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Latitudinal limit not a cold limit: Cold temperatures do not constrain an endangered tree species at its northern edge

Authors:

Abstract

Aim A strong influence of climate on species’ range is often assumed, and forms the basis for projecting many future range shifts with changing climate. Particularly at poleward latitudinal or elevational edges, abiotic conditions are thought to play a major role in limiting distributions. We estimated the roles of climate and landscape features in shaping habitat at the northern distributional edge of a critically threatened mountain tree species. Location British Columbia and Alberta, Canada. Taxon Pinus albicaulis (Engelm.) Methods We used a hierarchical Bayesian model (HBM) to combine multiple scales, sources, qualities and types of species data. We jointly examined the climate influence on occupancy across scales, and on juvenile and adult abundance to quantify habitat quality at two life history stages. Results We found that cold temperature was the strongest predictor of whitebark pine occurrence at regional scales, with colder areas being better (i.e. the sign was negative). Occupancy at local scales was best predicted by low growing degree‐days and declining precipitation as snow. These relationships with occupancy across scales indicate that suitable climatic and topographic habitats currently exist beyond the northern edge of whitebark pine's current range. We found high adult abundance was predicted in sunny, cool habitats with little climatic drought, whereas high juvenile densities were associated with higher precipitation as snow and more climatic drought. Main conclusions The negative relationship to temperature and the ample suitable habitats predicted to exist poleward of the current species’ range limit indicates whitebark pine is not limited by cold temperatures. We suggest that not all species’ ranges are cold limited at high latitudes or elevations. For whitebark pine this means warming temperatures may not directly result in a northern range expansion as a result of warming habitat.
1398  
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Journal of Biogeography. 2020;47:1398–1412.wileyonlinelibrary.com/journal/jbi
Received: 12 June 2019 
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Revised: 4 De cember 2019 
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Accepted: 20 D ecember 2019
DOI: 10.1111/jbi.13822
RESEARCH PAPER
Latitudinal limit not a cold limit: Cold temperatures do not
constrain an endangered tree species at its northern edge
Alana J. Clason1| Eliot J. B. McIntire2| Philip J. Burton3
© 2020 Her Majes ty the Queen in Right of Can ada. Reproduced with permission of the Mini ster of Natur al Resources Cana da
1Natural Resources and Environme ntal
Studies I nstitute, Universit y of Nor thern
British Columb ia, Prince Geor ge, BC, Canad a
2Natural Resources Canada, Canadian Forest
Service, Government of Canad a, Pacific
Forestry Centre, Victoria, BC, C anada
3Ecosystem Scien ce and Management,
University of No rthern British Columbia,
Terrace, BC , Cana da
Correspondence
Alana J. Clason, B ulkley Valley Cent re
for Natur al Resources Research and
Managem ent, 3731 1s t Avenue, B ox 4274,
Smithe rs, BC V0J 2N0, Canada.
Email: ajclason@gmail.com
Funding information
Pacifi c Institute for Climate Solutions;
ESRI Canada; Northern Scie ntific Training
Program; Univer sity of North ern Bri tish
Columbia; Cana dian Forest Ser vice;
Natural Sciences and Engineering Research
Council of Canada; Alberta Conser vation
Association
Handling Editor: Jack Williams
Abstract
Aim: A strong influence of climate on species’ range is often assumed, and forms
the basis for projecting many future range shifts with changing climate. Particularly
at poleward latitudinal or elevational edges, abiotic conditions are thought to play a
major role in limiting distributions. We estimated the roles of climate and landscape
features in shaping habitat at the northern distributional edge of a critically threat-
ened mountain tree species.
Location: British Columbia and Alberta, Canada.
Tax o n: Pinus albicaulis (Engelm.)
Methods: We used a hierarchical Bayesian model (HBM) to combine multiple scales,
sources, qualities and types of species data. We jointly examined the climate influ-
ence on occupancy across scales, and on juvenile and adult abundance to quantify
habitat quality at two life history stages.
Results: We found that cold temperature was the strongest predictor of whitebark
pine occurrence at regional scales, with colder areas being better (i.e. the sign was
negative). Occupancy at local scales was best predicted by low growing degree-
days and declining precipitation as snow. These relationships with occupancy across
scales indicate that suitable climatic and topographic habitats currently exist beyond
the northern edge of whitebark pine's current range. We found high adult abundance
was predicted in sunny, cool habitats with little climatic drought, whereas high juve-
nile densities were associated with higher precipitation as snow and more climatic
drought.
Main conclusions: The negative relationship to temperature and the ample suita-
ble habitats predicted to exist poleward of the current species’ range limit indicates
whitebark pine is not limited by cold temperatures. We suggest that not all species’
ranges are cold limited at high latitudes or elevations. For whitebark pine this means
warming temperatures may not directly result in a northern range expansion as a
result of warming habitat.
KEYWORDS
cold range limits, hierarchical bayes, latitudinal limit, niche limits, range limits, species at risk,
species distribution model
  
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CLA SON et AL .
1 | INTRODUCTION
Despite theory and evidence sug gesting that the abiotic and biotic
components of a species’ niche should all contribute to its range
limits (Sexton, McIntyre, Angert, & Rice, 2009), the underlying as-
sumption of climate equilibrium in most species distribution models
(SDM) implies that the climatic environment can often be informa-
tive in predicting species current and future ranges (Franklin, 2009).
However, some species ranges end before they have reached their
climatic limit, and some end beyond those of regionally defined cli-
mate limits. A meta-analysis indicates 75% of plant species trans-
plant studies observe a decline in fitness beyond current range
edges, but only half (46%) of the range limits tested coincided with
abiotic niche limits (Hargreaves, Samis, & Eckert, 2014). It may be
that the potential climatic niche is not filled as a result of dispersal
limitation (Hargreaves et al., 2014; Svenning & Skov, 2004), distur-
bance history or biotic interactions.
