Of Lemmings and Mussels: Trophic Cascade Drives Population Dynamics of Long-Tailed Ducks Breeding in Siberia

Migratory animals experience very different environmental conditions at different times of the year, i.e., at the breeding grounds, during migration, and in winter. The long-tailed duck Clangula hyemalis breeds in the Arctic regions of the northern hemisphere and migrates to temperate climate zones, where it winters in marine environments. The breeding success of the long-tailed duck is affected by the abundances of predators (mainly Arctic fox Alopex lagopus) and their main prey species, lemmings Lemmus sibiricus and Dicrostonyx torquatus, whose population uctuation is subject to climate change. In the winter quarters, long-tailed ducks mainly eat the blue mussel Mytilus edulis. We examined how North-west Siberian lemming dynamics affect long-tailed duck breeding success via predation pressure and how nutrient availability in the Baltic Sea inuences long-tailed duck population size via mussel biomass and quality. The long-tailed duck population dynamics was predator-driven on the breeding grounds and resource-driven on the wintering grounds. Nutrients from fertilizer runoff from farmland stimulate mussel stocks and quality, supporting high long-tailed duck population sizes. The applied hierarchical analysis combining several trophic levels can be used for evaluating large-scale environmental factors that affect the population dynamics and abundance of migrants from one environment to another. in the previous year, and variability in precipitation and temperature in North-western Siberia inuenced the proportion of juveniles at the wintering grounds in the southern Baltic Sea. For the processes occurring at the wintering grounds we analysed how nutrient amounts, in the form of dissolved nitrogen and phosphorus, and winter climate inuenced long-tailed duck juvenile proportions and spring migration population size. Using a hierarchical Bayesian 49,50 model, implemented with the above listed environmental variables, we show how lemming dynamics affected the proportion of juveniles in autumn and winter and how these together with nutrient availability explained spring migration numbers of the long-tailed duck the following spring. This study exemplies how to analyse complex dynamical systems based on heterogeneous and partly incomplete time-series data.


Introduction
Migratory organisms spend part of the year at the breeding grounds before moving to winter quarters that are often located thousands of kilometres away 1 . Changes in environmental conditions at the breeding grounds or winter quarters in uence performance of migrants in the same or the other habitat 2,3 . The long-tailed duck Clangula hyemalis is globally threatened and classi ed as Vulnerable on the IUCN Red List. It winters in North Europe and migrates along the Gulf of Finland to and from the breeding areas in Western Siberia 4 . Spring migration counts at Söderskär, Finland in the 1940s and 1950s showed a 90% reduction of the long-tailed duck population in the Baltic Sea wintering area 5,6 . During the Second World War, oil spills were suggested to be the main reason for the decline 5,7,8 . The wintering population gradually recovered as environmental conditions improved, with over half a million migrants. Spring counts peaked during 1991-1996 in Finland 8 and Estonia 9 , followed by severe declines during the 2000s with recent numbers of migrants being only one-third of peak-year numbers (190,000 vs. 570,000 individuals). The North-west Siberian/North European winter population of the long-tailed duck was estimated at 4,700,000 birds based on co-ordinated surveys 1992-1993 6,10 , of those numbers the Baltic Sea winter population declined from 4,272,000 to 1,482,000 birds until 2009 6 .
Population characteristics of many species of aquatic birds that breed in the Arctic covary with population cycles of Arctic lemmings (Lemmus sibiricus and Dicrostonyx torquatus). These rodents are important prey for Arctic foxes, skuas and raptors, and thus form an essential component of the Arctic ecosystem 11 . Vole and lemming populations exhibit cyclic dynamics, particularly in northern regions 12 , with population peaks occurring every 3-5 years [13][14][15] often followed by almost total absence of individuals 13,15−18 . Years with high abundance of lemmings lead to an increase in predator populations that show cycles that track those of their rodent prey [19][20][21][22] such that predators are abundant the year following a rodent peak year while their populations are low after such lemming years 16,23 . In the year following a rodent peak, when predator populations are high, these predators exploit alternative prey 8,24−28 such as bird eggs and young of species such as the long-tailed duck 26,29,30 , leading to large-scale breeding failure in these birds 26,31,32 and fewer juveniles recruiting into the winter population 8, 15,33 .
