Tree line population monitoring of Pinus sylvestris in the Swedish Scandes, 1973–2005: implications for tree line theory and climate change ecology


Leif Kullman (e-mail


  • 1Demographic trends of Pinus sylvestris L. (Scots pine) tree line populations are reported for a 32-year monitoring period (1973–2005). Functional and projective aspects of tree line performance were analysed by relating temporal variability and change of vital population parameters, such as natality/mortality, vigour, injuries, height growth and seed viability to contemporary variations in air and soil temperatures.
  • 2The size of the entire sampled population increased by 50% during the 32-year observation period and thereby pine has become a more prominent element on the landscape. This reverses a natural multicentennial or even millennial trend of tree line decline and recession.
  • 3Contrasting population trends were recorded for the subperiods 1973–87 and 1988–2005, viz. decline and increase, respectively. Mean summer temperatures (JJA) did not change perceivably over and between these intervals, although some exceptionally warm summers from 1997 onwards have contributed to population expansion by increased seed viability and seedling emergence. Winter temperatures (DJF) decreased significantly over the first subperiod and were consistently higher during the second, which has significantly lowered the mortality rates.
  • 4A functional link to winter temperature conditions was particularly stressed by the aetiology of individual plant vigour, injuries and final mortality. Classical symptoms of winter desiccation correlated significantly with low winter temperatures. This negative impact occurred with a high frequency during the decline phase and virtually ceased during the expansion phase from 1988 onwards, when winter air and root zone temperatures were raised to a consistently higher level.
  • 5Winter and summer temperatures in the air and soil, as well as positive feedback mechanisms and nonlinear responses, must be taken into account in the search for global or regional mechanical explanations for the tree line phenomenon. This insight helps to generate realistic tree line models for a high-CO2 world, when winter warming is usually predicted to be particularly large.


Projected human-induced climate warming over the 21st century (IPCC 2001) stands out as a potential driver towards profound mountain landscape transformation (Theurillat & Guisan 2001; Beniston 2003; Kullman 2004a; 2006a,b). The alpine (upper) tree line is a key subject in this context, both for detection and for the understanding of climate-dependent ecological processes of vital concern for biodiversity patterns and ecological services to the human society. In fact, it is increasingly evident that upward tree line migration is already becoming a global phenomenon, although the magnitude and rate of advancement, population growth and stand densification also depend on local topoclimatic conditions (Kullman 1981, 2001, 2004b; Meshinev et al. 2000; Sturm et al. 2001; Moiseev & Shiyatov 2003; Lloyd 2005; Mazepa 2005).

Despite important progress (e.g. Tranquillini 1979; Körner & Paulsen 2004), conclusive functional explanations, which connect climate and vegetation, are not defined in detail, particularly with respect to tree line formation, maintenance and change (cf. Woodward 1987; Grace et al. 2002; Kjällgren & Kullman 2002; Holtmeier 2003; Smith et al. 2003). This circumstance has precluded the generation of ecologically valid landscape-scale projections of tree line evolution and high-altitude arboreal change under the influence of various prescribed (model-based) scenarios of future anthropogenic (or natural) climate change. In particular, the relative roles and interactions of winter and summer temperatures for tree line life are still not fully understood and need further scrutinity (cf. Grace & Norton 1990; Lavoie & Payette 1992; Kullman 1997; Juntunen et al. 2002). These aspects will be in special focus when analysing the data acquired in this study and their relevance is particularly great as both global and regional climate change models envisage the largest temperature rises during the winter period (IPCC 2001; Räisänen et al. 2003).

As a complement to correlative (‘climate envelope’) and small-scale, short-term manipulative approaches, the present study seeks to uncover causal mechanisms by observing and analysing an experiment by nature in the form of responses of natural tree line populations to variable climatic conditions over more than 30 years of time. This time-scale is reasonably relevant when discussing evolution of climate and vegetation under the common assumption of enhanced human-induced climate warming throughout the present century. The observation period is by far longer than any other analogous study. For the first time, direct observations of decadal tree line population responses (marked seedlings/saplings) are reported. Thus, important suggestions for future scientific inquiry may emerge, as well as due considerations for refinement of climate-driven high-mountain vegetation models. Moreover, the current focus on the establishment phase is in line with a growing insight that realistic forecasts of potential tree line trajectories critically rely on mechanisms and trends of natality, mortality and growth during early life stages (e.g. Germino et al. 2002; Graumlich et al. 2005).

