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R E V I E W A N DS Y N T H E S I S Causes and consequences of variation in plant
population growth rate: a synthesis of matrix
population models in a phylogenetic context
Yvonne M. Buckley,1,2� Satu
Ramula,3*� Simon P. Blomberg,1
Jean H. Burns,4 Elizabeth E.
Crone,5 Johan Ehrlen,6 Tiffany M.
Knight,7 Jean-Baptiste
Pichancourt,8 Helen Quested6
and Glenda M. Wardle9
Abstract
Explaining variation in population growth rates is fundamental to predicting population
dynamics and population responses to environmental change. In this study, we used
matrix population models, which link birth, growth and survival to population growth
rate, to examine how and why population growth rates vary within and among 50
terrestrial plant species. Population growth rates were more similar within species than
among species; with phylogeny having a minimal influence on among-species variation.
Most population growth rates decreased over the observation period and were negatively
autocorrelated between years; that is, higher than average population growth rates tended
to be followed by lower than average population growth rates. Population growth rates
varied more through time than space; this temporal variation was due mostly to variation
in post-seedling survival and for a subset of species was partly explained by response to
environmental factors, such as fire and herbivory. Stochastic population growth rates
departed from mean matrix population growth rate for temporally autocorrelated
environments. Our findings indicate that demographic data and models of closely related
plant species cannot necessarily be used to make recommendations for conservation or
control, and that post-seedling survival and the sequence of environmental conditions
are critical for determining plant population growth rate.
Keywords
Comparative analysis, demography, fire, herbivory, matrix population models,
MCMCglmm, population dynamics, population growth rate, spatial and temporal
variation, temporal autocorrelation.
Ecology Letters (2010) 13: 1182–1197
I N T R O D U C T I O N
In nearly all natural systems, environmental conditions
fluctuate over time. This environmental variation influences
population growth rates and consequently species abun-
dance and distribution. Environmental variation is typically
thought to elevate extinction risk. However, in perennial
plants with high adult survivorship, environmental variation
1School of Biological Sciences, University of Queensland,
Queensland 4072, Australia2CSIRO Sustainable Ecosystems, 306 Carmody Rd, St Lucia,
Queensland 4067, Australia3Section of Ecology, Department of Biology, University of
Turku, 20014 Turku, Finland4Center for Population Biology, University of California, Davis,
CA 95616, USA5Department of Ecosystem and Conservation Sciences, College
of Forestry and Conservation, University of Montana, Missoula,
MT 59812, USA
6Department of Botany, Stockholm University, Stockholm
10691, Sweden7Biology Department, Washington University in St. Louis,
St. Louis, MO 63130, USA8CSIRO Entomology, Indooroopilly, Qld 4068, Australia9School of Biological Sciences, University of Sydney, Sydney,
NSW 2006, Australia
*Correspondence: E-mail: [email protected]�These authors contributed equally to this work.
Ecology Letters, (2010) 13: 1182–1197 doi: 10.1111/j.1461-0248.2010.01506.x
� 2010 Blackwell Publishing Ltd/CNRS
that leads to rare episodes of high recruitment may promote
persistence (Higgins et al. 2000). Understanding how pop-
ulation growth rate varies in space and time in natural plant
populations, and identifying the sources of that variation is
fundamental to predicting species responses to environ-
mental change (e.g. climate change) and other environmen-
tal factors (Gotelli & Ellison 2006; Morris et al. 2008;
Dahlgren & Ehrlen 2009; Dalgleish et al. 2010).
Variation in population growth rates is due to differences
in underlying vital rates, such as birth, growth, reproduction
and death. Vital rates are in turn influenced by multiple
environmental factors (e.g. fire, herbivores, weather) and
their contributions to population dynamics depend on the
life history of the focal species (Silvertown et al. 1993, 1996;
de Kroon et al. 2000; Ramula et al. 2008a). Population
dynamics may vary substantially among populations and
years within the same plant species (e.g. Pascarella &
Horvitz 1998; Warton & Wardle 2003; Jongejans &
de Kroon 2005) and this variation may be related to
changes in population density. In general, we would expect
average population growth rates to be stable but patterns of
variation in population growth rates to differ among species.
Variation in population growth rates is likely to depend on
species life-form and lifespan (Garcıa et al. 2008; Dalgleish
et al. 2010), with herbs and grasses more likely to exhibit
variable population growth rates than trees and shrubs. If
similar environmental factors cause both spatial and
temporal variation, then understanding spatial variation in
population dynamics might allow understanding of temporal
variation, informing also under what circumstances (if any)
spatial dynamics might be substitutable for temporal
dynamics.
In randomly fluctuating environments, vital rates are
expected to vary from year to year in an unpredictable way.
However, in many natural environments fluctuations occur
non-randomly over a longer period of time causing
significant temporal autocorrelation. For example, succes-
sion results in a sequence of environmental conditions and
positive temporal autocorrelation in vital rates (e.g. Pasca-
rella & Horvitz 1998). Temporal autocorrelation can also be
negative such that a good year is followed by a bad year, for
instance, because of synchronized flowering and associated
costs of reproduction (Crone et al. 2009). Due to the rarity
of long-term demographic studies for plants (Menges 2000),
temporal autocorrelation is rarely included in predictions of
population performance (but see Pascarella & Horvitz 1998;
Quintana-Ascencio et al. 2003; Menges et al. 2006), although
in some cases, it has been shown to have a large effect on
predicted population dynamics (Pike et al. 2004; Tuljapurkar
& Haridas 2006).
Vital rates are most commonly linked to population
growth rate using matrix population models that describe
individuals classified by age, size or life-stage moving
through the life-cycle (Caswell 2001). Due to similar
construction and standard parameter estimation, matrix
population models have been widely used to quantify
population dynamics across plant species with different life-
histories, including rare and invasive species (e.g. Silvertown
et al. 1993, 1996; Ramula et al. 2008a; Burns et al. 2010). A
large and growing number of techniques exist for incorpo-
rating variation in vital rates into population growth rate
estimates (Tuljapurkar 1990; Fieberg & Ellner 2001; Kaye &
Pyke 2003; Tuljapurkar et al. 2003; Doak et al. 2005b;
Dahlgren & Ehrlen 2009). However, fewer studies have to
date examined the sources of variation and the importance
of realized levels of vital rate variation for population
growth rates of natural populations.
Closely related species often show more similarity in their
traits or geographic distributions than less related species
(e.g. Darwin 1859; Garland et al. 1993; Freckleton et al. 2002;
Blomberg et al. 2003; Cadotte et al. 2009; Diez et al. 2009),
and may therefore be expected to have more similar
population dynamics than non-related species, making
phylogeny a potential predictor of patterns of variation in
vital rates and population growth rates. If it is possible to
predict patterns of variation in population growth rate based
on species relatedness, phylogeny might be a useful tool for
identifying species that are likely to become endangered or
invasive, and for designing management when detailed
demographic information is not available. However, most
studies examining variation in plant population growth rate
have focused on a single or a few species and we do not
know enough about variation above the species level to be
able to say whether phylogeny is an important predictor of
population dynamics.
