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“Tempora mutantur et nos mutamur in illis”
— Lothair I
While environmental variation is an ubiquitous phenomenon in the natural world, recent
changes in the climate (IPCC 2007) have begun to increase attention in ecological
(McCarty 2001; Walther et al. 2002;
Williams et al. 2008), economical (Stern
2006), political and sociological ramifications of global climate change. It has been
predicted that long-term climate change is
likely to increase the frequency and magnitude of extreme climatic events, such as
drought and tropical hurricanes, and
strengthen and modify important atmospheric
oscillations, such as El Niño (Easterling et al.
2000; IPCC 2007), which will have an important impact on natural systems as well as
human societies worldwide.
In addition to quantitative variation in
fluctuation magnitude — which has the potential to lead to regime shifts in the composition of natural communities (van Nes &
Scheffer 2004) — global climate change can
also have a qualitative influence on the temporal behaviour of environmental factors,
such as air temperature (Wigley et al. 1998).
The temporal autocorrelation of environmental variation (see Glossary Box for words
in italics), characterising the rate of shortterm change in conditions, has a crucial role
in altering the eco-evolutionary dynamics of
species populations and entire communities
(Ruokolainen et al. 2009).
Climate warming has already resulted in
documented changes in ecosystem functioning, with direct repercussions on ecosystem
services (e.g., O'Reilly et al. 2003). While
predicting the influence of ecosystem
changes on vital ecosystem services can be
extremely difficult (Carpenter et al. 2006),
knowledge of the organisation of ecological
interactions within natural communities can
help us better understand climate driven
changes in ecosystems (Tylianakis et al.
2008). This thesis aims at developing theoretical understanding of how ecological
communities respond to changes in the regime of environmental fluctuations.
0101 6#7&%"#,*#$-8/ -($"5"%%*8-$&"#/ &#/
Spatio-temporal variation in the physical environment constantly operates to modify biological processes in nature. The way that biological systems are affected by environmental stochasticity can crucially depend on
environmental autocorrelation (defined
above), i.e., colour (Ruokolainen et al.
2009). The term colour comes from the analogy with visible light that varies between
blue and red depending on the dominant frequency. A blue data-series (over time or
across space) is characterised by highfrequency (rapid) fluctuations, whereas a
reddened data-series is dominated by lowfrequency (slow) variation (Fig. 1a). In a
white data-series all frequencies have equal
contribution and hence temporal variation is
entirely random. In the real world environmental factors (e.g., temperature and precipitation) tend to be positively autocorrelated in
their fluctuations over time (Steele 1985;
Vasseur & Yodzis 2004).
Autocorrelation (with lag 1) describes the average degree of similarity (correlation)
between consecutive observations in a data series.
An eigenvalue is a property of a square matrix (a table with an equal number of rows
and columns). In, e.g., community models, the stability of a system that is governed
by a matrix A can be found by considering the eigenvalues of this matrix. An eigenvalue is a unique solution to a characteristic equation: |A – !I| = 0, where ||!indicates
the determinant, ! is an eigenvalue and I is an identity matrix (a matrix with ones on
the main diagonal and zeros everywhere else).
In the context of environmental stochasticity, colour usually refers to temporal (spatial)
autocorrelation (or spectral exponent). The concept of colour comes from an analogy
with visible light, where different dominating frequencies correspond to different colours. Positively autocorrelated variation is said to be red, due to domination of low
frequencies, whereas negatively autocorrelated variation is called blue, due to domination of high frequencies. White noise has an equal mix of frequencies (none dominates).
In multi-species communities, each species has its specific response to environmental stochasticity. Species-specific environmental responses can be either independent (IR), uniformly correlated (CR), or hierarchically correlated (HR) between species. IR refers to a situation where each species responds to environmental fluctuations independently of all other species (" = 0). CR indicates that species-specific
responses are positively correlated ("ij = " > 0; negative equivalency is only possible
in a two-species community), while with HR the correlation between species-specific
responses reflects the ecological similarity of community members ("ij " "ik).
Community feasibility is closely related to dynamical stability. In a feasible community
all species have a positive density at the equilibrium. In mathematics it is possible
that a dynamical system has an equilibrium, either partly or entirely, in a negative
quadrant. However, this is meaningless in biological systems (species cannot have
negative densities) and thus such systems are termed unfeasible. In an unfeasible
community, if all species are initiated with positive densities, some species show exponential decline in the absence of any perturbations.
This term comes from economics, indicating that if a community is diversified among
many species, the relative fluctuation in biomass of the entire community may be
much smaller than the relative fluctuation in the biomass of the constituent species. A
related phenomenon is the ‘covariance effect’, which indicates increased community
stability through decreased covariance between species fluctuations. Together, these
mechanisms can be referred to as the ‘insurance effect’ of biodiversity.
This measure corresponds to the slope of logarithmic spectral density (relative dominance of different frequencies) against logarithmic frequency in a data series. A positive slope corresponds to blue (negatively autocorrelated) variation, while a negative
slope indicates reddened (positively autocorrelated) variation.
Stability in ecological systems can be divided to two main categories: 1) dynamical
stability and 2) biomass stability. Dynamical stability considers the existence of an
equilibrium point (steady state) for a specific system, which can be either stable or
unstable. After a small perturbation, a system will return to a stable equilibrium and
diverge from an unstable one. Biomass stability can be measured in various ways,
but it generally refers to the variability of population fluctuations over time.
ac = 0.10
Fig. 1. (a) Environmental variation of different colours. (b) Values for the January North Atlantic Oscillation index (NAO)
from 1823 to 2009 and their
long-term distribution. The NAO
time-series (solid line) has a
mean of 0.64 (dashed line), variance of 3.33 and an autocorrelation of 0.10. The distribution of
January NAO indices is normally distributed.
%&#$ %&"$ %&'$ %&&$ %($$ %(#$ %("$ %('$ %(&$ #$$$
%$ #$ 3$
The influence of large-scale climatic variation on biological systems can be approximated by applying climatic indices, such as
the El Niño (ENSO) and North Atlantic Oscillation index (NAO) (Stenseth et al. 2003).
Empirical evidence suggests that NAO influences ecological dynamics in both marine
and terrestrial systems, at different levels of
organisation (at the individual, population
and community levels; Ottersen et al. 2001).
Considering large-scale climatic fluctuations,
the time-scale at which ecological processes
operate and empirical studies are conducted
can have an important influence on the observed temporal autocorrelation
(Ruokolainen et al. 2009). For instance,
while the NAO index (Fig. 1b) tends to be
white in colour over relatively long timescales, it can exhibit either blue, white or red
fluctuations on relatively short time-scales
(Ruokolainen et al. 2009).