Study area

The study is located in the Handölan Valley in the southern Scandes of Sweden, 63°14′ N, 12°25′ E (Fig. 1). The valley floor is about 670 m a.s.l. and the surrounding mountains reach 1300–1500 m a.s.l. The monitoring plots are distributed within an area of 6 km2 between 680 and 715 m a.s.l. and comprise most of the existing solitary old-growth pines. The studied pine tree line is positioned in the lower reaches of the subalpine belt of predominant mountain birch (Betula pubescens Ehrh. ssp. tortuosa (Ledeb.) Nyman). This is approximately 200 m below the tree line of this species, which currently forms the forest–alpine tundra interface in this region. Phytogeographically, the area belongs to the Northern Boreal zone (Ahti et al. 1968).

Figure 1.

Location of the study area and the sampled pine stands (0).

The bedrock of amphibolites and gneisses is overlain with glacial till, fluviglacial and peat deposits. These form small-scale topographic outcrops (1–10 m in amplitude), where the pine outposts preferentially grow on south-facing minor slopes, i.e. spots with a relatively dry, warm and snow-poor local climate. The landscape is a mosaic of extensive mires, treeless and windswept heaths and mountain birch woodlands with small, isolated stands or solitary trees of pine and spruce (Picea abies (L.) Karst.). More continuous pine stands prevail 3–5 km to the north of the southernmost pine trees in the valley.

The climate is transitional between oceanic and continental types. The nearest meteorological station is Storlien/Visjövalen (642 m a.s.l., 20 km north-west). Mean temperatures (1961–90) for January, July and the year are −7.6, 10.7 and −1.1 °C, respectively. Total annual precipitation is approximately 850 mm, of which 45% falls as snow.

Past and present human impact and fire disturbance, with relevance for the modern tree line history and regeneration dynamics appear essentially negligible. Reindeer grazing occurs in the area, but this represents a chronic disturbance factor, well integrated in this ecosystem.


population trends

During the summer of 1973, a total of 20 permanent plots were established a few tens of metres below the pine tree line in the Handölan Valley (Fig. 1), defined as the uppermost trees with a height of at least 2 m. At that time, this boundary zone had the character of widely scattered, solitary old-growth pine trees (250–500 years old, 6–8 m high) in a matrix of mountain birch forest and mires.

The old pines represented remnant outliers and the last survivors from the most recent phase of continuous elevational tree line retraction, which had proceeded in response to gradual cooling since the early Holocene and accelerated during the past millennium until the onset of the 20th century (Kullman 2005a; Kullman & Kjällgren 2006). A striking lack of medium-aged trees manifested that successful regeneration had not taken place for some centuries or more. However, most of the moribund veteran pines were narrowly surrounded by more or less dense sapling populations of quite recent age, i.e. mid-20th century (Fig. 2). This clearly suggested a significant trend break in the tree line evolution, which prompted inquiry and follow-up of future population trajectories. For that purpose, the permanent plots concerned here were established and a long-term monitoring project was launched.

Figure 2.

Pine population representing one of the sample plots and which comprised only one tree-sized pine until quite recently. By the mid-1970s, a cohort of saplings originating from the late 1950 and early 1960s had emerged. During the past two decades, many of the saplings have attained tree stature and reproductive maturity. Photo: 4 April 1976.

Each plot (10 × 10 m) was centred on an old-growth pine tree and its offspring sapling population underneath and somewhat outside the vertical crown projection. All live pines, irrespective of size or age, were mapped in order to enable continuous monitoring of regeneration, vitality and height growth at the individual level. Since 1973, censuses of population parameters have been carried out annually, often by mid-July. During the monitoring period, two of the original plots had to be deleted from the monitoring programme due to physical disturbance from military activities.