We constructed a database of demographic models with
both spatial and temporal replication from 50 species of
terrestrial plants and a corresponding phylogeny to examine
how potential sources of variation (e.g. vital rates,
phylogeny, life-form, rare or common distribution, envi-
ronmental factors) influence population growth rates. We
asked the following specific questions: (i) How do plant
population growth rates vary within species and among
species, and how does phylogeny contribute to that
variation? (ii) What are the sources of variation in
population growth rates? We examine how temporal
variation in vital rates (survival, growth, fecundity) contrib-
utes to population growth rate, and how rare or common
distribution, population density and environmental factors
(fire, herbivory) are related to variation in population
growth rate. (iii) What is the importance of realized
temporal variation in population growth rates to predicted
population dynamics? We compare deterministic and
stochastic population growth rates and examine the role
of temporal autocorrelation. If realized temporal variation
in population growth rates is unimportant, we would expect
Review and Synthesis Plant population dynamics in space and time 1183
� 2010 Blackwell Publishing Ltd/CNRS
average deterministic growth rate to be similar to stochastic
population growth rate.
We found that populations within a species are more
similar to each other than populations among species, with a
minimal influence of phylogeny above the species level. Our
findings indicate that the population growth rate of any
particular species cannot be substituted for that of a closely
related species to predict population dynamics. Most plant
populations studied had a decreasing trend in population
growth rates over the observation period and population
growth rates between years were negatively autocorrelated.
Population growth rates varied more through time than
space regardless of life-form. Temporal variation in a subset
of species for which we had environmental data was partly
explained by time-since-fire and herbivory. Deterministic
and stochastic population growth rates were highly corre-
lated for randomly fluctuating environments but differed for
temporally autocorrelated environments, particularly for rare
species with strong positive or negative autocorrelations.
Our results raise new questions about the causes and
consequences of temporal variation in vital rates, and
suggest that simple population models with uncorrelated
environmental variation may not adequately capture sto-
chastic population dynamics for strongly autocorrelated
environments.
M E T H O D S
We first summarize our database on matrix population
models and variables calculated to analyse population
dynamics. We then describe statistical analyses used to
answer the three main questions addressed above.
Database
The database, obtained from the literature and some
unpublished material from the authors and their collabora-
tors, contains matrix population models for 50 perennial
plant species in which multiple populations (‡ 2) and
multiple matrices per population (‡ 2) were available.
A total of 708 matrices for 38 herbaceous species (herbs
and grasses) and 120 matrices for 12 other species (trees,
shrubs and succulents) was assembled. This database is
unique as it includes both spatial and temporal population
dynamics for each species, allowing a detailed comparison
within and among species. Different subsets of the data
were used for analyses depending on which data were
available (detailed under specific analyses outlined below).
Species were categorized as common (including three
invasive species) or rare, or as common, restricted range
rare and wide range rare (i.e. locally rare but regionally
widespread), depending on the analysis. Species were
classified based on the author�s description. Matrix dimen-
sion was recorded at the species level as a factor with three
levels, small (£ 4 matrix dimensions), medium (£ 7) and
large (> 7); category boundaries were chosen to ensure
adequate replication within each category. Treating matrix
dimension as a categorical variable enabled simpler inter-
pretation of interactions than treating it as a continuous
variable with polynomial terms. Species were also classified
as clonal or not and having a seedbank or not. Spatial
locations of populations were sourced from the literature
where available and through personal communications with
the authors.
Calculation of variables
Population matrices were analysed using standard methods
(Cochran & Ellner 1992; Caswell 2001), implemented within
a custom built MATLAB program 7.1 (The MathWorks, Inc.,
Natick, MA, USA). In cases where the original papers
incorporated a seedbank incorrectly leading to a spurious
one-year delay in the life-cycle (Silvertown et al. 1993:
p. 467; Caswell 2001: p. 61), the matrix was corrected before
analysis was carried out. In a few species, some matrices
were reducible (Caswell 2001) because a matrix element
involving growth from one of the smallest stages was zero.
In these cases, we added a small value (10)20) to the matrix
(Ehrlen & Lehtila 2002).
Variation and sources of variation in population growth rates
For analyses of variation in population growth rates within
and among species, we used a subset of data for each
species in which the same consecutive years were surveyed
for every population (i.e. if some populations were studied
longer than others for a species, only a subset of the data
were used; this reduced our data set to 49 species, 197
populations, totalling 736 matrices; Table S1). This avoids
confounding spatial and temporal variation, gives a clearer
comparison of whether spatial or temporal variation in
population growth rates is greater and allows straightfor-
ward interpretation of temporal autocorrelation. We
calculated the long-term deterministic population growth
rate (log kdet) for each matrix according to Caswell (2001,
p. 108) and estimated standard deviation of population
growth rates across years for each population (rlog kdet).
Based on all annual matrices from each population, we
calculated standard deviation for five demographic rates
(hereafter denoted vital rates) across years: post-seedling
survival, growth to stages with a greater reproductive value
conditional on survival, retrogression to stages with a
lower reproductive value conditional on survival, the
number of seeds entering the seedbank and the number
of seedlings produced. Post-seedling survival was estimated
as the weighted mean of the survival of individuals not
included in the seed bank or the first non-seed stage (often
1184 Y. M. Buckley et al. Review and Synthesis
� 2010 Blackwell Publishing Ltd/CNRS
equivalent to the seedling stage). To take population
structure into account, we used the proportion of
individuals in the respective stage in the stable stage
distribution as weighting factors. For Taxus floridana, where
seedlings of different ages were present in multiple stages
(Kwit et al. 2004), we excluded only the first of these
stages in a matrix for our estimates of post-seedling
survival. Similar to post-seedling survival, we excluded the
first non-seed and non-dormant stage (often the seedling
stage) in each matrix from the calculations of growth and
retrogression. We used average variation of growth and
retrogression (hereafter denoted growth) to avoid losing
matrices and species with missing growth or retrogression
transitions. Since actual seed and seedling production
varied greatly among species, we calculated the coefficient
of variation for both these variables to standardize the
scale (Sokal & Rohlf 1995; CV for small samples eq. 4.9).
We used average variation in seed and seedling production
when both variables occurred simultaneously in a matrix;
otherwise variation in either seed or seedling production
was used depending on which variable was presented for a
given species.
As the exact location of populations was rarely available,
we used the approximate distance between populations for
each species (available for 43 species; Table S1) to examine
whether populations in close proximity were more similar
in population growth rate than more distantly located
populations. Where available we calculated average plant
density per m2 for each population and year (21 species)
and noted habitat type and environmental factors (time-
since-fire and herbivory). Data on environmental factors
affecting population growth rate were only available for a
few species, time-since-fire was recorded for three species
and herbivory intensity was recorded for four species
(Table S4).
Importance of temporal variation in plant population growth rates
The full 50 species dataset and all available populations with
multiple years were used. For each population of each
species, we constructed a mean matrix by averaging multiple
annual matrices and calculated deterministic population
growth rate (log kmean). This estimate is based on average
vital rates over time and can sometimes be used to describe
average population performance (Doak et al. 2005a).
However, mean matrix population growth rate often differs
from the long-term stochastic population growth rate
(Tuljapurkar et al. 2003; Boyce et al. 2006), and differences
between these two rates can be regarded as a measure of the
influence of temporal variation in vital rates on population
growth rates.