North-west Siberian/North European long-tailed ducks have declined since the 1990s 6 , coinciding with reductions in lemming abundances throughout the Arctic and northern alpine areas [34][35][36] that has been linked to global climate warming, which particularly affects the Arctic. Indeed, changes in snow conditions due to climate change may explain why lemming populations show fewer peaks 37 . Snow hardness and humidity in the High Arctic, in uenced by changing weather conditions, are critical for winter survival and reproduction in lemmings [37][38][39] .
The blue mussel, Mytilus edulis, constitutes the main food item for long-tailed ducks during winter [40][41][42] . Wintering success of long-tailed ducks declines with declining stocks of blue mussels Mytilus edulis in the southern Baltic Sea 43 . Mussel abundance is affected by climate, with cold winter temperatures stimulating reproduction in blue mussels, which may increase mussel stock sizes and thus sea duck populations a few years later 44 . Mussel abundance is also affected by fertiliser runoff in two ways.
Fertilizer runoff from farmland increases dissolved nutrient levels, which increases primary production in the Baltic Sea 45,46 and stimulates a bottom-up trophic cascade in coastal areas 44,47,48 . However, this also causes hypoxia and bottom death, which reduces abundance and availability of mussels in large areas of the Baltic Sea where there is poor mixing or in ux of fresh, oxygenated water 45 and where longtailed ducks spend the winter.
Here we identify and quantify the ecological processes and their contributing environmental factors that in uence the population dynamics of long-tailed ducks during both breeding and winter. For processes occurring at the breeding grounds, we tested how predation risk, estimated from lemming abundances in the previous year, and variability in precipitation and temperature in North-western Siberia in uenced the proportion of juveniles at the wintering grounds in the southern Baltic Sea. For the processes occurring at the wintering grounds we analysed how nutrient amounts, in the form of dissolved nitrogen and phosphorus, and winter climate in uenced long-tailed duck juvenile proportions and spring migration population size. Using a hierarchical Bayesian 49,50 model, implemented with the above listed environmental variables, we show how lemming dynamics affected the proportion of juveniles in autumn and winter and how these together with nutrient availability explained spring migration numbers of the long-tailed duck the following spring. This study exempli es how to analyse complex dynamical systems based on heterogeneous and partly incomplete time-series data.

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This article does not contain any experiments on animal subjects performed by any of the authors.
Observations of long-tailed ducks Spring migration counts of long-tailed ducks have taken place at Söderskär (60°07´N, 25°24´E, Fig. 1), Gulf of Finland each spring 1968 -2014. These counts are generally assumed to re ect population size 8 , and there is no indication that the main migration corridor for Baltic long-tailed ducks has changed during the study. However, wind direction and velocity at Söderskär can force migrating birds off their preferred migration route 51,52 , thereby causing variation in migrant bird counts. To control for this error source, we used daily wind direction and velocity measures at Söderskär during spring migration counts.
We developed a weighted wind direction and velocity factor to be implemented into the observation model of the long-tailed duck to correct long-tailed duck population size estimates by reducing noise due to the effect of wind on spring migration counts 53,54 (details in Supplementary Methods).
We estimated recruitment from the number of juvenile (1st to 2nd calendar year individuals) in relation to the number of adult female birds shot by hunters in autumn and winter (juvenile proportion in year t refers to bags from October in year t until February in year t+1) from the Danish Wing Survey data 55,56 and related this to lemming abundance (of the year t-1) in North-western Siberia during breeding and climate conditions in breeding and wintering grounds (Supplementary Methods).

