mass in children: a bias-adjusted meta-analysis of prospective studies[END_REF][START_REF] Wilks | Objectively measured physical activity and obesity prevention in children, adolescents and adults: a systematic review of prospective studies[END_REF] .

F o r R e v i e w O n l y 6
Six studies fulfilling the eligibility criteria were found [START_REF] Delany | Energy expenditure and substrate oxidation predict changes in body fat in children[END_REF][START_REF] Figueroa-Colon | Paternal body fat is a longitudinal predictor of changes in body fat in premenarcheal girls[END_REF][START_REF] Johnson | Aerobic fitness, not energy expenditure, influences subsequent increase in adiposity in black and white children[END_REF][START_REF] Moore | Does early physical activity predict body fat change throughout childhood?[END_REF][START_REF] Salbe | Assessing risk factors for obesity between childhood and adolescence: II. Energy metabolism and physical activity[END_REF][START_REF] Treuth | Predictors of body fat gain in nonobese girls with a familial predisposition to obesity[END_REF] . They are characterised by heterogeneity in populations studied, age and sex groups recruited, follow-up times, measures of physical activity level and body composition, and which confounders are adjusted for. One of the studies is summarised in Table 1, and will provide a running example in this paper. Most studies measured percentage of total weight as body fat (%BF) at baseline and follow-up, and regressed change in %BF on baseline physical activity level and confounders. Results from these regression analyses were presented in various ways, for example either a partial regression or a partial correlation coefficient with a p-value, and often without a direct measure of uncertainty such as a standard error or confidence interval.

Target setting and categories of bias

The overall approach to identify and quantify the biases of original studies in relation to a target setting is depicted in Figure 1. For each original study undertaken, an idealised version is described that is not subject to any internal biases. This separates the internal biases from the external biases, which are themselves broken down into components so that they can be more easily assimilated and opinions about their magnitude elicited.

The key components of a well-defined target setting in our example were considered to be the population, the measure of physical activity, the measure of change in adiposity, and the duration of follow-up. The specific target setting chosen is shown in Table 2, in order to address the most relevant public health question in the UK. While some aspects (for example the choice of change in %BF as the outcome measure) were well represented within the studies undertaken, others were not (all the studies were conducted in the USA but the target population was the UK). Also shown in Table 2 is the idealised version of the example study from Table 1. The idealised study uses the same design, population, measures and context as the original study, but is not subject to any internal biases (for example no loss to follow-up, proper control of confounding). There is no subjectivity involved in defining the idealised study; it does not have to be practicable but

F o r R e v i e w O n l y
7 is merely a mechanism to enable internal and external biases to be separated. The differences between the original and idealised study represent internal biases, and differences between the idealised study and the target setting (Table 2) represent potential external biases.

The sources of internal bias were put into six categories (Figure 1): selection bias (whether the sample recruited was representative of the intended population), control of confounding (whether essential confounders have been adjusted for), exposure measure (problems in assessing physical activity), attrition (loss to follow-up), outcome measure (problems in measuring change in adiposity), and any other biases (for example when the statistical analysis used was thought to have introduced bias). These six categories of bias were generally mutually exclusive, so that each potential bias in each study could be placed in one category, and considered to operate independently of each other. The external biases were in four categories (population, exposure measure, outcome measure and follow-up time) that relate to the definition of the target setting. To help itemise the specific biases for each study, a checklist was developed (Figure 2) based on previous work [START_REF] Von Elm | The Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) statement: guidelines for reporting observational studies[END_REF][START_REF] Turner | Bias modelling in evidence synthesis[END_REF][START_REF] Downs | The feasibility of creating a checklist for the assessment of the methodological quality both of randomised and non-randomised studies of health care interventions[END_REF] and this was completed for each study.

The choice of appropriate confounders to adjust for is a difficult issue. Rather than attempt to say whether the choice of a particular set of confounders was 'correct', we judged the bias from the adjustment presented in relation to using a standard set of confounders (namely age, sex, ethnic group, sexual maturity, baseline fat mass and baseline lean mass). Moreover we did not consider the effects of within-subject variation over time in the assessment of physical activity. Thus the target parameter to be estimated in the meta-analysis is that for the association between change in %BF and observed baseline physical activity energy expenditure (PAEE) adjusted for a specific set of confounders.

