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Study areasNine large forest dynamics plots of areas between 20 and 50 ha were used in the present study (Supplementary Table 1). The forest plots are part of the ForestGEO network4 and are situated in Asia and the Americas at locations ranging in latitude from 9.15° N to 45.55° N. Tree species richness among the plots ranges from 36 to 468. All free-standing individuals with diameter at breast height (dbh) ≥1 cm were mapped, size measured and identified. We focused our analysis here on individuals with dbh ≥ 10 cm (resulting in a sample size of 131,582 individuals) and focal species with more than 50 individuals (resulting in 289 species). The 10 cm size threshold excludes most of the saplings and enables comparisons with previous spatial analyses20,35,47,48. Shrub species were also excluded.Some of our analyses require estimation of the ratio βfi/βff that describes the relative individual-level competitive effect18 of individuals of species i on an individual of the focal species f. We used for this purpose phylogenetic distances49 based on molecular data, given in Myr, that assume that functional traits are phylogenetically conserved19,26,27. In this case, close relatives are predicted to compete more strongly or to share more pests than distant relatives26. To obtain consistent measures among forest plots, phylogenetic similarities were scaled between 0 and 1, with conspecifics set to 1, and a similarity of 0 was assumed for a phylogenetic distance of 1,200 Myr, which was somewhat larger than the maximal observed distance (1,059 Myr). This was necessary to avoid discounting crowding effects from the most distantly related neighbours26.Observed spatial patterns at species-rich forestsFigure 1 and Supplementary Data Table 1 show the intraspecific variation in our three crowding indices nkff, nkfh and nkfβ that can be approximated by gamma distributions. To assess how well the gamma distribution described the observed distribution, we used an error index defined as the sum of the absolute differences of the two cumulative distributions divided by the number of bins (spanning the two distributions). The maximal value of the error index is one, and a smaller value indicates a better fit.Equations (6, 8 and 9) relate the measures of the emerging spatial patterns (that is, kff, kfh and Bf) to macroscale properties and conditions for species coexistence. Even though our multiscale model (equation (7)) is simplified, it allows for a direct comparison with the emerging patterns in our nine fully stem-mapped forest plots. We estimate the key quantities of equations (8) and (9) directly from the forest plot data (Fig. 4), with the exception of the carrying capacities Kf, which were indirectly estimated from the observed species abundances (assuming approximate equilibrium; equation (8) and Supplementary Data Table 1). This allowed us to estimate the feasibility index µf (equation (9)). Because statistical analyses with individual-based neighbourhood models19,26 based on neighbourhood crowding indices have shown that the performance of trees depends on their neighbours for R between 10 and 15 m, we estimate all measures of spatial neighbourhood patterns with a neighbourhood radius of R = 10 m. Analyses with R = 15 or R = 20 gave similar results.The spatial multispecies model and equilibriumWe use a general macroscale model to describe the dynamics of a community of S species:$$frac{{N_fleft( {t + {Delta}t} right) – N_fleft( t right)}}{{{Delta}t}} = N_fleft( t right)left[ {left( {r_f – 1} right) + s_fexp left( { – alpha _{ff}N_fleft( t right) – mathop {sum }limits_{i ne f} alpha _{fi}N_i(t)} right)} right]$$
(11)
where rf is the mean number of recruits per adult of species f within time step Δt, sf is a density-independent background survival rate of species f and the αfi are the population-level interaction coefficients, yielding αff = c γff kff βff and αfi = c γfβ kfh βff Bf (equation (6)). The βfi are the assumed individual-level interaction coefficients between individuals of species i and f; kff = Kff(R) / π R2 and kfh = Kfh(R) / π R2 measure intraspecific clustering and interspecific segregation, respectively, with Kff(R) being the univariate K function for species f and Kfh(R) the bivariate K function describing the pattern of all heterospecifics ‘h’ around individuals of species f. A is the area of the observation window.Following equation (5), Bf can be estimated as$$B_f = frac{{bar n_{fbeta }}}{{bar n_{f{mathrm{h}}}}} = frac{{mathop {sum }nolimits_{i ne f} left[ {ck_{fi}N_ileft( t right)} right]frac{{beta _{fi}}}{{beta _{ff}}}}}{{mathop {sum }nolimits_{i ne f} left[ {ck_{fi}N_ileft( t right)} right]}} = frac{{mathop {sum }nolimits_{i ne f} k_{fi}N_ileft( t right)frac{{beta _{fi}}}{{beta _{ff}}}}}{{k_{f{mathrm{h}}}mathop {sum }nolimits_{i ne f} N_ileft( t right)}},$$