Both theoretical and empirical studies
have demonstrated how environmental autocorrelation can influence the dynamics of
(Petchey et al.
1997; Petchey 2000; Laakso et al. 2001;
Heino & Sabadell 2003; Laakso et al. 2003a;
Laakso et al. 2003b; Pike et al. 2004;
Schwager et al. 2006) and multi-species
communities (Gonzalez & Holt 2002; Ripa &
Ives 2003; Gonzales & De Feo 2007; Long et
al. 2007; Matthews & Gonzales 2007;
Hiltunen et al. 2008). An important implication of coloured environmental stochasticity
is that it influences biomass stability (affecting, e.g., population extinction risk, see section 1.4) across different levels of structural
complexity (Ruokolainen et al. 2009). From
the perspective of the human society, longterm stability of population and/or community biomass is desirable, e.g., in fish stocks
and field crops.
01;1 65"8"<&5-8/ &#$*%-5$&"#)/ &#/ ):*5&*)/ tems, non-trophic interactions (within a trophic level; such as competition, mutualism
and facilitation — where one species changes
Fundamentally, ecology is a science of inter- the living conditions to allow colonisation of
actions. Biological organisms interact with another species) are also dynamically imporeach other and the ambient physical envi- tant for food webs — yet remain understudronment and ecologists study how these in- ied (Berlow et al. 2004). This thesis concenteractions result in the distribution and abun- trates on the influence of environmental stodance of species in nature. Ecological inter- chasticity on non-trophic, competitive comactions between organisms come in many munities.
forms (Begon et al. 1996); they can be either
Most of the theory on competitive combidirectional (competition, predation/ munities assumes that between-species interparasitism and mutualism) or unidirectional actions are linear (changes in the abundance
(amensalism and commensalism), positive of species A have a constant influence on the
[mutualism (+/+) and commensalism (+/0), per-capita growth rate of species B) and that
where either both or just one of the counter- the strength of these interactions is unafparts benefit from the interaction, respec- fected by other links in the species network.
tively], negative [competition (–/–) and However, it is likely that interactive links
amensalism (–/0), where the interaction is within a community are not independent of
harmful for either both or just one of the each other (Neill 1974; Abrams 1983; Billick
counterparts, respectively] or both (natural & Case 1994; Wootton 1994), nor constant in
enemies, +/–). Natural food webs incorporate time (Jiang & Morin 2004) in the real world.
all of these different types of interactions, in Nevertheless, as disentangling the true strucdifferent proportions, at different trophic lev- turing of species assemblages has turned out
to be challenging (Billick & Case 1994;
At the population level, it is assumed that Wootton 1994; Laska & Wootton 1998),
the presence of interspecific interactions in- proxies for, e.g., the relative competitive abilfluences the per capita growth rate (births ity of different species (Fowler 2005; I),
and deaths) of species (Royama 1992). might be useful for applied purposes.
Therefore, whether a species is able to survive under given conditions depends on the 01>1 +:*5&*)/*?$$&"#)
combined effect of intrinsic and extrinsic biotic and abiotic factors acting upon popula- Understanding the risks of population extinction renewal. For example, in the absence of tion is not only of theoretical interest to
interspecific competition each species would population biologists, but it is also a central
reach their specific carrying capacities, while practical issue for conservation biologists
the presence of competitive species interac- and wildlife managers concerned with saving
tions reduce the long-term density of each populations. The famous ‘evil quartet’ of the
species away from its carrying capacity to a most pronounced sources of extinction risk
new state (May 1974). Whereas consumer- includes: overkill, habitat destruction and
resource (and host-parasite) relationships are fragmentation, impact of introduced species,
of undoubted importance in natural ecosys- and extinction cascades (Diamond 1984).
Here, I briefly review the relevance of these
different sources of extinction risk for my
Demographic stochasticity is the primary
mechanism leading to local population extinction. Small populations are especially
susceptible, e.g., to vagaries in birth and
death events and fluctuations in sex-ratio.
Environmental fluctuations additionally increase the risk of extinction arising from
demographic accidents alone (Pimm et al.
1988). Natural populations are often small
due to restricted ranges (Johnson 1998;
Purvis et al. 2000). However, while extinction risk will be most pronounced in species
that have both small ranges and low abundance, range size and abundance may compensate for one another in determining how
prone a species is to extinction (Johnson
1998). Due to the close connection between
range and population size, an important anthropogenic cause of decreased population
size is habitat fragmentation (Diamond
1984). A related, major source of population
extinction at local (and global) scale is habitat destruction, which is estimated to result in
extinction rates as high as 0.8% per year in
tropical forest regions (Hughes et al. 1997).
Due to large fluctuations in the density of
many populations (due to demographic
stochasticity, environmental variation, or
both; Lande 1993), weak dispersal abilities
are likely to be associated with increased extinction risk (Pimm et al. 1988; Fagan et al.
2001). In addition, body size (which
correlates positively with longevity and
negatively with intrinsic growth rate; Pimm
et al. 1988) is repeatedly pointed out as an
important proxy of increased extinction risk
in animal populations (e.g., Pimm et al.
1988; Purvis et al. 2000; Fagan et al. 2001;
Cardillo et al. 2005). A final point to the list
of the most important causes population extinctions is added by species invasion
(Caughley 1994; Clavero & García-Berthou
2005). Exotic species can exterminate native
species by, for example, competing with
them, preying upon them, or destroying their
There is no doubt that global climate
change drives population extinctions at both
local and global scales. Changes in climatic
regimes result in geographical changes in
suitable living conditions for a considerable
amount of species on the planet. Furthermore, many of the most severe impacts of
climate-change are likely to stem from interactions between extinction threats (Walther et
al. 2002; Thomas et al. 2004). For example,
the ability of species to reach new climatically suitable areas will be hampered by
habitat loss and fragmentation, and their ability to persist in appropriate climates is likely
to be affected by new invasive species (as
well as remnant populations from previous
climatic conditions in that location).
Overexploitation and habitat degradation act
to decrease local population densities and
hence increase the frequency of local extinctions (Diamond 1984). However, most of the
benefits biodiversity confers on human society are dependent on large numbers of species populations. This is because each population ordinarily provides an incremental
amount of an ecosystem good or service
(Hughes et al. 1997), such as seafood, timber, water purification, generation/maintenance of soil fertility, pest control, mitigation
of floods and droughts, and regulation of
Ecosystem functioning can crucially depend on the organisation of species communities within the ecosystem (e.g., Loreau et
al. 2001; Thebault et al. 2007), which inevitably influences the impact of extinctions on
ecosystem functioning. Consequently, many
local extinctions may be due to changes in
community composition (Paine 1966;
Diamond 1984), where an initial extinction
of one species leads to so called secondary
extinctions of other species from the system
(e.g., Lundberg et al. 2000; Dunne et al.