Extracting results

The principal quantitative result extracted from each study, which would form the basis for the meta-analysis, was chosen to be as close as possible to an estimate of the target parameter. Then the extent to which biases would have to be assessed was minimised.

For example adjusted associations were chosen if available, and reported associations with PAEE were preferred over associations with total energy expenditure. Since the exposure and outcome variables were on different scales in different studies, and because results were presented in different formats, it was necessary to convert all extracted results to a common scale. Moreover standard errors were not always provided. Our solution was to transform all associations into correlation coefficients using, if nothing else were available, the sample size and the p-value to derive these.

We use the result that the Fisher-transformation of a correlation coefficient r , namely

0.5ln[(1 ) /(1 )] = + - z r r
, has an approximate normal distribution with standard error

1/( 3) - n
where n is the sample size [START_REF] Armitage | Statistical Methods in Medical Research[END_REF] . Thus the relevant (2-sided) p-value reported in the paper is first converted into a standard normal score S taking due regard of the sign of the association in the paper, the Fisher-transformed correlation derived as

1/( 3) = × - z S n
, and the correlation as

Bias assessments

The process of eliciting biases was as follows, for each study in turn. The same subject- After the group discussion, each assessor individually considered biases in each category (Figure 1). A first qualitative stage was to consider whether the bias was potentially large, medium, small, or negligible, and in what direction. They then indicated their view about the magnitude of an additive bias, and their uncertainty about this, on the upper scale in Figure 3. This required marking an interval on the untransformed correlation scale such that they believed there was a two-thirds chance that the bias lay inside this interval, and a one-third chance that it lay outside. To help guide these judgements, Figure 4 shows the impact of different biases on the magnitude of the confidence interval for the correlation according to sample size. From this, a guideline was suggested that additive biases of magnitude more than 0.2 were large, those between 0.1 and 0.2 were moderate, and those less than 0.1 were small. If an assessor had no opinion about the direction of the bias, then the interval would be placed symmetrically about zero. If an assessor thought that the bias would tend to favour a negative correlation, the centre of the interval would be on the left hand side of the upper scale in Figure 3, and vice-versa for a bias favouring a positive correlation. If there was thought to be no or negligible bias, the 'interval' became a point at zero on the scale. Biases considered proportional by the group were indicated on the lower scale in Figure 3

Meta-analysis

We performed meta-analysis of correlation coefficients on the Fisher-transformed scale because the distribution of z is more symmetric than that of r. We incorporated assessments of the biases elicited on the correlation scale but transformed onto the z scale.

Since the range of z is from minus to plus infinity, this has the theoretical advantage that additive biases cannot produce impossible values of the underlying correlation. However, in our context where correlations are modest in magnitude, this is of limited practical importance because the values of z and r are numerically close in the range -0.3 to +0.3.

The calculations for including the bias assessments in the meta-analysis follow published methods [START_REF] Turner | Bias modelling in evidence synthesis[END_REF] , and Stata code is available [START_REF] Sharp | Bias adjustment methods for meta-analyses of published observational studies: Stata code[END_REF] . In brief, a bias assessment interval marked on the scales in Figure 3 is considered to be an estimated bias ± one standard deviation (SD), since this corresponds to a two-thirds (67%) interval for a normal probability distribution.

For each study and assessor, the total internal additive bias is calculated by adding the individual bias estimates and summing their variances (squared SDs). The total internal proportional bias and estimated variance for each study and assessor are also calculated [START_REF] Turner | Bias modelling in evidence synthesis[END_REF] .

These two quantities are combined to give a total internal bias and variance. This total bias for each assessor and study is subtracted from the observed study result, and the total variance of the bias added to the study result variance, to give an internal bias-adjusted estimate and variance for each study and each assessor. The external biases are then incorporated using a similar procedure. These adjusted estimates for each study are then averaged across assessors by median pooling [START_REF] Clemen | Combining probability distributions from experts in risk analysis[END_REF] , taking the median of the bias-adjusted estimates and the median of the variances; this corresponds to a 'typical' assessor.