(12)
and is the weighted average of the relative individual-level interaction coefficients βfi/βff between species i and the focal species f, weighted by the mean number of individuals of species i in the neighbourhoods of the individuals of the focal species (that is, c kfi Ni(t)). For competitive interactions, Bf ranges between zero and one; Bf = 1 indicates that heterospecific and conspecific neighbours compete equally, and smaller values of Bf indicate reduced competition with heterospecific neighbours. The denominator can be rewritten in terms of segregation kfh to all heterospecifics and the total number of heterospecifics ∑i≠f Ni(t).The analytical expression of the equilibrium (equation (8)) relies on the assumption that the values of Bf are approximately constant in time. This assumption may not apply in our model during the initial burn-in phase of the simulations if the βfi/βff show large intraspecific variability (Supplementary Text and Figs. 1–5). The underlying mechanism is the central niche effect introduced by Stump45 where a species has reduced average fitness if it has high niche overlap with competitors.Finally, the factors γff = ln(1 + bff βff) (bff βff)−1 and γfβ = ln(1+ bfβ βff) (bfβ βff)−1 describe the influence of the variance-to-mean ratios bff and bfβ of the gamma distribution of the crowding indices nkff and nkfβ, respectively. For high survival rates during one time step (for example, >85%), the values of γff and γfβ are close to one; in this case the exponential function in equation (1a) can be approximated by its linear expansion and γff = γfβ = 1.In equilibrium we have (Nf(t + Δt) ‒ Nf(t))/Δt = 0, which leads, with equation (7), to:$$N_f^{ast} = left( {K_f – frac{{alpha _{f{mathrm{h}}}}}{{alpha _{ff}}}J^{ast} } right) left( {1 – frac{{alpha _{f{mathrm{h}}}}}{{alpha _{ff}}}} right)^{-1}$$
(13)
with (K_f = – {mathrm{ln}}left( {frac{{1 – r_f}}{{s_f}}} right) left( alpha _{ff} right)^{-1}) and the total number of individuals being (J^{ast} = sum _iN_i^{ast}). Rewriting equation (13) yields (frac{K_f}{J^{ast}} = left( frac{N_f^{ast}}{J^{ast}} right) left(1- frac{alpha_{f{mathrm{h}}}}{alpha_{ff}}right) + frac{alpha_{f{mathrm{h}}}}{alpha_{ff}}). For αfh/αff  More

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This large-scale survey study of over 9000 pet dogs suggests that aggressive behaviour toward people is affected by behaviour, demography, and environment. The studied factors daily time spent alone, and weaning age were novel, and factors living environment, family size, dogs in the family, dog experience, daily exercise, have previously been studied only in few articles14,15,20,21,22. Dogs showing aggressive behaviour were more often fearful, small-sized, males, owner’s first dogs and the only dogs in the family. In addition, probability of aggressive behaviour increased with age, and we found that the probability of aggressive behaviour differed between dog breeds. These findings suggest that improvements in the owner education and breeding practices of pet dogs could alleviate aggressive behaviour toward people. The identified factors should also be considered when planning studies that aim for the discovery of the associated hereditary factors.Fearfulness had the strongest association with aggressive behaviour. Fearful and noise-sensitive dogs have been found to behave more aggressively toward unfamiliar people than dogs with no anxieties11. In the study of Dinwoodie et al.28, the dogs with fear/anxiety problem had more biting incidences than other dogs, and they also found remarkable comorbidity between fear/anxiety and overall aggressive behaviour. Similarly, in the study of Salonen et al.12, comorbidity between fearfulness and aggressive behaviour was strong: aggressive dogs were over three times more often fearful than non-aggressive dogs. Aggressive behaviour commonly stems from fearfulness, as fear-related aggressive behaviour is a type of undesired aggressive behaviour13,29. Here, we could not separate fear-related aggressive behaviour from other types of aggressive behaviour. Therefore, it is possible that majority of the dogs in this study show fear-related aggressive behaviour.We found a significant association between sex and aggressive behaviour. Male dogs had a higher probability of aggressive behaviour than females. This association has been found before in some studies1,28,29, but Hsu et al.14 found this association only with aggressive behaviour toward the owner and Bennett and Rolf15 did not find association with unfriendliness/aggressiveness. In addition, in the study population of Guy et al.30, female dogs were more likely to have bitten than male dogs. Thus, more studies are needed to reveal the association of sex and aggressive behaviour.The probability of aggressive behaviour increased with age, and