2002; Fowler & Lindström 2002; Fowler
2005). How such extinction cascades propagate through a community may depend on
community structure (Dunne et al. 2002;
Fowler & Lindström 2002) and the location
of the primary extinction in a food web
(Thebault et al. 2007). An important implication for conservation biologists is that species
exclusion from a community can lead to
community closure (Lundberg et al. 2000);
the inability of the excluded species to successfully reinvade the community.
<@*195*139- %1,2- $9:- +9D1%39#+9*$=- ,*35($,Y
Finally, I will consider the influence of environmental variation on population extinction
risk, which is one of the main scopes of this
thesis. As noted before, the role of environmental variation as an agent mediating population extinctions is likely to become increasingly important in the present scenarios of
global climate change (Thomas et al. 2004;
In general, a community’s response to environmental stochasticity can depend on trophic structure in a food web (Ives et al. 2003;
Greenman & Benton 2005; Vasseur 2007)
and the similarity in species-specific responses to environmental conditions
(Roughgarden 1975b; Ripa & Ives 2003;
Greenman & Benton 2005; I – IV), where
the response of a given species can be modified by the presence of other species in the
community (Ives 1995b; Gonzales &
Descamps-Julien 2004). In general, adding
more variables (between-species links,
within-population structure, space, etc.) increases the number of possible routes environmental variation can enter a system
(Greenman & Benton 2005), which inevitably makes the impact environmental variation more complex (Ruokolainen et al.
Previous studies on single species populations suggest that population extinction risk
depends on an interaction between density
dependence and environmental autocorrelation (Ripa & Lundberg 1996; Kaitala et al.
1997; Petchey et al. 1997; Schwager et al.
2006). That is, environmental reddening is
predicted to increase (decrease) extinction
risk in populations with undercompensatory
(overcompensatory) dynamics (Ripa &
Heino 1999). While investigation of multispecies communities indicate that correlated
between species-specific responses to environmental variation (environmental response;
see Glossary Box) can reverse this relationship for overcompensating populations (Ripa
& Ives 2003; Greenman & Benton 2005),
patterns reported for single populations are
likely to hold over multiple scales over structural complexity (Ruokolainen et al. 2009)
and across different underlying processes
generating environmental fluctuations (VII).
In this thesis I investigate the behaviour of
multi-species communities in stochastic environmental conditions. I will specifically concentrate on the following questions:
in resource use (III, IV) and how this
interacts with community size (IV).
(iii) What are the consequences of environmental variation and ecological drift on
community persistence and composition? First I ask how mechanistically introduced variation in species vital rates
affects community persistence and the
occurrence of ‘emergent neutrality’ in
competitive communities (V). Next I
consider the prevalence of different realistic ecological drift processes operating
at local and global scales in metacommunities and how they will influence
dynamics in the composition of structurally neutral and non-neutral (nichebased) communities (VI).
(i) How do simple competitive communities
respond to environmental variation of
different colour? This is addressed using
both randomly constructed communities
with competitive asymmetry (I) and diffuse communities (II). Of particular interest is the abundance rank of species
affected by environmental variation (I)
and the statistical properties of environmental stochasticity (II).
(ii) How does the degree of similarity in
species-specific responses to environmental variation influence the dynamics
of niche-structured communities? Here I
compare different covariance structures
in species-specific responses to stochasticity (I, III, IV). I also address the importance of migration in maintaining diversity under different regimes of environmental stochasticity (III). A special
interest is on a scenario where the similarity in species-specific responses to
stochasticity is related to their similarity
(iv) Finally I will ask how general is the relationship between population dynamics
and environmental autocorrelation, with
respect to the noise generating process.
The aim is to test whether different,
commonly used methods to generate
coloured environmental variation lead to
qualitatively different predictions regarding changes in population extinction risk
with variation in environmental colour
The truth about the behaviour of ecological
communities lies out in the natural world.
Therefore, reliable understanding about
community dynamics in fluctuating conditions can only be established through empirical data. This task is not straightforward as,
for example, temperature-dependent varia-
tion in interaction strength may make it extremely difficult to predict responses to
warming, even in simple communities (Jiang
& Morin 2004). Immense amounts of data
may also be required for reliably analyzing
species networks, even in static conditions,
which will take a lot of time. Therefore, theo-
Fig. 3. A schematic illustration of interspecific
interaction, using Darwin’s finches as an example
(Grant 1999; Grant & Grant 2006). The curves
represent each species’ ability to utilize seeds of
different size in their diet. The shaded area represents overlap in the diets of species 2 and 3. In
terms of interaction strength (entries in matrix A)
this area gives a value for !23.
retical predictions are necessary and very
useful in laying outlines for future empirical
research as well as conservation plans.
1 '/ '
The work presented in this thesis relies on
theoretical models of competitive communities. I model these communities using a
multi-species version of the Ricker function
for population renewal (Ricker 1954), incorporating Lotka-Volterra type interactions between species. In this model the renewal of
population density N in species i (S in total)
from time t to t + 1 follows:
N i ,t +1 = N i ,t exp % ri
! ij N j ,t &( ,
which can be written in matrix form as:
Nt +1 = Nt ! exp #$r ! (1 " ANt /K ) %& .
In eqn. (1.a) ri and Ki are the species-specific
intrinsic growth rate and carrying capacity,
respectively. Parameter !ij defines the per
capita effect of species j on the renewal of
species i. The !ij values combine to form an
interaction matrix A (Levins 1968; May
1974). The A matrix is usually standardised
such that its main diagonal elements (!ii) are
set equal to 1 and the off-diagonal (!ij) elements fall between [0, 1]. An exception is
made in chapter IV, where interspecific
competition is allowed to exceed intraspecific competition in a more mechanistic form
of the model. It is traditional to consider the
!’s in eqn. (1) as measures of niche overlap
between species, e.g., along different reFigure 3.
source gradients (e.g., MacArthur 1970),
where the degree of interspecific competition
depends on the degree of shared resources
(Fig. 3). In this thesis, competition is linked
to niche theory in chapters III – VI. Eqn.
(1.b) gives eqn. (1.a) in matrix notation,
where N, r, and K are vectors (S ! 1 in size)
containing species specific densities, growth
rates and carrying capacities, respectively.
The ! and / signs represent elementwise
multiplication and division, respectively.
In the simplest form, parameters r and K
are set equal for all species, and the ! coefficients are set equal for all species pairs. In
this case competition is called diffuse and the
identity of species is irrelevant for population
dynamics (II). This should not, however, be
confused with neutral competition, which
implies the equivalency of kin and non kin in
competitive interactions (e.g., Bell 2001).