Throughout, the following life stages are defined: seedlings, < 0.1 m; saplings, 0.1–2.0 m; trees, > 2 m.

foliage vigour: winter desiccation

Each annual census included a visual assessment by the present author of the percentage needle mortality of each individual pine as a result of desiccation during the past winter/spring, relative to the total foliar biomass. These data are pooled and accounted for as the annual frequency of pine saplings with more than 20% of the foliage killed in this manner. In addition, these assessments included records on other types of injuries and diseases, relevant for the mortality analyses (below).

mortality causes

The biographies of individual pines, which died during the monitoring period, were traced back in the annual records in an attempt to define the ultimate and proximate causes of premature mortality.

seed viability

By late winter every year, i.e. when seeds are normally shed, 25 cones were collected from the S-facing aspect of the crown of each old-growth parent tree, in all the 18 study plots. The cones were pooled together and air-dried for approximately 2 weeks. Thereafter, the seeds were easily extracted from the cones by shaking them in a plastic bag, which yielded the vast majority of the seeds originally contained in the cones. Viability testing in the laboratory was carried out according to Kullman (1984).

ground temperature records

Long-term root zone temperature monitoring has been carried out in one of the studied plots at two spots, about 25 m apart and with a modest S-facing aspect. These records embrace the period 1985–2005, i.e. only the second half of the observation period. The ground cover was an intact mat of Empetrum hermaphroditum Hagerup, growing on podzolic soil. Typically, for these small outlier pine populations, the maximum snow depth is usually thin (< 0.2 m) and normally snow disappears completely early in the spring.

Resistance thermistors (TO-03R, manufactured by T. Johnsson Inc., Umeå, Sweden) were installed in mineral soil, with the sensors at a depth of 30 cm below the surface, i.e. in the zone where most of the fine roots are located. At this depth, short-term temperature fluctuations are significantly damped, as evidenced by daily measurements during some shorter periods during all seasons. Thus, readings, which have been carried out one to two times per month, are supposed to provide reasonably accurate and integrative views of ecologically relevant annual variations in soil temperature regimes (cf. Harris 2001). An annual index of summer and winter soil temperature is calculated as the mean from the two measuring spots, representing the highest and lowest readings from July–August and February–March, respectively.


climate change and variability

When evaluating ecological responses to altered climatic conditions one has to consider that the observation period 1973 through 2005 is nested within a somewhat longer context, when some of the ecological structures considered here were founded.

The longest instrumental air temperature record is provided by the Storlien/Visjövalen meteorological station (see above), where data exist since 1901.

Winter temperatures (December–February) have shown a large interannual scatter over the past century. A weak, although not significant, linear warming trend (+0.5 °C), is evident on that timescale. A conspicuous and lasting rise of the winter temperature took its start in 1988 (Fig. 3). The period 1973–87 (henceforth termed A) was characterized by distinct cooling, which sharply contrasts with the subsequent interval 1988–2005 (henceforth termed B), which stands out as a consistent sequence of exceptionally mild winters, although no trend appeared (Fig. 3). The mean winter temperatures for these subperiods differ substantially: –7.5 ± 2.4 °C and –5.3 ± 1.6 °C, respectively.

Figure 3.

Linear regression of winter air temperatures (December–February) for the period 1902–2005 and for the monitoring period, split into two subunits, viz. 1973–87 and 1988–2005.

The summer period (June–August) displays a significant linear warming trend of 1.1 °C over the period 1901–2005 (Fig. 4). However, the factual course of the temperature is more complex, with shorter periods of both warming and cooling. Concerning the 32-year observation period, no trend can be gleaned, neither for the entire period, nor for A or B (Fig. 4), although the mean during B was slightly warmer than during A, 10.8 ± 1.3 and 10.1 ± 0.8, respectively. The summers of 1997, 2002 and 2003 were exceptionally warm within the perspective of the past century.

Figure 4.

Linear regression of summer air temperature (June–August) for the period 1901–2005 and for the monitoring period, split into two subunits, viz. 1973–87 and 1988–2005.

In this region, precipitation has increased steadily throughout the past century, although no reliable local data exist. There is also a regional tendency for increasing spring temperatures and associated earlier snowmelt (Moberg et al. 2005).

Locally recorded maximum and minimum ground temperatures, during the summer and winter periods, respectively, have warmed significantly over the period 1985–2005. Particularly during the winter, warming of the ground has been substantial, with a net temperature rise of c. 2.5 °C (Figs 5 and 6). This is approximately the same magnitude as recorded for the winter air temperature between 1988 and 2005, relative to 1973–87 (see above).

Figure 5.

Linear regression of summer maximum soil temperature recordings (July–August), 1985–2005.

Figure 6.