thus, older dogs were more likely aggressive than young dogs. A similar association between age and aggressiveness/unfriendliness has been found earlier10,15. However, in the study of Hsu and Sun14, age influenced only aggressive behaviour toward the owner, and the difference was significant only when comparing dogs over 10 years of age to dogs under 5 years of age. In contrast, in the study Casey et al.10, only the probability of aggressive behaviour toward strangers increased. Study of Col et al.1 found no association between age and aggressive behaviour, and it is possible that old dogs have had more opportunities to show aggressive behaviour, reflecting to our finding. As aggressive behaviour can be a sign of pain5, it is possible that older dogs have painful conditions or disorders which make them more aggressive. For example, hip dysplasia is a common disease which can cause pain-related aggressive behaviour in dogs7. In addition, some disorders, such as the blinding eye disease cataract which is common in older dogs31, can decrease the ability to perceive approaching people. This can make the dog feel insecure and increase the chance of an aggressive response. Thus, yearly health checks might reduce pain- or other disease-related aggressive behaviour.We found differences between dog breeds in the probabilities of aggressive behaviour toward people. From all the studied breeds, Rough Collie had the highest probability of aggressive behaviour. Rough Collies also commonly suffer from another behavioural problem, fearfulness32 and thus, it seems that Rough Collies would likely benefit from more behaviour-focused breeding. Besides Rough Collies, other breeds with high probability of aggressive behaviour included the Miniature Poodle, Miniature Schnauzer, German Shepherd Dog, Spanish Water Dog, and Lagotto Romagnolo. In previous studies (Miniature) Poodle19 and Miniature Schnauzer14 have scored above the average in aggressive behaviour toward strangers, and Lagotto Romagnolo in aggressive behaviour toward family members11. The two breeds having the lowest probabilities of aggressive behaviour in our study were Labrador and Golden Retrievers. These breeds have also scored low in previous studies14,19. However, some of our breed-wise results differ from previous studies. For example, in the study of Duffy et al.19, Chihuahua and Jack Russell Terrier exhibited the most severe signs of aggressive behaviour, such as biting, but in our study, when taking the other factors account (e.g. body size), these breeds were among the least aggressive breeds. Duffy et al.19 did not take other factors into account which probably explains the difference between these results. To be noted, Staffordshire Bull Terrier, which is one of the restricted breeds, for example, in Ireland2, was not among the most aggressive breeds in this study. In the future, we will also consider breeding lines among the breeds, for example, separate German Shepherd Dog to working and show line types, since the purpose that dogs were bred for can also affect behaviour33. Furthermore, some breeds are more prone to, for example, skeletal disorders, which can cause pain-related aggression34 and influence these observed breed differences.Small dogs were more prone to aggressive behaviour than large or medium-sized dogs. Association of small size and aggressive behaviour is in line with some previous studies: taller and heavier dogs were found to be less aggressive toward the owner and strangers than small dogs17, and Ley et al.35 reported that heavier dogs have higher amicability than lighter dogs. In contrast, Khoshnegah et al.9 found that large breeds displayed more aggressive behaviour toward strangers, and Bennett and Rohlf15 did not find any association between the dog’s body size and unfriendliness/aggressiveness. To be noted, however, both in our study and in the study of McGreevy et al.17, the body size estimates were based on the breed standards, not the actual height of the individuals, which can affect the results. Even though we found no multicollinearity between the breed and body size, we also ran the model without body size and obtained the same results. Thus, we think that the association of body size with aggression mainly comes from the “other breeds” group, which included 6360 individuals from breeds with different body sizes.Nevertheless, previous studies have also associated small size with fearfulness9,17,36 and thus, it seems that small dogs are more vulnerable to behavioural problems in general. Interestingly, owners handle small dogs differently than larger dogs, which can partly explain the higher proportion of behaviour problems in smaller dogs. Owners of small dogs play with and obedience train their dogs less frequently than owners of large dogs37,38, and small dogs are also less often house-trained39. We