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Scaling up phenotypic plasticity with hierarchical population models 1
The original publication is available at www.springerlink.com
http://dx.doi.org/10.1007/s10682-009-9340-2
Evolutionary Ecology (2010) 24:585-599
Scaling up phenotypic plasticity with
hierarchical population models
12 3 1 1
Eelke Jongejans ’ ’ , Heidrun Huber and Hans de Kroon
1. Department of Experimental Plant Ecology, Radboud University Nijmegen,
Heyendaalseweg 135, 6525 AJ Nijmegen, the Netherlands
2. Nature Conservation and Plant Ecology group, Wageningen University,
Droevendaalsesteeg 3a, 6708 PB Wageningen, The Netherlands
3. E.Jongejans@science.ru.nl, tel. +31-24-3652114, fax +31-24-3652409
Keywords (4-6): Life history components, life table response experiments, matrix projection
models, trait-trait covariances, vital rates
A bstract
Individuals respond to different environments by developing different phenotypes, which is
generally seen as a mechanism through which individuals can buffer adverse environmental
conditions and increase their fitness. To understand the consequences of phenotypic plasticity it
is necessary to study how changing a particular trait of an individual affects either its survival,
growth, reproduction or a combination of these demographic vital rates (i.e fitness components).
Integrating vital rate changes due to phenotypic plasticity into models of population dynamics
allows detailed study of how phenotypic changes scale up to higher levels of integration and
forms an excellent tool to distinguish those plastic trait changes that really matter at the
population level. A modeling approach also facilitates studying systems that are even more
complex: traits and vital rates often co-vary or trade-off with other traits that may show plastic
responses over environmental gradients.
Here we review recent developments in the literature on population models that attempt
to include phenotypic plasticity with a range of evolutionary assumptions and modeling
techniques. We present in detail a model framework in which environmental impacts on
population dynamics can be followed analytically through direct and indirect pathways that
importantly incorporate phenotypic plasticity, trait-trait and trait-vital rate relationships. We
illustrate this framework with two case studies: the population-level consequences of phenotypic
responses to nutrient enrichment of plant species occurring in nutrient-poor habitats and of
responses to changes in flooding regimes due to climate change. We conclude with exciting
prospects for further development of this framework: selection analyses, modeling advances and
the inclusion of spatial dynamics by considering dispersal traits as well.
Introduction
Plants can adapt to variable environments by changing their phenotype which typically is
expected to increase individual fitness (Pigliucci 2001; Sultan and Stearns 2005; Bradshaw
2006). Despite the expectation that phenotypic plasticity (i.e. environmentally induced trait
variation) will have important consequences for population dynamics at the local and landscape
scale (Sultan 2007), studies of phenotypic plasticity typically focus on individual fitness. The
effect of phenotypic plasticity across environments on fitness components like reproduction or
survival can be analyzed statistically with path models or structural equation models. Path
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Scaling up phenotypic plasticity with hierarchical population models 2
models fit hypothesized networks of causal relationships between ecological drivers, individual
traits and one or more fitness components to data (Huber et al. 2004; Pigliucci and Kolodynska
2006; Picotte et al. 2007; de Vere et al. 2009). However, finding effects of phenotypic plasticity
on a fitness component does not automatically allow for conclusions at the population level
(Metcalf and Pavard 2007). The relationship between phenotypic plasticity and population
dynamics is unlikely to be straightforward: phenotypic shifts in one trait may have indirect
fitness consequences through positively or negatively (e.g. trade-offs) correlated traits (Tonsor
and Scheiner 2007). Furthermore, changes in individual fitness rarely translate linearly into
population size fluctuations (Ehrlen 2003), partly because not all fitness components are equally
important for local population growth and partly because not all individuals will respond in the
same way.
Evaluation of the population-level consequences of phenotypic plasticity requires
computer simulations or, more elegantly, analytical population models (Caswell 1983). Matrix
population models have proven to be very useful because they transparently represent the life
cycle of a species by including all the year-to-year transitions between the various age or size
stages in which individuals can be classified (Caswell 2001). These annual transitions are made
up of vital rates (i.e. fitness components) such as stage-specific survival and reproduction rates
and growth rates of surviving individuals that reach other stages. The mathematical
characteristics of matrices have clear biological interpretations such as the projected population
growth rate (i.e. the dominant eigenvalue of the transition matrix) and the relative contributions
of matrix elements or vital rates to population growth (i.e. elasticity values) (de Kroon et al.
