projection models for different environmental conditions
The deterministic growth rates calculated from matrices representing different habitats varied from 0·85 (poor) to 1·63 (good), which seems plausible, as the year-to-year variation in natural populations, probably augmented by some sampling error, may even exceed that range (e.g. λ = 0·3–3·0; computed from a 30-year time series in Feichtner 1998). Thus our three matrix models seem to represent reasonable combinations of (positively correlated) vital rates in wild boar, and may serve as a valid base on which to address both basic and applied questions concerning the population ecology of this species.
Under fluctuating conditions, such as variation in food resources and climate, the relative importance of each vital rate for population growth may change (Benton & Grant 1996; Caswell 2001). Interestingly, our analysis indeed revealed such a change in the ranking of elasticities (Fig. 2). While the elasticity of λ to juvenile survival e(P1) was the highest among all vital rates under good conditions, the elasticity of λ to adult survival e(P3) was highest in a poor environment, and both elasticities were almost equal in intermediate habitats. These changes in the ranking of elasticities may be viewed as moves along the fast–slow continuum scale of mammalian life histories (Oli & Dobson 2003; Oli 2004).
As outlined by Oli & Dobson (2003), the ratio of overall fertility (F̄) to the onset of reproduction (α) may be useful for ordering species along this fast–slow continuum. Typically, in ‘fast’ mammals the ratio F̄/α is > 0·6 and in ‘slow’ mammals F̄/α is < 0·15 (Oli & Dobson 2003). On this scale wild boar indeed adjust their life-history tactics from an intermediate type under poor environmental conditions (F̄/α ratio = 0·52) to a fast life history under intermediate (F̄/α ratio = 0·68) and good (F̄/α ratio = 1·06) conditions (calculated from equation 14 in Oli & Zinner 2001). Interestingly, the summed elasticity of λ to changes in fertility exceeded the elasticity of λ to either juvenile or adult survival (P1, P3; cf. Fig. 2) under good conditions (high F̄/α ratio) but not under poor conditions (low F̄/α ratio). This finding clearly supports the prediction by Oli & Dobson (2003) that the sensitivity of λ to perturbations in fertility should increase as the F̄/α ratio increases (i.e. towards the fast end of the continuum).
Rapid shifts between slow and fast life-history tactics in wild boar may reflect the adaptation of this species to an important but unpredictable food resource, i.e. the mast of beech or oak. While under conditions of poor food availability, juvenile fecundity decreases and, thus, the trade-off between early reproduction and survival is shifted in favour of survival, fecundity of adult animals is less influenced by environmental conditions. This age class represents a reservoir of individuals with high survival rates that dampens negative effects of unfavourable conditions on population size. Under good conditions, on the other hand, population growth is primarily driven by juveniles, which contribute twofold. First, we observed a more than threefold increase in the elasticity of λ to juvenile fertility (Fig. 2). Juveniles under good conditions have an enormous potential to gain weight (which may explain why pigs have been domesticated; Briedermann 1990) and puberty in wild boar depends more on weight than on age (Briedermann 1990; Fernandez-Llario, Carranza & Mateos-Quesada 1999). Secondly, the elasticity of λ on juvenile survival under good conditions was higher than any other elasticity. Thus juveniles have the potential to cause large and rapid increases in λ.
It seems that documented cases of crossovers in elasticities, as observed here, are relatively rare (Mills, Doak & Wisdom 1999). Typically, population growth and elasticities are derived from a single mean or ‘best-guess’ matrix for many species, because data on vital rates under fluctuating environmental conditions are often not available. For example, Oli & Dobson (2003) computed elasticities of λ to changes in different vital rates for 142 natural populations of mammals, but only in six cases was more than one set of life-history variables used (Oli & Dobson 2003). From our analysis it is clear that in wild boar conclusions based on elasticities from a single matrix of vital rates, for instance that for intermediate conditions, would be quite misleading if mean long-term environmental conditions (such as the frequency of mast years) should change. Also, management measures that seem optimal, given a certain ranking of elasticities, in one year, may be inappropriate in another (see below). These results support the view that, while elasticity analysis is a useful tool for applied ecology, elasticities should be interpreted with considerable care, especially when they are obtained from a single mean matrix (Mills, Doak & Wisdom 1999; Ehrlén, van Groenendael & de Kroon 2001; Mills, Doak & Wisdom 2001).
If long-term environmental conditions stay constant, on the other hand, the pure effects of stochasticity on the properties of wild boar populations seem moderate. Mean and stochastic elasticities in our simulations were highly similar (Table 4), which seems quite typical (Benton & Grant 1996; Caswell 2001; but see Tuljapurkar, Horvitz & Pascarella 2003). This similarity was unaffected by the somewhat unusual type of environmental noise in beech mast that contained a significant negative autocorrelation. As expected on theoretical grounds (Caswell 2001), the deterministic λm computed from the mean matrix in our simulation of environmental fluctuations was slightly higher than the actual stochastic λs (Table 4). Our estimate of a λs of 1·05, i.e. steady population growth under a realistic sequence of environmental fluctuations, was probably affected by the fact that Briedermann's (1990) set of vital rates was mainly obtained from populations in eastern Germany, which underwent a long-term population increase. Different combinations of vital rates obtained from other populations may easily lead to lower growth rates, i.e. λ= 0·98 (Oli & Dobson 2003; based on vital rates published in Jezierski 1977 and Ahmad et al. 1995).