speculate that small size can make a dog easier to control even when they act aggressively, and people do not necessary feel threatened by small dogs. Therefore, the owners may not try to treat nor seek professional help for aggressive behaviour so willingly than owners of larger dogs. Professional help, however, have shown to decrease incidence of undesirable behaviours, such as aggression towards strangers, in young dogs40. In addition, we speculate that, as people may not feel threatened by small dogs, they might not consider behaviour important when making breeding decisions. Further, a recently published study associated several problematic behaviours with genetic variants known to cause small body size41.The dogs whose owners have had at least one dog before had a lower probability of aggressive behaviour than owners’ first dogs. This finding replicates previously found associations of owner’s dog experience and dominance-type aggressive behaviour21 as well as general aggressive behaviour20. It is possible that experienced owners are more aware of the importance of socialisation. Previous experience can also help owners to identify a problem at early stage, when the problem can be treated more efficiently. Furthermore, if the owners had problems with their first dogs, they may be more careful when choosing a new dog.Company of other dogs was associated with a lower probability of aggressive behaviour; dogs living with other dogs were less likely aggressive than dogs living without other dogs. Number of household dogs also decreased aggressive behaviour toward the owner in a study of Hsu and Sun14. They suggested that dogs in multi-dog families compete with each other for owners’ attention, with the best behaving dog acquiring more attention and thus, dogs are striving to be obedient. Similarly, dogs living in multi-dog households showed less aggressive behaviour toward the owner and other dogs in a more recent study of Serpell and Duffy20. Canine companions may offer something that owners cannot, such as the daily opportunity of intraspecific communication. For example, playing with other dogs could decrease aggressive behaviour emerging from frustration. On the other hand, owners of aggressive dogs may choose not to acquire another dog to avoid possible conflicts between the dogs and ease the handling of the aggressive dog.This study has some limitations. One of the limitations is that we could not examine aggressive behaviour towards family members and strangers separately due to a small number of dogs showing aggressive behaviour in many breeds. This may affect the reliability of the results, as the study of Salonen et al.12 showed distinct breed differences in the aggressive behaviour sub-traits. This also made comparisons between this study and previous ones challenging, because in many other studies aggressive behaviour was divided to sub-traits. In addition, as we did not have any health information from the dogs, we could not identify the individuals having health problems. Owners’ participation to the study was voluntary and thus, the data can be somewhat biased; owners of highly aggressive dog may have not wanted to participate to the study, or, on the other hand, they may have wanted to participate more willingly than owners of non-aggressively behaving dogs. It is also possible that owners did not report all information precisely, for example the breed of the dog. Moreover, as the questionnaire was available only online, participation required basic computer skills and access to the Internet. Finally, this study is cross-sectional and therefore, the causality of the associations discovered cannot be inferred. In the future, it is important to collect even larger datasets, to include health information and to design longitudinal studies, enabling the study of aggressive behaviour sub-traits, associations with health issues and the causal effects.Our results replicate findings of previous studies in an independent study population and suggest that aggressive behaviour is a complex trait associated with several demographic, environmental, and behavioural factors. The prevalence of aggressive behaviour could be decreased by preferring less aggressive individuals in breeding, since aggressive behaviour has been suggested to be heritable42,43. Furthermore, prevalence of aggressive behaviour could also be decreased by using only non-fearful dogs in breeding, as these traits were highly associated and may share a genetic component. Dog owners may decrease the chances of aggressive behaviour by carefully selecting the right breed for their lifestyle and by having multiple dogs. Since aggressive behaviour can be a consequence of pain, yearly health checks could also decrease aggressive behaviour especially in older dogs. More

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