2000; Franco and Silvertown 2004). Matrix models have continued to develop rapidly and now
include stochasticity (Tuljapurkar et al. 2003) and a spatial dimension (Neubert and Caswell
2000), while still retaining all useful analytical properties.
Matrix population models have already been used to investigate the consequences of the
outcome of phenotypic plasticity, for instance reduced variability in demographic rates due to
dampening of the impact of environmental fluctuations (Caswell 1983). Temporal variation in
demography is generally thought to decrease population growth (Tuljapurkar 1990; Boyce et al.
2006), although that still depends on the specific response (e.g. linear or convex) of a vital rate to
an environmental driver (Koons et al. 2009). It has therefore been hypothesized that natural
selection has led to the reduction of the variation of especially those vital rates that contribute
most to the population growth rate (Pfister 1998; Morris and Doak 2004). However, these studies
did not specifically include the plastic traits that may underlie vital rate variability.
In this paper, we develop a framework of hierarchical population models (HPMs) to
analyze the effects of phenotypic plasticity on demographic and dispersal traits at the population
level. In this context we will investigate plastic changes of morphology, biomass accumulation,
flowering probability and reproductive effort; traits are directly and indirectly linked with
demography and dispersal processes. In essence, HPMs bring together two research lines: that of
studying the effects of phenotypic plasticity with path models and that of spatial and non-spatial
population modeling. This approach of coupling relationships between individual traits and vital
rates inside matrix models was already pioneered by van Tienderen (2000) with an hypothetical
plant species, and applied to and extended for animal field data by Coulson and coworkers
(Coulson et al. 2003; Coulson et al. 2006; Pelletier et al. 2007; Coulson and Tuljapurkar 2008).
Here we develop HPMs for perennial plants and add spatial dynamics to the equation. We will
illustrate how HPMs can be used to answer the following important questions: what are the
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Scaling up phenotypic plasticity with hierarchical population models 3
population-level consequences of trait-trait covariance and how does phenotypic plasticity
change the effect of environmental fluctuations on local and spatial population dynamics.
H ierarchical population models
HPMs can be schematically represented (as for instance in Fig. 1) in the same way as path
models: environmental factors (i.e. ecological drivers such as flooding, nutrient availability,
weather, or population density) influence traits of individuals, which in turn affect vital rates (or
fitness components such as survival, growth and reproduction) that together can be used to build
population models (e.g. a population transition matrix). Thus, each of these lower-level
parameters (i.e. environmental factors, traits of individuals, vital rates) can influence population
dynamics. Vice versa (from right to left in Fig. 1) the arrows leading to a model parameter
indicate which lower-level parameters contribute to that higher-level parameter. Like in path
models covariances between individual traits can be included in HPMs. Trade-offs among traits
result in negative covariances. Depending on how individual traits of interest are defined, HPMs
may also include direct effects of environmental factors on vital rates (V in Fig. 1). It is also
possible that the changes in the environment affect how an individual trait contributes to a vital
rate (i.e. the vital rate function of that trait changes with the environment).
However, to our knowledge no such complex hierarchical population models including
the relationships described above (Fig. 1) have been performed so far. In the next section we will
present the results of a case study (Fig. 2) for which we have data and for which we show
numerically what insights can be gained from a HPM approach. Thereafter we will explore a
more complex, hypothetical case study which includes various environmental effects and trait-
trait covariation.
Eutrophication effects on the population dynamics of 4 grassland species
The first case study is an example of how an HPM can be constructed and analyzed. We
analyzed the population-effect of eutrophication, which has caused declines in species richness
in many grasslands (Neitzke 2001; Stevens et al. 2004). We focused on four perennial plant
species (Centaurea jacea, Cirsium dissectum, Hypochaeris radicata and Succisa pratensis) of
which the demography has been studied in nutrient-poor grasslands (Jongejans and de Kroon
2005; Jongejans et al. 2008).
To study the importance of lower-level parameters we formulated an HPM (see Fig. 1 for
details) with the following plant traits: plant size (zj), threshold size for flowering (z2) and seed
production per unit plant size (z3). With zj we fit linear models to the following vital rates: the
number of clonal offspring per non-flowering (w4) and per flowering rosette (W5 ) and the number
of seeds produced per flowering rosette (w9). The slope of the latter seed production model is the
plant trait z3, the number of seeds per unit plant size. For adult survival (w2, w 3) and flowering
(w6, w 7, w8) we performed generalized linear models with a logit-link and plant size as the
explanatory variable. We inserted the average of observed plant sizes into these functions to
obtain average vital rate values for the field scenario (see Supplementary Material for details).
