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Detailed model description
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Overview
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The yearly metapopulation demography is simulated based on four events: reproduction,
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dispersal, survival and aging, in this order. Reproduction, dispersal and survival are based on
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population density and habitat quality. Perceived habitat quality is controlled by time and
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location specific temperature, and the individual’s genome. As such we simulate the effect of
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stochastic temperature zone shifts on the distributions and individual numbers of the different
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genotypes in the metapopulation.
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Landscape
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The landscape we use in the model has dimensions of 15 km from east to west by 2000 km
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from north to south. The east and west side are merged to create a cylindric landscape. The
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landscape contains 3000 circular habitat patches of 50 ha each, so consists of a total of 5%
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habitat. When generating the landscape, patches were placed in random positions in the
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landscape, yet only allowed if they were at a minimum distance of 150 m from existing
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patches. Five landscape variants with different habitat positions were randomly generated in
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this way.
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Climate
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Climate is incorporated in the model through habitat quality. Where climate is optimal for the
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species, habitat quality equals 1, and where climate is unsuitable for the species, habitat
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quality is 0 (see equation HQ below). Climate change scenarios are based on temperature
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increase predictions (I °C year-1) by the Hadley Centre of 0.0167 and 0.0333 °C year-1, and
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we also included a scenario with a temperature increase of 0.084 °C year-1. Besides, the used
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scenarios include weather variability increase assumptions as temporal stochasticity in the
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temperature (the current standard deviation of the average temperature t (°C), 0.59 °C
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(Schippers et al., 2011)). Climate in our model is thus defined as the temperature in year t and
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at location Y. Climate change is then the speed with which temperature isoclines travel north
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(T km year-1) and the yearly fluctuation of these lines (σd km). We use a climatic gradient
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from south to north of G (ºC km-1) to get to:
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T = I / G, and
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𝝈d = 𝝈t / G
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This results in a current yearly fluctuation of the temperature isoclines σd of 140 km, and we
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further included scenarios with yearly fluctiations σd of 0 km and 280 km. We can then
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calculate the location of the optimal temperature in north-south direction (Yopt) in a certain
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year as:
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Yopt,t = Yopt,0 + T * t + 𝝈d * Nt
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with Nt is the yearly random number drawn from a standard normal distribution.
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We obtain a normal habitat quality distribution with this optimal coordinate Yopt in its centre
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by defining habitat quality (HQ) as
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HQpatch, t, ind = HQfactorgen * exp[-0.695(Yopt,t - Ypatch)2 / Hgen2]
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Hgen is an indicator of the temperature tolerance of the specific genotype, and defined as the
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distance from the temperature optimum at which habitat quality is 0.5. See Table 1.
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HQfactorgen determines the perceived habitat quality of the individual with its specific
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genotype. This factor serves as a trade-off for the larger temperature tolerance of the climate
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generalist genotype GG.
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Species
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We modelled a woodland bird, parameterised as the middle spotted woodpecker
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(Dendrocopus medius). Parameters were based on biological information (Hagemeijer &
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Blair, 1997, Kosenko & Kaigorodova, 2001, Kosinski et al., 2004, Kosinski & Ksit, 2006,
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Michalek & Winkler, 2001, Pasinelli, 2000, Pettersson, 1985a, Pettersson, 1985b) and on the
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interpretation by Schippers et al. (2011)(see Table 1). The model distinguishes 2 sexes and 2
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life stages: adults and juveniles. The yearly life cycle consists of recruitment, dispersal, and
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survival, in this order. Lastly, all juveniles age to adults. Recruitment, dispersal and survival
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are all dependent of life stage, population density (PD) and habitat quality (HQ).
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PD = NI / CC,
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with NI: number of individuals in patch,
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CC: carrying capacity of patch, and
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HQ: see section Climate in this appendix.