The ecological niche defines the conceptual space in which
an organism can meet its requirements to survive (Franklin,
2009; Guisan & Zimmermann, 20 00; Hutchinson, 1959). The
‘fundamental niche’ describes the broadly suitable physical en-
vironment, such as that defined by climate (precipitation, tem-
perature), whereas the ‘realized niche’ describes the actual
occurrence of a species based on constraint s on the fundamen-
tal niche, such as biotic interactions (competition) or dispersal
(Franklin, 2009; Guisan & Thuiller, 2005). Patterns in species
occurrence are influenced by a hierarchy of drivers across multi-
ple spatial and temporal scales (Guisan & Thuiller, 2005; Mackey
& Lindenmayer, 2001) controlling this niche space. Climate may
greatly influence species, communities, ecosystems or biomes
at the coarsest scales, but factors such as land cover (Pearson,
Dawson, & Liu, 2004), topography (Dobrowski, 2011) and soils
(Beauregard & de Blois, 2014) will be important drivers of spe-
cies patterns at finer scales due to the hierarchical struc ture of
ecosystem drivers (Pearson & Dawson, 2003; Whittaker, Willis,
& Field, 2001). Biotic interactions affect species distributions
at local scales, but outcomes of these interactions can be ob-
served both locally (Brown & Vellend, 2014) or at regional scales
(Heikkinen, Luoto, Virkkala, Pearson, & Körber, 2007; Meier
et al., 2010). Drivers operating at different scales within a de-
pendent ecological hierarchy will act simultaneously in natural
sy s te m s. Inc orp o rat ing th e se dri ver s at mult i ple sc a les is us efu l in
quantifying species–habitat relationships (Pearson et al., 2004).
Thus, a spatially hierarchical model—where a diversit y of poten-
tial drivers from different scales is used simultaneously, not as
alternative models for each scale—would likely improve accuracy
when predicting species occurrence.
At latitudinal range edges, the broad assumption of climatic
equilibrium suggests species are generally limited by cold, or in-
teractions with cold climates, with maladaptation to colder en-
vironments further towards the poles. However, evidence from
empirical studies on North American trees suggests multiple po-
tential causes for northern distributional limits, including climate.
For example, disturbance (Asselin, Payette, Fortin, & Vallée, 20 03;
Flannigan & Bergeron, 1998), stand history (Zhang, Bergeron,
Zhao, & Drobyshev, 2015), substrate (e.g. an affinity for rock y
outcrops (Meilleur, Brisson, & Bouchard, 1997)) or for coarse
till (Drobyshev, Guitard, Asselin, Genries, & Bergeron, 2014), or
the interaction between disturbance and site (Tardif, Conciatori,
Nantel, & Gagnon, 2006), can interact with climate to result in
northern distributional limits in the absence of climatic limits
alone. Other investigations have confirmed climatic limits to some
North American trees due to phenological maladaptation (lack of
fruit ripening; Chuine & Beaubien, 2001; Morin, Augspurger, &
Chuine, 2007) or decreased germination (Hobbie & Chapin, 1998).
The assumption of northern cold limitation underlies the general
prediction of northward range expansion with warming climates
(Chen, Hill, Ohlemüller, Roy, & Thomas, 2011). As northern cli-
mates warm, habitats should become suitable beyond northern
range edges, resulting in a northward shift in range. However, ev-
idence of northward expansion from the “cold” edge with climate
change is mixed (Chen et al., 2011; Harsch, Hulme, McGlone, &
Duncan, 2009; Kerr et al., 2015; Walther et al., 2002), suggest-
ing a better understanding of the processes controlling latitudinal
range edges is required, particularly to forecast range shifts with
a warming climate.
In predicting distributions using species distribution models
(SDMs), given the hierarchical structure of ecological systems,
species responses should be observed at appropriate scales and
viewed in relation to relevant processes. For instance, climate will
influence species at coarse scales, requiring observations of spe-
cies response at a similarly coarse scale (Pearson & Dawson, 2003).
This is the case for trees where coarse climatic variables may not
describe plot-level variation in tree abundance (Canham & Thomas,
2010; Zhu, Woodall, Ghosh, Gelfand, & Clark, 2014), but may ade-
quately describe occurrence (Lalonde, Morin, & Currie, 2012). This
can be the re su lt when occur re nc e and abu nd an ce are dr iven by di f-
ferent processes, requiring an analytical approach that can capture
these different processes and responses simultaneously (Nielsen,
Johnson, Heard, & Boyce, 2005). Furthermore, estimating how de-
mographics vary with ecological drivers can provide greater insight
into how these processes result in range limits (Eckhart et al., 2011)
or may result in distributional change with climate (Dolanc, Thorne,
& Safford, 2013; Zhu, Wood al l, & Cla rk, 2012). Par ti cu la rl y fo r lo ng-
lived sessile organisms such as trees, growth rates of established
individuals are often less sensitive to climate (Canham & Murphy,
2016) compared with juvenile recruitment, suggesting a broader
fundamental niche for adults compared with juveniles (Jackson,
Betancourt, Booth, & Gray, 2009). Estimating drivers of multiple
species responses (occurrence, abundance, reproductive success)
at appropriate scales could then provide greater understanding of
the processes controlling current species distributions (Dallas &
Hastings, 2018), resulting in improved predictions of future distri-
butional change.
The need to incorporate multiple responses and associated pro-
cesses at appropriate scales requires structuring SDMs to mirror
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this ecological structure. The data required to do this may vary in
quality and availability, particularly for species of conservation con-
cern (Camaclang, Maron, Martin, & Possingham, 2015). However,
accurately defining species–habitat relationships to estimate future
trajectories and extinction risk is essential for conservation planning
(Camaclang et al., 2015). Here, we use the flexibility available within
a hierarchical Bayesian statistical modelling approach to evaluate
drivers of occurrence and abundance of whitebark pine (Pinus al-
bicaulis Engelm.) in a broad geographic area that includes its “cold”
edge. The hierarchical Bayes approach accommodates the ecological
st ruc tu re an d pr ese nt s an op por tun it y to incor por at e da ta fr om mul-
tiple studies in a single statistical framework (Clark, 2005). Although
other processes may also contribute to range limitation (i.e. biotic
interactions), this mechanistic SDM will define suitable climatic habi-
tat for the current northern distribution of whitebark pine, informing
current management and future planning for a species at risk under
a changing climate.
2 | MATERIALS AND METHODS
2.1 | Study species and area
Whitebark pine is an endangered tree species, occupying high-ele-
vational habitats in western North America, ranging from California
to northern British Columbia. Whitebark pine has experienced sig-
nificant mor tality range wide over the last century, largely due to
the exotic pathogen, white pine blister rust, Cronartium ribicola J.C.