Linear regression of winter minimum soil temperature recordings (February–March), 1985–2005.

demographic changes

A composite of all 18 permanent plots accounts for demographic change and regeneration dynamics on an annual basis over the period 1973–2005 (Fig. 7). The pooled population increased from 142 to 214 living pines, i.e. by 50.1%, during these years. It stands out clearly that a marked break in the demographic evolution took place during 1987–88. Before and after that point of time, the trend was significantly negative and positive, respectively. The population expansion, which started in 1988, is particularly noteworthy and has tended to accelerate by massive recruitment since 1997. This pattern is the net outcome of both natality and mortality over the years. Both these aspects are accounted for separately (Figs 8 and 9). Mortality was largely confined to A, while recruitment of new pines took place mainly during B, in particular after 1997.

Figure 7.

Results of annual censuses of the pooled population size, i.e. all pines within the 18 plots. Linear regressions are shown separately for the subperiods 1973–87 and 1988–2005.

Figure 8.

Natality, expressed as the number of pine saplings that emerged during a specific year.

Figure 9.

Mortality, expressed as the number of pines that died during a specific year.

All pines, which died during the observation period, belonged to the initial population, which prevailed in 1973 and had mainly (c. 75%) established during the time period 1941–55. The decrease of this cohort was 49.3% over the entire observation period. The average size of the population members has increased from 1.64 ± 1.2 m in 1973 to 2.3 ± 2.1 m in 2005. Most of the survivors from the initial population have attained tree size during the study period and the height of this cohort has increased to 4.5 ± 2.5 m. Thereby, small pine tree groves have rapidly emerged in the lower reaches of the mountain birch forest where only widely scattered solitary pines had existed for centuries (Fig. 10). However, the main birch forest matrix, between the small, centrifugally expanding pine exclaves, supports only a very low density of young pines (< 1 ha−1).

Figure 10.

Typical view of the pine groups, which have been the subject of annual demographic monitoring. Here (675 m a.s.l.), three distinct generations are clearly visible. A 450-year-old tree appears to the right. The tree in the centre germinated in the 1930s and the dense group to the left became established in the 1950–60s. In addition, some young saplings < 10 years of age thrive in the ground cover. Photo: 4 April 2006.

It is important to stress that the first recordings of new recruits were rarely first-year seedlings. Such specimens are easily overlooked in the dense ground cover of dwarf-shrubs in plots of the current size. Thus, the assigned years of natality usually lag behind the true natality year. This discrepancy was estimated to be in the order of 1–5 years and in a few cases even more. This temporal uncertainty is shared with the mortality records. In causative terms, mortality was usually not an annual event but the final outcome of a recessional process over several prior years (see below). These circumstances imply that rigorous statistical analyses, correlating demographic trends with annual climatic parameters, are precluded. The nature of any such relationships has to be inferred in broader terms.

foliage winter desiccation

As the general appearance of each pine was carefully recorded in the mid-summer, it could be ascertained that substantial needle discoloration (‘reddening’) was not reversible, as sometimes happens during high solar radiation/cold stress periods in spring (cf. Ensminger et al. 2004).

Results from the annual censuses of the amount of foliage mortality due to needle desiccation during the past winter/spring are displayed in Fig. 11. During A, this was a type of injury that persistently removed a considerable part of the living biomass. After 1994, this previously more or less chronic stressing agent virtually ceased to exist. Some pine saplings, which were severely defoliated (> 80% of the needle mass) during A, have recovered remarkably well and attained tree size by the end of B (Fig. 12). On two occasions, viz. 1987 and 1994, i.e. after exceptionally cold winters, the mature parent trees within virtually all the 18 plots suffered from extensive winter/spring needle desiccation (reddening). Despite losses of 50–75% of the needle mass (Kullman 1997), all trees survived and in 2005 they showed no obvious external signs of these episodes. On the contrary, and particularly since 2000, it was remarked each year that pines in general had taken on a particularly healthy and vigorous appearance, with exceptionally long needles and terminal leaders (0.4–0.5 m).

Figure 11.

Results of annual assessments of the frequency (18 plots) of pines that had suffered more than 20% defoliation (winter desiccation).

Figure 12.