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Recruitment function
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The number of nests in a patch in each generation is equal to the number of unique adult pairs
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of opposite sex in this patch, with a maximum of 10. The number of offspring per nest is then
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found with:
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𝑁𝑂 = 𝑁𝑂_𝑃𝐷0 𝐻𝑄1 ∗ (1 − (1 −
𝑁𝑂_𝑃𝐷0 𝐻𝑄0
𝑁𝑂_𝑃𝐷1 𝐻𝑄1
) ∗ (1 − 𝐻𝑄)) ∗ (1 − (1 −
) ∗ 𝑃𝐷)
𝑁𝑂_𝑃𝐷0 𝐻𝑄1
𝑁𝑂_𝑃𝐷0 𝐻𝑄1
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with 𝑁𝑂_𝑃𝐷0 𝐻𝑄1 : number of offspring at population density (PD) = 0 and
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habitat quality (HQ) =1, and similar for 𝑁𝑂_𝑃𝐷0 𝐻𝑄0 and 𝑁𝑂_𝑃𝐷1 𝐻𝑄1 . See Table 1.
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Dispersal function
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Determines for each individual the yearly chance that it leaves its patch to go on dispersal, PD.
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𝑃𝐷 = 𝑃𝐷𝑃𝐷1 𝐻𝑄1 (−1 + 𝐻𝑄 + 𝑃𝐷) + 𝑃𝐷_𝑃𝐷1 𝐻𝑄0 (1 − 𝐻𝑄) + 𝑃𝐷_𝑃𝐷0𝐻𝑄1 (1 − 𝑃𝐷)
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with 𝑃𝐷𝑃𝐷1𝐻𝑄1 : dispersal rate at population density (PD) = 1 and habitat quality (HQ) =1, and
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similar for 𝑃𝐷_𝑃𝐷1 𝐻𝑄0 and 𝑃𝐷_𝑃𝐷0 𝐻𝑄1 . See Table 1.
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Survival function
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Determines for each individual the chance that it survives the current year, PS.
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𝑃𝑆 = 𝑃𝑆_𝑃𝐷0𝐻𝑄1 ∗ (1 − (1 −
𝑃𝑆𝑃𝐷1 𝐻𝑄1
𝑃𝑆_𝑃𝐷0 𝐻𝑄0
) ∗ 𝐻𝑄) ∗ (1 − (1 −
) ∗ (1 − 𝑃𝐷))
𝑃𝑆_𝑃𝐷0 𝐻𝑄1
𝑃𝑆𝑃𝐷0 𝐻𝑄1
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with 𝑃𝑆_𝑃𝐷0 𝐻𝑄1 : survival rate at population density (PD) = 0 and habitat quality (HQ) =1, and
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similar for 𝑃𝑆_𝑃𝐷0𝐻𝑄0 and 𝑃𝑆_𝑃𝐷1 𝐻𝑄1 . See Table 1.
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If an individual disperses, we need to determine where it goes. From their origin patch
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individuals can go in every direction, along a straight line. Connectivity to other patches is
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determined by destination patch radius (r) and distance to there (d). So the chance to disperse
from patch A to patch B is:
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PAB = (2* arcsin [(rB+l)/dAB]) / 2π
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with l is 150 m, the maximum distance from where an individual can detect suitable habitat.
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The maximum dispersal distance is 15 km, so habitat patches that are separated by more than
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this distance are not directly connected. Our model does not allow dispersers to ignore a
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nearer patch, so more distant patches are located in the shadow of the nearer patch. An
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individual may arrive in a patch with a population size larger than carrying capacity twice per
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dispersal event, and is then allowed to disperse again. Should it fail to reach a habitable patch
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within a total of three dispersal rounds, it dies.
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Explicit fitness responses to selection coefficients
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Based on the above equations and the parameters in Table 1, we here show examples of the
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explicit fitness responses to the selection induced by the average location of the temperature
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optimum. All graphs refer to the specific case of adult individuals in populations at 0.5
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carrying capacity, so with a population density of 50%.
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Survival probability
0.8
0.75
0.7
0.65
GG
0.6
SS
0.55
0.5
0
200
400
600
Distance to temperature optimum
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800
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Figure S1. The average survival probabilities of the SS (specialist) and GG (generalist) individuals, relative to
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the location of the temperature optimum, resulting from their perceived habitat qualities (see Figure 1).