Random-effects meta-analysis across studies was undertaken on the Fisher-transformed correlation scale. The impact of heterogeneity was summarised by the I

Results

To explain the process, we first consider the biases, elicitations and adjustments performed for the one example study [START_REF] Figueroa-Colon | Paternal body fat is a longitudinal predictor of changes in body fat in premenarcheal girls[END_REF] summarised in Table 1. The study result extracted was based on a sample size of 39 and a reported p-value of 0.04 from a multiple regression for the association of baseline PAEE and other covariates with change in %BF , yielding a calculated (partial) correlation of -0.33 (95% CI -0.59 to -0.01).

The internal biases reflect differences between the study undertaken and the idealised version of the study (Table 2); the elicited internal biases are shown in Figure 5 (top).

Since there was little information about recruitment, it is possible that the girls in the example study were not representative of the population intended. The resulting selection bias was considered an additive bias; the assessors generally had no opinion about the direction of the bias but some were more uncertain about its impact than others. The reported result included adjustment for age and baseline fat-free mass but not ethnic group or baseline fat mass; the assessors generally thought that the resulting bias was quite modest (compared to the standard specified set of confounders), with no strong opinion about its direction. There were no differences in implementation of the exposure and outcome measures between the actual study and the idealised study, so no biases were recorded for these items. Only 39 out of the original 47 study entrants had the requisite follow-up data, and there was no comment in the published study about whether the girls omitted were similar to those included in the analysis. The assessors again did not have an opinion about the direction of the resulting bias. Finally, the study reported results from a stepwise regression, where non-significant effects had been excluded. The assessors regarded this as a proportional bias, generally likely to exaggerate the size of the reported association between PAEE and change in %BF.

For the external biases, the idealised version of the study is compared with the target setting ( The assessors generally thought that the PAEE measurement used in the study might diminish the association as compared to the target setting, but the other biases were generally thought to be small (proportional bias near 1).

The effect of adjusting for these biases, pooled over assessors, is shown in Table 3. The anticipated direction of the internal biases overall brings the correlation slightly nearer zero, and the confidence interval width increases to reflect the uncertainty in the biases.

The effect of the external biases is to further increase the confidence interval width, but the correlation estimate remains almost the same. These results are also shown in Figure 6 (second study).

A similar exercise was undertaken for each of the six studies in our example, leading to bias-adjusted results for each study and corresponding meta-analyses (Figure 6, Table 3).

The meta-analysis of unadjusted correlations gave a summary estimate of -0.04 (95% CI -0.21 to 0.14), but with substantial heterogeneity (I 2 =78%). This heterogeneity reflects both the different study designs and measures used, but also the effect of biases.

Adjusting for the internal biases reduced the heterogeneity (I 2 =15%). After also taking into account the external biases, there was no apparent heterogeneity (I 2 =0%) and the pooled correlation was -0.01 (95% CI -0.18 to 0.16). The overall conclusion from the bias-adjusted meta-analysis, now consistently expressed in terms of the correlation between PAEE and subsequent change in %BF, is that there is little or no association. To help interpretation, the pooled correlation can be converted to a regression coefficient; using published standard deviations of PAEE and change in %BF [START_REF] Delany | Energy expenditure and substrate oxidation predict changes in body fat in children[END_REF] , the estimated biasadjusted regression coefficient was -0.05 (95% CI -1.00 to 0.91) change in %BF per 1 MJ/d (239 kcal/d) increase in PAEE.

After adjustment for the biases, the relative weights the different studies receive in the meta-analysis change. For example, the fourth study [START_REF] Moore | Does early physical activity predict body fat change throughout childhood?[END_REF] in Figure 6 This in part reflects the uncertainty in the external biases for this study, since accelerometer counts were used as a measure of physical activity rather than a direct measure of PAEE, and skinfold thickness as a measure of body composition rather than %BF.

To investigate the consistency across assessors, we repeated the bias adjustments for each of the internal bias assessors separately, and then for each of the five external bias assessors. The results from the meta-analysis (Figure 7) show consistency across assessors, and do not change the overall conclusion based on a 'typical' assessor (Figure 6, Table 3).

Discussion

We have presented a method of obtaining an overall quantitative summary in a systematic review of observational studies, where numerous potential biases may operate. This is in contrast to the common approach where a vague and non-committal qualitative conclusion is drawn, because of the poor quality, reporting or relevance of the component studies. This apparently daunting task has been achieved by breaking it down into small manageable steps as follows: (i) define a target question, (ii) describe an idealised version of each study, (iii) separate internal from external biases, (iv) separate categories of these biases, (v) compile a checklist of the possible biases in each study, (vi) agree this checklist within a group of assessors, (vii) elicit the biases and their uncertainty from assessors independently for each category of bias for each study, and (viii) perform a bias-adjusted meta-analysis. Although this is a time-consuming process, there are no obvious alternatives, since empirical evidence on the size and uncertainty of all the biases is not available.