Environmental variables
(1) Nutrient levels. Dissolved inorganic nitrogen (DIN), considering the sum of the oxidized nitrogen and ammonium pool, and phosphorus (DIP) have been estimated for the Baltic Sea major basins each year from 1970 to 2016 46 . We tested the effects of total DIN and DIP recorded from the southern Baltic Sea, the Baltic Proper and the Danish Straits major basins 46 (Fig. 1), covering the main wintering area of the long-tailed duck, on the population dynamics of this species. Nutrient effects can be positive, because additional DIN stimulates primary production and thereby growth of mussels, the primary food of this species during winter [40][41][42] , or negative, because of hypoxia and bottom death that can occur at low DIN:DIP ratios 46 in areas of poor mixing 45 . We used the total annual amount of fertilizer applied by Danish farmers during 1965-2016 as a predictor of marine nutrient pools in the southern Baltic Sea because this variable is a reliable proxy for total nitrogen runoff into the marine environment 47  (2) Lemming abundances. The majority of long-tailed ducks wintering in the Baltic Sea originate from the part of North-western Siberia including the Yamal and Taimyr Peninsulas 57 . Lemming abundance across the entire breeding area should in uence the dynamics of the long-tailed duck population, but such data are lacking. However, information on lemming abundance exists from three separate, long-termed surveys in the Western Taimyr Peninsula, North-western Siberia, which allow us to quantify regional population changes in lemmings (Fig. 1 (3) North-west Siberian climate. We extracted annual (1965-2017) monthly climatological variables (precipitation and temperature) from a database of high spatial resolution global weather and climate data 58,59 (data downloaded from www.worldclim.org) for the three regions in Western Taimyr for which lemming abundance data were available. Climate variation was averaged for the three areas corresponding to the three rodent surveys (Fig. 1). We tested if climate variability affected rodent population sizes 37 , which may in uence the breeding success and population dynamics of the longtailed duck 8 . Similarly, for estimating climate effects on recruitment, we averaged annual precipitation and temperature scores for North-western Siberia (Fig. 1). For processing the climatological map data, we used the R package 'raster' 60 . winter temperatures and high levels of precipitation in the Baltic Sea 61 . NAOI data were obtained from https://climatedataguide.ucar.edu/climate-data/hurrell-north-atlantic-oscillation-nao-index-pc-based. We estimated the effects of winter NAOI on the proportion of juveniles killed by Danish hunters and on population dynamics of long-tailed ducks.
(5) Abundance and quality of blue mussels. Long-tailed ducks feed on blue mussels. Though no longterm data exist for mussel stocks in the Baltic Sea, such data are available from the Wadden Sea although this is outside the core winter grounds of the long-tailed duck 6 . Two arguments justify the use of mussel stock data from the Wadden Sea as a proxy for the missing mussel stock data from the Baltic: First, population trends of mussel stocks are comparable over areas covering several hundred kilometres 63 , and, second, the eider Somateria mollissima, another sea duck, also feeds primarily on blue mussels and winters in the Baltic Sea. Winter body condition of eiders in the Baltic is positively correlated with mussel stock estimates for the Wadden Sea 64,65 .
In the Baltic Sea, in the western part of the Finnish Archipelago, blue mussels grow from larvae to 10 mm within 3-4 years 66 so we expect mussels in the southern Baltic Sea ecosystem to attain the size of 9 mm preferred by long-tailed ducks 43 in about the same period after spawning. Annual blue mussel stocks were estimated for the intertidal zone of the Danish (1986-2007, and 2017) and Schleswig-Holstein (Germany, 1998-2015) parts of the Wadden Sea ( Fig. 1) during autumn by ground sampling on mussel beds and estimation of mussel beds from aerial photography 67,68 . Mussel stock data are available for both areas from1998-2007 and annual biomass showed a positive correlation between the areas (r = 0.920, N = 10).
Data were available for blue mussel quality, measured as esh to shell ratio 69 , each autumn from 1998 to 2013 from 19 sites in the Baltic and Wadden Sea. The reduction in mussel esh content during winter (October-March) due to temperature-dependent respiration was estimated for the Baltic Sea 70 . This allowed us to estimate long-tailed duck food resources by predicting mussel numbers and quality as a function of the amount of fertilizer applied by Danish farmers (see Supplementary Methods) and winter and spring temperatures along the Wadden Sea coastline, using the same global climate database as described above (see "North-west Siberian climate").

Hierarchical modelling
We used an integrated hierarchical model 71 , which is a complex stochastic system partitioned into a dependent sequential set of simpler sub-models dynamically affecting the performance of the main system of interest 71 . In the following system, the state-space model, equation (1), expressing log-scale long-tailed duck dynamics (1968-2014) is written brie y as: in which n ( t ) is the population size estimate of long-tailed ducks in year t that has a negative binomial error structure 49,72 around the expected population size n ( t ) . R ( t − 1 ) = 1 + p ( t − 1 ) is a variable for recruitment based on estimated juvenile proportion (p ( t − 1 ) ), from equation (2), in autumn and winter preceding spring migration. Terms a and ϵ ( t ) are intrinsic growth rate (intercept) and random environmental disturbance terms, respectively. cis a density-dependent parameter whose value can vary from zero to one. Dissolved nitrogen DIN ( t − 1 ) and phosphorus DIP ( t − 1 ) describe annual nutrient pools in the southern Baltic Sea (outputs from equation (4a)). The nutrient series implemented into equation (1) were scaled to have a mean of zero and variance of one. w D weights nutrient effects and β R quanti es the effect of juvenile proportion in autumn and winter on subsequent spring migration counts; these parameters are beta distributed varying between zero and one (uninformative prior beta-distribution with α = 1 and β = 1). β D is normally distributed regression coe cient. The observation model for equation (1) is speci ed with Gaussian errors and a priori assumed environmental disturbances (wind) as: , where γ is a parameter for east-west aspect winds x ( t ) , and τ is the standard deviation of a random observation-error process (Supplementary Methods). The joint-likelihood 71 of the integrated hierarchical model combining equations (1), (2) and (3) is summarized with Supplementary Table S1.