The field scenario (i.e. control, nutrient-poor conditions) was contrasted with an
eutrophication scenario, which was based on the field scenario, but altered at five points: the
three plant traits (zj, z2, z3), and two direct effects (vj, v2) on the vital rates survival and seedling
establishment. For the changes in plant traits and survival we used the relative effects that were
found in a garden experiment in which these four plant species were grown amidst a hexagon of
tussocks of the competitive grass M olinia caerulea (Jongejans et al. 2006). Half of the plots in
the garden were annually fertilized, and by comparing survival and the sizes of the survivors
between the enriched and control plots we were able to estimate how much nutrient enrichment,
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Scaling up phenotypic plasticity with hierarchical population models 4
as applied in the garden experiment, affects the mentioned plant traits and the adult survival rate.
For the calculation of the vital rates of the eutrophication scenario we changed the mean plant
traits of the field scenario proportionally to the experimental fertilization effect sizes which can
be found in Table 2 (see Supplementary Material for details). For the relative effect of
eutrophication on seedling establishment (w1o) we used the ratio of the establishment rate in high
productive field sites and the establishment ratio in low productive field sites as found in a
published seed addition experiment involving 20 sites (Soons et al. 2005).
Next we wanted to know how these different effects of eutrophication on plant traits and
vital rates contributed to the difference (AX) between the projected population growth rate of the
E C
eutrophication scenario (X ) and that of the default field scenario (X ). We therefore decomposed
AX with a so-called fixed-effect LTRE (i.e. Life Table Response Experiment; Horvitz et al. 1997;
Caswell 2001; Jongejans and de Kroon 2005) to investigate at each level what caused the
difference between XC and Xe. LTREs approximate these contributions to AX with the products of
1) the sensitivity of X to changes in a parameter and 2 ) the deviation of the value of that
parameter from its control value (see Supplementary Material for the sensitivity and LTRE
equations used for the trait, vital rate and matrix element levels). LTRE contributions of
underlying parameters quantify the importance of those parameters for the given difference in X
and together the contributions sum up to the total X-difference observed. First we decomposed
AX at the level of the matrix elements (aij), then at the level of the underlying vital rates (wk), and
finally at the level of the involved plant traits (zr). The last level also included the contributions
of changes in direct environmental effects (vh) on vital rates (see Fig. 1). This way the sum of the
LTRE contributions at each level approximated AX.
Eutrophication had a larger impact on X of the two shorter-lived species: AX was -0.626
(from XC=0.960 to X=0.334) for Hypochaeris radicata and -0.496 (from 1.007 to 0.511) for
Cirsium dissectum, while only -0.059 (from XC=0.986 to XE=0.928) for Centaurea jacea and
even +0.045 (from XC=1.237 to XE=1.282) for Succisapratensis. Furthermore, the LTREs clearly
showed that nutrient enrichment affected the population dynamics of these four grassland species
differently (Fig. 2): at the level of matrix elements we see that the steep decline in X in the
eutrophication scenario for the short-lived species was mostly caused by decreased survival (and
by decreased clonal propagation for C. dissectum). However, reduced sexual reproduction had
the largest negative contributions to AX in the two longer-lived species (C. jacea and S.
pratensis), although this was more than compensated in S. pratensis by positive contributions of
matrix elements that represented the fate of surviving individuals.
At a lower level we see that this negative contribution of sexual reproduction in the long-
lived species is mainly caused by reduced seedling establishment
(w1o).
At this vital rate level it
becomes clear that the largest buffering of the lower establishment rate in S. pratensis actually
takes place within the sexual reproduction matrix elements by increased seed production (w9).
The vital rate analysis also shows that it is not the survival rate itself that contributed to a higher
X in the eutrophication scenario, but that this was caused by higher flowering probabilities of
surviving plants (w<5, W7). For the short-lived species it was mainly the reduction in the survival
rate of non-flowering plants (w2) that caused the X-declines.
Direct effects (v1 and v2) of eutrophication had the largest negative contributions at the
lowest level (see right column of Fig. 2). These negative effects on X were to some extent
buffered by positive contributions by changed plant traits, showing that plastic responses to
eutrophication of plants that are growing amidst competitors can indeed be beneficial for