Internal network structure can be modified
by allowing these parameters to differ between species (I, III – VI).
In the system described by eqn. (1), the
community equilibrium can be found as
N* = A !1K .
If any of the elements in N* is less than or
equal to zero, the community is said to be
unfeasible. In this thesis I will consider both
feasible and locally stable (I, II), and unfeasible communities (III – VI). Communities
that are feasible and locally unstable are not
considered here, since they are liable to loose
species in the presence of disturbances, except under certain conditions (Fowler 2009).
In the special case of S = 1, the singlespecies equilibrium of eqn. (1) is equal to K
and the local stability of this equilibrium is
controlled by r (Roughgarden 1975a; May &
Oster 1976). Population dynamics are stable
when 0 < r < 2. If r < 1 population growth is
said to be undercompensating, which means
that if the population is perturbed away from
its carrying capacity, it will return monotonically to that point. When r > 1 population
dynamics are overcompensatory. In the range
1 < r < 2 the population approaches K with
successive over- and undershoots, resulting
in dampened oscillations. Finally, for r > 2
the population (equilibrium) is unstable (see
Glossary Box) and perturbations away from
the equilibrium will result is different forms
of sustained oscillations, such as periodic
cycles and chaos (May & Oster 1976).
Finding the stability of a multi-species
community can be analysed by linearising
eqn. (1) around the equilibrium point. In matrix form this becomes:
x t +1 = Bx t ,
where x is a vector of linearised (log-transformed) population densities and B is the Jacobian matrix, summarising linearised effects
of community members upon each other. The
elements bij in the community Jacobian are
found by taking a partial derivative of the
equation for species i with respect to species
j and evaluating this derivative at the equilibrium (Roughgarden 1975b):
# ij ri N *j
The main diagonal elements of B (bii) become 1 + bij. In the simple case of diffuse
competition (i.e., ri = r, Ki = K, !ij = !) the
diagonal elements become bii = 1 – r / [1 +
(S – 1)!] and on the off-diagonal we have bij
= – ! r / [1 + (S – 1)!].
By analysing the eigenvalues of B one is
able to tell whether the community equilibrium is stable or not (May 1974; Caswell
2001). Stability is contingent on the eigenvalue that is maximum in absolute value,
which is often called the dominant eigenvalue, !1. If |!1| > 1 the equilibrium is unstable and if |!1| < 1 the equilibrium is locally,
asymptotically stable (for a distinction
between local and global stability, see May
1974). In the simplest case, for a diffuse
competition system (when ! < 1), the dominant eigenvalue only depends on r, !1 = 1 – r.
Whether the entire community reacts in an
undercompensating or an overcompensating
manner following a perturbation depends on
the subdominant eigenvalues of the system
(Ives et al. 1999).
>1>1 E*,"<%-:9&5/ -#4/ *#7&%"#,*#$-8/ where " is the correlation coefficient between
all pairs of environmental time series and " is
the autocorrelation coefficient. Setting " < 0
produces ‘blue’ noise with high fluctuation
In natural conditions the survival and repro- frequency, " = 0 results in ‘white’ noise with
duction of individuals is not guaranteed. This random fluctuation frequency, and finally " >
brings uncertainty into population demogra- 0 yields ‘red’ noise associated with low flucphy, in direct proportion to population size, a tuation frequency (Fig. 1a). The terms #t and
process that is referred to as demographic $i,t are standard normal random components,
stochasticity. This becomes especially impor- where # is common for all time series i and
tant in small populations that can go extinct $ is independent between them. Parameter %
due to chance alone. A common approach to is a scaling factor ensuring that noise variintroduce demographic uncertainty into ance remains independent of #. This method
population models is to draw population denscales the noise time-series to its (desired)
sities in the next generation from a Poisson
asymptotic variance (&i2) independently of
distribution (Ranta et al. 2006): N’i, t+1 = noise autocorrelation (Heino et al. 2000). If
Poisson(Ni, t+1), where Ni, t+1 is the expected only one time series is required, eqn. (5) revalue of the Poisson distribution, given by duces to 't+1 = "'t + (1 – "2)1/2. I mainly ineqn. (1). This method allows explicit extinc- troduce environmental variation into populations to take place [Poisson(Ni, t+1) = 0], tion carrying capacities. In order to avoid
which are not otherwise observed in eqn. (1) negative K‘s, noise time series are truncated
where populations asymptotically approach such that 99% of values fall between [–w,
zero and explicit extinctions are only due to
w], where 0 < w < 1. Any values exceeding
this range are then truncated to the limits.
Other methods for generating coloured
I+9+%$*19F- *1#+- ,+%1+,- 3>- +9D1%39#+9*$=- environmental stochasticity also exist (Halley
1996; Haccou & Valutin 2003; Wichmann et
All the work presented in this thesis is, in one al. 2003; Mankin et al. 2004), where the
way or another, related to environmental sto- most popular alternative for AR noise is the
chasticity. I generally model environmental so called 1/f noise (e.g., Halley & Inchausti
variation as autoregressive (AR), coloured 2004) that is considered to capture a wide
noise (Ripa & Lundberg 1996). Single or range of different environmental processes
multiple noise time-series (") can be found (Cuddington & Yodzis 1999). However, it
can be shown that previously noted qualitaby the following method (II):
tive difference between results produced by
AR and 1/f noise are due to changes in noise
$ t + %& i ,t
! i ,t +1 = "! i ,t + 1 # " 2
Environmental variation in population models is often assumed to affect all individuals
in the population equally. If the environment
affects reproduction, mortality or dispersal
rates, a common approach is to adjust the per
capita growth rate (pgr). This can be done by
multiplying the deterministic prediction of a
model with exp("t) (Brännström & Sumpter
2006). Environmental factors can also affect
the amount of suitable habitat or intraspecific
competition (density dependence). These features are in fact related (Royama 1992), since
the strength of density dependence determines the carrying capacity in many models.
In both cases, we can again consider the effect as being multiplicative. This can be
modelled with a temporally varying carrying
capacity Kt = K (1 + 't), where K is the deterministic carrying capacity in the absence
of stochasticity. Thus, if environmental stochasticity is thought to affect per capita
growth rate, we have:
N i ,t +1 = N i ,t exp % ri
! ij N j ,t &( exp #$) i ,t &' , (7.a)
x t +1 = Bx t + ! t ,
where et is a vector of species-specific environmental noise terms. Eqn. 8 assumes that
noise is introduced into pgr (eqn. 7.a). If
noise is introduced into K, eqn. 8 becomes
xt+1 = Bxt + r!N*!et. Using time series
data from natural populations, eqn. (8) can be
recovered by applying multiple linear regression, where the resulting regression coefficients correspond to the elements in B and et
represents the residuals (Ives 1995a).