We constructed a logit model to generalize the variations of juvenile proportions during the period 1967-2017, based on the number of juveniles per adult female shot by Danish hunters: Here, p ( t ) is the expected proportion of juveniles (in autumn and winter) affecting subsequent spring migration numbers (population size n ( t + 1 ) , equation (1)) of long-tailed ducks. z ( t − 1 , j = 1 ) is an estimate for (log) lemming population size in the previous year based on the longest series of lemmings (Kara Sea, j = 1) from equation (3).
terms quantify the effects of precipitation (k = 1) and temperature (k = 2) in North-western Siberia in May and June on juvenile proportions, and these were weighted, e.g. for precipitation (P), as S t , 1 = w June , 1 1 − P May + w June , 1 P June . a p and b X are estimated regression coe cients, and r p ( t ) controls for random effects (full description in Supplementary Methods).
Lemming population dynamics z ( t , j ) estimated using three separate population time-series (j) of lemming abundances in the Western Taimyr Peninsula (1965-2017, t = 0 refers to 1965) was estimated based on the following state-space model:

Results
The output of the hierarchical Bayesian state-space models in long-tailed ducks and lemmings, as well as generalized linear models for juvenile proportions in long-tailed ducks and nutrients (DIN and DIP), are reported in Supplementary Tables S1a-c and S2, and Figures 2-4 visualize estimated dynamical trends and relations between model variables. Figure 5 summarizes the directions and strengths of variable effects and causalities between lemmings and long-tailed duck juvenile proportions, and spring migration counts {n}_{\left(t\right)} as estimated with equations (1) -(3). For most parameters, Bayesian probability, p-value (or degree of belief, cf. statistical signi cance) was high implying that the probability for a parameter coe cient being smaller or, respectively, larger than zero converged close to one.
The magnitude of lemming population peaks in the western Taimyr Peninsula have declined over time (Fig. 2) and the 3-year cyclic regularity was broken after 1994 (Supplementary Table S1a, Supplementary Methods). Equation (3) shows that lemming populations declined with increasing autumn precipitation in the previous year and increased weakly when early summer precipitation was high (Supplementary Table  S1a). The autumn precipitation affected particularly the Kara Sea population. The estimates for climate effects were highly convincing, with climate variation explaining 29% of the total lemming population variance. Of these climate variables, autumn precipitation had the stronger effect, explaining 84% of the lemming population variation due to climate (Supplementary Table S1a).
Colder and wetter springs and summers in North-western Taimyr led to fewer long-tailed duck recruits on the wintering grounds in the Baltic. This effect was stronger for variation in precipitation (Fig. 3a) than temperature (Fig. 3b) and was the strongest for May precipitation. Together the North-west Siberian climate variables explained 26% of the total variation in juvenile proportions. The proportion of juveniles declined the year following lemming peaks (Fig. 3c), implying that lemming population troughs that followed abundance peaks were poor years for long-tailed duck recruitment. Lemming population variation explained 9% of juvenile proportions (Supplementary Table S1b). High NAOI was followed by declines in juvenile proportion with a three-year lag (Fig. 3d), suggesting poor recruitment three years after a warm winter. Together, the climate parameters (Fig. 3) explained 39% of the total variance estimated for the long-tailed duck juvenile proportion (Supplementary Table S1b).
The observation process variation (i.e., sampling error or observation error) of spring migration counts was affected by east-west aspect winds such that observed counts decreased with strengthening west winds during the annual census period. The details of wind effects on the observations, which delineated the performance of the population model given in equation (1), are reported in Supplementary Methods. After correcting for measurement errors, number of spring migrant long-tailed ducks showed relatively smooth annual variation and increased from the end of the 1960s up to 1991 followed by a steep decline from 1992 until the end of the 2000s. Some recovery took place in the beginning of the 2010s (Fig. 4d).
The whole system modelled for and around the long-tailed duck is summarized in Fig. 5.