To examine the importance of temporal variation in plant
population growth rates to predicted population dynamics,
we compared log kmean to stochastic population growth
rates calculated for randomly fluctuating environments. We
calculated stochastic population growth rates for each
population using a simulation which started from the stable
stage distribution derived from the mean matrix with 1000
individuals. All simulations were based on a matrix selection
method which is suitable for a small number of matrices
(Ramula & Lehtila 2005). In these simulations, each matrix
had an equal probability of being selected at each time
step and population dynamics were predicted for 500 years
with 10 000 iterations per year. Stochastic population
growth rate (ks) was calculated as log[(Nt ⁄ N0)1 ⁄ t ], where
N is population size at time t (Caswell 2001). In addition to
the simulations, we used Tuljapurkar�s analytical approxi-
mation for uncorrelated environments (Caswell 2001;
eq. 14.72), which estimates the stochastic population growth
rate (kTulja) from observed matrices and covariances among
matrix entries. This method provides an alternative to
simulations but may not describe population dynamics
accurately if there is a lot of variation in vital rates over time
(Morris & Doak 2002).
Both the simulation and Tuljapurkar�s method ignore
temporal autocorrelation, assuming uncorrelated population
growth rates over time. To estimate population growth rates
for temporally autocorrelated environments, we used matri-
ces from each population in the same sequence they were
observed in the field and calculated population growth rate
(kseq) by taking the n-th root of the greatest positive
eigenvalue of the matrix product [AnAn)1…A1] where A
denotes annual matrices over time and n the total number of
matrices per population. Throughout the paper, we use log-
transformed mean matrix growth rates to enable compari-
sons between them and stochastic population growth rates,
with population growth rates < 0 denoting decreasing
populations and population growth rates > 0 denoting
increasing populations.
Analyses
Variation in population growth rates within species and among species
To examine the effect of phylogeny on variation in
population growth rates, we generated a phylogeny using
the seed plant phylogeny available via phylomatic (reference
tree #R20050610), which references the angiosperm phy-
logeny website, the most recent, and constantly updated,
summary of the angiosperm phylogeny available (phylomatic
version 2; Webb C.O. 2005; Webb et al. 2008; Stevens 2009).
This topology was then assigned branch lengths based on
fossil calibration following Wikstrom et al. (2001) using the
bladj command in phylocom (version 4.0.1b), which approx-
imates branch lengths in millions of years (Webb et al. 2008;
see Fig. S1).
As we had multiple levels of random effects: species
within a phylogeny, populations within species and years
Review and Synthesis Plant population dynamics in space and time 1185
� 2010 Blackwell Publishing Ltd/CNRS
within populations, we used the R library MCMCglmm
v.1.10 to test for effects of phylogeny. MCMCglmm is a
Markov chain Monte Carlo sampler for multivariate
generalized linear mixed models with special emphasis on
correlated random effects arising from pedigrees and
phylogenies (Hadfield & Nakagawa 2010). MCMCglmm
enables the inclusion of a phylogeny, equivalent to a
pedigree in quantitative genetics studies, as a variance ⁄co-variance matrix in a generalized linear modelling Bayes-
ian framework. The MCMCglmm model also enables
random effects to be fit at the species and below species
levels. We fit species and populations nested within species
as random effects for models of deterministic population
growth rate (log kdet), and a random effect of species for
models of standard deviation of population growth rate
(rlog kdet) and comparisons of mean matrix and stochastic
population growth rate. We used weak proper priors on the
grouping variables (variance v > 0, degree of belief n = 1)
and assessed an arbitrary range of different values for the
prior variances (0.001 ) 1). We also assessed the effect of
prior selection on datasets where the response variable was
randomized. The adequacy of models with and without
phylogeny was assessed by comparing the Deviance
Information Criterion (DIC) of the two models (Spiegel-
halter et al. 2002).
The phylogenetic effects have expected (co)variances
proportional to the phylogenetic covariance matrix con-
structed from the phylogenetic tree (Fig. S1) for the
MCMCglmm models (Hadfield & Nakagawa 2010). The
within group errors were assumed to be independent and
identically normally distributed (IID), with mean 0 and
variance r2, except where a within group correlation
structure was explicitly applied. The random effects were
also assumed to be IID for different groups, with mean 0
and covariance matrix w. IID assumptions for residuals and
random effects were assessed using plots of the within
group errors and random effects (Pinheiro & Bates 2000:
p. 174–196). Chains mixed well with little autocorrelation,
indicating good convergence.
We examined the effect of phylogeny on population
growth rate (log kdet) using a model which included all
predictors (see Table 1) as well as a simpler version of the
model which only retained significant terms from the non-
phylogenetic models (see below). Autocorrelation of errors
to account for autocorrelation between time periods within
a population could not be fitted in the MCMCglmm
models for testing phylogeny and was therefore omitted.
Similarly, we examined the effect of phylogeny on standard
deviation of population growth rate (rlog kdet) and
stochastic population growth rates (ks, kTulja, kseq) using
a model which included several predictors and variance
at the species level (see Tables 2 and 3 for predictors
fitted).
Sources of variation in population growth rates
As the inclusion of phylogeny was not supported for
models of population growth rate (log kdet) (see Results and
Table S2), we used models without phylogeny to test
hypotheses about the structure and partitioning of variation
between spatial and temporal components for log kdet.
Simple variance components analysis of log kdet was used
initially to assess the effects of population level vs. year level
random effects (nested within species) to determine the
relative contributions of spatial vs. temporal effects.
Population and year effects could not be included in the
same model due to the lack of replicates at the within
population, within year level. As population level variation
may partly depend on spatial distances among the study
populations with populations closer together exhibiting
more similar dynamics, we also fitted models only including
species with populations at least 1 km apart (24 species) to
explore the effect of spatial distances among the popula-
tions on variation in population growth rates (i.e. whether
the results differ from those when all populations are
included).
To better model temporal effects on population growth
rate, we constructed a general linear mixed effects model
which included a fixed effects structure, a random effects
structure and autocorrelation between errors for sequences
of years within a population. For all of the following
non-phylogenetic linear mixed effects models, random
Table 1 Predictor variables and their significance in non-phyloge-
netic models for deterministic population growth rate, log kdet.
Variables retained in the simplest adequate model are in bold.
Fixed effects were assessed using likelihood ratio tests and
maximum likelihood estimates. Random effects were assessed
using likelihood ratio tests and restricted maximum likelihood
estimates. The random effect of species was not tested as
populations were nested within species and were retained in the
model. Data were from 49 species
Predictor variables LR testd.f., P-value
Year LR1 = 10.7, < 0.005
Matrix dimension (small, medium, large) LR2 = 0.4, < 0.85
Life-form (herb, other) LR1 = 0.7, < 0.5
Clonality (binary) LR1 = 0.1, < 0.96
Seedbank (binary) LR1 = 1.5, < 0.3
Distribution (common, rare restricted,
rare widespread)
LR2 = 0.1, < 0.95
Year : life-form LR1 = 2.1, < 0.2
Year : clonality LR1 = 3.2, < 0.3,
Year : seedbank LR1 = 2.5, < 0.2
Year : distribution LR2 = 2.6, < 0.3
r2species (intercept) Not tested
r2population (intercept) LR2 = 39.5, < 0.0001
r2population (slope of year) LR2 = 11.4, < 0.004
Autocorrelation of residuals (AR1) LR1 = 20.7, < 0.0001
1186 Y. M. Buckley et al. Review and Synthesis
� 2010 Blackwell Publishing Ltd/CNRS
effects were estimated using restricted maximum likelihood
(REML) and likelihood ratio (LR) tests, where the v2
distribution was used to determine P-values. Where the
errors from sequences of years within a population were
assumed to be distributed according to an auto-regressive
process of order 1 (AR1) (i.e. for temporal autocorrelation),
autocorrelation of errors was tested using REML tests
between models with and without the autocorrelation. Fixed
effects were assessed using maximum likelihood and
likelihood ratio tests (Bolker et al. 2009). We used the nlme
library in R (v. 2.9.2) (Pinheiro et al. 2009) to include
autocorrelation between errors for consecutive years.