If environmental variation is a stationary
process, as is the case for AR (and 1/f) noise,
population densities will converge to a stationary distribution over time (e.g., Ives et al.
2003), i.e., the mean and variance of population fluctuations remain constant over time.
For a multi-species community the variancecovariance matrix of this can be approximated by applying eqn. (8) (Greenman &
Vec (C ) = I ! " 2B # B I ! " 2I # B
N i ,t +1 = N i ,t exp , ri &
, &% K i 1 + ! i ,t
# j =1 ij j ,t )) // , (7.b)
if we consider the environment to affect
population carrying capacities. The choice
between eqns. (7.a) and (7.b) can have a
quantitative influence on the size of population fluctuations, but no qualitative difference is expected (II, VII).
The behaviour of communities in the vicinity of the equilibrium can be approximated via linearisation (eqns. 3, 4) also in the
presence of environmental stochasticity
(Ripa & Ives 2003; Greenman & Benton
2005). The linearisation yields (Ripa et al.
(I ! " B # I) (I ! B # B)
Vec (S )
where Vec(C) is the vectorised variance–covariance matrix; I is an identity matrix; and
Vec(S) is a vectorised variance–covariance
matrix for the environmental noise (diagonal
elements equal to noise variances &2i and offdiagonal elements equal to "ij&2i, where "ij is
the correlation between species-specific
noise terms). The ! symbol indicates the
Kronecker tensor product (producing all possible combinations between the elements in
two matrices) and " indicates a matrix product (e.g, AB). This method of finding population asymptotic variances in different environmental conditions is contrasted with
simulation results in chapter II.
Fig. 4. Environmental variation
affecting population carrying
capacities across a resource gradient. Environmental fluctuations are either filtered through
tolerances (a), or affect population carrying capacities directly
w = 0.2
In chapter V coloured environmental
variation is modelled as a random walk along
a circular (periodic) resource gradient, affecting species-specific carrying capacities, intrinsic growth rates and interaction coefficients depending on the position of species
resource optima along the gradient. In this
model (as well in those used in III – VI) species take their carrying capacities from a resource distribution. The maxima of this distribution
!$' the"resource gradient
as: µt = µt–1 + ('t , where µ indicates the
mean position of the resource distribution
and $ is the rate at which µ changes along the
gradient. Increasing temporal autocorrelation
(reddening) in µt is observed as ( approaches
zero as a limit. When considering environmental variation along a resource gradient,
stochasticity can be introduced in two dis-
tinct ways: horizontally across the gradient,
which affects all species simultaneously (Fig.
4a), or vertically, affecting each species separately (Fig. 4b). In the former case, environmental variation is filtered through species
environmental tolerances (Gaussian responses along the gradient), modifying the
environmental signal (Fig. 4a) (Laakso et al.
2001). This filtering does not occur in the
latter case (Fig. 4b).
The mathematical models (eqn. 7) for community dynamics are used to generate time
series data of simulated population densities.
Different metrics are calculated from this
data, depending on the specific question of
interest. All of the metrics used here are ei-
ther commonly applied tools in empirical
community ecology, or are easily applicable
to empirical data. Most of the work within
this thesis deals with community dynamics
and population persistence. This includes recording actual extinction events, as well as
estimating the variability in population densities (I, II, VII). Variability is measured as the
coefficient of variation, which scales fluctuation magnitude with respect to the mean
population density [CV = s.d.(N)/mean(N)].
This is necessary, as multiplicative effects,
such as environmental variation, scale with
population size. Another useful measure,
considering community dynamics, is the
evenness in population densities (Pielou
" p ln pi ,
ln S i=1 i
where p is the proportion of all individuals in
a community belonging to species i and S is
community size (number of species). J ranges
between [0, 1], where 0 indicates that all individuals belong to a single species and 1
indicates an even distribution of individuals
across all S species. In addition to its application to measure ecological diversity, species
evenness is also considered as a useful proxy
for biomass stability (Gonzales & De Feo
2007). Species evenness is used to measure
species diversity, along with actual species
richness, in chapters III – V.
Species extinction risk/probability can be
measured in many different ways, such as the
expected time to extinction (e.g., Lande
1993; Cuddington & Yodzis 1999), or the
extinction probability in a given time
(Morales 1999; Heino et al. 2000). I utilise
two different measures for extinction propensity; extinction probability (I, II), taken as
the proportional frequency of extinction
events (Heino et al. 2000), and extinction
risk (II), measured as the proportional time
(T = time series length) spent below an extinction threshold (NiE = 0.01!Ni*):
< N iE
t =1 i=1
When considering time series data from real
populations one can incorporate information,
e.g., about the minimum viable population
size, by changing the value of NiE.
Chapter VI considers local community
assembly within metacommunities — a collection of local communities linked by dispersal (Leibold et al. 2004). The ecological
similarity between replicated communities
(assembled under identical environmental
conditions) is compared using the Steinhaus
index of similarity (Pielou 1977; Legendre &
where W indicates a sum of the minimum
densities of species shared by samples i and
j, and A and B indicate the total densities for
species present in samples i and j, respectively. This community metric is often referred to as percent similarity, as it returns a
proportional association between samples.
Steinhaus similarity is the complement of the
commonly used Bray & Curtis dissimilarity
measure (S = 1 – BC).
“I try to think but nothing happens”
drift processes for community organisation and dynamics (VI).
— Esa Ranta
Although the models investigated here are
relatively simple, the response of these
model communities becomes rather complex
when environmental stochasticity is introduced in different ways. Therefore it is not
necessarily easy to derive general patterns
from the results presented. Therefore, the following results and discussion do not strictly
follow those in the thesis chapters, but rather
intend towards a clearer synthesis of my thesis. The main results are:
(1) Environmental correlation (i.e., correlation between species responses to environmental variation) is an important
characteristic of competitive communities, affecting the persistence (I, II) diversity (III) and temporal stability (IV)
of these communities. Environmental
correlation influences the community
response to variation both in the magnitude and temporal autocorrelation of environmental fluctuations. Qualitative
predictions regarding species diversity
are maintained between simple, diffuse
communities (II) and hierarchically
structured communities (III).
