Volume 108, Issue 1 p. 107-121
RESEARCH ARTICLE
Free Access

Tree survival and growth responses in the aftermath of a strong earthquake

Robert B. Allen

Corresponding Author

Robert B. Allen

Independent Researcher, Lincoln, New Zealand

Correspondence

Robert B. Allen

Email: [email protected]

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Darryl I. MacKenzie

Darryl I. MacKenzie

Proteus, Outram, New Zealand

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Peter J. Bellingham

Peter J. Bellingham

Manaaki Whenua – Landcare Research, Lincoln, New Zealand

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Susan K. Wiser

Susan K. Wiser

Manaaki Whenua – Landcare Research, Lincoln, New Zealand

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Elise A. Arnst

Elise A. Arnst

Manaaki Whenua – Landcare Research, Lincoln, New Zealand

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David A. Coomes

David A. Coomes

Department of Plant Sciences, University of Cambridge, Cambridge, UK

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Jennifer M. Hurst

Jennifer M. Hurst

Independent Researcher, Christchurch, New Zealand

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First published: 02 July 2019
Citations: 8
Handling Editor: Frank Gilliam

Data Availability Statement: The data are archived within and can be requested from New Zealand's National Vegetation Survey Databank at https://nvs.landcareresearch.co.nz/data/search using the string ‘harper/avoca forest stem diameter’.

Abstract

  1. The infrequent and unpredictable nature of earthquakes means that their landslide-generated impacts on forests are rarely investigated. In montane forests, landslides are the main cause of tree death and injury during earthquakes. Landslides range from soil movements that uproot and bury trees over extensive areas to rock falls that strike individual trees. We examined unexplored relationships between tree survival and distance from an epicentre, soil-available phosphorus (P) as an indicator of soil development and tree diameter. We expected decreased tree growth in damaged forests because of tree injury.
  2. We used a plot network, established in 1974 and resurveyed regularly ever since, to quantify survival and growth responses 6–30 km from the epicentre of a 1994 earthquake in New Zealand's Southern Alps. Our Bayesian analysis used 8,518 trees from 250 plots that representatively sampled a naturally monospecific Nothofagus forest. As the time-scales over which responses could emerge were unknown, we compared relationships for a pre-earthquake period with 0–5 years post-earthquake, and with 5+ years post-earthquake.
  3. Not all plots were affected by the earthquake. We found that 0–5 years post-earthquake survival increased logarithmically with distance from the epicentre with lowered survival up to 20 km from the epicentre. Survival was low on plots with high soil-available P. An inverted U-shaped relationship between survival and diameter pre-earthquake was not found 0–5 years post-earthquake. This was because of surprisingly high survival by large trees. The earthquake most often suppressed 0–5 years post-earthquake growth up to 15 km from the epicentre, but this was only apparent after accounting for more general growth differences among periods. The positive relationship between growth and soil-available P pre-earthquake and 5+ years post-earthquake reflected enhanced growth on young soils. This contrasted with a negative effect of soil-available P on growth 0–5 years post-earthquake.
  4. Synthesis. Soil-available P, tree diameter and distance from the epicentre independently determined how tree survival and growth responded to an earthquake. The impacts on survival and growth largely occurred 0–5 years post-earthquake and suggests a level of resilience in mountain beech forests.

1 INTRODUCTION

Disturbance has profound long-term impacts on the structure, composition and functioning of forest ecosystems (Attiwill, 1994; Millar & Stephenson, 2015). Developing an understanding of disturbance impacts is particularly challenging when they are large, infrequent and sometimes unpredictable (Turner, Baker, Peterson, & Peet, 1998). Earthquakes are one such event, affecting forests throughout the world's tectonically active regions. Seismic shaking can damage trees directly (e.g. by snapping the stems of individuals) and indirectly (e.g. by generating landslides and altering hydrology). Damage caused by earthquake-induced landslides is the main source of tree death and injury in montane regions (Figure 1; for example, Allen, Bellingham, & Wiser, 1999; Veblen, González, Stewart, Kitzberger, & Brunet, 2016). Landslides include soil movements that uproot, move and bury trees over extensive areas and damage root systems. Soil movement on steep slopes can also deposit debris on flood plains that dam streams and submerge forest in valley bottoms (Cui, Lin, & Chen, 2012; Speight, 1933; Veblen & Ashton, 1978). Surface ruptures can fracture roots and split trees. Rock movements include sliding on shear surfaces through to free falling rocks that damage individual trees upon impact (Keefer, 1984b; Liu, Liu, & Ge, 2010).

Details are in the caption following the image
Large earthquake-induced landslide that denuded forested slopes over a large area (A) and with lesser landslides in the foreground (B) causing smaller scale disturbance, Easy Stream, 7 km from the epicentre ((a); February 1995). Dead mountain beech trees that were deposited on lower slopes by earthquake-induced landslides (C) with more intact forest beyond (D), Basin Creek, 10 km from the epicentre ((b); January 1999). Note much of the scree area above tree line pre-dates the earthquake [Colour figure can be viewed at wileyonlinelibrary.com]

Understanding what controls tree survival and growth responses is necessary to determine the impacts of earthquakes. Landscape-level characteristics (e.g. topographic position) often regulate the damage that earthquakes cause to montane forests. Irrespective of magnitude, the number of earthquake-induced landslides decreases logarithmically with distance from the epicentre (Keefer, 2000; Qiu et al., 2015; Walker & Shiels, 2013). Given this, we hypothesise that post-earthquake tree survival will increase logarithmically away from the epicentre. Variability around any distance decay in landslide damage will occur because of other landscape-level characteristics (e.g. Bekker, Metcalf, & Harley, 2018; Keefer, 1984a; Marc, Hovius, Meunier, Uchida, & Hayashi, 2015). For example, the number of earthquake-induced landslides varies with slope and landform (Keefer, 1984a; Kitzberger, Veblen, & Villalba, 1995; Rosser & Carey, 2017). We hypothesize that there will be low survival on steep slopes and on lower slope landforms subject to landslide debris deposition (Garwood, Janos, & Brokaw, 1979; Keefer, 1984a). Landslides alter soils through physical losses, gains and mixing as well as through chemical changes (Cheng, Yang, Yu, Li, & Zhang, 2012; Lin et al., 2017). Chemical weathering of minerals in freshly exposed rocks, particularly of apatite, can lead to greater concentrations of available phosphorus (P) in young soils (Eger et al., 2018; Peltzer et al., 2010). With time P is leached from soils or occluded into unavailable forms during soil development (Peltzer et al., 2010). We hypothesize that landslides would recur on unstable, young soils so that post-earthquake survival will be low on sites with high soil-available P.

Tree survival is strongly related to size where, if all else is equal, both small and large trees have lower survival thus forming an inverted U-shaped relationship (Goff & West, 1975; Hurst, Allen, Coomes, & Duncan, 2011). This pattern is thought to largely reflect neighbourhood competition for light, causing the relatively low survival of small trees, and with disturbance the relatively low survival of large trees, whereas trees of intermediate size are less affected by either process (Coomes, Duncan, Allen, & Truscott, 2003). Earthquake-induced landslides may decrease the survival of trees regardless of size (Allen et al., 1999). We hypothesise that this should lead to the loss of any inverted U-shaped relationship post-earthquake. Similarly, landslide-related tree death should reduce any influence of neighbourhood competition on survival post-earthquake (Hurst et al., 2011), but this negative influence will re-emerge once competitive hierarchies re-establish.

Earthquakes also cause above- (e.g. branch breakage through rock fall) and below-ground (e.g. fractured roots through soil movement) injury to many trees in montane forests (Allen et al., 1999; Jacoby, Bunker, & Bensen, 1997). Injury is the usual reason given for suppressed tree growth after earthquakes (Bekker et al., 2018; Jacoby et al., 1997; Wells, Duncan, & Stewart, 2001). Sometimes, however, trees may exhibit a growth increase after earthquakes because the death of adjacent trees leads to a reduction in neighbourhood competition and increased resources (Kitzberger et al., 1995; Veblen, Kitzberger, & Lara, 1992; Wells et al., 2001). It remains unclear which of these two processes dominates. We hypothesize that post-earthquake tree growth will most often decrease near an epicentre due to injury of many surviving trees. Injury-related decreased growth post-earthquake is also hypothesized to occur on steep slopes, landforms on lower slopes and on young soils with high soil-available P (coincident with landslide disturbance). We do expect growth will be high pre-earthquake on young soils with high soil-available P (Coomes, Bentley, Tanentzap, & Burrows, 2013).

Tree growth is often positively related to size (Coomes & Allen, 2007a), but we hypothesize that this relationship will be lost post-earthquake if reduced neighbourhood competition leads to increased growth of survivors, particularly for small individuals. This is because competition, in the absence of disturbance, can be most intense for small individuals (Coomes & Allen, 2007a). A negative effect of neighbourhood competition on growth found pre-earthquake may also be lost post-earthquake if survivors are injured when neighbours are killed by earthquakes.