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Number of offspring
2.5
2
1.5
GG
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SS
0.5
0
0
200
400
600
800
Distance to temperature optimum
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Figure S2. The average numbers of offspring of the SS (specialist) and GG (generalist) females, relative to the
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location of the temperature optimum, resulting from their perceived habitat qualities (see Figure 1).
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Dispersal probability
0.5
0.4
0.3
0.2
GG
0.1
SS
0
0
200
400
600
800
Distance to temperature optimum
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Figure S3. The average dispersal rates of the SS (specialist) and GG (generalist) individuals, relative to the
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location of the temperature optimum, resulting from their perceived habitat qualities (see Figure 1).
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The subjective habitat quality leads to different dispersal rates for generalist and specialist
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individuals at the same location. The dispersal rate of an individual increases with decreased
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perceived habitat quality. This means that, as the optimum temperature shifts, individuals
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whose genotypes are in mismatch with their location relative to the temperature optimum, will
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become more dispersive. This increases their chance of reaching a habitat patch with better
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quality.
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Initialisation
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At initialisation of the model, all habitat patches were filled with 10 adult individuals,
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equaling half the carrying capacity. Each individual was randomly given 2 alleles. The
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climate optimum Yopt was initialised at 400 km from the southern landscape edge.
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Burn-in
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After initialisation the model was run for 3000 generations, thus 3000 years. During these
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3000 years burn-in, the model runs with temperature isocline speed T equaling 0 in the
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equation for Yopt,t. After this burn-in we started our experiments.
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Experiments
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In the experiments the temperature isoclines were simulated to move northward for 600 years,
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under the different scenarios in Table 1. Each parameter setting was run twice in each
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landscape variant (10 runs in total). For studying trends in numbers of individuals we
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averaged these per parameter setting. We stored and analysed data for several points in time
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(Table 1). To investigate the distribution of the genotypes we cut the landscape in ranges of
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50 km and summed the numbers of individuals with the SS, SG, and GG genotypes in the
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combined populations in each 50 km range.
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Additional figure
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Figure S4. The distributions and numbers of the GG (black bars), SG (dark gray bars), and SS (light gray bars)
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genotypes in time through the model space under the temperature isocline shift rate of 4 km/year, with standard
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deviation of 140 km. The lengths of the bars indicate the sum of the local numbers of individuals. The thin
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horizontal lines represent the model space, cut into ranges of 50 km. The bold black lines in the model space
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indicate the locations of the average temperature optimum along the total range of 2000 km in time, which is
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indicated in the lower right corners of each of the figures. The temperature increase was stopped after 300 years.
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In this particular run, in year 100 there were several SG-individuals at the range front, indicated by the arrow.
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These could establish as a result of their selective advantage and their increase in numbers was subsequently
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enhanced by the founder effect, leading to high numbers of specialists and intermediates throughout the range.
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100
200
400
600
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References
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Hagemeijer WJM, Blair MJ (1997) The EBCC Atlas of European Breeding Birds, T. & A.D.
Poyser.
Kosenko SM, Kaigorodova EY (2001) Effect of habitat fragmentation on distribution, density
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and breeding performance of the middle spotted woodpecker Dendrocopos medius
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(Alves, Picidae) in Nerussa-Desna Polesye. Zoologichesky Zhurnal, 80, 71-78.
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Kosinski Z, Kempa M, Hybsz R (2004) Accuracy and efficiency of different techniques for
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censusing territorial Middle Spotted Woodpeckers Dendrocopos medius. Acta
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Ornithologica, 39, 29-34.
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Kosinski Z, Ksit P (2006) Comparative reproductive biology of middle spotted woodpeckers
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Dendrocopos medius and great spotted woodpeckers D-major in a riverine forest. Bird
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Study, 53, 237-246.
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Michalek KG, Winkler H (2001) Parental care and parentage in monogamous great spotted
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Pasinelli G (2000) Oaks (Quercus sp.) and only oaks? Relations between habitat structure and
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home range size of the middle spotted woodpecker (Dendrocopos medius). Biological
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Conservation, 93, 227-235.
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Pettersson B (1985a) Extinction of an isolated population of the Middle Spotted Woodpecker
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Pettersson B (1985b) Relative importance of habitat area, isolation and quality for the
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