(2) Reddened environmental stochasticity
and ecological drift processes (such as
demographic stochasticity and dispersal
limitation) have important implications
for patterns in species relative abundances (V, VI) and community dynamics
over time and space (VI). Our understanding of patterns in biodiversity at
local and global scale can be enhanced
by considering the relevance of different
(3) The underlying process generating fluctuations in environmental conditions
does not qualitatively (nor quantitatively) affect the results presented here
=101 !",,(#&$./ %*):"#)*)/ $"/ *#7&V
%"#,*#$-8/ %*44*#&#</ [email protected]/ -)/ )&,V
An important characteristic of multi-species
communities in fluctuating environmental
conditions is the similarity in species-specific
responses to these fluctuations (Roughgarden
1975b; Ives et al. 1999; Ives et al. 2000;
Ripa & Ives 2003; Greenman & Benton
2005; Vasseur & Fox 2007). As in single species populations (Kaitala et al. 1997; Ripa &
Heino 1999), environmental reddening amplifies (dampens) undercompensating (overcompensating) population dynamics in multispecies communities (Greenman & Benton
2005). However, results by Ripa & Ives
(2003) on competitive communities suggest
that overcompensating populations can respond differently to environmental reddening, depending on ‘environmental correlation’ (covariation between species-specific
environmental responses). If species are independent in their responses to environmental variation, environmental reddening
increases population variability, whereas correlated responses result in decreased variability. This pattern is also recovered by the analytical tools of Greenman & Benton (2005)
(II). My results show that these relationships
can depend on both the properties of environ
mental variation and community structure
Fig. 5. Population variability (coefficient of variation CV = s.d.(N) / mean(N); a proxy for extinction risk) varies with environmental reddening, depending on the severity (w) of environmental fluctuations in diffuse competitive communities (II). Species-specific responses to environmental variation (species equivalency) are either independent or correlated (#) between species. Parameter values:
K = 1, ! = 0.5, r = 1.8.
(I – III).
!1#)=+- 53##"91*1+,- K1*(- :1>>",+- 53#)+*1Y
Investigation of diffuse competitive communities of overcompensating populations (II)
recovered the qualitative results of Ripa &
Ives (2003); environmental reddening has an
opposite effect on population extinction risk
when species environmental correlation is
zero or highly positive (Fig. 5). One potential
explanation for the contrasting results regarding the relationship between environmental
reddening and population extinction risk
(Ripa & Ives 2003; Greenman & Benton
2005; I, II) lies in the strength of interspecific interactions (Ruokolainen et al. 2009);
weak interactions lead to patterns similar to
those in single species models (I), independently of the correlation between species environmental responses, while relatively strong
interactions result in qualitatively different
patterns depending on similarity between en-
vironmental responses (II).
The importance of the strength of between-species interactions for community stability has been been recognized previously
(Kokkoris et al. 1999; 2002; Jansen &
Kokkoris 2003). My results indicate that in6.
teraction strength can interact withFigure
environmental correlation in affecting community stability under coloured environmental fluctuations. More work is needed for
a better understanding of the general patterns
in and the exact mechanism be hind community responses to environmental reddening.
The amplitude (severity, w) of environmental fluctuations also has a considerable
influence on the relationship between environmental reddening and extinction risk, under different environmental correlations (Fig.
5). For example, while weak noise leads to a
negative relationship between environmental
reddening and extinction risk with highly
correlated environmental responses (Fig. 5a),
increasing noise severity can change this re-
Fig. 6. Increasing environmental
autocorrelation (%) increases (decreases) population extinction
probability in competitive communities ,where species are characterised by their relative abundance
ranks, with undercompensatory (r
= 0.25, grey lines) or overcompensatory (r = 1.75, black lines) equilibrium dynamics (I). Speciesspecific responses to environmental
variation are either independent (a)
or identical (b) between species.
" [email protected]!"A
lationship from negative to positive under
relatively high environmental autocorrelations (Fig. 5b, c). Interestingly, the relationship between environmental reddening and
population variability can be nonmonotonic,
depending on noise severity and the similarity between environmental responses (Fig.
5), which is in some cases also predicted by
linear approximation techniques (II). Increasing noise severity acts to increase the
discrepancy between results from simulationand analytical models (II), which supports
the application of stochastic simulations over
linear approximations (Greenman & Benton
2005) in more reliably predicting population
and community responses to environmental
fluctuations (Bjørnstad et al. 2004; Reuman
et al. 2006). The fact that these results arose
in a simple model where local stability =
global stability emphasizes the need for
simulations in more complex models.
veys no qualitative influence to population
extinction probability (EP) in locally stable
communities with asymmetric competition
(I). Assuming independent species-specific
responses to environmental variation, noise
colour has an important effect on extinction
probability (Fig. 6a); red noise leads to
higher (lower) extinction probability in association with undercompensating (overcompensating) dynamics than blue noise does.
When species respond identically to the environment, noise colour is only important in
association with overcompensating
ics, while evaluating species extinction probability (Fig. 6b). There is a much stronger
contrast between blue and red noise in respect to extinction risk, compared to independent responses to environment.
In these communities species identity
(relative abundance) can have important consequences for population extinction risk. If
only a single species is forced by environ7$9:3#- 53##"91*1+,- K1*(- 53#)+*1*1D+- mental stochasticity, the presence of inter$,&##+*%&
specific interactions can interfere with the
Contrary to previous predictions by Ripa & interaction between noise colour and populaIves (2003), variation in the similarity be- tion density dependence (I). This indicates
tween species environmental responses con- that community interactions and the scale of
disturbance within a community play a considerable role in affecting the extinction risk
of community members, with potential implications to population management, such as
harvesting (e.g., Enberg et al. 2006). In addition, species position in an abundance hierarchy influences their population dynamics
(colour and variability) and extinction probability, confirming that abundance rank can
provide a useful proxy for relative competitive ability (Fowler 2005).
The results presented above (I, II) assume
that environmental variation can be modelled
as a stationary autoregressive (AR) process.
However, as previous work using autoregressive (Petchey et al. 1997; Ripa & Heino
1999; Schwager et al. 2006) and sinusoidal
1/f noise (Cuddington & Yodzis 1999;
Morales 1999) have reported differing predictions regarding population extinction risk
with environmental reddening, it is worth
asking how general our results are? In chapter VII we compare population variability
when forced either by AR or 1/f noise, while
controlling for the variance in the environmental time series. The results show clearly
that there are no qualitative difference in
population variability when subjected to
forcing by different noise generating processes. Even the quantitative differences are
minor while considering population extinction risk in association with environmental
reddening. This finding allows us to better
compare results between different studies and
generalise the reported relationships between
environmental autocorrelation and population dynamics (e.g., Ruokolainen et al. 2009
and references therein).
=1;1 !",,(#&$./ %*):"#)*)/ $"/ *#7&V
%"#,*#$-8/ %*44*#&#</ ILJK/ <*$$&#</
All the previous work comparing the correlation structure between species environmental
responses and its influence on population extinction risk and biomass stability in communities has assumed that the environmental
correlation remains the same for all species
pairs (Roughgarden 1975b; Ives et al. 2000;
Ripa & Ives 2003; Vasseur & Fox 2007).