This paper examines how landscape- and tree-level characteristics regulate survival and growth responses to the 1994 Arthur's Pass earthquake (Mw = 6.7; moment magnitude scale; Arnadottir, Beaven, & Pearson, 1995) in New Zealand's Southern Alps (Figure 1). We investigate these demographic responses using tagged individuals on 250 permanent plots that randomly sample a 9000-ha elevational band of mountain beech (Nothofagus solandri var. cliffortioides Nothofagaceae, also referred to as Fuscospora cliffortioides) forest 6–30 km from the earthquake's epicentre. This forest is naturally monospecific (Wiser, Hurst, Allen, & Wright, 2011), in contrast to most forests in earthquake-affected regions (e.g. Simonett, 1967; Kitzberger et al., 1995), allowing us to investigate responses without the confounding effects of species interactions. Plot resurveys allowed us to determine survival of all trees present before the earthquake as well as the growth of all trees present before and after the earthquake. Such details are not available from common approaches used to study earthquake impacts on forests where the consequences are reconstructed decades or even centuries later using only long-term survivors and recruitment in subjectively selected stands (e.g. Kitzberger et al., 1995; Wells et al., 2001) or using remote sensing to characterize landslides above a certain size (e.g. Garwood et al., 1979; Chou, Lin, & Lin, 2009). Moreover, our representative sample of many trees on many plots allowed us to incorporate the variable nature of tree survival and growth, both spatially and temporally (Coomes & Allen, 2007a, 2007b; Hurst et al., 2011), into an understanding of earthquake impacts. We used joint survival and growth modelling within a Bayesian framework to examine hypothesized post-earthquake changes in the relationships between annual survival probability (hereafter survival) and annual diameter growth (hereafter growth) of trees in relation to distance from the epicentre, slope, landform index and soil-available P of plots as landscape-level (hereafter plot-level) characteristics and basal area of nearby trees (a local measure of neighbourhood competition) and diameter size as tree-level characteristics. We determined whether plot- and tree-level characteristics independently determined variability around any distance-decay in tree survival and growth and whether tree-level characteristics explained responses above and beyond those explained by plot-level characteristics. The time-scales over which responses would emerge were unknown, particularly as earthquakes can lead to ongoing landscape instability (Saba, van der Meijde, & van der Werff, 2010). Because of this, we compared relationships using plot data from three periods: pre-earthquake (1974–1993), 0–5 years post-earthquake (1993–1998) and 5+ years post-earthquake (1999–2015).

2 MATERIALS AND METHODS

2.1 Study area

Mountain beech is an evergreen tree species, living up to 250–350 years, that dominates comparatively dry (<2,000 mm/year precipitation) montane forests in eastern parts of New Zealand. These old-growth forests (‘Black/mountain beech forest (subalpine)’ of Wiser et al., 2011) occur as a band between the valley bottoms at c. 650 m and tree line at c. 1,350 m elevation (Figure 1). Mountain beech occurs with few other sub-canopy tree or shrub species (<0.4% of tagged individuals). The mountainous terrain has been glacially steepened but also contains extensive morainal, fluvioglacial and periglacial slope deposits (Mosley, 1979). Lower slopes and valley bottoms have extensive alluvial and colluvial deposits. In general, the greywacke-derived soils have low P (Brandtberg, Davis, Clinton, Condron, & Allen, 2010), although geomorphic processes such as landslides have resulted in landscape variability in the availability of soil P (Brandtberg et al., 2010; Coomes & Allen, 2007a). There is also a temporal variability in soil P as stands recover from disturbance (Brandtberg et al., 2010). Annual precipitation increases from 1,500 mm in the east to 2,500 mm on the western edge of the study area (Griffiths & McSaveney, 1983).

Before 1980 these forests were subjected to wind, snow and pathogen damage (Hurst et al., 2011; Wardle & Allen, 1983). This led to a pattern of dispersed, low-intensity disturbance, which resulted in many plots losing basal area between 1974 and 1987 (Hurst et al., 2011). Following disturbance to mountain beech forest there is usually widespread seedling recruitment, self-thinning and biomass accumulation in developing stands (Coomes, Holdaway, Allen, Kobe, & Lines, 2012; Osawa & Allen, 1993). Survival and growth during stand development are, in part, driven by neighbourhood competition and tree diameter size (Coomes & Allen, 2007a; Hurst et al., 2011). Stand development led to a positive trajectory in mean plot basal area from 1987 until the 1994 earthquake.

Strong earthquakes (Mw = 6.0–6.9) have return times of <300 years in the study area (Stirling, McVerry, & Berryman, 2002). The epicentre of the 18 June 1994 earthquake was c. 6 km north of the north-western corner of the forests sampled in the study area and there were numerous aftershocks, with the largest (Mw = 6.1) occurring 1 day after the main event (see map in Appendix S1; Arnadottir et al., 1995). In a sub-catchment near the epicentre, 24% of trees were killed immediately and 23% were injured (Allen et al., 1999). The key role of earthquake-induced landslides in causing this damage is supported by a comparison of landslides on aerial imagery taken of this sub-catchment in 1986 and 1996. New landslides affected 22% of the forest area in this sub-catchment. These landslides varied in area from <0.1 ha to 11.9 ha (Thomas Schickedanz unpubl. data). Rosser and Carey (2017) estimated landslides occurred over a 170 km2 area but considered this was an underestimate because aerial surveys miss small landslides. Various forms of landslides killed 70% of the trees that died (Allen et al., 1999). It appeared that tree injury affected subsequent survival as basal area has declined since 1994 over the study area (Hurst et al., 2011). This may be because mountain beech is poorly adapted to root damage and inundation by soil movement and does not sprout after main stem breakage (Wardle, 1984). Although trees of this species can survive on earthquake-induced soil rafts on steep slopes (Allen et al., 1999).

2.2 Data collection

The 250 permanent plots were located along 98 transect lines (see Hurst & Allen, 2007). The origin of each transect line was located randomly along a stream. The side of the stream sampled by the transect line was also selected randomly. The direction of the transect line (the compass bearing) was then selected as towards the nearest tree line according to a topographic map or, if there was no tree line, to the nearest dominant ridge. Plots were established at 200-m intervals along the transect line until the tree line or a ridge was reached. Each transect line had one to eight plots. The 0.04 ha (20 m × 20 m) plots were each subdivided into 5 m × 5 m subplots (16 per plot) using tapes between opposing boundaries that ensured the correct shape and area of plots. There were in total 4,000 (16 × 250) subplots of size 5 m × 5 m. Within each plot, the diameter at breast height (Diameter) of each tree stem ≥30 mm size was surveyed and recorded by species and subplot. In the austral summer starting in 1974, all trees were uniquely tagged at survey height. Subsequent resurveys of all plots identified recruited and dead trees based on tags during the austral summers starting in 1976, 1978, 1980, 1983, 1985, 1987, 1999, 2004 and 2009. A resurvey during the austral summer starting in 1993—that is, 6 months before earthquake—assessed only 216 plots with the other 34 plots resurveyed during the austral summer starting in 1994—that is, 6 months after earthquake. Additional resurveys of a 62-plot subset (sub-catchments close and distant from the epicentre) were undertaken in the austral summers starting 1995, 1996, 1997, 1998 and 2015.

Geographic co-ordinates of the earthquake epicentre and Geographic Positioning System locations of each plot were used to determine distance (km) of each plot from the epicentre (range 6–30 km). The predominant slope (degrees) was determined for each plot in 1974 and, in 1993 and 1994, we calculated a mean angle to the horizon (degrees) from horizon angles measured from the plot centre at 45° compass bearing intervals (eight values). This was used as a simple landform index with the lowest mean values corresponding to exposed ridge crests and the highest values to landforms on lower slopes and valley bottoms (McNab, 1993). In 1992, we collected eight soil samples (c. 60 mm diameter) systematically over each plot from the top 100 mm of mineral soil, and composited these to form a single sample. Composites were air-dried, sieved (<2 mm), and analysed for Bray 2 exchangeable P (μg/g) as a measure of soil-available P (Nicholson, 1984). P was selected as the nutrient of interest because of its well-documented decline in availability during soil development and its important role in forest nutrient dynamics on low P soils (Peltzer et al., 2010; Richardson, Allen, & Doherty, 2008). A crowding index was calculated for each tree, as a measure of neighbourhood competition, for each survey, based upon the local basal area (m2/ha) of all neighbours within a 15 m × 15 m square centred on the 5 m × 5 m subplot within which the tree was recorded (Coomes & Allen, 2007a; Hurst et al., 2011). Thus, survival and growth modelling was only undertaken for trees in the four central 5 m × 5 m subplots.