Application of more fertilizer to Danish farmland led to higher DIN and DIP in the southern Baltic Sea the following year. This 1-year lagged effect (lag=1) was returned from 94.25% of the simulation updates (Supplementary Table S2).
High winter temperature was followed by lower mussel stocks in the Wadden Sea 2-3 years later (more weight for 2-year lag). Mussel biomass increased with the increasing use of fertilizers (Fig. 6a) in previous years, most strongly 1-2 years before. Simulation chains revealed frequencies for the lags of 0,  Table S3a). More demographic variance caused by local disturbances affecting mussel dynamics was found for the population in the Danish than the Schleswig-Holstein part of the Wadden Sea (Supplementary Table  S3a). Population trends were not perfectly parallel in the two areas (Fig. 6b). Together, mussel biomasses showed large variation during the period 1986-1998, entering steep decline from the turn of the 1990s and recovering from 2011 up to 2017 (Fig. 6b). The quality of blue mussels in autumn in terms of (log) esh/shell ratio of the total biomass, i.e. {\begin{array}{c}logit\end{array}f}_{p\left(t\right)} from equation (6), increased with the previous winter's temperature (19% variance partition proportion, Supplementary Table S3b) and fertiliser use over the two previous years (42% variance partition proportion, Fig. 7a, b) but spring temperatures had no effect on mussel quality. These results suggest that mussels in the Wadden Sea were in better condition, as measured in autumn, during the years of high nutrient availability and after warm winters. The system modelled for the blue mussel esh/shell ratio and biomass is summarized in Fig. 8.

Discussion
This integrated hierarchical model for the long-tailed duck population investigates a complex stochastic system affected dynamically by sub-systems that are also stochastic and regulated by independent variables 71,76 . This model allowed us rst, to correct for population estimate errors due to variation in wind velocity and direction at Söderskär, Gulf of Finland, during spring migration, which accounted for 51% of the total observation error variance. This result underlines that ignoring wind effects on counts would have led to serious misspeci cations in the state-space model for long-tailed ducks.
This model allowed us to identify and quantify the variables contributing to population size variation of the long-tailed duck by using sub-models for trophic processes driven by nutrient and climate factors occurring at both the breeding and the wintering grounds. We were able to attribute 51% of total variation in long-tailed duck population size, estimated from spring migration counts, to ecological processes occurring at the breeding or overwintering grounds (Fig. 5). The processes that in uence long-tailed duck populations in these two habitats are driven by different ecological interactions, for example predatordriven on the breeding grounds 26,77,78 and resource-driven on the wintering grounds 44,64,65,79 with very different climatic and environmental controls, for example, precipitation that in uences lemming dynamics on the breeding grounds and temperature and nutrient runoff from the land that affect mussel reproduction, growth and survival on the wintering grounds.
On the breeding grounds, lemming population cycles affected the number of new recruits of long-tailed ducks, estimated from the proportion of juvenile birds killed by hunters in the winter. The year following high lemming years have few recruits while those following low lemming years show many (Fig. 3c). This is expected if predator numbers are high the year after a lemming peak and these predators switch to eggs and nestlings if lemmings are rare 11,26,80 . Western Taimyr lemming dynamics was driven by climate, particularly autumn and winter precipitation 37 (Fig. 5). High autumn precipitation was associated with low lemming population size the next year. Heavy autumn precipitation may cause ice formation at the soil surface in the subnivean space, reducing the insulation properties of snow 38,39 , which leads to poor lemming winter success 18,37,81−83 .
High late spring and early summer precipitation with low temperatures in North-western Siberia were directly related to decreases in juvenile proportions in long-tailed ducks (Fig. 5). This may be linked to varying nesting areas and predation pressure during snow melt: more precipitation during cold springs delays snow melt 84,85 , which limits open areas for nesting and thus enhances predation on birds' nests during early breeding season 85 .
Recruitment, as estimated from juvenile proportion of hunters' returns, though it is the raw material of population growth and renewal, explained 5% of variation in spring migration numbers. This is unremarkable for a long-lived species like the long-tailed duck 86 , where adult survival drives population dynamics more than does fecundity 87-90 . Furthermore, juvenile proportion of hunters' returns is probably representative of the population. Long-tailed duck juveniles resemble mature females in autumn and winter so hunting pressure is unlikely to be age dependent, as for some other quarry species 91 .