Fisch. (McDonald & Hoff, 2001), but also accelerated by outbreaks
of the endemic mountain pine beetle, Dendroctonus ponderosae
Hopkins (Campbell & Antos, 2000). Climate change is anticipated to
favour more competitive tree species (Keane, Holsinger, Mahalovich,
& Tomback, 2016), and interactions with disturbance agents to fur-
ther accelerate decline (Logan, Macfarlane, & Willcox, 2010; Wong
& Daniels, 2017). The northern populations of whitebark pine in
British Columbia and Alberta are as susceptible to disturbances
and stresses as populations further south (Clason, Macdonald, &
Haeussler, 2014), but the survival of northern populations may be
important for the long-term persistence of the species, given an-
ticipated climate warming scenarios. As with many species, climate
change is expected to reduce suitable growing space for whitebark
pine at its “warm” edge, while providing new habitat at the “cold”
edge (Hamann & Wang, 20 06). Understanding the role of climate in
shaping the distribution of the current northern distributional limit
of whitebark pine will be important for recover y under a changing
climate.
The study region in western Canada extends from 114°W in
Alberta to 132°W in British Columbia (BC), and from 52 to 57°N,
covering >43 million ha. The distribution of whitebark pine in the
study area falls into two distinct sub-regions: the Rock y Mountains
and associated interior mountain ranges in the east, and the Central
Coast, Skeena and Omineca Mountains in the west (Figure 1, and
Appendix S1 in Suppor ting Information).
2.2 | Response data
We used two types of response dataset s in this study to cap-
ture the influence of climate and topography on occurrence and
abundance: a new whitebark pine range map and whitebark pine
plot data. The whitebark pine range map (the derivation of which
is documented along with the resulting map in Appendix S1 in
Suppor ting Information) was converted into a raster map of pres-
ence (1) and absence (0) at a resolution of 2.5 km pixels for the
study area (Figure 1).
Whitebark pine plot data came from field collections as part
of this study in 2011 and 2012 (132 transects), and quantitative
presence, cover or abundance measurements (637 plots) made by
other researchers or conducted as part of government agency sur-
veys. For the new data collected here, we measured transects at
locations across the study area (Figure 1; Table 1). We established
transects haphazardly in whitebark pine or non-whitebark pine
habitat, recording whitebark pine density (juveniles and adults). All
other whitebark pine plot data used here were collected by other
researchers or government organizations from 1977 to 2014, with
variation in collec tion method (Table 1). To be included in this study,
data on the number and type (juvenile or adult) of whitebark pine
individuals within a recorded area were required, along with geo-
graphic coordinates for the location of the plot.
Three whitebark pine response types were possible from the plot
data: (a) presence/absence of whitebark pine, (b) abundance of regen-
eration (<1.3 m in height = “juveniles”) and (c) abundance of whitebark
pine sap li ng s and tre es (>1.3 m in hei gh t = “ad ult s” ). Within the juven il e
and adult response types, there were two types of abundance esti-
mates: (a) density (stems/ha) and (b) cover (% ground cover). Cover data
ca me fr om th e BC go ver n m ent biog e ocli m at ic ecosy s tem cl ass i f icat ion
(BEC) programme, and included areas within and beyond the current
northern limit for whitebark pine in BC. BEC plots were queried for
presence of whitebark pine (n = 160), and an additional 7,367 absence
plot s that did not cont ain whi te bar k pi ne and were abo ve 80 0 m in ele -
vation were extr acted from the BEC plot database (MacKenzie, 2017).
Including this absence data, the total plot data available for presence/
absence analysis were n = 8,160: for juvenile abundance n = 8,085
and for tree abundance n = 7,975 (Table 1). Juvenile density ranged
from 0 to 17,00 0 seedlings/ha, whi ch was simila r to studies from oth er
regions of the species’ range (Larson & Kipfmueller, 2010), and adult
density ranged from 0 to 3,467 stems/ha.
2.3 | Predictor variables
We selected two sets of predictor variables to explore the influ-
en ce of clima te (re gio na l and lo cal) an d top ogr aphy (l oca l) on white-
bark pine across the two scales of analysis (Table 2). We selected
variables based on ecological relevance and lack of correlation be-
tween these variables (Elith & Leathwick, 2009; Franklin, 2009) at a
give n sca le (s ee Ap p en d ix S2 in Su ppo r tin g Infor mat ion for de scr ip -
tion of predic tor variable selec tion). We used 2.5-km resolution to
  
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CLA SON et AL .
capture regional climate, and to capture the effect of landscape
position in highly varied mountainous terrain where whitebark pine
occurs, we used a resolution of 250 m at the local scale.
We selected climate variables from 213 annual, seasonal and
monthly variables generated by ClimateWNA (v.5.2.1; (Wang,
Hamann, Spittlehouse, & Murdock, 2012)). ClimateWNA down-
scales PRIS M da ta (Da ly, Gibson, Taylor, Johns on , & Paster is , 20 02),
creating scale-free actual and derived climate variables using lat-
itude, longitude and elevation with weighted correlations among
weather stations from 1961 to 1990 baseline data (Wang et al.,
2012). We averaged (using bilinear resampling, ArcGIS v.10.0) cli-
mate variables created at a resolution of 250 m, producing climate
layers at 2.5 km resolution for the regi ona l scale sub-mod el. We se-
lected mean annual temperature (MAT) and precipitation (MAP) at
the regional scale (2.5 km) to underst and the influence of regional
climate on whitebark pine occurrence (Table 2). We derived topo-
graphic variables from a 250-m-resolution digital elevation model
(DEM) produced using Canadian Digital Elevation Data (Natural
Resources Canada, http://geogr atis.gc.ca/api/en/nrcan-rncan/
ess-sst/3A537 B2D-7058-FCED-8D0B-76452 EC9D0 1F.html, ac-
cessed June 2012). We used ArcGIS spatial analyst (v.10.0, ESRI) to
estimate solar radiation (Fu & Rich, 2002) and the geomorphome-
try and gradient metrics toolbox (v.1.01; Evans, Oakleaf, Cushman,
& Theobald, 2014) to derive a compound topographic index
(Table 2). Predictor variables for the local occurrence and abun-
dance su b- model s we re growin g degre e- da ys (GDD, 5°C th re shold ),
precipitation as snow (PAS), climatic moisture deficit (CMD), com-
pound topographic index (CTI) and solar radiation (SOL; Table 2).