2.3 Joint survival and growth modelling

Survival and growth were modelled using a total of 8,518 trees measured across surveys in the four central 5 m × 5 m subplots of the 250 plots. The number of trees used from a survey ranged between 641 in 1994 (one of the years when 62 plots were resurveyed) to 5,375 in 2009 (one of the years when all 250 plots were resurveyed). The mean (range) number of trees on each plot was 37.6 (1–534) and their mean diameter was 148 mm (30–740 mm). The total number of trees found across surveys in the four 15 m × 15 m neighbourhoods was 32 918. The total for a survey year ranged between 2,693 (in 1994) and 20,484 (in 2009). The mean basal area of the four 15 m × 15 m neighbourhoods across surveys was 49.5 m2/ha (0–136.8 m2/ha). The plot-level covariates used in the modelling were constant over time with mean distance from the earthquake epicentre, slope, landform index and soil-available P being 18.1 km (5.6–30.2 km), 29.3° (1.0–60.0°), 20.7° (9.0–33.0°) and 23.1 μg/g (2.6–191.4 μg/g) respectively. In contrast, local basal area and diameter, had tree- and resurvey year-level values.

The survival and growth of a tree between surveys can be conceptualized with two components. At unit time intervals (e.g. annually), a tree may be alive (or not), and if alive it may survive until the next time interval with some survival probability. When a tree is alive, it may grow at a certain rate between survey periods. These two demographic components can be described more formally as follows.

Let urn:x-wiley:00220477:media:jec13238:jec13238-math-0001 be a binary (i.e. Bernoulli) random variable indicating whether tree urn:x-wiley:00220477:media:jec13238:jec13238-math-0002 in plot urn:x-wiley:00220477:media:jec13238:jec13238-math-0003 is alive (urn:x-wiley:00220477:media:jec13238:jec13238-math-0004) or dead (urn:x-wiley:00220477:media:jec13238:jec13238-math-0005) at time urn:x-wiley:00220477:media:jec13238:jec13238-math-0006 (Table 1). The probability of the tree surviving from time urn:x-wiley:00220477:media:jec13238:jec13238-math-0007 to urn:x-wiley:00220477:media:jec13238:jec13238-math-0008 (in years) is defined to be urn:x-wiley:00220477:media:jec13238:jec13238-math-0009 if the tree was alive at urn:x-wiley:00220477:media:jec13238:jec13238-math-0010, and 0 otherwise. That is, once a tree dies, it remains dead (i.e. the random variable urn:x-wiley:00220477:media:jec13238:jec13238-math-0011 cannot change from a 0 to a 1). In statistical terms, this can be expressed as:
urn:x-wiley:00220477:media:jec13238:jec13238-math-0012(1)
urn:x-wiley:00220477:media:jec13238:jec13238-math-0013(2)
Table 1. Notation and definition of terms used in models
Notation Definition
urn:x-wiley:00220477:media:jec13238:jec13238-math-0014 Tree index within plot
urn:x-wiley:00220477:media:jec13238:jec13238-math-0015 Plot index
urn:x-wiley:00220477:media:jec13238:jec13238-math-0016 Survey number (1, 2, … etc)
urn:x-wiley:00220477:media:jec13238:jec13238-math-0017 Years between survey urn:x-wiley:00220477:media:jec13238:jec13238-math-0018 and urn:x-wiley:00220477:media:jec13238:jec13238-math-0019
urn:x-wiley:00220477:media:jec13238:jec13238-math-0020 Initial survey when tree urn:x-wiley:00220477:media:jec13238:jec13238-math-0021 in plot urn:x-wiley:00220477:media:jec13238:jec13238-math-0022 was measured ≥30 mm
urn:x-wiley:00220477:media:jec13238:jec13238-math-0023 Tree urn:x-wiley:00220477:media:jec13238:jec13238-math-0024 alive, in plot urn:x-wiley:00220477:media:jec13238:jec13238-math-0025 at time urn:x-wiley:00220477:media:jec13238:jec13238-math-0026 (= 1 if alive, = 0 if dead)
urn:x-wiley:00220477:media:jec13238:jec13238-math-0027 Probability of tree urn:x-wiley:00220477:media:jec13238:jec13238-math-0028, in plot urn:x-wiley:00220477:media:jec13238:jec13238-math-0029, surviving from time urn:x-wiley:00220477:media:jec13238:jec13238-math-0030 to urn:x-wiley:00220477:media:jec13238:jec13238-math-0031
urn:x-wiley:00220477:media:jec13238:jec13238-math-0032 Diameter of tree urn:x-wiley:00220477:media:jec13238:jec13238-math-0033, in plot urn:x-wiley:00220477:media:jec13238:jec13238-math-0034 at time urn:x-wiley:00220477:media:jec13238:jec13238-math-0035
urn:x-wiley:00220477:media:jec13238:jec13238-math-0036 Growth of tree urn:x-wiley:00220477:media:jec13238:jec13238-math-0037, in plot urn:x-wiley:00220477:media:jec13238:jec13238-math-0038 at time urn:x-wiley:00220477:media:jec13238:jec13238-math-0039

Note that urn:x-wiley:00220477:media:jec13238:jec13238-math-0040 is annual survival probability. Where there is an unequal time interval of length urn:x-wiley:00220477:media:jec13238:jec13238-math-0041 between surveys, then the survival probability between surveys can be calculated as urn:x-wiley:00220477:media:jec13238:jec13238-math-0042.

Let urn:x-wiley:00220477:media:jec13238:jec13238-math-0043 be the diameter of tree urn:x-wiley:00220477:media:jec13238:jec13238-math-0044 in plot urn:x-wiley:00220477:media:jec13238:jec13238-math-0045 when it was first recorded on a plot. This tree was first surveyed at time urn:x-wiley:00220477:media:jec13238:jec13238-math-0046. The subsequent expected diameter of the tree urn:x-wiley:00220477:media:jec13238:jec13238-math-0047 surveys later will be:
urn:x-wiley:00220477:media:jec13238:jec13238-math-0048(3)
where urn:x-wiley:00220477:media:jec13238:jec13238-math-0049 is the annual diameter growth rate (mm/year) for tree urn:x-wiley:00220477:media:jec13238:jec13238-math-0050 in plot urn:x-wiley:00220477:media:jec13238:jec13238-math-0051, and urn:x-wiley:00220477:media:jec13238:jec13238-math-0052 is the length of time between surveys urn:x-wiley:00220477:media:jec13238:jec13238-math-0053 and urn:x-wiley:00220477:media:jec13238:jec13238-math-0054. To allow for potential measurement error, the measured diameter for tree urn:x-wiley:00220477:media:jec13238:jec13238-math-0055, in plot urn:x-wiley:00220477:media:jec13238:jec13238-math-0056 at time urn:x-wiley:00220477:media:jec13238:jec13238-math-0057 was assumed to be normally distributed with mean urn:x-wiley:00220477:media:jec13238:jec13238-math-0058 and variance urn:x-wiley:00220477:media:jec13238:jec13238-math-0059 (i.e. urn:x-wiley:00220477:media:jec13238:jec13238-math-0060).

urn:x-wiley:00220477:media:jec13238:jec13238-math-0061 and urn:x-wiley:00220477:media:jec13238:jec13238-math-0062 were modelled using a combination of plot-level and tree-level effects, and should be interpreted as tree survival or growth, respectively, between the times t and t + 1. Diameter was included as a covariate for survival and growth, hence the joint nature of the analysis. An explanation of priors and the Bayesian modelling is outlined below.