consequences of changes in food availability and climate
The classifications of our three matrix models were based on both food availability and winter climate (Briedermann 1990) but the time pattern of our stochastic fluctuations simulated typical temporal sequences of tree masting only. This was justified by several analyses of long-term data sets showing a clear association between beech or acorn crop availability, winter survival and yearly population growth rates (Okarma et al. 1995; Jedrzejewska et al. 1997; Feichtner 1998). The abundance of tree seeds appears to be a limiting ecological factor in several species (reviewed by Silvertown 1980). For example, in the edible dormouse Glis glis L. entire populations skip reproduction in years with a failure of beech and/or oak mast (Bieber 1998; Pilastro, Tavecchia & Marin 2003; Fietz et al. 2004). While the arboreal dormouse may predict the seeding of trees, at least within 1 year, from the presence of seed buds on branches (one of their food items) in spring, wild boar probably respond entirely opportunistically to this fluctuation in food resources. Also, the bearded pig Sus barbatus Müller, a species under threat in parts of its range, is known to be strongly affected by seeding in dipterocarps (Hancock, Milner-Gulland & Keeling 2005). Pulsed resources may also affect densities of secondary consumers, such as mammalian and avian predators, that respond to population fluctuations in mast consumers (for an overview see Ostfeld & Keesing 2000). Rapid population growth in these predators can have a strong impact on other prey, including rare or endangered species (e.g. effects of stoats on endemic birds in New Zealand; Ostfeld & Keesing 2000). Thus pulses of heavy seed production are widespread and may have important consequences for the population dynamics of several species within an ecosystem.
Our evaluation of long-term beech mast time series showed that the temporal sequence of masting is largely random, except that full mast years are generally followed by a year of very low levels of seed production (Piovesan & Adams 2001). Seed production is induced by certain climatic conditions, i.e. moist, cool summers followed by a dry early summer in the next year (Piovesan & Adams 2001), which apparently occur at random intervals. Interestingly, masting of trees seems to be a large-scale phenomenon that occurs synchronously in the northern hemisphere (Piovesan & Adams 2001). Hence, wild boar and other populations within large areas will be affected simultaneously. Our evaluation of the impact of changes in seeding pattern on population growth in wild boar indicated that an increase in the frequency of full mast years should lead to a rapid acceleration of population growth (Fig. 4).
We do not intend to suggest, however, that the seeding of beech and oak is the single environmental factor determining population dynamics in this species, nor that it fully explains the past increase in the number of wild boar in many areas. Historical hunting bag statistics indicate that population densities in central Europe have apparently been stable during most of the last two centuries but have increased dramatically during the past five to six decades (W. Arnold, personal communication). However, we found no statistically significant increase of beech masting frequency over that period in the time series analysed here. Also, it should be noted that our modelling of stochastic environments was based on good, intermediate and poor conditions, which reflected not only food availability but also additional factors such as winter temperatures and snow cover (Briedermann 1990). Thus, our analyses incorporate climatic influences, namely a clear positive effect of mean annual temperatures on vital rates, and consequently on population growth (Briedermann 1990; Jedrzejewska et al. 1997). These effects suggest that one of the decisive factors contributing to the widespread increase in wild boar population densities may have been the well-known rise in global mean annual air temperatures over the last century (global warming; Root et al. 2003). In addition, the simultaneous intensification of agriculture has provided increased food resources for wild boar, which buffers environmental fluctuations and further augments reproductive output (Andrzejewski & Jezierski 1978).
implications for management
Our study has direct relevance for hunting strategies in wild boar. It is clear that, rather than relying on a general management strategy derived from an average elasticity analysis, hunting, as a measure to control populations, should be adjusted to changing environmental conditions (cf. Mills, Doak & Wisdom 1999). In growing populations under good environmental conditions, particularly following a full mast of trees, yearly survival of juveniles should be reduced most, to approximately 15% (including natural postnatal mortality), assuming 60% survival in yearlings and 70% in adults, in order to limit growth rate to λ ≤ 1 (Fig. 3). High hunting pressure on juveniles as an effective measure to control population growth was also recommended by Briedermann (1990) and Neet (1995). However, in many parts of Europe juveniles are rarely hunted because of tradition and difficulties in finding them (Boitani, Trapanese & Mattei 1995). Our analysis shows that preferential hunting of adults in favourable habitats would be ineffective, because even if survival of adults was below 10% (assuming 50% survival in juveniles and 60% survival in yearlings) population growth would not drop to λ = 1 (Fig. 3). For poor environments, on the other hand, our elasticity analysis indicated that decreasing adult survival would lead to the most effective reduction of population growth and should be considered, for instance, if the aim is to reduce or even remove a population from a certain area.
Regarding the practicability of these recommendations, it should be noted that the three age classes chosen for our analyses are easy to distinguish visually in the field. Also, data on the current mast situation in beech and oak and winter climate (e.g. snow cover) are simple to register. Thus, our recommendations are applicable management measures. However, reducing yearly survival rates of juveniles to approximately 15% in favourable habitats might be a difficult task to fulfil. In that case, simultaneously increasing hunting pressure on all other age classes will be necessary. Moreover, should important environmental factors, such as mean annual temperatures and masting frequency of trees, continue to increase (cf. Hofmann et al. 1992), controlling growth and spreading of wild boar populations will require major increases in total hunting effort and harvest rates.
In conclusion, we suggest that management strategies in species that are strongly affected by mast seeding or other pulsed resources should, whenever possible, be based on the analysis of vital rates obtained under various environmental conditions, such as peak and minimum food abundance. In species showing large population fluctuations because of resource variation, management measures merely based on ‘average’ vital rates will almost certainly be less effective.