However, in an evolutionary context it is reasonable to assume that the similarity between
species environmental responses should reflect the overall ecological similarity between species (e.g., Grant & Grant 2006;
Johansson & Ripa 2006). The implications of
this assumption on species diversity in fluctuating conditions was tested in chapters III
and IV, where I compared open (dispersal
linked) communities with a hierarchical
niche structure that are subjected to different
scenarios regarding the correlation between
species environmental responses.
Environmental variation is known to promote
species coexistence when species have dif
ferent optima along an environmental gradient and when resource availability varies
along that gradient (Chesson 2000; Lehman
& Tilman 2000). In such conditions increasing species richness may in turn increase
species evenness (a good proxy for biomass
stability; Gonzales and De Feo 2007), due to
the so called insurance effect of biodiversity
(e.g., Doak et al. 1998; Yachi and Loreau
1999). In these hierarchically structured sysems competitively inferior species may have
periodic outbreaks at different ends of the en
vironmental gradient, especially if fluctuations along that gradient are positively auto-
! // / !
Fig. 7. Species evenness (a) and richness (b) are
affected differently by environmental autocorrelation (%), depending on the correlation between
species environmental responses. HR = hierarchical responses (" is a function of |xi – xj|, distance between species niche optima). Parameter
values: r = 1.8 is used to allow comparison with
Fig. 5., noise severity w = 0.5, community size S
correlated (Gonzalez and Holt 2002; Holt et
al. 2003; Long et al. 2007). Therefore it is
surprising that species diversity was previously observed to decreases with environmental reddening (Hiltunen et al. 2006;
Gonzales & De Feo 2007). My results are in
contrast with those from earlier studies, as
they show a clear increase in diversity with
environmental reddening (Fig. 7) (III), as
predicted by the ‘inflation effect’ (Gonzalez
& Holt 2002; Holt et al. 2003). The discrepancy between my and previous results can be
related to the strength of interspecific competition (III).
The results in III also show that the correlation structure in species environmental responses is important for species diversity in
hierarchical systems, as in simpler communities (I, II). In addition, the relative importance of different scenarios of environmental
correlation can depend on 1) the severity and
2) temporal autocorrelation of environmental
fluctuations (III). Species-specific changes
in population variability differ considerably
between (i) uniform environmental responses
across a community and (ii) hierarchical responses (HR), due to the non-linear filtering
of environmental variation through species
environmental tolerances (Laakso et al.
2001) in the latter case (Fig. 4). With overcompensating population dynamics, independent (positively correlated) responses
lead to a decrease (increase) in species diversity with environmental reddening (Fig. 7),
as predicted by previous results from nonhierarchical, diffuse systems (II). As noted
above, HR is associated with increased diversity with environmental reddening. However, hierarchical responses result in lower
diversity than independent (IR) or positively
correlated responses (CR), due to higher
variability in species-specific environmental
The results presented here indicate that the
negative relationship between species evenness and environmental reddening (Hiltunen
et al. 2006; Gonzales & De Feo 2007) is not
general, but applies only under limited dynamical scenarios in hierarchically structured
systems. An important result is that when
competition is hierarchically organised in a
community, the correlation structure in spe-
cies environmental responses can critically
influence community dynamics and diversity
in coloured environments (III).
stantially modify the variance-covariance
structure in population fluctuations (Ranta et
al. 2008a, b).
Differences in species environmental responses also have implications for the relationship between biomass stability and community size (IV). In this system, increasing
community size is associated with an increase in biomass stability, in agreement with
previous results (Tilman 1999; Yachi &
Loreau 1999; Lehman & Tilman 2000;
Lhomme & Winkel 2002). My results also
agree with the observation that the correlation between species environmental responses has an effect on the relationship between diversity and biomass stability in
communities (Doak et al. 1998; Ives et al.
1999; Ives et al. 2000; Fowler 2009). I demonstrate that hierarchical environmental responses (HR) promote biomass stability in
comparison with independent responses (IR),
when stability is measured as species evenness, whereas independent responses have a
stronger stabilizing effect on biomass variability (IV).
The relative importance of different scenarios of species environmental correlation
(HR, IR) also depends on the interaction between colour and amplitude of environmental
fluctuations (II, IV) Furthermore, my results
indicate that while the positive diversitystability relationship would be due to the
‘portfolio effect’ (Tilman et al. 1998; see
Glossary Box) and the ‘covariance effect’ of
competition (Lehman & Tilman 2000), this
can be difficult to show in ecologically realistic conditions. This is because such factors,
as environmental reddening and correlation
between environmental responses, can sub-
=1>1 !",,(#&$./ :*%)&)$*#5*/ -#4/ 5",V
In chapter V, I studied community dynamics
in a system where fluctuating availability of
limited resources affected species vital rates
(K’s, r’s and !’s). In this model environmental variation changes the availability of
different resources along a resource gradient.
In the absence of resource limitation (and
environmental variation) this model framework has been shown to generate aggregated
species abundance distributions along the
resource gradient (Scheffer & van Nes 2006;
Pigolotti et al. 2007), with pronounced gaps
between the species clusters that are maintained by competition. Such nearly neutral
patterns have also been reported for other
systems with host-parasite (Bonsall &
Mangel 2004) and spatial (Gravel et al.
2006) dynamics. This ‘emergent neutrality’
arises because small differences in species
traits lead to extremely long times for competitive exclusion to occur (Holt 2006) and it
is increasingly likely to occur with increasing
species richness (Purves & Pacala 2005; Holt
Previous models reporting ‘emergent neutrality’ in the form of species aggregates
along ecological gradients have assumed
constant environmental conditions. However,
when linking these predictions to the real
world, this assumption is no longer valid,
since biological systems are constantly buffeted by fluctuations in ambient conditions.
Fig. 8. The influence of dispersal rate (p; a, b), landscape
size (L; c, d), and initial
community size (S; e, f) on
the distribution of similarities
calculated between replicated
community samples of neutral
and non-neutral communities.
Dashed lines = local dispersal, solid lines = global dispersal.
In agreement with previous reports, my
model — even with limited resource availability — predicts multiple species clusters in
the absence of stochasticity (V). In contrast,
introducing environmental variation to the
system prevents the emergence of sustained
species clusters. While there still appears to
be aggregation of population abundances in a
single cluster, this is simply due to concentrated resource availability. Stochasticity also
prevents convergence to any competitive
quasi-equilibrium, as the competitive advantages between highly similar species constantly change across time. Changes in patterns of species abundance over time depend
on the rate of change in environmental conditions, i.e., environmental colour; rapid (blue)
changes promote long-term community per-
sistence, while slower (red) changes increase
population extinction risk due to low resource availability and increased competition.