2.4 Survival

Tree survival was modelled as:
urn:x-wiley:00220477:media:jec13238:jec13238-math-0063(4)
where urn:x-wiley:00220477:media:jec13238:jec13238-math-0064 is the mean survival probability, urn:x-wiley:00220477:media:jec13238:jec13238-math-0065 is the plot-level effect for plot urn:x-wiley:00220477:media:jec13238:jec13238-math-0066 at time urn:x-wiley:00220477:media:jec13238:jec13238-math-0067, urn:x-wiley:00220477:media:jec13238:jec13238-math-0068 is standardized log-diameter (standardization is explained below) and urn:x-wiley:00220477:media:jec13238:jec13238-math-0069 is the basal area of the measured trees at time urn:x-wiley:00220477:media:jec13238:jec13238-math-0070 in the nine subplots surrounding the subplot of tree urn:x-wiley:00220477:media:jec13238:jec13238-math-0071. A quadratic relationship with standardized diameter was assumed (see Hurst et al., 2011), with the a priori expectation that survival would peak for middle-sized trees and be lower for smaller and larger trees (i.e. urn:x-wiley:00220477:media:jec13238:jec13238-math-0072. Diameter (in mm) was standardized as urn:x-wiley:00220477:media:jec13238:jec13238-math-0073, where urn:x-wiley:00220477:media:jec13238:jec13238-math-0074 to ensure positive diameter values (as normal distribution assumed; more discussion below). Log diameter was used in the standardization to provide some asymmetry to the quadratic relationship on the real scale and a recognition that small trees were more numerous than large trees. The value of 25 mm is approximately the median value of the natural log of the recorded diameter for all trees, hence subtracting that value means the median of urn:x-wiley:00220477:media:jec13238:jec13238-math-0075 will be approximately 0. This reduces the correlation between the estimated values of urn:x-wiley:00220477:media:jec13238:jec13238-math-0076 and urn:x-wiley:00220477:media:jec13238:jec13238-math-0077 with other model parameters and can improve the convergence of the Markov Chain Monte Carlo (MCMC) chain. Note that as some plot resurveys were partial, the diameter value for some trees is unknown for some surveys. In these cases, the imputed (i.e. a predicted) value for urn:x-wiley:00220477:media:jec13238:jec13238-math-0078 was used according to the growth model.
The plot-level effect, urn:x-wiley:00220477:media:jec13238:jec13238-math-0079, was modelled with the inclusion of several plot-level characteristics as covariates, the effect of which may be different in the pre-earthquake, 0–5 years post-earthquake and 5+ years post-earthquake periods:
urn:x-wiley:00220477:media:jec13238:jec13238-math-0080(5)
where urn:x-wiley:00220477:media:jec13238:jec13238-math-0081 denotes the period associated with survey urn:x-wiley:00220477:media:jec13238:jec13238-math-0082 (pt = pre-earthquake years, 0–5 years post-earthquake or 5+ years post-earthquake); urn:x-wiley:00220477:media:jec13238:jec13238-math-0083, urn:x-wiley:00220477:media:jec13238:jec13238-math-0084, urn:x-wiley:00220477:media:jec13238:jec13238-math-0085 and urn:x-wiley:00220477:media:jec13238:jec13238-math-0086 are the standardized distance from the earthquake epicentre, slope, landform index and soil-available P of plot urn:x-wiley:00220477:media:jec13238:jec13238-math-0087 respectively. Two alternative distance measures, urn:x-wiley:00220477:media:jec13238:jec13238-math-0088, were considered as two separate models that were fit to the data: either the linear distance or the natural logarithm of distance from a plot to the epicentre. urn:x-wiley:00220477:media:jec13238:jec13238-math-0089 is a normally distributed plot-level random effect on survival (i.e. urn:x-wiley:00220477:media:jec13238:jec13238-math-0090). The corresponding effect sizes (e.g. urn:x-wiley:00220477:media:jec13238:jec13238-math-0091) allow the size of the effect to be different in each period. The term urn:x-wiley:00220477:media:jec13238:jec13238-math-0092 allows survival at the point where all other covariates are 0 to be different in each period. urn:x-wiley:00220477:media:jec13238:jec13238-math-0093 was set to 0 to ensure urn:x-wiley:00220477:media:jec13238:jec13238-math-0094 was identifiable.

All covariates were standardized to reduce the correlation of model parameters, and some were log-transformed (Table 2).

Table 2. Standardization used for each covariate employed to model survival and growth, and corresponding units for interpretation of estimated effect sizes
Covariate Standardization Units Description
urn:x-wiley:00220477:media:jec13238:jec13238-math-0095 (1) urn:x-wiley:00220477:media:jec13238:jec13238-math-0096 ln (km) Natural logarithm of distance from epicentre
urn:x-wiley:00220477:media:jec13238:jec13238-math-0097 (2) urn:x-wiley:00220477:media:jec13238:jec13238-math-0098 10 km Linear distance from the epicentre
urn:x-wiley:00220477:media:jec13238:jec13238-math-0099 urn:x-wiley:00220477:media:jec13238:jec13238-math-0100 Degrees° Slope
urn:x-wiley:00220477:media:jec13238:jec13238-math-0101 urn:x-wiley:00220477:media:jec13238:jec13238-math-0102 Degrees° Landform index
urn:x-wiley:00220477:media:jec13238:jec13238-math-0103 urn:x-wiley:00220477:media:jec13238:jec13238-math-0104 ln (µg/g) Natural logarithm of soil-available P
urn:x-wiley:00220477:media:jec13238:jec13238-math-0105 urn:x-wiley:00220477:media:jec13238:jec13238-math-0106 m2/ha Basal area
urn:x-wiley:00220477:media:jec13238:jec13238-math-0107 urn:x-wiley:00220477:media:jec13238:jec13238-math-0108 mm Natural logarithm of diameter at breast height
urn:x-wiley:00220477:media:jec13238:jec13238-math-0109 urn:x-wiley:00220477:media:jec13238:jec13238-math-0110 mm Diameter at breast height

Note

  • Brief description of covariate is also given.

2.5 Growth

Growth was modelled as:
urn:x-wiley:00220477:media:jec13238:jec13238-math-0111(6)
where urn:x-wiley:00220477:media:jec13238:jec13238-math-0112 is the mean growth rate, urn:x-wiley:00220477:media:jec13238:jec13238-math-0113 is the plot-level effect for plot urn:x-wiley:00220477:media:jec13238:jec13238-math-0114 at time urn:x-wiley:00220477:media:jec13238:jec13238-math-0115 and urn:x-wiley:00220477:media:jec13238:jec13238-math-0116 is standardized diameter, urn:x-wiley:00220477:media:jec13238:jec13238-math-0117 is the basal area of the measured trees in the nine subplots surrounding the subplot of tree urn:x-wiley:00220477:media:jec13238:jec13238-math-0118 as a tree-level covariate and urn:x-wiley:00220477:media:jec13238:jec13238-math-0119 is a tree-level normally distributed random effect term (urn:x-wiley:00220477:media:jec13238:jec13238-math-0120. For growth, diameter was standardized as urn:x-wiley:00220477:media:jec13238:jec13238-math-0121, where 122 mm is approximately the median value of the recorded diameter for all trees, hence subtracting that value means the median of urn:x-wiley:00220477:media:jec13238:jec13238-math-0122 will be approximately 0. This reduces the correlation between the estimated values of urn:x-wiley:00220477:media:jec13238:jec13238-math-0123 with other model parameters and can improve the convergence of the MCMC chain. Note that as some plot resurveys were partial, the diameter values for some trees are unknown for some surveys. In these cases, the imputed (i.e. a predicted) value for urn:x-wiley:00220477:media:jec13238:jec13238-math-0124 was used according to the growth model.
The plot-level effect urn:x-wiley:00220477:media:jec13238:jec13238-math-0125 for growth was modelled as:
urn:x-wiley:00220477:media:jec13238:jec13238-math-0126(7)
where urn:x-wiley:00220477:media:jec13238:jec13238-math-0127 and the plot-level covariates are defined as above (Table 2); and urn:x-wiley:00220477:media:jec13238:jec13238-math-0128 is a plot-level normally distributed random effect on growth (i.e. urn:x-wiley:00220477:media:jec13238:jec13238-math-0129). The corresponding effect sizes (e.g. urn:x-wiley:00220477:media:jec13238:jec13238-math-0130) allow the size of the effect to be different in each period. The term urn:x-wiley:00220477:media:jec13238:jec13238-math-0131 allows growth at the point where all other covariates are 0 to be different in each period. urn:x-wiley:00220477:media:jec13238:jec13238-math-0132 (pre-earthquake) was set to 0 to ensure urn:x-wiley:00220477:media:jec13238:jec13238-math-0133 was identifiable.

A Bayesian analysis of the tree survival and growth data using the above models was conducted using the JAGS software via the R package jagsUI. Prior distributions defined for the model parameters are given in Table 3. The prior distribution for urn:x-wiley:00220477:media:jec13238:jec13238-math-0134 was centred at 3.0 as survival was expected a priori to be very high (a prior centred at 0.0 implies a prior distribution for survival centred near 0.5). The approximate posterior distributions of the model parameters were obtained using Markov Chain Monte Carlo techniques in JAGS. Three chains were used of 10,000 iterations with the first 1,000 iterations being discarded as the burn-in period. Traceplots and the Gelman and Rubin (1992) R-hat statistic for both survival and growth models indicated that three chains, for each parameter, converged to the same range of values. Models were fit using all possible covariates.