Table 1 shows the variables fitted for population growth
rates (log kdet). We tested the slope of year as a fixed effect
and variance about the slope of year as a random effect. The
random effects structure included species, populations
nested within species and variance about the slope of year
at the population level with temporal autocorrelation
between errors (AR1). To examine the consistency of
autocorrelation for longer time series, we tested autocorre-
lation between errors (AR1) using a subset of our data that
contained populations with ‡ 3 consecutive year matrices
per population (610 matrices from 28 species). This subset
of data produced qualitatively and quantitatively similar
results to the full data set and we therefore report results
based on the full dataset only.
We examined the roles of vital rates, environmental
factors, habitat and population density as drivers of
population growth rates (log kdet). To investigate direct
relationships between population growth rate (log kdet) and
the vital rates of survival, growth and fecundity, we used a
model with autocorrelation of errors (31 species, 601
matrices due to missing data). We tested fire and herbivory
as drivers of variation in population growth rates using data
from three species (35 populations) for fire and four species
(25 populations) for herbivory. Time-since-fire or herbivory
(as linear and quadratic effects) was used as an explanatory
variable in linear mixed effects models to test for its effect
Table 2 Predictor variables and their significance in non-phyloge-
netic models for standard deviation of population growth rate,
rlog kdet. Variables retained in the simplest adequate model are in
bold. Fixed effects were assessed using likelihood ratio tests and
maximum likelihood estimates. Random effects were assessed
using likelihood ratio tests and restricted maximum likelihood
estimates. The random effect of species was not tested as
populations were nested within species and were retained in the
model. There were missing data for Campanula americana, Alnus
incana and Astragalus alopecurus, models were therefore run including
47 species. Note that simplified models including log rgrowth
instead of log rsurvival were structurally identical; however, models
with log rsurvival were strongly preferred to models with
log rgrowth (DAIC > 10)
Predictor variables LR testd.f., P-value
Log kmean LR1 = 10.1, < 0.002
Matrix dimension (small, medium, large) LR1 = 4.3, < 0.2
Distribution (common, rare restricted,
rare widespread)
LR1 = 0.01, < 0.95
No. matrices per population LR1 = 6.0, < 0.015
Life-form (herb, other) LR1 = 0.2, < 0.7
Seedbank (binary) LR1 = 0.8, < 0.4
Log rsurvival LR1 = 28.0, < 0.0001
CV fecundity LR1 = 1.7, < 0.2
r2species (intercept) Not tested
r2population (intercept) Not tested
r2population (slope of log rsurvival) LR2 = 13.6, < 0.0015
Table 3 Non-phylogenetic models for three measures of stochastic population growth rate (ks, kTulja and kseq) for 50 species. Variables
retained in the simplest adequate model are in bold. Fixed effects were assessed using likelihood ratio tests and maximum likelihood estimates.
Random effects were assessed using likelihood ratio tests and restricted maximum likelihood estimates. Some explanatory variables were not
tested because of significant interactions
Predictor variables ks kTulja kseq
Log kmean Not tested LR1 = 111.2, P < 0.001 Not tested
Matrix dimension (small, medium, large) LR2 = 8.2, P < 0.02 LR2 = 6.3, P < 0.05 LR2 = 6.4, P < 0.05
No. years per population LR1 = 1.35, P < 0.3 LR1 = 0.9, P < 0.4 LR1 = 1.8, P < 0.2
Life-form (herb, other) LR1 = 0.26, P < 0.7 LR1 = 0.26, P < 0.7 LR1 = 0.3, P < 0.6
Seedbank (binary) LR1 < 0.0001, P < 1 LR1 = 0.07, P < 0.8 LR1 = 3.4, P < 0.07
Distribution (common, rare) Not tested LR1 = 8.2, P < 0.005 Not tested
Log kmean : no. years per pop LR1 = 0.04, P < 0.85 LR1 = 1.3, P < 0.3 LR1 = 1.7, P < 0.2
Log kmean : matrix dimension LR2 = 0.75, P < 0.7 LR2 = 4.0, P < 0.2 LR2 = 0.08, P < 0.96
Log kmean : life-form LR1 = 0.4, P < 0.6 LR1 = 0.64, P < 0.5 LR1 = 0.04, P < 0.9
Log kmean : seed bank LR1 = 0.21, P < 0.7 LR1 = 1.8, P < 0.2 LR1 = 1.3, P < 0.3
Log kmean : distribution LR1 = 5.0, P < 0.03 LR1 = 2.3, P < 0.2 LR1 = 13.1, P < 0.001
r2species (intercept) Not tested Not tested Not tested
r2species (slope of log kmean) LR2 = 20.7, P < 0.001 LR2 = 33.8, P < 0.001 LR2 = 56.7, P < 0.001
Review and Synthesis Plant population dynamics in space and time 1187
� 2010 Blackwell Publishing Ltd/CNRS
on population growth rate across species. We also tested
for autocorrelation between years. As time-since-fire and
year were confounded, we did not include year in the fire
model. For the herbivory model, we included year as a fixed
effect and variance about the slope of year as a random
effect to account for possible temporal trends. We note that
all three species with data available for fire were from the
same geographic region (Central Florida, USA). We
examined the effect of habitat on log kdet. Habitat data
were available for 483 matrices and two categories of
habitat had sufficient species level replicates, grassland
(15 species, 53 populations) and forest (18 species, 86
populations). Finally, we tested whether density affected
log kdet for a subset of 207 matrices (21 species, 58
populations). We constructed models including density, year
and random effects of species and population (with
variance about the intercept and slope of density at the
population level to account for context specific effects of
density) with autocorrelation of errors (AR1) for sequences
of years within populations.
For analyses of standard deviation in population growth
rate, rlog kdet, we used the same predictors as for analyses of
log kdet (see Table 2 for predictors). In addition, we
examined the contributions of temporal variation in vital
rates (standard deviation of survival and growth and CV of
fecundity) in a subset of species (n = 47) for which these
data were available. Plots and initial modelling indicated
that variation in survival and growth (log rsurvival and
log rgrowth) were co-linear, therefore the sources of variation
in population growth rates was analysed using a model which
included the predictors in Table 1 and either log rsurvival or
log rgrowth; the better predictor was assessed using AIC. The
random effects structure included variance about the
intercept and about the slope of log rsurvival or log rgrowth
at the species level. As phylogeny was not important, we used
linear mixed effects models (nlme library in R).