In the hierarchical model, we fit each variable with the qua-
dratic term (xi + x
i
2), approximating a Gaussian species response
curve (Oksanen & Minchin, 20 02), allowing a nonlinear response to
environmental gradients (Guisan & Zimmermann, 2000). We cen-
tred and scaled all predictor covariates prior to analysis to facilitate
model convergence and to compare covariate importance by exam-
ining the relative size of their parameter estimates. We log-trans-
formed squared covariate terms prior to scaling to reduce skewness.
Predictor covariates were edited in ArcGIS (version 10.0; ESRI) and
in R (R Core Team, 2019) with the raster package (Hijmans, 2019).
FIGURE 1 The study area (grey) extends from 52–57°N in central British Columbia and Alber ta, C anada and encompasses all
mountainous terrain within that range. Polygons (red) represent the current range map of whitebark pine (Appendix S1). The study area
contains the northern-most whitebark pine
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2.4 | Model description
We used the flexibility of a hierarchical Bayesian statistical model-
ling framework (Clark, 2005) to combine multiple scales, sources and
qualities of data in one statistical model (Appendix S2 in Supporting
Information). We directly integrated these multiple pieces of evidence
fo r be t t er ov e r a ll in fer e n ce of sp e c ies–hab ita t re lati ons h i ps, as we l l as
estimates of uncertainty around all parameters (Talluto et al., 2016).
The integrated model struc ture included two spatial scales (regional
and local), three response types (presence/absence, density, cover)
for two life history stages (adult, juvenile). The model estimates oc-
currence probability and abundance of whitebark pine.
TABLE 1 Summary of plot whitebark pine data sources and types
Data source No. plots General location Date Data type
Mean adult
density (#/ha)
Mean juvenile
density (#/ha)
Min/ Max
elevation (m)
Alberta Parks 15 Willmore, Alberta 2006–2008 P, AD, JD, H 777 394 1754/ 2, 210
A. Clason 132 B.C., A lberta 2011–2012 P/A, AD, JD, H 213 481 996/ 2,262
MFLNRO 2B.C. 2013 P, AD, JD, H 245 1,063 1536/ 1841
S. Haeussler, A.
Clason
6 Smithers, B.C . 2007–2009 P, AD, JD, H 78 1,033 782/ 1,017
BEC 160 B.C . 19 7 7–20 0 8 P, AC, JC 5.63a1. 29a675/ 2,233
BEC 7, 3 67 B.C. 19 7 7–20 0 8 A, AC , JC 0a0a412/ 2,276
C. Wong 95 Jasper, Willmore, Albert a 2006–2007 P/A , AD, JD 341 3,134 1553/ 2,127
E. Campbell 4 (averaged) McBride, Smithers 1995 P, AD, JD, H 4 81 418 1403/ 1712
M. Gelderman 69 Jasper, Willmore, Albert a 2012–2013 P, JD n/a 1,398 1574/ 2,230
National Parks 34 Jasper, Banf f, Alber ta 2003–2009 P, AD, JD 1,035 291 1590/ 2,739
R. Moody 171 Jasper, Banff, Albert a 2004–2005 P/A , AD, JD, H 17 38 1465/ 2,14 0
S. Zeglen 75 B.C. 1998–2000 P, H n/a n/a 944/ 2,337
Note: Adult >1.3 m, Juveniles <1.3 m.
Abbreviations: A, absence; AC, adult cover ; AD, adult densit y; H, health; JC , juvenile cover; JD, juvenile density; P, presence; P/A, presence and
absence.
Sources: Carmen Wong (Wong , 2012); Randy Moody (Moody, 1997); Alberta Parks; Elizabeth Campbell (Campbell & Antos, 2000); Matthew
Gelderman (Gelderman, Macdonald, & G ould, 2016); Canada National Parks; Sybille Haeussler (Haeussler, et al., 20 09); British Columbia Ministr y of
Forest s Lands and Natural Resource Operations; Alana Clason (Clason et al., 2014) and Stefan Zeglen (Zeglen, 2002).
aIndicates mean % cover estimate instead of #/ha.
TABLE 2 List of climate (from ClimateWNA; Wang et al., 2012) and landscape predictor variables used in the regional- and local-scale
sub-models
Regional sub-model Local sub-models
MAP Mean annual precipitation (mm).
Sum of annual precipitation
(mean from 1961 to 1990).
PAS Precipitation as snow (mm). This is based on average monthly air temperature and total
precipitation for each month from the start of September to the end of May.
MAT Mean annual temperature (°C).
Sum of annual temperature
(mean from 1961–1990).
GDD Growing degree-days over 5°C . This measure of cumulative heat sums c aptures both
growing season and temperature. Those site s with higher average monthly temperatures
will have a greater GDD value than those sites that may have a longer growing season,
but with lower temperatures.
CMD Climatic moisture deficit (mm). Calculated as the difference between monthly evaporation
and precipitation when evaporation > precipitation. A value of 0 indicates no moisture
deficit , with higher values indicating greater CMD. This measure is adjusted for the
effec t of latitude on water evaporation.
SOL Average annual solar radiation (WH/m2). Solar radiation quantif ies the energy from light,
taking into account atmospheric interference, latitude, elevation, slope steepness,
aspect, sun angle shifts throughout the year and shadows as a result of surrounding
topography (Fu & Rich , 2002)
CTI Compound topographic index . A wetness index correlated with soil moisture (Gessler,
Moore, McKenzie, & Ryan, 1995). Small water catchment s, steep slope s or hills would
have low values of CTI . Large catchments, gentle slopes, depressions or plains would
have high values of CTI.
  
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CLA SON et AL .
Integrating multiple scales, qualities and types of response re-
quires careful consideration of the ecological system and statistical
framework. In this case, we represented ecological relationships
based on the assumption that local occurrence is a reflection of both
the regional and local environment. For instance, analysing local oc-
currence alone may suggest that an observed absence is driven by
local processes, when in fact larger-scale habitat suitability defined
by regional climate may be significantly contributing to the observa-
tion. In other words, we consider the observation of local presence or
absence as the joint probability of regional and local occurrence. We
vi e w the pr oce s ses dr i vin g occu r renc e and th o se dr i vin g ab u nda nce as
two connected ecol ogical pr ocesses, ac count ing for the se explic it ly in
the model structure on the observation of local abundance (Figure 2).