Other methods of adjusting for biases in meta-analysis have previously been proposed.

Some have adjusted for specific biases by specifying a model with parameters that together determine the bias in the target effect [START_REF] Eddy | Meta-analysis by the confidence profile method: the statistical synthesis of evidence[END_REF] [START_REF] Wolpert | Adjusted likelihoods for synthesizing empirical evidence from studies that differ in quality and design: effects of environmental tobacco smoke[END_REF] and uncontrolled confounding [START_REF] Greenland | Multiple-bias modelling for analysis of observational data (with Discussion)[END_REF] , using a full or approximate likelihood approach. Others have used distributions to represent directly the overall internal and external biases in the effect of interest in each study [START_REF] Spiegelhlater | Bayesian approaches to multiple sources of evidence and uncertainty in complex cost-effectiveness modelling[END_REF] . Like the former more complex methods [START_REF] Eddy | Meta-analysis by the confidence profile method: the statistical synthesis of evidence[END_REF][START_REF] Wolpert | Adjusted likelihoods for synthesizing empirical evidence from studies that differ in quality and design: effects of environmental tobacco smoke[END_REF][START_REF] Greenland | Multiple-bias modelling for analysis of observational data (with Discussion)[END_REF] , we model biases due to individual sources, but like the latter simpler method [START_REF] Spiegelhlater | Bayesian approaches to multiple sources of evidence and uncertainty in complex cost-effectiveness modelling[END_REF] we assume a direct form for the bias in the target effect. Our aim has been to present generic methods that can be used in a routine setting. Specifically, we have extended a previous approach for intervention studies where the outcome scale was relative risk [START_REF] Turner | Bias modelling in evidence synthesis[END_REF] , tailored to the context of observational studies where the outcome scale is correlation. In contrast, simple methods based on weighting by quality scores are known to be inadequate [START_REF] Greenland | On the bias produced by quality scores in meta-analysis, and a hierarchical view of proposed solutions[END_REF] .

For the example considered, we conclude that there is little or no relationship between physical activity and subsequent change in percent body fat in children, since the estimated pooled correlation is almost zero with tight confidence limits. While physical activity is no doubt important for various aspects of health, a policy focusing on increasing physical activity alone, without changing dietary habits, is unlikely to be effective in reducing obesity in children [START_REF] Wilks | Objectively measured physical activity and fat mass in children: a bias-adjusted meta-analysis of prospective studies[END_REF] . Before biases are considered, the results of the different studies were severely heterogeneous, which makes a pooled result very difficult to interpret. After adjusting for internal biases, the results are less heterogeneous across studies, but the pooled result still refers to the associations between the measures of physical activity and change in adiposity used in the different studies. After also adjusting for external biases, the correlation refers to that between PAEE and change in percent body fat, as in the target setting, and so is directly interpretable. The lack of heterogeneity between studies at this stage is what one would expect if the bias adjustment process was working as intended. The confidence interval for the pooled correlation now incorporates the uncertainty about the magnitudes of the biases, rather than the heterogeneity between studies as in the unadjusted analysis.

In the example presented, the pooled estimate and confidence interval are quite similar between the unadjusted and bias-adjusted meta-analyses.

In other examples we have undertaken the bias-adjusted pooled estimate or its precision were rather different from the unadjusted values. In a meta-analysis of intervention studies of the effect of routine antenatal anti-D prophylaxis on maternal sensitization, bias adjustments led to a similar overall odds ratio but a substantially wider confidence interval [START_REF] Turner | Bias modelling in evidence synthesis[END_REF] . In a meta-analysis of observational studies of the relationship between dietary energy density and subsequent changes in adiposity in children, bias adjustments made the correlation both more positive and more imprecise, suggesting that the near-null rather precise unadjusted association might be misleading [START_REF] Wilks | Dietary energy density and adiposity: a bias-adjusted meta-analysis of prospective studies[END_REF] .