Importance of temporal variation in population growth rates
To examine the importance of realized temporal variation in
plant population growth rate for randomly fluctuating
environments, we compared mean matrix population
growth rate (log kmean) to stochastic population growth
rates (ks and kTulja), and further examined the role of
temporal autocorrelation in plant population dynamics by
comparing mean matrix population growth rate to kseq. As
the inclusion of phylogeny was not supported in any of the
models (see Results), we used linear mixed effects models
(lme4 library in R to ensure model convergence) with
variance about the intercept and the slope of mean matrix
population growth rate (log kmean) with species as a random
effect to estimate model parameters (Table 3).
To determine whether the magnitude of the temporal
autocorrelation explained differences between stochastic
population growth rates for randomly fluctuating and
temporally autocorrelated environments, we constructed a
model for a subset of species with at least three consecutive
matrices (n = 26) with kseq as a response variable and the
following explanatory variables: ks, temporal autocorrelation
of annual population growth rates (as linear and quadratic
effects), distribution (rare, common) and their interactions.
Species was used as a random effect.
Normality and homogeneity assumptions were examined
for each model visually from residual plots and were well
supported. Exceptions were models of stochastic popula-
tion growth rates, where the differences between mean
matrix and stochastic population growth rates were mostly
in one direction only, leading to asymmetric distribution of
residuals. However, fitting heterogeneous variances by
species distribution (common ⁄ rare) or matrix dimension
was not supported by LR tests, indicating that the model
assumptions about homogenous variances were not severely
violated.
R E S U L T S
Variation in population growth rates within speciesand among species
The effect of phylogeny on all response variables was weak,
i.e. the phylogenetic relationship between species was
unrelated to deterministic population growth rate, standard
deviation of population growth rate, or the relationship
between mean matrix and stochastic population growth
rates. In analyses of deterministic population growth rate
(log kdet), the non-phylogenetic model was preferred
(DDIC > 7.5 for all priors tested). The proportion of
variance explained by phylogeny was very sensitive to the
priors selected, ranging from < 1 to 28% for the model of
log kdet and was similar to that for randomized log kdet
where phylogeny should convey no information (< 1–18%;
Table S2). A value of 0 indicates the grouping conveys
no information, up to 100% where all members of a group
are identical (Gelman & Hill 2007). The proportion of
variance explained by species was insensitive to prior
selection (c. 14% for all priors tested). Similarly, in analyses
of the standard deviation of population growth rate and
stochastic population growth rates, the models without
phylogeny were either identical to the models with
phylogeny (DDIC < 1) or models without phylogeny were
strongly preferred (DDIC > 6.5).
Sources of variation in population growth rates
Populations within a year were more similar to each other
than the same population across years, although this pattern
depended on spatial scale and temporal autocorrelation.
1188 Y. M. Buckley et al. Review and Synthesis
� 2010 Blackwell Publishing Ltd/CNRS
Variance components analysis of population growth rate
used to determine spatial and temporal effects revealed that
the population level effect when nested within species was
small (missing middle grey bar in Fig. 1a), whereas when
year was nested within species it explained a similar
amount of variance in population growth rates as species
(Fig. 1a). However, when species with populations ‡ 1 km
apart were analysed, the proportion of variance explained
by population increased (middle grey bar in Fig. 1b),
indicating that population growth rates were more similar
within a population through time, i.e. the year effect
weakened and the population effect strengthened. For both
cases, the inclusion of autocorrelation between years
increased the explanatory power at the population
level and reduced the residual variance (black bars in
Fig. 1a,b).
The effect of year on population growth rate (log kdet)
was significant and negative, indicating a decreasing trend in
population growth rate over time (Table 1, Fig. 2 for
predicted values, Table S3 for parameter estimates). Popu-
lation growth rates decreased through time at different rates
for different populations (Fig. 2); variance about the slope
for year within population was significant (Table 1). Despite
the overall negative trend in population growth rate through
time most populations remained increasing (log kdet > 0)
throughout the studies (Fig. S2). Around these average
trends in population growth rates, autocorrelation of annual
residuals was highly significant (Table 1) and negative
(u = )0.3), meaning that years with higher than average
population growth rates tended to be followed by years with
lower than average population growth rates and vice versa.
When autocorrelation of errors within populations and
population-specific temporal trends were included in the
model, the proportion of variance explained at the
population level increased substantially relative to the simple
variance components analysis (Fig. 1a,b). Appropriate mod-
elling of within population temporal processes was therefore
important.
To explore possible mechanisms for temporal autocor-
relation in annual population growth rates, we examined
autocorrelations (AR1, using the acf function in R) for 133
populations with > 3 years of data from consecutive years
and found that autocorrelations in survival (LR1 = 14.2,
P < 0.0005) and fecundity (LR1 = 8.56, P < 0.004) had
significant additive positive contributions to autocorrela-
tions in population growth rate.
Examination of direct relationships between vital rates
and population growth rate revealed that log(survival)
contributed to population growth rate significantly when
tested in a model including autocorrelation of errors and
varying slopes for survival (LR1 = 68.6, P < 0.0001);
varying slopes for year could not be included due to model
convergence issues. Log(growth) was significant when
included in a model with autocorrelation and varying slopes
for year (LR1 = 5.97, P < 0.02). Fecundity was not
significant.
Both time-since-fire and herbivory intensity explained part
of the temporal variation in population growth rate. There
was a significant effect of the quadratic term of time-since-
fire (LR1 = 19.5, P < 0.0001), with no significant population
level variation in the slope (LR1 = 0.0003 P > 0.9) (Fig. 3).
This indicates that population growth rates can be expected
to decline after fire until reaching more stable dynamics.
There was also a significant negative autocorrelation between
years, similar in magnitude to the autocorrelation found in
the full dataset (u = )0.38, LR1 = 15.8, P < 0.0001).
Population growth rate declined linearly with increasing
herbivory intensity (herbivory: LR1 = 9.8, P < 0.002 and
year: LR1 = 6.59, P < 0.02, Fig. 4). Autocorrelation of
errors (LR1=0.6, P > 0.5) and population level random
effects (LR1=0.05, P > 0.9) were not statistically significant.
Models with and without habitat were very similar
(DAIC = 0.6), with little support for retaining habitat in
YearPopulationAutocorr
Species0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Pro
port
ion
of v
aria
nce
expl
aine
d
Year/population Residual
(a)
(b)
Figure 1 Variance components analysis of deterministic popula-
tion growth rate (log kdet) for three models: (i) years nested within
species (YEAR), (ii) populations nested within species (POPULA-
TION) and (iii) population nested within species, in a model
including autocorrelation of errors between sequential years
(AUTOCORR). (a) Data from 49 species and (b) data from 24
species with populations ‡ 1 km apart.
Review and Synthesis Plant population dynamics in space and time 1189
� 2010 Blackwell Publishing Ltd/CNRS
the model for this subset of the data. Finally, our analyses
revealed no evidence for density dependence in population
growth rates. The random effect of varying slopes for density
at the population level was not significant (LR2 < 0.001,
P > 0.9) and a fixed effect of density and habitat were also
not significant (LR1 = 0.8, P < 0.4 and LR1 = 2.6, P < 0.1,
respectively).
Variation in survival and growth rather than variation in
fecundity explained temporal variation in population
growth rates (rlog kdet). Variation in rlog kdet increased
with mean population growth rate (log kmean), the number
of matrices and the standard deviation of survival
(log rsurvival) (Fig. 5, Table 2, Table S3 for parameter
estimates).