Reddened environmental stochasticity, in
particular, can increase drift in community
composition, compared to static conditions
(V), which may give a false impression of the
unimportance of species-specific differences
for community dynamics, i.e., neutrality
(Bell 2001; Hubbell 2001). In chapter VI, I
investigate the importance of ecological drift
(both in deterministic and variable environmental conditions) on the similarity of replicated community samples that are generated
using either neural or niche-based commu-
nity assembly models in a metacommunity (a
collection of local communities connected by
dispersal). The range of community similarities generated by the different models is affected by dispersal rate between patches in a
metacommunity (Fig. 8a, b), the size of the
metacommunity (Fig. 8c, d), and the number
of species initially present in each local
community (Fig. 8e, f). On top of these factors dispersal scale (local or global) has a
considerable influence on community repeatability (Fig. 8). These results support empirical findings indicating that reducing the connectivity between patches increases drift in
community composition (Chase 2003, 2007),
as species are more likely to be found in their
preferred habitats (Pulliam 2000).
Whether community composition can be
understood based on species traits (Diamond
1975) or neutral drift (Hubbell 2001), is an
important and timely question in community
ecology (e.g., Dornelas et al. 2006; Volkov et
al. 2007; Leibold 2008). It is well-known
that neutral patterns can arise through nonneutral processes (Chave et al. 2002; Purves
& Pacala 2005; Alonso et al. 2006; Scheffer
& van Nes 2006; Walker 2007). Consequently, teasing apart observed community
patterns (such as species relative abundance)
and underlying processes can be quite difficult in practice (Adler et al. 2007). Chapter
VI is an attempt to unify the previous under-
standing and provide guidelines for planning
experiments for understanding the relative
role of equalizing and stabilizing processes
(Chesson 2000; Holt 2006) driving community dynamics in nature.
My findings indicate that the relation between pattern and process can be understood
by consideration of the following ecological
drift processes (VI): A) variation in population densities due to (i) demographic stochasticity and (ii) interspecific competition
(Purves & Pacala 2005); B) variation in species composition (presence/absence) in local
communities due to local extinctions and
dispersal limitation; C) drift in the global
species pool that provides immigrants to each
local community as a result of global extinctions; and finally D) reddened environmental
stochasticity increases drift in local population densities (due to the ‘inflation’ of
population densities in subdominant species;
Gonzalez & Holt 2002), which is only realized in non-neutral communities. The relative
importance of different sources of drift determines whether a non-neutral process resembles a neutral process in terms of community similarity metrics. An important aspect of the results is that niche-structuring
(i.e., a non-neutral model) tends to amplify
heterogeneity in community composition in
association with localized dispersal, compared with the neutral model (Fig. 8).
While stochastic population and community
models incorporating environmental variation have been analysed for over a decade,
there still remains many important questions
left unanswered (Ruokolainen et al. 2009).
Here I will briefly go through a couple of
topics I personally find worth pursuing in the
The work presented in this thesis only
scratches the surface of community responses to environmental variation. I have
investigated relatively simple systems that
comprise only a single trophic level. One of
the many opportunities for future work is to
explore how different assumptions regarding
environmental noise entering trophically
structured systems influence stability and
function of food webs (Vasseur & Fox 2007).
Additional work is also required even with
the simple communities investigated here (I,
II). For example, it is not clear under what
conditions do environmental reddening result
in increased and decreased extinction risk in
association with overcompensatory population dynamics.
The influence of the covariation between
species-specific responses to environmental
variation is well studied in closed communities (Ives et al. 1999; Ripa & Ives 2003; I, II)
and explored also for open communities
(Hiltunen et al. 2006; Gonzales & De Feo
2007; Long et al. 2007; III, IV). However, it
is not clear how such covariation in space
and time will interact with environmental
reddening in metacommunities. Developing
this field is an important challenge for future
research. Another interesting research direction both in closed systems and metacommunity framework is to investigate how, e.g.,
environmental reddening affects coevolution
in species assemblages.
I dedicate this thesis to my supervisor and
friend, Esa Ranta. A lot was left undone after
Esa’s unexpected death in August of 2008. I
especially miss our discussions, flavoured
with French culture and classical music. With
joy I remember our excursion to Beijing in
2007, with all the medicinal cognac (due to
heavy jetlag), funny coincidences with taxi
drivers not really knowing where they should
take us, great culinary experiences at down
town (our hotel was situated in the middle of
nowhere in the countryside and it took nearly
an hour to transport to the city centre), and
not so great wine (despite the great name;
Great Wall). I also had the greatest time in
Scheffield in 2008, when our group made a
trip there to visit local peers. Again, unforgettable gastronomic experiences, excellent ‘refreshments’ and magnificent company. Esa,
you really made my stay at IKP memorable,
interesting and exciting.
What comes to my thesis, I have a lot to
thank Mike for. He was there for my when I
desperately needed help and he also took the
effort to teach me valuable things about presentation, writing and modelling. Most importantly, Mike cheered me up after those endless rejection letters, telling me that the
comments I thought were fatal could be easily handled. I really enjoyed our collaboration and I hope we will continue doing so
(unless I’ll end up delivering newspapers). I
would also like to thank Veijo, who took over
the responsibility of my supervision after
Esa. I could always trust in the help of Veijo
when I had mathematical problems reaching
beyond my capabilities. Every time we had
meeting, the conversation might start on scientific matters, it always ended up on more
Academic work is mentally extremely
challenging. Thus, it was very kind and
thoughtful of Annukka to let me have my
weekly escape from reality in form of floorball (given that my legs were OK, none of
the children were sick, there we no more im-
portant activities, etc.), even it meant spending also the evening with two children after a
long day. You have my respect, and I will try
to make this all up to you somehow. These
Wednesday nights at Kumpula provided a
valuable sanctuary in the middle of work and
family life. I am thankful to Suvi for organising the sähly and all the other players for tolerating my sometimes too intense playing.
My warm thanks also go to my Mother
and Father, who have stood by me throughout my academic studies and later career. Al
of that would have been much more difficult
without your financial — and mental — sup-
port. As I’m writing this in my office in Toronto Canada, I’m expecting you to arrive for
a visit in a couple of days.
I am most grateful to my dear wife Annukka for keeping our family together, she
knows I was not always up the task after
hard, frustrating days in front of my computer. My family also helped me to detach
from work (at least to some extent) in the
free time, preventing a complete nervous
breakdown. I could not have done this without your support and help, Annukka, Eelis
and Alma. I love all of you some much and
I’m privileged to share this life with you.
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