There are of course limitations to the approach we have adopted which add uncertainty around the final conclusions. First, the elicited biases are subjective. Assessors may not agree with each other, and different assessors might have reached different judgements, including for example whether a particular bias is best represented as additive or proportional. Assessors might also not be consistent in how they judge the same bias on different occasions. We have minimised these problems by involving assessors who are experienced in the biases being judged (either methodological or subject-matter specialists), by using independent judgements from a group of assessors, and basing results on median pooling (which corresponds to a 'typical' assessor and eliminates extreme judgements). Moreover, in general, the judgements of the different assessors were quite similar (Figures 5 and7), and using more assessors would not have reduced the uncertainty about the views of a typical assessor. The method would be improved if it were better informed by empirical evidence, for example from meta-epidemiological studies [START_REF] Welton | Models for potentially biased evidence in meta-analysis using empirically based priors[END_REF] , or if authors themselves investigated the potential for bias in their studies [START_REF] Fox | Creating a demand for bias analysis in epidemiological research[END_REF] .

Analyses of individual participant data, when these are available for at least one of the contributing studies, can help in the assessment of biases, for example in investigating the potential impact of missing data, of adjustment for different confounders, or of categorising a continuous exposure [START_REF] Wilks | Dietary energy density and adiposity: a bias-adjusted meta-analysis of prospective studies[END_REF] .

A second issue relates to the limits necessarily placed on the process. We consider results in terms of correlations, since these can always be derived from just the sample size and reported p-value. Any approximations in extracting results from a published paper (for

F o r R e v i e w O n l y 16
example rounded p-values, uncertain sample sizes, or unclear analytical methods) can be considered as an additional internal bias. Although meta-analysis of correlations or regression coefficients is an established method [START_REF] Peterson | On the use of beta coefficients in meta-analysis[END_REF][START_REF] Prevost | Allowing for correlations between correlations in random-effects meta-analysis of correlation matrices[END_REF] and has been used before in the field of nutrition and energy expenditure [START_REF] Carpenter | Influence of body composition and resting metabolic rate on variation in total energy expenditure: a meta-analysis[END_REF] , it is conceptually a somewhat difficult scale on which to elicit biases. Hence we provided some guidance, derived from Figure 4, on what might be considered small or large additive biases. Our process assesses confounding bias relative to a pre-specified set of confounders, and considers only the published studies available and so does not address publication or dissemination biases [START_REF] Song | Extent of publication bias in different categories of research cohorts: a meta-analysis of empirical studies[END_REF] . It also does not adjust for biases resulting from within-person variability over time, in either the exposure or confounders, since these "multivariate measurement error" effects are very hard to judge. This is an example where parametric modelling of individual biases using empirical evidence [START_REF] Wolpert | Adjusted likelihoods for synthesizing empirical evidence from studies that differ in quality and design: effects of environmental tobacco smoke[END_REF][START_REF] Greenland | Multiple-bias modelling for analysis of observational data (with Discussion)[END_REF] would be more reliable. For these reasons, one needs to be somewhat cautious in making a causal interpretation from the summarised results.

The work we have presented could be further developed, and it would be beneficial if our methods were applied to other examples by independent investigators in the future. Webbased software could be developed to aid the elicitation process and subsequent analysis.

Ideally our approach needs validation, either against empirical evidence or for example in the context of a systematic review that pre-dates a planned large definitive study, where the design of the latter provides the relevant target setting. Most fundamentally, experience with the method needs to be gained in terms of real policy decision making, for example in national public health intervention assessments [START_REF]Developing NICE public health guidance[END_REF]

Population bias

Study subjects in idealised study drawn from population identical to target population, with respect to age, sex, health status etc.?

Exposure bias (external)

Exposure in idealised study identical to target exposure?

Outcome bias (external)

Outcome in idealised study identical to target outcome?