2.4.1 | Regional occurrence
The first model component evaluates the probability of whitebark
pine occurrence within and beyond the current northern range limit
based on climate and landscape position, as in a standard zero-in-
flation model. This component was comprised of two sub-models
representing two ecologically significant scales: regional and local.
The regional sub-model is described by:
where Xr represents a vector of climate covariates (Table 2) with pa-
rameters αr and vector of
Br
estimating the probability of occurrence
of whitebark pine at the regional scale (
ψreg
). Dr represents the range
map presence/absence data used to fit regional predicted probability
of occurrence (
ψreg
), drawn from a Bernoulli distribution (0 or 1), with
ψcreg
representing the probability of regional occurrence centred to-
wards 0.5. We do this centring to account for asymmetric sampling of
presences and absences.
(1)
logit (
ψreg
)
=𝛼r+
Br×Xr
(2)
Dr
Bern
(
ψ
reg)
(3)
ψ
c
reg
=inverse.logit
(
logit
(
ψ
reg)
logit
(
ψ
reg))
FIGURE 2 The struc ture of the hierarchical Bayesian model (HBM). The numbers in brackets describe which equation in the text
corresponds to which parameter estimate
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2.4.2 | Local occurrence
The local-scale sub-model is described by:
where Xl represents a vector of climate and topography covariates
(Table 2) with parameters αl, and vectors of slope parameters (
Bl
) es-
timating the probabilit y of local whitebark pine occurrence (
). We
suggest that observed local occurrence (
Dl
) is a reflection of the joint
probability of occurrence from regional and local environments, result-
ing in observed plot data (
Dl
; presence/absence n = 8,160) being fit to
the joint probability of occurrence (
ψjoint
) via the Bernoulli distribution,
as opp os ed to the loc al pr ob abi li t y of occ ur ren ce (
) alon e. The prob -
ability of local occurre nce (
ψloc),
estimated from loc al covaria tes
Bl
, was
centred on the mean (
). When multiplied by the centred probabil-
ity of occurrence from the regional sub-model (
ψcreg
) and an unknown
scaling factor (s, to be estimated), (
ψloc)
contributes to the joint prob-
ability of occurrence,
ψjoint
. The joint probability of occurrence (
ψjoint
)
was also centred on the mean
(
ψ
joint)
to acc ou nt for prevalen ce of pres-
ence in the observed dataset, and this centred joint occurre nce (
ψcjoint
)
was linked to abundance sub-models below.
2.4.3 | Adult and juvenile abundance
The second model component predicts seedling or adult tree density
adjusted by the joint probability of a given plot being located in suit-
able habitat (based on both regional and local scales). Abundance
data were obser ved as either density (stems/ha) or cover (% ground
cover). To use all available data, we considered cover an estimate
of density and so included an observation model on the juvenile
and adult cover datasets to conver t cover estimates to equivalent
density. In this way, we used both cover and density data to simul-
taneously estimate local predicted abundance. The advantage of
doing this within a Bayesian model is that the uncertaint y around
the conversion parameters is estimated, and this uncertainty can
be included in estimating the influence of climate and landscape on
abundance. We estimated abundance using four sub-models. The
two sub-models estimating whitebark pine juvenile or adult densit y
(stems/ha) both had the same structure:
where N is the de nsity es timated from intercept (α) and vector of slope
parameters (
B
) on vec to r of cov ar iates (Xl). For compactness, we do not
show the identical set of equations and represent each with subscript
q, denoting juvenile or adult. The density estimate N was constrained
by the joint probabilit y of occurrence based on regional and local
sub-models (
ψcjoint
). These zero-inflated abundance models (both den-
sity and cover) accounted for zeros based on estimated probability of
occurrence in Equations 1-8, which prevented over-fitting unsuitable
habitat (zeros) in the density sub-models. We fit the density sub-mod-
els using a negative binomial distribution as it is well suited for count
data that contain zeros as well as extreme values (Bolker, 2008). The
stochastic model (Equation 11) fits the observed abundances (S), and
is described by a negative binomial distribution parameterized by the
mean (
Nd
) and size (Z) parameters.
The observation sub-models on juvenile and adult per cent cover
are described by:
where
Nc
is estimated cover, F is a scaling parameter to conver t be-
tween per cent cover (0–100) and estimated density
Nq
, thus assuming
a linear conversion. Estimated cover (
Nc
) was also influenced by the
probability of whitebark pine occurrence (
ψcjoint,
), and was thus a ze-
ro-inflated model similar to the density models above. The stochastic
model for cover data C was fit to a negative binomial distribution with
a mean of
Nc
and size K. We considered using a beta distribution for
these dat a bu t th e JAG S implementation employ ed (Su & Yajima, 2015)
do es not allo w va lue s of exa c tly 0, an d as vir tuall y al l of the valu es were
less than 40% cover, the behaviour was adequate with the unbounded
negative binomial.
We used normally distributed, uninformative priors for all
parameters Normal(0, 100), except for the size parameters of
the negative binomial distributions (Z, K), as well as the scaling
parameters (G,s, and F, Appendix S2 in Supporting Information),
for which we gave a uniform, uninformative prior Uniform(0.001,
1,00 0) to ensure draws of positive values. We ran three chains
with 200,00 0 iterations each, 150,0 00 discarded for the burn-in
for each chain, with resulting iterations thinned to produce 1,000
post-convergence (Rhat = 1; ry, 2010) iterations per chain. We
assessed model fit (predictive performance; Franklin, 2009) using
goodness of fit (R2) for juvenile and adult abundance sub-models
with plot-level data. We used threshold-dependent contingency
tables (Liu, White, & Newell, 2011) and threshold-independent
AUC (area under the receiver operator curve) for the occurrence
sub-models (Franklin, 2009). We describe the 2.5%, 50% and
97.5% quantile estimates of parameter values from 3,000 total
post-convergence iterations to generate predictions and for test s
of model fit.