Importance of variation in population growth rates
Mean matrix population growth rate (log kmean) was a good
predictor of all measures of stochastic population growth
rate (ks, kTulja and kseq) (Table 3). However, mean matrix
population growth rate tended to be greater relative to ks
and kTulja for rare species and species with medium and
small matrix dimensions (Fig. 6). Departure from a 1 : 1
relationship with mean population growth rate was most
1 3 5
–0.2
A. spicata
1 2 3 4 5
–0.1
0
A. eupatoria
1.0 2.0 3.0
–0.1
5
A. incana
3.0 4.5 6.0
0.0
A. fecunda
1.0 2.0 3.0
0.00
A. elliptica
1.0 1.4 1.8
0.00
A. triphyllum
1.0 2.5 4.0
–0.1
A. bipartita
1 2 3 4 5
–0.4
A. canadense
1.0 2.5 4.0
0.0
A. alopecurus
1 2 3 4 5
–0.2
A. scaphoides
2 4 6 8
–0.6
A. tyghensis
1.0 1.4 1.8–0.0
05
B. excelsa
1.0 2.5 4.0
–0.2
C. ovandensis
1.0 1.4 1.8
1.0
C. americana
1.0 2.0 3.0
–1.0
C. keyensis
1.0 2.5 4.0
–0.2
C. elata
1.0 2.0 3.0
–0.2
C. palustre
1.0 2.0 3.0
0.1
C. hirta
1.0 1.4 1.80.
0
C. scoparius
1.0 1.4 1.8
–0.4
D. sericea
1.0 1.4 1.8
–0.3
D. purpurea
1.0 1.4 1.8
–0.0
6
E. latifolium
1 3 5
–0.2
E. cuneifolium
1.0 1.4 1.8
0.00
E. edulis
1.0 1.4 1.8
0.00
G. reptans
1.0 2.0 3.0
–0.0
6
G. rivale
2 4 6 8
–0.5
H. radiatus
1.0 1.4 1.8
–0.0
1
H. acuminata
1 2 3 4 5
–0.5
H. cumulicola
1.0 2.0 3.0
–0.1
L. vernus
1 3 5 7
–1.0
L. bradshawii
1 2 3 4 5
–0.4
L. cookii
1.0 1.4 1.8
–0.0
5
M. magnimamma
1.0 2.0 3.0
–0.6
M. cardinalis
1.0 2.0 3.0
–0.4
M. lewisii
1.0 1.4 1.8
0.00
P. quinquefolium
1.0 2.5 4.0
–0.1
4
P. media
1.0 2.0 3.0
–0.1
5
P. farinosa
2.0 2.4 2.8
–0.3
P. veris
1.0 1.4 1.8
0.0
P. vulgaris
1.0 1.4 1.8
–0.0
4
P. gaumeri
3.0 4.0 5.0–0.0
40
P. subintegra
1.0 2.5 4.0
–0.1
5
S. europaea
1.0 1.4 1.8
–0.0
6
S. pulcherrima
1.0 2.5 4.0
–0.2
S. cotyledon
1.0 2.0 3.0
–0.3
S. pratensis
1.0 2.5 4.0
–0.0
35
T. floridana
1.0 1.4 1.8
–3.0
T. pratensis
2.0 3.0 4.0
–0.1
5
T. grandiflorum
Year
Log
(pop
ulat
ion
grow
th r
ate,
λde
t)
Figure 2 Deterministic population growth
rate (log kdet) for 49 species, points are
observed data from multiple populations
and lines are the predicted values for each
population from the multi-level mixed
effects model (Table 1).
1190 Y. M. Buckley et al. Review and Synthesis
� 2010 Blackwell Publishing Ltd/CNRS
noticeable for rare species where stochastic population
growth rate was calculated taking autocorrelation into
account (kseq) (Fig. 6). Mean matrix and stochastic popula-
tion growth rates sometimes predicted opposite population
dynamics; for 14 of 222 populations (6%) log kmean
indicated an increasing population, whereas kseq indicated
a declining population and vice versa for four of 222
populations (2%).
The contribution of temporal autocorrelation to kseq was
nonlinear (LR1 = 9.3, P < 0.01 for the ks · quadratic auto-
correlation interaction) and depended on species distribution
and the magnitude of ks (LR1 = 20.9, P < 0.0001 for the
distribution · ks · autocorrelation interaction). Both large
positive and negative autocorrelations caused departure from
an expected 1 : 1 relationship between ks and kseq especially
for rare species (Table S6 for parameter estimates), showing
that the strength of autocorrelation is important. In our
dataset, the six data-points that departed most strongly from
the expected 1 : 1 relationship had large negative autocorre-
lations and for the five rare species ks was substantially higher
than kseq (Fig. 7).
D I S C U S S I O N
Plant population growth rates exhibit a signal of species
For our dataset of 50 perennial plants, we found species to
be an important predictor of population dynamics with
phylogeny above the species level having a little or no
explanatory power. This indicates that patterns of variation
in plant population growth rates are evolutionarily labile
above the species level for the species sampled in this study,
suggesting that we cannot predict population dynamics
based on phylogenetic relatedness alone. Although our
database is taxonomically sparse with few species per genus,
other studies using larger databases have also reported a
negligible effect of phylogeny on the evolution of plant life-
histories, vital rates, and hydrological niches in plant
Chamaecrista keyensis
Time-since-fire
Eryngium cuneifolium
0 5 10 15 20 25
5 10 15 20 25
30
0 5 10 15 20 25 30
–0.5
–0.6
–0.2
–0.4
–0.2
0.0
0.2
0.4
0.0
0.2
0.4
0.0
0.5
1.0
1.5
Hypericum cumulicola
Log
(pop
ulat
ion
grow
th r
ate,
λde
t)
Figure 3 Effect of time-since-fire on population growth rate
(log kdet) for three species. Points are k estimates for each matrix
and the lines are fitted values with the BLUPs for each species.
Population level variation in the intercept was significant (LR1 = 5.4,
P < 0.03) but very low and for clarity is not shown here.
1 2 3 4 5 6
Actaea spicata
Year
MinMeanMax
Cirsium palustre
2.0 2.2 2.4 2.6 2.8 3.0 1.0 1.5 2.0 2.5 3.0
1.0 1.5 2.0 2.5 3.0
3.5 4.0
–0.0
5
–0.0
50.
05–0
.2–0.2
–0.1
0.1
0.0
0.2
0.0
0.4
–0.1
5
0.05
0.15
Lathyrus vernus Trillium grandiflorum
Log
(pop
ulat
ion
grow
th r
ate,
λde
t)Figure 4 Effect of year and herbivory on population growth rate
(log kdet) for four species. Lines are predicted values (BLUPs) for
min, mean and max herbivory (%) within each species (see
Table S5 for min, mean and max values).
Review and Synthesis Plant population dynamics in space and time 1191
� 2010 Blackwell Publishing Ltd/CNRS
communities (Silvertown et al. 2006; Kuster et al. 2008;
Burns et al. 2010); therefore, we consider the lack of a
phylogenetic signal on population dynamics found here to
be biologically reasonable. We note however that a more
fine scale sampling of genera (i.e. a larger number of species
per genus) could still reveal a phylogenetic signal on patterns
of variation in population growth rates.