Timescale bias

Follow-up time in idealised study identical to target follow-up time? [START_REF] Delany | Energy expenditure and substrate oxidation predict changes in body fat in children[END_REF][START_REF] Figueroa-Colon | Paternal body fat is a longitudinal predictor of changes in body fat in premenarcheal girls[END_REF][START_REF] Johnson | Aerobic fitness, not energy expenditure, influences subsequent increase in adiposity in black and white children[END_REF][START_REF] Moore | Does early physical activity predict body fat change throughout childhood?[END_REF][START_REF] Salbe | Assessing risk factors for obesity between childhood and adolescence: II. Energy metabolism and physical activity[END_REF][START_REF] Treuth | Predictors of body fat gain in nonobese girls with a familial predisposition to obesity[END_REF] for the association between physical activity and subsequent change in adiposity on the correlation scale. Results are shown unadjusted for any biases, adjusted for internal biases, and adjusted for both internal and external biases. : Meta-analysis of six studies [START_REF] Delany | Energy expenditure and substrate oxidation predict changes in body fat in children[END_REF][START_REF] Figueroa-Colon | Paternal body fat is a longitudinal predictor of changes in body fat in premenarcheal girls[END_REF][START_REF] Johnson | Aerobic fitness, not energy expenditure, influences subsequent increase in adiposity in black and white children[END_REF][START_REF] Moore | Does early physical activity predict body fat change throughout childhood?[END_REF][START_REF] Salbe | Assessing risk factors for obesity between childhood and adolescence: II. Energy metabolism and physical activity[END_REF][START_REF] Treuth | Predictors of body fat gain in nonobese girls with a familial predisposition to obesity[END_REF] for the association between physical activity and subsequent change in adiposity on the correlation scale. Results are shown using the internal bias adjustments from each of 6 internal bias assessors (IA1-IA6) separately, the overall internal bias-adjusted result, and adjusted for internal and external biases using the external biases from each of 5 external bias assessors (EA1-EA5) separately, and the overall result adjusted for both internal and external bias.

  of particular biases relevant to an individual study[START_REF] Welton | Models for potentially biased evidence in meta-analysis using empirically based priors[END_REF] . The magnitude of biases always of course remains uncertain, and quantifying this uncertainty is part of the elicitation process. Here we extend this work on intervention studies to the more problematic context of observational studies.

  coefficient and a p-value, our derived correlation agreed well with the published value.

  matter specialist and one statistician reviewed each study's publication, defined the idealised version of the study, and completed the checklist in Figure2by qualitatively describing each potential source of bias. The internal biases were then assessed by a group of six quantitatively-trained assessors (primarily statisticians) and the external biases by a group of five subject-matter specialists (primarily physical activity Having read the paper and checklist, the group agreed any modifications to be made to the checklist, but avoided discussing the seriousness or magnitude of potential biases. Each bias was classified by the group as operating either additively or proportionally on a correlation scale. An additive bias could introduce a correlation where none were in truth present; examples included inadequate control of confounding or biases caused through missing data or loss to follow-up. A proportional bias would change the magnitude but not the sign of the correlation, thus exaggerating or attenuating a true effect; examples included differences between populations, and biases caused by undertaking stepwise regression and retaining only statistically significant predictors.

  in a similar way, indicating exaggeration or attenuation of effect.

  unadjusted meta-analysis but only 2% in the fully adjusted meta-analysis.

Figure 1 : 24 Figure 2 : 25 Figure 2

 1242252 Figure 1: Overview of bias adjustment method: separating internal and external biases

26 Figure 3 : 27 Figure 4 :Figure 5 : 29 Figure 6 :

 2632745296 Figure 3: Elicitation scales for additive and proportional biases

30 Figure 7

 307 Figure7: Meta-analysis of six studies[START_REF] Delany | Energy expenditure and substrate oxidation predict changes in body fat in children[END_REF][START_REF] Figueroa-Colon | Paternal body fat is a longitudinal predictor of changes in body fat in premenarcheal girls[END_REF][START_REF] Johnson | Aerobic fitness, not energy expenditure, influences subsequent increase in adiposity in black and white children[END_REF][START_REF] Moore | Does early physical activity predict body fat change throughout childhood?[END_REF][START_REF] Salbe | Assessing risk factors for obesity between childhood and adolescence: II. Energy metabolism and physical activity[END_REF][START_REF] Treuth | Predictors of body fat gain in nonobese girls with a familial predisposition to obesity[END_REF] for the association between physical activity and subsequent change in adiposity on the correlation scale. Results are shown using the internal bias adjustments from each of 6 internal bias assessors (IA1-IA6) separately, the overall internal bias-adjusted result, and adjusted for internal and external biases using the external biases from each of 5 external bias assessors (EA1-EA5) separately, and the overall result adjusted for both internal and external bias.