Table 3. Prior distributions assumed for model parameters
Component Parameter Distribution
Survival urn:x-wiley:00220477:media:jec13238:jec13238-math-0135 urn:x-wiley:00220477:media:jec13238:jec13238-math-0136
urn:x-wiley:00220477:media:jec13238:jec13238-math-0137 urn:x-wiley:00220477:media:jec13238:jec13238-math-0138
urn:x-wiley:00220477:media:jec13238:jec13238-math-0139 and urn:x-wiley:00220477:media:jec13238:jec13238-math-0140 urn:x-wiley:00220477:media:jec13238:jec13238-math-0141
All other urn:x-wiley:00220477:media:jec13238:jec13238-math-0142’s urn:x-wiley:00220477:media:jec13238:jec13238-math-0143
Growth urn:x-wiley:00220477:media:jec13238:jec13238-math-0144 urn:x-wiley:00220477:media:jec13238:jec13238-math-0145
urn:x-wiley:00220477:media:jec13238:jec13238-math-0146 urn:x-wiley:00220477:media:jec13238:jec13238-math-0147
urn:x-wiley:00220477:media:jec13238:jec13238-math-0148’s and urn:x-wiley:00220477:media:jec13238:jec13238-math-0149’s urn:x-wiley:00220477:media:jec13238:jec13238-math-0150
All other urn:x-wiley:00220477:media:jec13238:jec13238-math-0151’s urn:x-wiley:00220477:media:jec13238:jec13238-math-0152

Note

  • urn:x-wiley:00220477:media:jec13238:jec13238-math-0153 denotes the uniform distribution with limits urn:x-wiley:00220477:media:jec13238:jec13238-math-0154 and urn:x-wiley:00220477:media:jec13238:jec13238-math-0155 and urn:x-wiley:00220477:media:jec13238:jec13238-math-0156 denotes the normal distribution with mean urn:x-wiley:00220477:media:jec13238:jec13238-math-0157 and variance urn:x-wiley:00220477:media:jec13238:jec13238-math-0158.

3 RESULTS

The Deviance Information Criterion for the natural logarithm of distance from the epicentre was 104 points smaller than a linear distance model, indicating a much better fit to all the data. Hence, only results from the survival and growth models using the natural logarithm of distance from the epicentre (hereafter distance from the epicentre) are presented. Plot- and tree-level covariates used in the models were not correlated (Table 4), and so were interpreted independently.

Table 4. Pearson correlation coefficients for each pair of covariates
  Plot-level Tree-level
Distance Slope Landform index Soil-available P Basal area Diameter
Plot-level
Distance 1.00 −0.12 −0.29 0.30 0.04 −0.04
Slope   1.00 0.36 −0.09 −0.01 0.00
Landform index     1.00 0.08 −0.33 −0.05
Soil-available P       1.00 −0.15 −0.15
Tree-level
Basal area         1.00 0.34
Diameter           1.00

Note

  • Plot-level covariates were assumed to be constant over time and include the natural logarithm of a plots distance from the epicentre (Distance), slope, landform index, and soil-available P. For tree-level covariates, based upon survey-specific values, correlation coefficients were summarized to a single value (mean) per plot. This mean was for the basal area of the four 15 m × 15 m neighbourhoods on each plot across years and for diameter at breast height (Diameter) of trees found in the four central 5 m × 5 m subplots across years. Covariates were correlated using the standardized values developed for the analyses.

3.1 Survival

Pre-earthquake mean tree survival was generally very high based on the posterior distribution (PD) for urn:x-wiley:00220477:media:jec13238:jec13238-math-0159 (Table 5). At the point where all the standardized covariates were zero pre-earthquake, mean survival was 0.99 (converted from Logit scale) but then decreased during 0–5 years post-earthquake (urn:x-wiley:00220477:media:jec13238:jec13238-math-0160) before marginally increasing 5+ years post-earthquake (urn:x-wiley:00220477:media:jec13238:jec13238-math-0161) (Table 5). However, there was considerable plot-level variation in survival after accounting for the effects of the other covariates (urn:x-wiley:00220477:media:jec13238:jec13238-math-0162).

Table 5. Summary of posterior distributions (PD) of parameters for survival model
Parameter Description Mean SD Percentiles
2.5% 97.5%
urn:x-wiley:00220477:media:jec13238:jec13238-math-0163 Mean survival pre-earthquake (logit scale) 4.3612 0.0560 4.2522 4.4708
urn:x-wiley:00220477:media:jec13238:jec13238-math-0164 Difference in mean survival 0–5 years post-earthquake −0.4057 0.0994 −0.5986 −0.2093
urn:x-wiley:00220477:media:jec13238:jec13238-math-0165 Difference in mean survival 5+ years post-earthquake 0.0997 0.0762 −0.0478 0.2508
urn:x-wiley:00220477:media:jec13238:jec13238-math-0166 SD of plot-level random effect 0.5342 0.0380 0.4632 0.6117
Plot-level
urn:x-wiley:00220477:media:jec13238:jec13238-math-0167 Pre-earthquake effect of distance from epicentre −0.1282 0.1139 −0.3501 0.0947
urn:x-wiley:00220477:media:jec13238:jec13238-math-0168 0–5 years post-earthquake effect of distance from epicentre 0.8039 0.1571 0.4936 1.1112
urn:x-wiley:00220477:media:jec13238:jec13238-math-0169 5+ years post-earthquake effect of distance from epicentre 0.4454 0.1304 0.1854 0.7001
urn:x-wiley:00220477:media:jec13238:jec13238-math-0170 Pre-earthquake effect of slope 0.0033 3.1905 −6.2730 6.2830
urn:x-wiley:00220477:media:jec13238:jec13238-math-0171 0–5 years post-earthquake effect of slope −0.0059 3.1605 −6.1931 6.1880
urn:x-wiley:00220477:media:jec13238:jec13238-math-0172 5+ years post-earthquake effect of slope −0.0161 3.1477 −6.2256 6.1840
urn:x-wiley:00220477:media:jec13238:jec13238-math-0173 Pre-earthquake effect of landform index −0.0246 0.0116 −0.0472 −0.0017
urn:x-wiley:00220477:media:jec13238:jec13238-math-0174 0–5 years post-earthquake effect of landform index −0.0351 0.0177 −0.0698 −0.0005
urn:x-wiley:00220477:media:jec13238:jec13238-math-0175 5+ years post-earthquake effect of landform index −0.0323 0.0142 −0.0604 −0.0044
urn:x-wiley:00220477:media:jec13238:jec13238-math-0176 Pre-earthquake effect of soil-available P −0.0321 0.0564 −0.1413 0.0796
urn:x-wiley:00220477:media:jec13238:jec13238-math-0177 0–5 years post-earthquake effect of soil-available P −0.0882 0.0886 −0.2619 0.0858
urn:x-wiley:00220477:media:jec13238:jec13238-math-0178 5+ years post-earthquake effect of soil-available P 0.1587 0.0661 0.0302 0.2882
Tree-level
urn:x-wiley:00220477:media:jec13238:jec13238-math-0179 Pre-earthquake linear effect of diameter 0.0658 0.0042 0.0576 0.0742
urn:x-wiley:00220477:media:jec13238:jec13238-math-0180 Pre-earthquake quadratic effect of diameter −0.0570 0.0049 −0.0665 −0.0472
urn:x-wiley:00220477:media:jec13238:jec13238-math-0181 0–5 years post-earthquake linear effect of diameter 0.0344 0.0099 0.0153 0.0539
urn:x-wiley:00220477:media:jec13238:jec13238-math-0182 0–5 years post-earthquake quadratic effect of diameter 0.0274 0.0121 0.0042 0.0516
urn:x-wiley:00220477:media:jec13238:jec13238-math-0183 5+ years post-earthquake linear effect of diameter 0.0371 0.0063 0.0249 0.0494
urn:x-wiley:00220477:media:jec13238:jec13238-math-0184 5+ years post-earthquake quadratic effect of diameter −0.0116 0.0072 −0.0257 0.0024
urn:x-wiley:00220477:media:jec13238:jec13238-math-0185 Pre-earthquake effect of basal area −0.0145 0.0021 −0.0187 −0.0103
urn:x-wiley:00220477:media:jec13238:jec13238-math-0186 0–5 years post-earthquake effect of basal area 0.0032 0.0040 −0.0045 0.0111
urn:x-wiley:00220477:media:jec13238:jec13238-math-0187 5+ years post-earthquake effect of basal area −0.0230 0.0026 −0.0281 −0.0179

Note

  • Parameters include those for the overall model as well as those for plot- and tree-level covariates. A description is given of each parameter followed by the mean, standard deviation (SD), and percentile values for the PD which are used to assess the effect size and strength of each parameter. Parameter values are for the point where other covariates in the model are zero on their standardized scales. As there was little correlation between covariates, the effect will be the same when other standardized covariates are not zero, but the magnitude will be different.