On the wintering grounds long-tailed ducks are feeding mainly on blue mussels 42,43,70 . Mussels reproduce more during cold than warm winters 44,70 . NAOI values that represent variation in winter temperatures showed the strongest association with juvenile long-tailed duck proportion at the wintering grounds in the southern Baltic Sea three years later. If mussels require two or three years to reach the preferred size for long-tailed duck food items 43,66 , then food on the wintering grounds will be scarce two or three years after a warm winter but abundant two or three years after a cold winter. In the Wadden Sea the best tting lag between cold winters and mussel biomass increase was two years (Fig. 8). Years of high food abundance on the wintering grounds should enhance female condition, increasing their fecundity and maternal investment 44,64 . Thus we would expect, as we nd, higher nesting and edging success three years after cold winters.
We detected effects of fertilizer runoff on long-tailed duck populations via the trophic cascade primed by dissolved nutrients 46 . Long-tailed duck populations increased with increasing DIN that translated into increased biomass and quality of mussels. However, the opposite trend was observed for DIP because increased DIP led to larger and more long-lasting hypoxia and bottom death 45,46,92  In conclusion, we used hierarchical Bayesian models to quantify the effects of population and observation processes on the estimation of the abundance of the long-tailed duck, an Arctic migratory bird. This approach allowed us to estimate the amount of variance accounted for by environmental conditions both the breeding and wintering grounds. At the Arctic breeding ground, predation limits nesting success when lemming predators shift to alternative prey such as the long-tailed duck. In the marine winter quarters fertilizer runoff from agriculture drives a bottom-up trophic cascade, stimulating food availability by increasing primary production and thereby mussel biomass and quality. However, phosphorus overload could limit food availability by inducing hypoxia and bottom death. These conditions at the wintering grounds affect juvenile survival and adult female body condition before spring migration to the Arctic breeding grounds. The originality of this study resides in our ability to quantify the effects at both breeding and wintering areas that present very different ecological and environmental conditions and challenges. This approach should be useful for analysing the dynamics of other migratory species confronted with divergent environmental conditions in winter and summer habitats.

Declarations Data availability
The data supporting the results of this study are provided as Supplementary Data (R workspace list-type objects printed as "data_*.docx" and "inits_*.docx" les) referenced in the Bayesian analyses (section "Program codes" in Supplementary Methods).

Acknowledgments
In Söderskär the following persons, whom we thank sincerely, have conducted Arctic migration censuses, and offered data for research: Esa Nikunen, Markku Nygård, Olli Paavilainen, Pekka Pamilo, Martti Santakari and Karl Selin. Several tens of other bird observers contributed to migration counts and the list of names is too long to mention here. Roland Vösa digitized the wind data from the original notebooks from Söderskär observatory. Also thank to Jakob Strand for data of mussel esh content collected during 1998-2013, and Thomas Kjaer Christensen for data of the Danish wing survey. We sincerely thank Jacqui Shykoff for providing suggestions, comments and editorial help on the nal version of the manuscript.    Summary of model parameters affecting long-tailed duck (LtD) Clangula hyemalis population size (Spring counts). Dissolved nitrogen (DIN) and phosphorus (DIP) in the southern Baltic Sea are affected by fertilizer use in the Danish farmland. Climate variables affect lemming Lemmus sibiricus and Dicrostonyx torquatus abundances and juvenile proportions of LtD. "Precipitation" and "Temperature" refer to Northwestern Siberia in June and July, and "NAOI" is the North Atlantic Oscillation Index. Precipitations in the Western Taimyr Peninsula affect lemmings. Red/blue arrows indicate a negative/positive effect. Solid lines indicate direct effects. Trophic cascades drive indirect effects from one trophic level to another (long dash lines). Mechanisms behind Siberian climate effects (short dash lines) on lemmings and juvenile proportions were out of the scope of this study and were not included in the general discussion. Black arrows denote random errors from unknown sources and circle arrow illustrates density dependence.
Percentages for DIN and DIP describe direct fertilizer plus smoother effects based on the fertilizer series.
Variance partition proportions (%) shown for the predictors. The sampling error proportion of the total LtD system (including sampling error variance) is in parentheses. Long-tailed ducks (female and hatchlings, and male and female on the sea), lemming L. sibiricus, and fertilizer-use symbol (crop) drawings by Kati Rintala.   Predicted, estimated using equation (6) and observed mussel quality from samples from the Baltic and Wadden Sea, given as esh/shell ratio, as a function of (a) Fertilizer application to Danish farmland in the previous year: In red, predictions with 68% con dence intervals. Observations from the Danish Wadden Sea are in blue. (b) Time in years from 1998-2013: The black line represents the predictions with 68% con dence limits in grey.