(4)
logit (
ψloc
)
=𝛼l+
Bl×X
l
(5)
ψ
c
loc
=inverse.logit
(
logit
(
ψ
loc)
logit
(
ψ
loc))
(6)
ψjoint cloc ×ψcreg ×s
(7)
Dl
Bern
(
ψ
joint)
(8)
ψ
c
joint
=inverse.logit
(
logit
(
ψ
joint)
logit
(
ψ
joint)) ,
(9)
log (
Nq)
q+
Bq,l×X
l
(10)
Ndq
=
Nq
×ψ
cjoint,q
(11)
Sq
negbinom
(
Nd
q
,Z
q)
(12)
Ncq
=
Nq
×
Fq
×ψ
cjoint,q
(13)
C
negbinom
(
Nc
q
,K
q)
  
|
 1405
CLA SON et AL .
2.4.4 | Predicting suitable habitat
An advantage of the integrated model structure is the ability to in-
terp ret each sub-model independently, and as a whole. Maps of pre-
dicted occurrence (
ψ
) were produced from the regional sub-model
(Equation 3), local sub-model (Equation 5) and the joint occurrence
probability (Equation 8, Figure 2) based on climate and topographic
data layers. These three maps were used to assess model fit and
evaluate whether fit improved with model integration (based on the
joint probability map).
All analyses were conducted in R (v 3.6.1; R Core Team, 2019)
using packages ‘R2jags’ (v.0.5-7; Su & Yajima, 2015), which accesses
JAGS (v.4.0; Plummer, 2003), ‘raster (v.2.9-23; Hijmans, 2019) and
‘SDMTools’ (v.1.1-221.1; VanDerWal et al., 2014). The R code can be
found in Appendix S3 (Supporting Information).
3 | RESULTS
3.1 |Occurrence
The integrated model structure resulted in three predictions of oc-
currence: regional, local and joint. Our results showed that white-
bark pine has a higher probabilit y of regional occurrence in areas
with moderate precipitation and low temperatures at the regional
scale (Table 3, Figure 3). The parameter estimate for the linear por-
tion of the temperature ef fect (−1.22) was twice as strong a predic-
tor as the linear portion of the precipitation effect (0.53 Table 3). All
four covariates in the regional sub-model were important predic tors
of regional occurrence as the 95% credible intervals did not over-
lap zero (Kéry, 2010). Local predicted occurrence of whitebark pine
was most influenced by precipitation as snow and growing degree-
days (Table 3). High growing degree-days and high levels of snow
precipitation had a negative effect on local whitebark pine occur-
rence ( Table 3). The strongly negative squared term in precipitation
as snow implies a less rapid decrease in occurrence at lower snow
values, but an increasingly negative effect with increasing snow
(Figure 5, Table 3).
The regional sub-model (Figure S1–S4 in supplementary mate-
rials) was a moderately good predictor of regional observed occur-
rence (AUC = 0.75). There was a 75% correct classification rate after
a threshold (sensitivity = specificity probability = 0.57) was applied
to determine predicted presence and absence from the continuous
probability output (Franklin, 2009). The regional sub-model was ef-
fective at predicting range absences, but less effective at predict-
ing presence. Of the 68,776 data point s used in the regional model,
62,110 were observed absences, and the vast majority (46,661) were
also predicted as absences from the regional model. The commission
error rate was 25% (predicted present when obser ved absent), as
was the omission error rate (predicted absent when observed pres-
ent). These error rates were largely driven by the regionally suitable
climate habitat north of the current range, where presence was pre-
dicted but none was observed (Table 4). The local sub-model (
ψcloc
)
TABLE 3 Parameter estimates (2.5%, 50% and 97.5% quantiles)
for α (intercept) and
B
(slope) parameters for each sub-model across
3,00 0 iterations after burn-in and thinning
Variable
2.5%
quantile
Median
Parameter
Estimate
97. 5%
quantile
Regional occurrence sub-model
Intercept −2.97 −2 .93 −2. 8 9
Precipitation 0.49 0.53 0.57
Precipitation2−0.63 −0.60 −0.58
Temperature −1. 26 −1 . 2 2 −1.1 7
Temperature2−0.23 −0.19 −0.16
Local occurrence sub-mo del
Intercept −3.30 −2 .52 −1 .76
Snow 0.39 0.85 1.44
Snow2−2 .81 −2 .04 −1. 4 3
Growing degree-days −1.9 7 −1.58 −1. 2 3
Growing degree-days20.16 0.39 0.66
Drought index 0.44 0.81 1.23
Drought index2−0.67 −0.35 −0.06
Solar radiation 0.45 0.63 0.85
Solar radiation20.15 0.38 0.58
Wetness index 0.88 −0.64 −0.41
Wetness index 20.29 0 .47 0. 67
Juvenile abundance
Intercept 7. 3 4 7. 8 3 8.31
Snow 0.81 1 .15 1. 52
†Snow2−0.37 −0.16 0.03
Growing degree-days −0.77 −0.39 0.0 0
†Growing degree-days2−0.38 −0 .14 0.09
Drought index 0.93 1.30 1.68
†Drought index2−0.37 0.14 0.07
†Solar radiation −0.01 0.12 0. 27
†Solar radiation2−0.30 −0.09 0.11
†Wetness index −0.41 0.17 0.05
†Wetness index 2−0.01 0.17 0.34
Adult abundance
Intercept 4.28 4.71 5.14
Snow −1.0 0 −0.57 −0.14
†Snow2−0.21 0.05 0.30
Growing degree-days 0.97 −0.58 0.17
Growing degree-days2−0.79 −0.50 0.23
Drought index −1. 18 0.71 0.23
†Drought index2−0.35 0.00 0.33
†Solar radiation −0. 24 −0.02 0.19
Solar radiation20.28 0.57 0.82
†Wetness index −0.23 0.02 0.30
†Wetness index 2−0. 27 −0.03 0.20
†represents parameters whose range of values overlap zero, suggesting
the variable does not contribute to the response.
1406 
|
   CLASON et AL .
(Figure S1–S4 in supplementary materials) predicted occurrence
moderately well using the local climate and landscape features
(AUC = 0.75). Based on the adjusted threshold value to separate
predicted presence from absence, 75% of plots were correctly clas-
sified (Table 4). The joint (
ψjoint
) sub-model was similarly accurate
(AUC = 0.75 ), with 76% pl ot s cor re c tly ide nti fi ed (thr esh ol d pro ba bil-
ity = 0.12). Improved model accuracy of the joint compared with the
local sub-model was through an improved prediction of observed
absences: A tot al of 5,705 corre ctly predicte d absence s (Join t), com-
pared to 5,652 (Local; Table 4).