Although several studies have shown that phylogenetic
relatedness or taxonomic groupings can be useful for
predicting rarity or invasiveness (Pysek 1998; Daehler 1998;
Daehler et al. 2004; Pheloung et al. 1999; Purvis et al. 2000;
Schwartz & Simberloff 2001; Diez et al. 2009; but see
Lambdon 2008), our results indicate that this does not likely
result from phylogenetic constraints on demography. Our
results suggest that demographic data of closely related
species may provide little information on demography for
the management of rare or invasive species.
Plant population growth rates decline through time
We found a negative temporal trend in population growth
rates for most of the populations. This trend held regardless
–8 –6 –4 –2
–8–6
–4–2
0
2 3 4 5 6 7 8 9
–8–6
–4–2
0
# matrices
–0.5 0.0 0.5
–8–6
–4–2
0
Log λmean
Log σsurvival
σ lo
g λ d
etσ
log λ d
etσ
log λ d
et
(c)
(b)
(a)
Figure 5 Temporal variation in population growth rate is partly
explained by (a) standard deviation of survival (log rsurvival), (b) the
number of matrices per population and (c) mean matrix population
growth rate (log kmean). Points are observed data from populations
within 47 species.
CommonRare
–0.5
0.0
0.5
1.0
–0.5
0.0
0.5
1.0
–0.5
0.0
0.5
1.0
1.5
–0.5
0.0
0.5
1.0
1.5
–0.5
0.5
1.0
–0.5
0.5
1.0
SmallMediumLarge
–0.5 0.0 0.5 1.0 –0.5 0.0 0.5 1.0
–0.5 0.0 0.5 1.0 –0.5 0.0 0.5 1.0
–0.5 0.0 0.5 1.0 –0.5 0.0 0.5 1.0
λ seq
λ Tul
ijaλ s
Log λmean
(c)
(a)
(d)
(e) (f)
(b)
Figure 6 Relationships between mean matrix population growth
rates (log kmean) and stochastic population growth rates (ks, kTulja
and kseq) for 50 species. The solid lines are expected 1 : 1
relationships between the population growth rates if log kmean and
the stochastic ks were exactly equivalent. Each row represents a
different stochastic population growth rate (a & b ks, c & d kTulja,
e & f kseq), the first column uses different symbols for common
and rare species (a, c, e) and the second column uses different
symbols for matrix dimensions (small, medium & large) (b, d, f).
1192 Y. M. Buckley et al. Review and Synthesis
� 2010 Blackwell Publishing Ltd/CNRS
of common or rare status; 51% of populations had positive
population growth rates at the beginning of a study period
but this reduced to 42% by the end of the study period. We
offer four possible explanations for this overall negative
trend in population growth rates, two of which reflect
sampling artefacts and two of which reflect actual declines in
abundance. The most obvious artefactual explanation would
be if the sampling process itself caused deterioration of the
vital rates determining population growth rate. We think this
is unlikely for studies of plant demography because these
typically involve minimal handling (few days per year).
Second, demographers may tend to start studies in
�best� sites with relatively high population densities,
increasing the likelihood of population declines. For
example, Bierzychudek (1999) identified density-dependent
population dynamics as a potential source of an unpredicted
population decline. However, in our dataset increasing and
decreasing populations were both equally likely at the
beginning of a time period (100 populations log kmean > 0
and 97 populations log kmean < 0), which is what we would
expect from a random sample of populations with stable
dynamics (log kmean = 0).
Therefore, we suggest that this general pattern reflects
more subtle causal factors. Researchers may choose to
terminate studies after a particularly bad year or run of years
leading to estimated declines in population growth rate.
Finally, it may be that habitat quality itself tends to fluctuate
over time. Fluctuating environmental conditions could
reflect successional dynamics (Menges 1990) or changes in
microbial communities, e.g. accumulation of pathogens or
less beneficial mychorrizae (Bever 1994). If demographers
tend to start studies in �best� sites with relatively high
population densities, then trends over relatively short
time periods would be biased toward declines. If this
mechanism were true, it would be necessary to establish
study plots or transects not only in the central parts of the
populations but also at the edges (i.e. sparser locations)
that might be those �best� locations in the future, to detect
true population-level trends. Further study of the charac-
teristics and locations of the studied populations may be
able to tease out broad landscape scale patterns correlated
with declining population growth rates (e.g. particular
land-use types or habitats). If sampling bias causes an
overly pessimistic view of population persistence, efficient
and effective conservation and restoration actions may be
compromised as, in the worst case, unnecessary manage-
ment will be implemented.
Sources of variation in plant population growth rates
Quantifying variation in plant population dynamics across
spatial and temporal scales is important for predictions of
species abundance and distribution. Our comparative study
based on a large number of plant species across different
habitats revealed quantitative and qualitative differences
between spatial and temporal variation in plant population
dynamics. Population growth rates varied more between
years than between populations, although the analysis of
populations > 1 km apart reduced the difference between
spatial and temporal variation, showing that greater temporal
variation in plant populations is partly scale-dependent and
caused by closely situated study populations within species.
Earlier studies have detected synchronized population
dynamics for short-lived grassland species (populations
situated within a few kilometers), with the magnitude of
synchrony clearly decreasing with increasing spatial distance
among populations (e.g. Ramula et al. 2008b; Kiviniemi &
Lofgren 2009). Our results suggest that synchronized
population dynamics might occur also for longer-lived
perennials, for instance, due to similar environmental factors
in closely situated populations. Unfortunately, the level of
detail on spatial locations reported was not adequate for us
to construct a spatial variance–covariance matrix to further
explore how distance between populations affects population
growth rate and this remains a question for future studies.
Observed temporal variation in population growth rates
was mainly due to variation in post-seedling survival
regardless of the life-form; a typical pattern for long-lived
perennials (Silvertown et al. 1993, 1996; de Kroon et al.
2000; Ramula et al. 2008a; Burns et al. 2010). In our case, we
–0.4
–0.4
–0.2
–0.2
0.0
0.0
0.2
0.2
0.4
0.4
0.6
0.6
Stochastic population growth rate
Seq
uent
ial p
opul
atio
n gr
owth
rat
e
Common
Rare
–0.76
–0.27
–0.45
–0.67
–0.74
–0.3
Figure 7 Relationship between stochastic population growth rates
for randomly fluctuating (ks) and temporally autocorrelated
environments (sequential population growth rate, kseq) in relation
to species distribution (rare, common) for 26 species. The solid line
is an expected 1 : 1 relationship between the population growth
rates if ks and kseq were exactly equivalent. The six largest
deviations from the expected 1 : 1 are identified with their
autocorrelation co-efficient.
Review and Synthesis Plant population dynamics in space and time 1193
� 2010 Blackwell Publishing Ltd/CNRS
cannot exclude the possibility that variation in plant growth
is related to variation in population growth rate because
variance in survival and growth were correlated. As
expected, some of the variation in population growth rates
was also explained by fire and herbivory because both these
environmental factors can dramatically alter population
dynamics over a short period of time. Although the effect of
herbivory on plant population dynamics also depends on the
timing of herbivory and the sensitivity of population growth
rate to the life stages attacked (e.g. Ehrlen 2002; Maron &
Crone 2006; Ramula 2008), our findings suggest that both
fire and herbivory influenced plant population dynamics
largely through changes in plant survival as temporal
changes in fecundity explained little variation in population
growth rates.