  [START_REF] Eccles | Research designs for studies evaluating the effectiveness of change and improvement strategies[END_REF] statistic[START_REF] Higgins | Measuring inconsistency in meta-analyses[END_REF] , which estimates the percentage of variation between study results explained by true heterogeneity rather than chance. Values of I 2 close to 0% represent little heterogeneity beyond that compatible with chance. Summary estimates and intervals were converted back to the correlation scale for presentation.

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Table 2

 2 , there is no bias for this component. The potential biases relate to differences in population (age range, gender and country), PAEE being measured under laboratory rather than free-living conditions, and a slight difference in follow-up interval.

	and target setting
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); the elicited external biases, which were all considered as proportional, are shown in Figure

5

(bottom). Since %BF was the outcome in both the idealised study

  . These methods have been developed, for

	example employing external empirical data, to address misclassification of exposure or
	outcome
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Table 1 :

 1 Characteristics of one example longitudinal study[START_REF] Figueroa-Colon | Paternal body fat is a longitudinal predictor of changes in body fat in premenarcheal girls[END_REF] of physical activity level and subsequent change in adiposity, and data extracted

	. It is exactly in this kind

Table 2 :

 2 Target setting for meta-analysis, and the idealised version of one example study[START_REF] Figueroa-Colon | Paternal body fat is a longitudinal predictor of changes in body fat in premenarcheal girls[END_REF]

		Target setting	Idealised version of one example
			study 18
	Population	General population of children	Normal weight girls aged 5-9
		aged 4-11years in the UK	years from Alabama, USA
	Exposure	Free-living PAEE objectively	PAEE measured by whole-room
		measured at baseline	indirect calorimetry (laboratory
			conditions)
	Outcome	Subsequent change in %BF,	Subsequent change in %BF
		objectively measured at baseline	measured at baseline and follow-
		and follow-up	up by dual-energy X-ray
			absorptiometry
	Time interval	Outcome assessed over a 2-year	Follow-up at 1.6 years
		period
	%BF percent body fat, PAEE physical activity energy expenditure

Table 3 :

 3 Unadjusted and bias-adjusted correlations between baseline physical activity level and change in percent body fat for one example study[START_REF] Figueroa-Colon | Paternal body fat is a longitudinal predictor of changes in body fat in premenarcheal girls[END_REF] , and meta-analysis of unadjusted and bias-adjusted correlations (95% CI)

		Correlation for one	Meta-analysis of correlations
		example study 18	in all six studies; I 2 for
			heterogeneity
	Unadjusted	-0.33 (-0.59 to -0.01)	-0.04 (-0.21 to 0.14); I 2 =78%
	Adjusted for internal biases	-0.26 (-0.62 to 0.19)	0.00 (-0.18 to 0.19); I 2 =15%
	(corresponds to idealised
	versions of each study)
	Adjusted for internal and	-0.27 (-0.68 to 0.26)	-0.01 (-0.18 to 0.16); I 2 =0%
	external biases (corresponds
	to target setting, Table 2)

Acknowledgement

This work was supported by the UK Medical Research Council Population Health Sciences Research Network (grant number PHSRN27). We thank two referees for useful comments. SGT is guarantor for the paper.

Confounding bias

Appropriate choice of confounders (i.e. based on importance rather than convenience)? Adjustment made for all known important confounders? [1] Objective method of measuring confounders? Confounders measured accurately? Appropriate timing for measuring confounders?

Exposure bias (internal)

Was the exposure measure appropriate? [2] Objective method of measuring exposure? Exposure measured accurately? Appropriate timing for measuring exposure? Was the way that the exposure measure was used in the analysis appropriate?

Attrition bias

Are the results unlikely to be affected by losses to follow-up? Are the results unlikely to be affected by exclusions from analysis (e.g. because of extreme values or missing values of confounders)?

Outcome bias (internal)

Was the outcome measure appropriate? [3] Objective method of measuring outcome? Outcome measured accurately? Appropriate timing for measuring outcome? Was the way that the outcome measure was used in the analysis appropriate?

Other bias suspected

Was the statistical analysis appropriate? [1] Known important confounders could be listed here. [2] Appropriate measures of exposure could be listed here. [3] Appropriate outcome measures could be listed here.