The pat terns in pre dicte d joint occur rence (Figure 4) sup port
observed distributional patterns for this species, being absent
from the wet, mild coastal climates and mild-low-elevational
interior climates (Arno & Hoff, 1989). The high predicted oc-
currence probability in the north of the study area is beyond
the current observed nor thern limit of whitebark pine (Figure 1,
Figure 4).
3.2 | Abundance
Adult abundance was predicted to be greatest on sites with low
degree-days, little climatic drought, high precipitation as snow
and high solar radiation. Juvenile abundance was predicted to be
greatest on site s w it h high pr ec ip it at ion as sn ow and hi gh climatic
drought ( Table 3). Precipitation as snow and climatic drought
were impor tant predic tors for both juveni le a nd a dults, but in op-
posite directions. More snow and increased climatic drought (rep-
resenting the difference between growing season precipitation
and estimated evaporation) were positively related to juvenile
abundance and negatively related to adult abundance (Table 3).
Growing degree-days had a negative effect on adult abundance
(Table 3).
Accuracy assessed by drawing from a negative binomial distri-
bution with juvenile or adult abundance estimates (Ψ) and size pa-
rameters (Z) from median rasters produced a predicted distribution
of values that included the observed dat a points of 67% of juvenile
plots (median of 1,000 iterations = 352/528) and 56% of adults ob-
served (median of 1,0 00 iterations = 232/418). Root mean square
deviation (RMSD, based on median parameter estimates) for the
adult model was 443 stems/ha, whereas the juvenile RMSD was
3,590 stems/ha. This describes the mean stems/ha deviation of pre-
dicted values from the obser ved (Piñeiro, Perelman, Guerschman, &
FIGURE 3 Frequency of pixels of suitable regional habitat for whitebark pine (black,>0.5 probabilit y) and available habitat (grey, <0.5
probability) across precipitation and temperature gradients
TABLE 4 Confusion matrix comparing obser ved and predicted
plot occurrence (presence or absence)
Predicted
Observed
Absent Present
Absent
Regional 5,284 185
Local 5,652 154
Joint 5,705 151
Present
Regional 2, 251 426
Local 1883 457
Joint 1,830 460
Note: Predicted occurrence was obtained by applying a threshold
(sensitivity = specificity) on the median parameter estimate for regional
(0.5), local (0. 57) and joint (0.12) occurrence sub-models to determine
predic ted presence (> threshold probability) and absence (< threshold
probability).
  
|
 1407
CLA SON et AL .
Paruelo, 2008), reflecting a low precision in predicted abundance.
Both sub-models had several parameter estimate values that over-
lapped zero (Table 3).
4 | DISCUSSION
Poleward and upper elevational range edges are commonly thought
to occur where the abiotic environment becomes too harsh for sur-
vival, while biotic factors, such as competition, may dominate limita-
tions at warm edges (Brown, Stevens, & Kaufman, 1996; MacArthur,
1972). The implication of this assumption is the highly anticipated
movement of species up-slope or poleward in response to warm-
ing climates (Chen et al., 2011; Parmesan & Yohe, 2003). However,
here we find a species that is not limited at its nor thern range by
cold climates. Integrating both regional- and local-scale abiotic con-
ditions predicts ample suitable habitat for whitebark pine north of
the range limit, suggesting other factors may currently drive the lati-
tudinal edge for this species. Dispersal limitation (Svenning & Skov,
2004), biotic interac tions (Mei er et al., 2010) and disturbance history
(Asselin et al., 2003; Flannigan & Bergeron, 1998) may all contribute
to the absence of this species in suitable climatic habitat. In addition,
if a species’ fundamental climatic niche contains climate space with
no modern analogue, a range limit may occur (Williams & Jackson,
2007). As a result of these possible drivers of the current range limit
of whitebark pine, using current species–climate relationships to
foreca st future range shift s wit h ch an gi ng cli ma te will be ina de qu at e.
The hierarchical statistical approach employed here estimated
the role of climate on habitat suitability across scales and response
variables, as well as enabled the integration of multiple data
sources in one an al ys is . High qu al it y and quantit ie s of data are lack-
ing for many species of conservation concern globally (Richardson
& Whittaker, 2010). However, waiting for more or better data to
understand population distribution or demographics while threats
such as habitat loss or disease outbreaks continue can severely
delay species conservation (Grantham, Wilson, Moilanen, Rebelo,
& Possingham, 2009). We demonstrate here that multiple types of
data can be used in a single analysis to generate a single predic-
tion of habitat requirements. The hierarchical structure also mir-
rored the ecological: large-scale climate should influence species
occurrence at broader scales, with the local-scale model refining
occurrence predictions within that broadly suitable space. Model
integration improved the accuracy in predicting plot presence/ab-
sence data from 70% with the regional model alone, to 75% with
the integration of regional and local scales (Table 4). The lack of
filling of suitable climate space nor th of the current range limit,
and the role of factors not included here, in shaping the distribu-
tion of whitebark pine, explain why our model only predicts 75%
of the data. Even with the flexibility and integration of the hier-
archical Bayesian model (HBM), additional fac tors are influencing
to whitebark pine's northern distribution. Seed dispersal by Clark's
Nutcrackers (Tomback, 1982), competitive dynamics (Campbell &
Antos, 2003) and disturbance history (Keane, Morgan, & Menakis,
1994) are all kn ow n to con tr ib ut e to the occurrence and abu nd ance
of whitebark pine. Incorporating these factors in this and other
species distribution model studies will help better understand the
current northern limit, and supports the inclusion of non-climatic
factors in species distributions more broadly (Araújo & Guisan,
FIGURE 4 Whitebark pine joint median occurrence probabilit y across its nor thern range in British Columbia and Alber ta, Canada, with
the current range map in black
1408 
|
   CLASON et AL .
2006). In addition, we did not include data from the entire range
of whitebark pine, which may have limited the fitting of abiotic
gradients, particularly regional temperature and precipitation at
the warm edge ( Titeux et al., 2017). However, all data t ypes used
here are not available for the entire range of the species, and as a
high-elevational species, the warm edge for whitebark pine (rep-
resented by it low-elevational habitat limits) occurs throughout its
latitudinal range.