Upper: Pine within one of the studied plots (705 m a.s.l.) and which germinated in the late 1950s. In 1986 it had grown to a size of 1.2 m, but at that time it was in a miserable condition after 5 years of severe defoliation. Lower: Since 1988 this pine has displayed a remarkable re-vitalization and height increment to reach 5.0 m in 2005.

Linear regression of the annual amount of needle desiccation (the same data as in Fig. 11) vs. relevant climatic parameters (e.g. Tranquillini 1979) revealed a significant negative relationship with winter temperature (December–February) of the same year (R2 = 0.24, P < 0.01), but no significant correlation with temperature during the previous summer.

mortality causes

For the vast majority (> 90%) of pines, which died during the observation period, winter desiccation was judged to be the ultimate cause. As a rule, saplings died 3–4 years after severe defoliation. Pines gradually weakened in this way were sometimes infected by the snow fungus Phacidium infestans Karst., which reasonably contributed to death as a secondary factor.

Causes of death of relatively less importance were snow breakage of main stems and mechanical damage caused by reindeer rubbing their antlers against saplings and small trees.

seed viability

Percentage pine seed viability of the studied population each year since 1973 is accounted for in Fig. 13. Seeds with a viability of 15–20% have been regularly produced. During the past decade, tree years, 1998, 2003 and 2004, stand out with the highest viability on record (40–60%). Viability correlated significantly with the mean June–August temperature and increased almost exponentially as the summer temperature exceeded 11 °C (Fig. 14).

Figure 13.

Results of annual censuses of pine seed viability (all 18 plots).

Figure 14.

Relationship between summer air temperature (June–August) and pine seed viability during the subsequent winter/spring.

Repeatedly over the past 10–15 years, most members of the initial population have copiously produced cones and filled seeds.


The obtained demographic trends of pine sapling populations, i.e. modest decline during A and strong increase during B, owe their existence to the balance of high mortality and low natality and low mortality and high natality, respectively. Notably, most of the pines that emerged during B are still in a vulnerable stage and the progressive trend may be reversed in the case of a series of colder winters (cf. Kullman 1997; Slot et al. 2005).

Ultimately, regeneration success presupposes seed viability, which is here shown to bear a strong and positive relationship with the summer temperature. A few years during the past decade have been particularly instrumental in this respect and no years with similarly high viability percentages occurred prior to 1988. Reasonably, the population expansion phase, which was initiated in 1988, has a partial relation to a raised frequency of summers warmer than normal and associated enhancement of seed viability. Moreover, the seed supply may have increased substantially as some members of the initial population have reached reproductive maturity during the monitoring period.

Unfortunately, the link between seed viability and natality cannot be elucidated statistically due to the lack of precise dating of recruitment, i.e. year of germination (see above). The mismatch between natality and viability at the annual scale (Fig. 8 vs. Fig. 13) illustrates this circumstance. Only careful observations within very small sample plots could shed light on this issue.

The time-series analysis indicates that seed viability, implicitly tree line dynamics, responds nonlinearly to summer temperature. Such relationships may cause great and rapid responses if and when future temperature passes critical threshold levels.

Except for the production of viable seeds and their germination, successful and lasting regeneration presupposes survival and height growth during the seedling/sapling phase. It appears that during B, winter temperatures have been particularly congenial in these respects, as winter desiccation of needles and shoots has virtually ceased as a chronic stressor and cause of mortality. To some extent, tree line progression during B relates to release from the constraint executed by winter desiccation, which had previously restricted the altitudinal range limit and high-elevation abundance of pine trees. This kind of injury and subsequent mortality agent, with their classical symptoms, are commonly found to relate to severe soil frost conditions, which cause needle and shoot desiccation and/or fine root mortality (Tranquillini 1979; Kullman & Högberg 1989; Sutinen et al. 1996; Kullman 1997). The recorded increase of root zone soil temperatures during B further supports the existence of a link between winter temperatures and survival rates of pine tree line populations.