Interestingly, population growth rates within populations
were negatively temporally autocorrelated, meaning that
good years were followed by bad years and vice versa.
Although both variation in survival and fecundity explained
negative autocorrelation in population growth rate, only
variation in survival contributed to temporal variation in
population growth rate. This indicates that fluctuating
survival was the main driver of variation and temporal
autocorrelation in plant population growth rates. Negative
temporal autocorrelation driven by survival may be related
to external (e.g. fire, herbivores) or internal (e.g. costs of
reproduction) factors that modify survival directly or
through correlations with the other vital rates.
Most stochastic population models assume that variation
is uncorrelated in time (Menges 2000; Pico & Riba 2002;
Kwit et al. 2004). However, a handful of studies point to the
potential importance of temporally autocorrelated stochas-
ticity (recently reviewed by Ruokolainen et al. 2009). These
studies have most often argued for positive autocorrelations
in population growth rates, due to resource storage, or
slower changes in the physical or biological environment that
buffer annual variation in environmental conditions (Halley
1996; Sabo & Post 2008). In contrast to both of these
expectations, we observed negatively autocorrelated popu-
lation growth rates. Negative temporal autocorrelation tends
to dampen environmental stochasticity, and slows down
extinction, resulting in a smaller extinction risk than positive
temporal autocorrelation or pure �white noise�. However, in
our dataset, realized population growth rates for ordered
environments were more often lower than expectations
without autocorrelations particularly for rare species with
large negative autocorrelations (Fig. 7). Therefore, the
temporal structure of variation in plant population dynamics
needs more attention in future research.
Although our dataset of 50 perennials is just a sample of
plant species and reflects any bias in the selection of species
for demographic studies, it includes species from temperate
ecosystems to the tropics and we therefore believe the
dataset allows generalizations to be made about plant
population dynamics. For instance, we can expect temporal
variation in survival rather than temporal variation in
fecundity to shape population dynamics of perennials, and
we can expect population growth rates to be temporally
autocorrelated. Departures from these generalizations may
occur for special cases, such as invasive species, although we
had insufficient invasive species to examine this in detail
here but see Ramula et al. (2008a). We encourage demog-
raphers to continue conducting demographic studies, and to
report detailed spatial and temporal information on their
study populations and environmental factors to enable
future comparative studies on plant population dynamics to
seek explanations for how populations respond to their
respective environments.
Consequences of realized temporal variation for plantpopulations
Deterministic population growth rates calculated from mean
matrices were generally good predictors of stochastic
population growth rates for randomly fluctuating environ-
ments, as others have also found (Boyce et al. 2006).
However, the inclusion of observed temporal autocorrela-
tion in population dynamics increased the difference
between deterministic and stochastic population growth
rates, and these differences were somewhat greater for rare
species and species with small to medium matrix dimen-
sions, where mean matrices usually produced more opti-
mistic estimates of population performance than the
stochastic methods. For our dataset, populations of rare
species with small sample sizes (e.g. 60–200 individuals for
Arabis fecunda, Astragalus scaphoides, Chamaecrista keyensis) were
often responsible for the greatest differences between
deterministic and stochastic population growth rates,
suggesting that the greater difference for rare species is
mainly because of larger sampling error. Larger sampling
error resulted from small sample sizes (c. < 300 individuals)
can lead to biased estimates of population growth rates
derived from matrix population models (Ramula et al. 2009).
Differences between deterministic and stochastic popula-
tion growth rates for autocorrelated environments are
important from a management point of view because small
differences in annual k estimates accumulate over time,
resulting in considerably different estimates of future
population size.
Lessons from variation in plant population dynamics
Our synthesis of population growth rates for perennial
plants has yielded important implications for understanding
and predicting plant population dynamics, showing that
environmental factors (e.g. fire and herbivory) strongly
1194 Y. M. Buckley et al. Review and Synthesis
� 2010 Blackwell Publishing Ltd/CNRS
influence population dynamics through space and time. The
lack of a phylogenetic signal on patterns of population
growth rates indicates that population dynamics can vary
greatly from species to species even within the same genus.
This makes it difficult to use demographic data from
close relatives (e.g. congeners) as a surrogate to produce
management recommendations when data for the target
species are lacking. The use of demographic data from
different populations within the same species would be
more appropriate, particularly if geographic distances among
populations are small and environmental factors similar.
However, simple space-for-time substitutions in plant
demographic analyses should be avoided. Greater temporal
variation than spatial variation in population growth rates
suggests that space-for-time data substitutions would
underestimate the true variation in population growth rates,
resulting in underestimated risk of extinction for declining
populations and consequently, over-optimistic predictions
of species performances.
Our results show that post-seedling survival is the key
vital rate contributing to temporal variation in population
growth rate and driving temporal autocorrelation of annual
population growth rates for perennial plants. Temporal
autocorrelation in population growth rates can rarely be
ignored in predictions of population dynamics as it occurs in
many plant populations and can change estimates of the
long-term population growth rate. For randomly fluctuating
environments realized variation in vital rates has a small
effect on plant population dynamics and mean matrix
and stochastic population growth rates are highly correlated,
although stochastic growth rates tend to be lower. However,
for temporally autocorrelated environments variation in
vital rates results in a slightly greater difference between
mean matrix and stochastic population growth rates. For
species with strong positive or negative autocorrelations,
stochastic population growth rates for temporally autocor-
related environments differed from those for randomly
fluctuating environments. This indicates that the sequence
of environmental conditions is essential for determining
plant population growth rate and should therefore be
incorporated into predictions of population dynamics.
Temporal autocorrelation in population dynamics necessi-
tates long-term observations over several years to produce
estimates of population performance, a finding that will be
particularly important in the face of future environmental
change.
A C K N O W L E D G E M E N T S
We thank the Australia–New Zealand Vegetation Function
Network for funding, Per Aronsson for database manage-
ment code, the editor, Mark Boyce and three anonymous
referees for helpful suggestions. YMB was funded by an
Australian Research Council Australian Research Fellowship
(DP0771387), SR by the Academy of Finland, JHB by
Tyson Research Center, the American Association of
University Women and the Center for Population Biology,
University of California, Davis.
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S U P P O R T I N G I N F O R M A T I O N
Additional Supporting Information may be found in the
online version of this article:
Figure S1 Phylogeny for 49 plant species used for
deterministic analyses.
Figure S2 Fitted population growth rates for all populations
of 49 plant species.
Table S1 Species included in the database.
Table S2 Model comparison with and without phylogeny for
log kdet.
Table S3 Parameter estimates for models of log kdet and
rlog kdet.
Table S4 Species with environmental factors.
Table S5 Herbivory levels for four species.
Table S6 Parameter estimates for the effect of temporal
autocorrelation on kseq.
As a service to our authors and readers, this journal provides
supporting information supplied by the authors. Such
materials are peer-reviewed and may be re-organized for
online delivery, but are not copy-edited or typeset. Technical
support issues arising from supporting information (other
than missing files) should be addressed to the authors.
Editor, James Grace
Manuscript received 7 April 2010
First decision made 10 May 2010
Manuscript accepted 20 May 2010
Review and Synthesis Plant population dynamics in space and time 1197
� 2010 Blackwell Publishing Ltd/CNRS