The relationships between survival and plot-level covariates changed in response to the earthquake. Pre-earthquake survival decreased slightly with distance from the epicentre (urn:x-wiley:00220477:media:jec13238:jec13238-math-0188) (Table 5) and median survival was >0.98 when plotted across the range of distances from the epicentre (Figure 2a). Post-earthquake survival increased away from the epicentre (i.e. higher mortality closer to the earthquake epicentre), with the effect being much stronger 0–5 years post-earthquake (urn:x-wiley:00220477:media:jec13238:jec13238-math-0189) than 5+ years post-earthquake (urn:x-wiley:00220477:media:jec13238:jec13238-math-0190) (Table 5; Figure 2c,e). Survival 0–5 years post-earthquake increased from c. 0.95 (5% annual mortality over 5 years) near the epicentre to >0.98 most distant from the epicentre, with lowered survival up to 20 km from the epicentre (Figure 2c). Plot slope did not affect survival: the PD for each slope-related parameter (urn:x-wiley:00220477:media:jec13238:jec13238-math-0191, urn:x-wiley:00220477:media:jec13238:jec13238-math-0192 and urn:x-wiley:00220477:media:jec13238:jec13238-math-0193) was centred near zero and each had a large standard deviation (SD) (Table 5). In fact, the PDs obtained are almost identical to the prior distributions used for these parameters (indicating little information about this relationship in the data) (Table 5). There was a small negative effect of landform index on survival pre-earthquake (urn:x-wiley:00220477:media:jec13238:jec13238-math-0194, that is, survival was lower on downslope plots (a high landform index) than those on ridges. The negative effect of landform index increased 0–5 years post-earthquake and was greater still 5+ years post-earthquake (urn:x-wiley:00220477:media:jec13238:jec13238-math-0195: the PD for each landform index-related parameter had a small SD. Soil-available P had little effect on survival pre-earthquake (urn:x-wiley:00220477:media:jec13238:jec13238-math-0196) (PD centred near zero and with a relatively large SD), a negative effect on survival 0–5 years post-earthquake (urn:x-wiley:00220477:media:jec13238:jec13238-math-0197), but a positive effect 5+ years post-earthquake (urn:x-wiley:00220477:media:jec13238:jec13238-math-0198) (Table 5). This positive effect resulted from high tree survival on plots with relatively high soil-available P 5+ years post-earthquake when compared with 0–5 years post-earthquake (Figure 3c cf Figure 3e).

Details are in the caption following the image
Median annual survival probability (Survival; (a), (c) and (e)) and median annual growth (Growth in mm/year; (b), (d) and (f)) in diameter plotted against distance from the epicentre (Distance) pre-earthquake (1974–1993), 0–5 years post-earthquake (1994–1998), and 5+ years post-earthquake (1999–2015) respectively. Note that survival and growth are denoted such that year t refers to the time period t to t + 1. The plots illustrate the effect of distance from the epicentre on survival and growth with standardized values of all other covariates used in the model set equal to zero. Because there was little correlation between covariates, the effect will be the same when the other standardized covariates are not zero, but the magnitude will be different. Tick marks on the X-axis indicate the distribution of plot values. Dark shaded area indicates 50% credible interval and light shaded area indicates 95% credible interval [Colour figure can be viewed at wileyonlinelibrary.com]
Details are in the caption following the image
Median annual survival probability (Survival; (a), (c) and (e)) and median annual growth (Growth in mm/year; (b), (d) and (f)) in diameter plotted against soil-available P pre-earthquake (1974–1993), 0–5 years post-earthquake (1994–1998) and 5+ years post-earthquake (1999–2015) respectively. Note that survival and growth are denoted such that year t refers to the time period t to t + 1. The plots illustrate the effect of soil-available P on survival and growth with standardized values of all other covariates used in the model set equal to zero. Because there was little correlation between covariates, the effect will be the same when the other standardized covariates are not zero, but the magnitude will be different. Tick marks on the X-axis indicate the distribution of plot values. Dark shaded area indicates 50% credible interval and light shaded area indicates 95% credible interval [Colour figure can be viewed at wileyonlinelibrary.com]

Pre-earthquake survival initially increased as diameter increased, then decreased for larger trees (Figure 4a). That is the PD for the quadratic, diameter-related parameter (urn:x-wiley:00220477:media:jec13238:jec13238-math-0199) had a negative value (Table 5) suggesting an inverted U-shaped relationship. The PD for the quadratic, diameter-related parameter changed to positive for the 0–5 years post-earthquake period (urn:x-wiley:00220477:media:jec13238:jec13238-math-0200) and then again negative for the 5+ years post-earthquake period (Table 5). Two features of the relationship between survival and diameter appear to drive these changes. Firstly, 0–5 years post-earthquake there was increased survival of trees with the smallest and largest diameter, as well as decreased survival of mid-sized trees, when compared with pre-earthquake (Figure 4c cf Figure 4a). Secondly, 5+ years post-earthquake the smallest trees again had lower survival, but the high survival of large-diameter trees was sustained (Figure 4e). Survival decreased with increasing basal area of neighbours pre-earthquake (urn:x-wiley:00220477:media:jec13238:jec13238-math-0201) but was little affected by basal area 0–5 years post-earthquake (urn:x-wiley:00220477:media:jec13238:jec13238-math-0202 (PD centred near zero and very small SD; Table 5). Five plus years post-earthquake, the negative effect of basal area on survival was even stronger than before the earthquake (again with a very small SD).

Details are in the caption following the image
Median annual survival probability (Survival; (a), (c) and (e)) and median annual growth (Growth in mm/year; (b), (d) and (f)) in diameter plotted against diameter pre-earthquake (1974–1993), 0–5 years post-earthquake (1994–1998) and 5+ years post-earthquake (1999–2015) respectively. Note that survival and growth are denoted such that year t refers to the time period t to t + 1. The plots illustrate the effect of diameter on survival and growth with standardized values of all other covariates used in the model set equal to zero. Because there was little correlation between covariates, the effect will be the same when the other standardized covariates are not zero, but the magnitude will be different. Tick marks on the X-axis indicate the distribution of plot values. Dark shaded area indicates 50% credible interval and light shaded area indicates 95% credible interval [Colour figure can be viewed at wileyonlinelibrary.com]

3.2 Growth

Mean pre-earthquake tree growth was 1.1 mm/year (based upon the PD for urn:x-wiley:00220477:media:jec13238:jec13238-math-0203; Table 6). Growth 0–5 years post-earthquake was marginally higher (urn:x-wiley:00220477:media:jec13238:jec13238-math-0204), but then 5+ years post-earthquake lower (urn:x-wiley:00220477:media:jec13238:jec13238-math-0205) when compared with pre-earthquake. There was substantial variation in growth among trees (i.e. urn:x-wiley:00220477:media:jec13238:jec13238-math-0206 is relatively large), when compared with among-plot variation in growth (urn:x-wiley:00220477:media:jec13238:jec13238-math-0207), after accounting for variation in growth related to plot-level covariates (Table 6). However, the normally distributed measurement error accounted for the greatest source of variation (urn:x-wiley:00220477:media:jec13238:jec13238-math-0208).

Table 6. Summary of posterior distributions (PD) of parameters for growth model (measured as mm/year)
Parameter Description Mean SD Percentiles
2.5% 97.5%
urn:x-wiley:00220477:media:jec13238:jec13238-math-0209 Mean growth pre-earthquake 1.1434 0.0305 1.0838 1.2037
urn:x-wiley:00220477:media:jec13238:jec13238-math-0210 Difference in mean growth 0–5 years post-earthquake 0.1810 0.0136 0.1544 0.2076
urn:x-wiley:00220477:media:jec13238:jec13238-math-0211 Difference in mean growth 5+ years post-earthquake −0.2830 0.0097 −0.3021 −0.2640
urn:x-wiley:00220477:media:jec13238:jec13238-math-0212 SD of random error on observation 2.3244 0.0081 2.3085 2.3404
urn:x-wiley:00220477:media:jec13238:jec13238-math-0213 SD of plot-level random effect 0.4172 0.0238 0.3723 0.4657
urn:x-wiley:00220477:media:jec13238:jec13238-math-0214 SD of tree-level random effect 0.7778 0.0076 0.7631 0.7927
Plot-level
urn:x-wiley:00220477:media:jec13238:jec13238-math-0215 Pre-earthquake effect of distance from epicentre −0.2834 0.0729 −0.4286 −0.1404
urn:x-wiley:00220477:media:jec13238:jec13238-math-0216 0–5 years post-earthquake effect of distance from epicentre −0.0477 0.0771 −0.2010 0.1034
urn:x-wiley:00220477:media:jec13238:jec13238-math-0217 5+ years post-earthquake effect of distance from epicentre −0.2720 0.0746 −0.4190 −0.1253
urn:x-wiley:00220477:media:jec13238:jec13238-math-0218 Pre-earthquake effect of slope 9.8429 4.0585 1.9914 17.8537
urn:x-wiley:00220477:media:jec13238:jec13238-math-0219 0–5 years post-earthquake effect of slope −25.1999 6.7912 −38.5386 −12.0398
urn:x-wiley:00220477:media:jec13238:jec13238-math-0220 5+ years post-earthquake effect of slope 4.8831 4.8567 −4.5843 14.4761
urn:x-wiley:00220477:media:jec13238:jec13238-math-0221 Pre-earthquake effect of landform index −0.0251 0.0069 −0.0387 −0.0115
urn:x-wiley:00220477:media:jec13238:jec13238-math-0222 0–5 years post-earthquake effect of landform index −0.0043 0.0074 −0.0187 0.0101
urn:x-wiley:00220477:media:jec13238:jec13238-math-0223 5+ years post-earthquake effect of landform index −0.0159 0.0071 −0.0298 −0.0020
urn:x-wiley:00220477:media:jec13238:jec13238-math-0224 Pre-earthquake effect of soil-available P 0.1252 0.0351 0.0563 0.1942
urn:x-wiley:00220477:media:jec13238:jec13238-math-0225 0–5 years post-earthquake effect of soil-available P −0.0224 0.0373 −0.0956 0.0511
urn:x-wiley:00220477:media:jec13238:jec13238-math-0226 5+ years post-earthquake effect of soil-available P 0.0489 0.0358 −0.0212 0.1193
Tree-level
urn:x-wiley:00220477:media:jec13238:jec13238-math-0227 Pre-earthquake effect of diameter 0.0042 0.0001 0.0040 0.0044
urn:x-wiley:00220477:media:jec13238:jec13238-math-0228 0–5 years post-earthquake effect of diameter 0.0050 0.0001 0.0047 0.0053
urn:x-wiley:00220477:media:jec13238:jec13238-math-0229 5+ years post-earthquake effect of diameter 0.0027 0.0001 0.0025 0.0030
urn:x-wiley:00220477:media:jec13238:jec13238-math-0230 Pre-earthquake effect of basal area −0.0295 0.0005 −0.0306 −0.0284
urn:x-wiley:00220477:media:jec13238:jec13238-math-0231 0–5 years post-earthquake effect of basal area −0.0295 0.0007 −0.0310 −0.0281
urn:x-wiley:00220477:media:jec13238:jec13238-math-0232 5+ years post-earthquake effect of basal area −0.0273 0.0006 −0.0284 −0.0261