We suggest that whitebark pine will not expand north with warming
climates (“pushing the grey bars to the right” in Figure 3), and already
occupies the coldest habitat available at the northern edge (i.e. there
are no available colder, unoccupied habitats (grey bars) to the left in
Figure 3). In other words, the poleward edge occupies the coldest hab-
itats available in the geographic space at the northern limit, but does
not occupy the warmer climate available. This would also be true for
any species whose northern limit is not a cold limit. This suggests that
an increase in temperature may not result in a range shift poleward and
highlights the need to consider how ubiquitous cold limitation is across
species, affecting predictions of future range shifts in a warming world.
The coldest climates available across its northern range are the habitats
most likely to be currently occupied (Figure 3, Figure 5) with abundant
juveniles and adults. Higher temperature locations in our study area
are accompanied by a steeper decline in adult compared with juvenile
abundance (larger negative slope), suggesting warm temperatures have
a larger negative effect on adult abundance. This suggests that the pre-
dicted decline in occurrence with increasing temperatures is a result of
stress or mortality impacting the successful transition from juveniles to
adults. This mechanism could be competitive disadvantage (Callaway,
FIGURE 5 Frequency and range of values for pixels (250 m) identified as suitable whitebark pine habitat (>0.5 probability, black) and
available (used or unused; grey) across the study area in the joint occurrence sub-model (based on median parameter values)
  
|
 1409
CLA SON et AL .
1998; Campbell & Antos, 2003) from slower growth rates in warmer
temperatures compared with that of competitors (McLane, 2011),
or other disturbance-caused mortality that may be more frequent in
warmer climates (Logan et al., 2010) or that interacts with climate to
increase mortality (Wong & Daniels, 2017). Incorporating other drivers
such as distance to seed sources (Moody, 2006), the health of seed
sources (Leirfallom, Keane, Tomback, & Dobrowski, 2015) as well as
masting/episodic seed production (Tomback, Sund, & Hoffmann,
1993), stand and canopy conditions (Larson & Kipfmueller, 2010),
and disturbance history (Campbell & Antos, 2003; Keane et al., 1994;
Morgan & Bunting, 1990) would improve predictions of abundance
across life stages, but especially at the juvenile stage. Other biotic in-
teractions, such as seed predation (Brown & Vellend, 2014), and the
absence of important mycorrhizae fungi (Nunez, Horton, & Simberloff,
2009; Wilkinson, 1998) could also be influencing establishment and
survival of whitebark pine at both its warm and cold elevational edges,
as well as the cold latitudinal edge captured here.
Tem per atu r e, an d its in flu e nce on the gr ow ing se aso n, is a st ron g
predictor of whitebark pine occurrence across scales and life his-
tory stages. The relationship between surface air temperatures and
whitebark pine is negative, with higher temperatures having a lower
probability of occurrence and fewer seedlings or trees expected.
This suggests two important predictions for understanding the role
of climate in shaping the distribution of this endangered species at
its northern limit: (a) cold temperature is unlikely the primary driver
of the curr en t nor t her n di str ibu tiona l bou ndary an d (b) war mer tem -
peratures with changing climate are unlikely to result in range ex-
pans io n nor th for this spec ie s. In the case of whi teb ar k pin e, th e lac k
of habitat that is “too cold” in the areas direc tly north of the current
range indicates that warming will not make more nor thern habit ats
available. Further studies of possible alternative drivers, including
biotic or dispersal limitations, are likely necessary to better under-
stand this northern range edge, particularly relevant for conserva-
tion planning for an endangered tree species. Indeed, subsequent
research has revealed a complex three-species interaction that may
explain some of the patterns observed here (Clason, 2017).
ACKNOWLEDGEMENTS
We thank NSERC for a Discover y Grant to EJBM and Postgraduate
Scholarship to AJC. We thank Pacific Institute for Climate Solutions
(PICS) for a graduate fellowship to AJC. We thank the Alberta
Conservation Association, Northern Scientific Training Program,
Alberta Parks, ESRI Canada, Canadian Forest Service and University
of Northern British Columbia (UNBC) for research support and
UNBC for scholarship support to AJC as well. We thank Laura Super,
Andrew Sheriff, Coralie Lenne, Nata de Leeuw, Mark Wong, Nikolas
Thum and Krystal Dixon for their help.
DATA AVAILAB ILITY STATE MEN T
Data from A.Clason (136 plots; Table 1) are openly available at the
Dryad Digital Repository https://datadryad.org/stash/dataset/
doi:10.5061/dryad.q83bk3jf9?
ORCID
Alana J. Clason https://orcid.org/0000-0003-2174-4925
Eliot J. B. McIntire https://orcid.org/0000-0002-6914-8316
Philip J. Burton https://orcid.org/0000-0002-5956-2716
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BIOSKETCHES
Alana J. Clason is an ecologist interested in the ef fect s of global
climate change on mountain ecosystems. She works to under-
stand the role of abiotic and biotic processes shaping species
distributions and forest communities. She is currently working
as a post-doctoral research associate with the Bulkley Valley
Research Centre www.alana clason.ca
Eliot J. B. Mc Intire is a co m p u t a tion al eco l o g ist who ha s wor ked in
forested and mountain ecosystems for 20 years. He is interested
in bringing mechanisms into phenomenological ecological mod-
els so that predictions can go beyond current conditions. He is
currently working on predictive applied ecology more generally
across a range of systems. http://predi ctive ecolo gy.org/
Philip J. Burton is a plant ecologist interested in all aspects of
vegetation dynamics and their response to natural disturbance,
climate change and human intervention. Based at UNBC’s
Terrace campus in north-western British Columbia, Phil is cur-
rently exploring issues of ecological resilience and mechanisms
of primary succession. https ://www.resea rchga te.net/profi le/
Philip_Burton2
Author contributions: This study was conceived by all authors.
AJC and EJBM designed, and AJC conducted the analyses. A JC
led the writing with significant input from PJB and EJBM.
SUPPORTING INFORMATION
Additional supporting information may be found online in the
Suppor ting Information section.
How to cite this article: Clason AJ, McIntire EJB, Bur ton PJ.
Latitudinal limit not a cold limit: Cold temperatures do not
constrain an endangered tree species at its northern edge.
J Biogeogr. 2020;47:1398–1412. htt ps ://doi.o rg /10.1111/
jbi.13822
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