These results, based on uniquely long-term observation of a natural experiment, add to general tree line theory by stressing that both winter and summer temperatures have to be taken into account in the search for some unifying mechanical explanation behind the tree line phenomenon (cf. Woodward 1987; Bonan & Sirois 1992; Payette & Lavoie 1994; Moiseev et al. 2004). This contention is further stressed and supported by substantial tree line advancement (Pinus peuce Griseb.) in Bulgaria, which is likewise found to relate primarily to winter warming since the early 1970s (Meshinev et al. 2000). In the light of that, generalizing theories, stressing a world-wide and overriding importance of growth period temperatures for broad-scale tree line patterns (Körner & Paulsen 2004), seem somewhat premature. Convincing evidence for a common causal basis, forming globally and climatically equivalent tree lines, has yet to be presented (cf. Crawford 2005). Reasonably, realistic models in this respect need to be more complex, integrating summer and winter temperatures as well as wind action (cf. Wardle 1985; Gamache & Payette 2004; Kullman 2004c). These conclusions have a definite bearing on ecological responses to projected climate transformation. As most models of human-induced warming suggest that the largest change at high elevations in the north will be during the winter (IPCC 2001; Räisänen et al. 2003), it appears that pine will benefit substantially by altitudinal advance and increasing abundance in the tree line ecotone. This process has already been initiated at a broad landscape scale in the Swedish Scandes, where the local pine tree line has risen by 150–200 m during the past century (Kullman 2004b; Kullman & Kjällgren 2006). Consequently, the initial stages in the formation of a discrete pine belt above the subalpine birch forest are already there.

The positive population trend, as illustrated by this study and related to climate warming, has reversed the long-term elevational recession of the pine tree line, which has been a modal state for several millennia (Kullman & Kjällgren 2006). The strict spatial confinement of young pine to the close proximity of old solitary tree line trees suggests that such individuals are of crucial importance for pine expansion in response to projected future climate warming. This complies with general observations that older trees often support regeneration of younger individuals in the boreal forest (e.g. Slot et al. 2005).

Evidently, tree line rise depends on seeds produced at the local tree line, rather than propagulae from more distant sources at lower elevations. The current spread of pine saplings to elevations up to 500–700 m above the tree line (Kullman 2004c; 2006a) coincides temporally with the population expansion phase (B) recorded here. Most likely therefore, this upward pine migration originates from these old outlier pines. Superimposed on microtopography and edaphic conditions, availability of viable seeds, rather than dispersal limitation, appears to govern the spatial structure and density of pine tree line vegetation.

The wide-crowned, old parent pines, aside from their role as seed source, enhance chances of establishment, survival and growth. Shading the ground by the canopy reduces winter/spring sun radiation and night time re-radiation, which reasonably reduces the risk of winter desiccation. Moreover, canopy interception and black body effect cause earlier snow melt, which is highly beneficial to tree line pine in general (Kullman 1981). The tree clusters, which expand on these premises, further facilitate the local regeneration potential in a positive feedback loop (cf. Germino et al. 2002; Kullman 2004b). However, as the studied pine stands are mainly restricted to local favourable sites (microclimate, edaphic conditions, etc.) it is likely that any further spread of pine vegetation will meet increasing resistance as less congenial conditions are centrifugally faced. The pace of this process is likely to depend also on the future trajectories of competing mountain birch forest. Given that the current tendency towards birch decline in response to summer soil drought will continue, the trend of increasing pine abundance and stand density on the landscape will be strengthened (Kullman 2006b). That inference is supported by the fact that pine has responded more abundantly in regions of the Swedish Scandes, where a subalpine birch forest belt is particularly poorly developed (Kullman 2004b, 2005b).

One implication of general scientific relevance concerns the near 50% reduction in size of the initial population. This originated mainly from the period 1941–55 and its present size is largely a function of subsequent winter mortality and bears only a subdued relation to conditions during the establishment period. This circumstance highlights the ambiguity of interpreting static age structures as a means of analysing past structural processes in boreal tree populations (cf. Johnson et al. 1994).

Another aspect from the obtained results, with methodological relevance for historical ecology, relates to the fact that population expansion since 1988 (B) is synchronous with a strong trend of radial growth decline, experienced by old-growth pine trees belonging to the studied population (Linderholm 2001). Also in a millennial-scale perspective, there is a striking mismatch between tree-ring responses and tree line population performance, as deduced from radiocarbon-dated wood remains (Kullman 2005a). Thus, long-term tree-ring chronologies may be poor predictors of population performance, e.g. tree line formation, which has a more complex and variable relation to climate than radial growth.


This study was defrayed by the Swedish Research Council for Environment, Agricultural Sciences and Spatial Planning (FORMAS). I am much obliged to two anonymous reviewers for valuable suggestions for improving the clarity of this paper.