Note

  • Parameters include those for the overall model as well as those for plot- and tree-level covariates. A description is given of each parameter followed by the mean, standard deviation (SD) and percentile values for the PD which are used to assess the effect size and strength of each parameter. Parameter values are for the point where other covariates in the model are zero on their standardized scales. As there was little correlation between covariates, the effect will be the same when other standardized covariates are not zero, but the magnitude will be different.

Pre-earthquake, there was a negative relationship between growth and the distance of a plot from the epicentre (urn:x-wiley:00220477:media:jec13238:jec13238-math-0233), no effect 0–5 years post-earthquake (urn:x-wiley:00220477:media:jec13238:jec13238-math-0234) (SD for the PD > Mean in Table 6) and then an almost identical relationship 5+ years post-earthquake (urn:x-wiley:00220477:media:jec13238:jec13238-math-0235) to that pre-earthquake (Table 6; Figure 2b,d,f). Growth 0–5 years post-earthquake was high at distances >20 km from the epicentre, when compared with that pre-earthquake or 5+ years post-earthquake, but not for distances of up to 15 km from the epicentre (Figure 2d cf Figure 2a,f). The lower 5+ years post-earthquake growth (urn:x-wiley:00220477:media:jec13238:jec13238-math-0236) largely appeared to be a consequence of decreased growth at distances >20 km from the epicentre (Figure 2f cf Figure 2b). Pre-earthquake growth was estimated to increase with increasing slope (urn:x-wiley:00220477:media:jec13238:jec13238-math-0237), strongly decrease with increasing slope 0–5 years post-earthquake (urn:x-wiley:00220477:media:jec13238:jec13238-math-0238), and to be little affected by slope 5+ years post-earthquake (urn:x-wiley:00220477:media:jec13238:jec13238-math-0239) because of a large SD for the PD (Table 6). The effect of landform index on growth was estimated to be similar and negative pre-earthquake (urn:x-wiley:00220477:media:jec13238:jec13238-math-0240) and 5+ years post-earthquake (urn:x-wiley:00220477:media:jec13238:jec13238-math-0241), but with no effect in the 0–5 years post-earthquake (urn:x-wiley:00220477:media:jec13238:jec13238-math-0242) (Table 6). Soil-available P was positively related to growth pre-earthquake (urn:x-wiley:00220477:media:jec13238:jec13238-math-0243), had a slightly negative effect immediately post-earthquake (urn:x-wiley:00220477:media:jec13238:jec13238-math-0244), before a small positive effect re-emerged 5+ years post-earthquake (urn:x-wiley:00220477:media:jec13238:jec13238-math-0245). The positive effect of soil-available P on pre-earthquake and 5+ years post-earthquake growth was driven by plots with the lowest soil-available P having low growth (Figure 3b,f).

A feature of the tree-level covariates was very small SDs for the PDs (Table 6) giving confidence in the parameter estimates. The effect of diameter on growth was positive for all three periods, with the effect being high 0–5 years post-earthquake and low 5+ years post-earthquake (Table 6; Figure 4f cf Figure 4b,d). Growth was estimated to decrease with basal area, and the estimated effect size was almost identical for all three periods (Table 6).

4 DISCUSSION

Spatially representative plot data collected from our mountain beech forest over 19 years before an earthquake allowed us to define a context for interpreting survival and growth responses measured in the aftermath of a strong, infrequent and unpredictable disturbance event. For example, pre-earthquake growth was related to distance from the epicentre and it was changes in the shape of that relationship that allowed us to identify the earthquake's suppression of growth near the epicentre 0–5 years post-earthquake. The changing nature of relationships between survival and growth with tree-level characteristics (which were uncorrelated with plot-level characteristics) show that demographic responses were not solely a function of landscape position (see Turner & Gardner, 2015). Tree survival and growth responses in relation to plot- and tree-level characteristics were often short term and usually the relationships returned to pre-earthquake patterns by 5+ years post-earthquake. In terms of these responses our mountain beech forest appears resilient although overall basal area remains depressed (Hurst et al., 2011). Resilience in survival and growth may be because although plots with high soil-available P were damaged by the earthquake, the trees on those plots displayed fast growth and high survival by 5+ years post-earthquake (Figure 3).

4.1 Survival

Our study is the first to analyse for a hypothesized logarithmic relationship between tree survival and distance from an earthquake's epicentre. Landslides are often used as a surrogate for tree death cause by earthquakes. In mountainous terrain, the number of landslides generated by an earthquake declines with distance from an epicentre (Keefer, 2000; Simonett, 1967) with the maximum distance from an epicentre at which landslides occur determined by earthquake magnitude (Keefer, 1984b; Owczarek, Opała-Owczarek, Rahmonov, & Mendecki, 2017). The 1960 Chile earthquake (Mw = 9.5), the most powerful recorded in modern times, caused landslide damage to forests >150 km from the epicentre (Veblen & Ashton, 1978). In the only other permanent plot-based study that is somewhat similar to ours, Qiu et al., (2015) measured plots before and after the 2008 Wenchuan earthquake (Mw = 7.9) in China, to examine spatial and temporal patterns in tree survival. In the hardest hit zone near the epicentre, that earthquake resulted in 5-year tree mortality rates that were 2.4 times higher than before and, at a distance >50 km from the epicentre, these rates were still significantly higher than before the earthquake (Qiu et al., 2015). For the much smaller 1994 Arthur's Pass earthquake (Mw = 6.7), effects on survival and injury were largely <20 km distance from the epicentre. This differs from tree growth ring studies for similar sized earthquakes which have detected responses >60 km from the epicentre (e.g. Carver et al., 2004; Owczarek et al., 2017). In the first 5 years following the Arthur's Pass earthquake approximately 25% of trees died nearest the epicentre (based upon annual survivorship being approximately 0.95 over five years in Figure 2c). Most of this tree death was immediate because Allen et al. (1999) showed that 24% of trees were killed within a year of the earthquake in a sub-catchment near the epicentre. This mortality is high near the epicentre when compared with only 9% of trees dying in the first 5 years following the Wenchuan earthquake in the hardest hit seismic zone (Qiu et al., 2015). The earthquake reported in our study markedly decreased mountain beech survival as longer term average annual tree survival was 0.98 (1974–2004) in these forests (Hurst et al., 2011).

Earthquake-induced landslides predominate on steep slopes in mountainous terrain (Keefer, 1984a; Zeng, Lu, Jenkins, Negrón-Juárez, & Xu, 2016), but there was no support for our hypothesis that lower survival would be concentrated on steep slopes. This was partly because of a higher likelihood that a tree on lower slope positions, which may not be steep, could be struck and killed by landslide deposits from steep upslope positions (Keefer, 1984a; Simonett, 1967). As hypothesized, the Arthur's Pass earthquake did accentuate a negative relationship between our landform index and survival found pre-earthquake, that is, lower survival on lower slope positions (Table 5). This was the only earthquake effect that was greatest 5+ years post-earthquake, rather than 0–5 years post-earthquake. This most likely reflected ongoing landscape instability on lower slope sites caused by the earthquake (Marc et al., 2015), rather than an outbreak of a fungal pathogen associated with native, wood-boring, pinhole beetles (Platypus spp.) reported in the past after an earthquake in New Zealand Nothofagus forests (Wardle, 1984). We did not notice a build-up of the pinhole beetles when plots were resurveyed after the Arthur's Pass earthquake. There was support for our hypothesis that decreased survival 0–5 years post-earthquake would be found on sites with high soil-available P because landslides would recur on sites with young soils. Decreased survival by trees on plots with high soil-available P plots supports a view that disturbance can both respond to landscape patterns in soil properties and then reinforce those same patterns (Rosser & Carey, 2017; Turner & Gardner, 2015). Landslides are the most likely cause of differences in soil P among eroding hillslope soils (e.g. Peltzer et al., 2010; Eger et al., 2018). Mountain beech has well-developed ectomycorrhizae that enhance uptake of P and other nutrients from infertile soils using a dense fine root network (Wardle, 1984). The positive relationship between survival and soil-available P 5+ years post-earthquake may be a consequence of enhanced P uptake on relatively fertile sites.

An inverted U-shaped relationship is sometimes observed between survival and tree diameter size when based upon measurements made over large areas or long timeframes (e.g. Lines, Coomes, & Purves, 2010) and this was so for our mountain beech forest pre-earthquake (Figure 4a; Hurst et al., 2011). At a local-scale, Holzwarth, Kahl, Bauhus, and Wirth (2013) showed the form of such a relationship varied with species and mode of tree death. In contrast, the inverted U-shaped relationship between survival and tree diameter 0–5 years post-earthquake was lost; instead the smallest and largest trees had relatively high survival. This is intriguing for two reasons. Firstly, disturbance is often invoked to explain reduced survival of large trees (e.g. Holzwarth et al., 2013) and, after the Wenchuan earthquake, larger trees in damaged stands had lower survival than those in undamaged stands (Zeng et al., 2016). However, large trees in our mountain beech forest had low survival during an outbreak of pinhole beetles in the 1970s (Wardle & Allen, 1983). It is therefore possible that many large trees sensitive to disturbance were killed well before the 1994 earthquake. Secondly, 0–5 years post-earthquake survival of small trees was higher than pre-earthquake (Figure 4c vs. Figure 4a). This may be more influenced by a developing cohort of recruitment after earlier wind, snow and pathogen disturbance. Hurst et al. (2011) considered that this high survival is because the largest, and most successful, of this cohort were being recruited. Basal area effects on survival were largely absent 0–5 years post-earthquake potentially due to the arbitrary nature of earthquake-induced mortality.

4.2 Growth

Growth responses by trees that survived earthquakes have been used to infer the timing of earthquakes (e.g. Owczarek et al., 2017; Wells et al., 2001) and how long afterwards tree growth was affected (e.g. Yadav & Bhattacharya, 1994). Trees that survive an earthquake may express responses as synchronous growth decreases caused by, for example, injury or they might increase growth through competitive release caused by the death of neighbours (e.g. Jacoby et al., 1997; Van Arsdale, Stahle, Cleaveland, & Guccione, 1998). Growth decreases and increases may occur among different trees in response to the same event (Gawior et al., 2017; Wells et al., 2001). In our study, using a very large number of randomly sampled trees, we showed that 0–5 years post-earthquake growth near the epicentre was similar to that pre-earthquake and 5+ years post-earthquake. However, we considered growth was more often decreased near the epicentre because growth distant from the epicentre was greater 0–5 years post-earthquake (Figure 2). This resulted in the relationship between growth and distance from the epicentre for 0–5 years post-earthquake having little slope, whereas there was a growth decrease with distance from the epicentre pre-earthquake and 5+ years post-earthquake. The reasons for this spatial pattern in growth remain unresolved. Differences in moisture availability may be a factor since distance from the epicentre coincides with a decrease in precipitation (Griffiths & McSaveney, 1983) but it is unlikely that growth is constrained by precipitation; photosynthetic rates were rarely constrained by leaf-level moisture deficits in the drier south-eastern part of our study area (Benecke & Nordmeyer, 1982). However, in that drier part, greater summer precipitation results in enhanced nitrogen (N) uptake and productivity in mountain beech (Smaill, Clinton, Allen, & Davis, 2011). It is plausible that growth differences among periods, as well as decreasing growth pre-earthquake and post-earthquake 5+ years with distance from the epicentre, reflect the effects of moisture-related N availability on growth. Alternatively, the spatial gradient in growth may reflect the historical imprint of previous disturbance events (Harcombe, Allen, Wardle, & Platt, 1998; Wardle & Allen, 1983). Whatever the cause, it is challenging to understand earthquake impacts without accounting for other factors driving spatial and temporal variation in demography.

Tree growth is immensely variable in natural forests (Canham, LePage, & Coates, 2004). We found a positive relationship between growth and slope pre-earthquake, and to a lesser degree 5+ years post-earthquake, but negative relationships between growth and landform index for the same periods (Table 6). Elsewhere slower growth has been demonstrated on sheltered lower slope positions (Herwitz & Young, 1994) but this is not always so (Bellingham & Tanner, 2000; Da Silva et al., 2002). Negative relationships between growth and landform index in our study area were unanticipated as we have previously shown that total above-ground tree stem biomass growth, using all trees in the same plots, increased with landform index (Harcombe et al., 1998). That relationship may be driven by a few fast-growing large trees on plots with high landform indices masking the slow growth of many small trees that are shaded and suppressed (Coomes & Allen, 2007a). As hypothesized the earthquake disrupted relationships between growth and slope, as well as between growth and landform index, 0–5 years post-earthquake (Table 6). Therefore, there was a strongly negative relationship between 0–5 years post-earthquake growth and slope, which may reflect injury-related slow growth on steep slopes. A positive relationship between pre-earthquake growth and soil-available P, and to a lesser degree 5+ years post-earthquake, may reflect enhanced growth on such relatively fertile soils (Figure 3). While P limitation in mountain beech has not been experimentally demonstrated, our study area does have low soil P (Brandtberg et al., 2010). Elsewhere soil-available P can relate positively to tree diameter growth (Coomes et al., 2013; Gradowski & Thomas, 2006). It is possible that plots with high soil-available P did not have high growth 0–5 years post-earthquake because the earthquake caused high levels of injury on such plots (Figure 3).

We hypothesized that a previously described positive relationship between growth and diameter (Coomes & Allen, 2007a) would be lost if the earthquake reduced survival, thereby decreasing neighbourhood competition, and in so doing increasing the growth of small individuals. This is because there is strong asymmetric competition for light in mountain beech stands (Coomes & Allen, 2007a). We instead documented increased growth (and survival) of large trees 0–5 years post-earthquake and suggest they were better able to capture any temporal patterns in resource availability. It was surprising that the relationships between growth and basal area were similar for the three periods because of the potential for widespread tree injury to effect growth.

5 CONCLUSIONS

A rich knowledge of forest dynamics has emerged from our mountain beech permanent plots over the last 45 years. These forests have so far been subject to a range of disturbance events including wind-throw, stem and branch breakage from snow, a native pathogen outbreak and more recently an earthquake. Elsewhere many studies have documented how tree growth and survival respond to human-related disturbances at global, regional and local scales (e.g. Adams et al., 2009; Trumbore, Brando, & Hartmann, 2015). In our study, a spatially extensive, representative plot network, including plots unaffected by the earthquake, gave confidence that the tree demographic responses portrayed were not a function of other potential causes (e.g. global change).

ACKNOWLEDGEMENTS

We thank John Wardle for establishing the plot network and Kevin Platt, Larry Burrows and many others who collected, checked and archived the data. John Barran provided the photograph of Easy Stream for Figure 1 and the Graphical Abstract photograph. The work was funded by the former New Zealand Forest Service, Ministry of Forestry, Foundation for Research, Science and Technology, and the Strategic Science Investment fund of the Ministry of Business, Innovation and Employment and the authors. There are no potential sources of any conflicts of interest.

    AUTHORS’ CONTRIBUTIONS

    R.B.A., D.I.M., P.J.B., S.K.W., D.A.C. and J.M.H. conceived the ideas and designed the methodology; R.B.A., P.J.B., S.K.W., J.M.H. and E.E.A. collected the data; D.A.M. analysed the data; R.B.A. led the writing of the paper. All authors contributed critically to the drafts and gave final approval for publication.

    DATA AVAILABILITY STATEMENT

    The data are archived within and can be requested from New Zealand's National Vegetation Survey Databank at: https://nvs.landcareresearch.co.nz/data/search using the string ‘harper/avoca forest stem diameter’.