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!"##$%& +(,,-%. 01 3#$%"4(5$&"# “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/ -($"5"%%*8-$&"#/ &#/ $9*"%./-#4/:%-5$&5* 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). U-G-V !"##$%& T8"))-%./L"?W% <,,+9*1$=-*+%#193=3F& @($"5"%%*8-$&"# 6&<*#7-8(* 6#7&%"#,*#$-8/ 5"8"(% 6#7&%"#,*#$-8/ %*):"#)* N*-)&'&8&$. U"%$C"8&"/*CC*5$ +:*5$%-8/ *?:"#*#$ +$-'&8&$. 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. U-T-V ac = 0.10 !"##$%& 8*: 3 A=,5/+B>C5 1;<=>?,@5 $ !3 3 0 3 DE>?5/+B>C5 -3 F5@/+B>C5 $ !3 $ #$ "$ '$ &$ %$$ G>;5H//! )*+,*-./012 89: Fig. 1. (a) Environmental variation of different colours. (b) Values for the January North Atlantic Oscillation index (NAO) from 1823 to 2009 and their long-term distribution. The NAO time-series (solid line) has a mean of 0.64 (dashed line), variance of 3.33 and an autocorrelation of 0.10. The distribution of January NAO indices is normally distributed. " # $ !# !" $ %&#$ %&"$ %&'$ %&&$ %($$ %(#$ %("$ %('$ %(&$ #$$$ %$ #$ 3$ 4-56,5+7. 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 single-species Figure populations (Petchey et al. 1. 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. U-W-V !"##$%& 01;1 65"8"<&5-8/ &#$*%-5$&"#)/ &#/ ):*5&*)/ tems, non-trophic interactions (within a trophic level; such as competition, mutualism -))*,'8-<*) 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 els. 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). U-X-V !"##$%& Here, I briefly review the relevance of these different sources of extinction risk for my work. ?+*+%#19$9*,-3>-,)+51+,-+@*195*139 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 habitat. 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). B(+-19C="+95+-3>-+@*195*139-39-+53,&,*+#, 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 biogeochemical cycles. U-A-V !"##$%& 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 *151*& 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; IPCC 2007). 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. 2009). 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). U-E-V !"##$%& ;1 @&,) 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 >1 (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 (VII). B*$9"4) 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- U-M-V $ !( 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 $ ( 1 K i " S ) ! ij N j ,t &( , ' j =1 (1.a) which can be written in matrix form as: Nt +1 = Nt ! exp #$r ! (1 " ANt /K ) %& . (1.b) In eqn. (1.a) ri and Ki are the species-specific intrinsic growth rate and carrying capacity, respectively. Parameter !ij defines the per capita effect of species j on the renewal of species i. The !ij values combine to form an interaction matrix A (Levins 1968; May 1974). The A matrix is usually standardised such that its main diagonal elements (!ii) are set equal to 1 and the off-diagonal (!ij) elements fall between [0, 1]. An exception is made in chapter IV, where interspecific competition is allowed to exceed intraspecific competition in a more mechanistic form of the model. It is traditional to consider the !’s in eqn. (1) as measures of niche overlap between species, e.g., along different reFigure 3. source gradients (e.g., MacArthur 1970), where the degree of interspecific competition depends on the degree of shared resources (Fig. 3). In this thesis, competition is linked to niche theory in chapters III – VI. Eqn. (1.b) gives eqn. (1.a) in matrix notation, where N, r, and K are vectors (S ! 1 in size) containing species specific densities, growth rates and carrying capacities, respectively. The ! and / signs represent elementwise multiplication and division, respectively. In the simplest form, parameters r and K are set equal for all species, and the ! coefficients are set equal for all species pairs. In this case competition is called diffuse and the identity of species is irrelevant for population dynamics (II). This should not, however, be confused with neutral competition, which implies the equivalency of kin and non kin in competitive interactions (e.g., Bell 2001). Internal network structure can be modified by allowing these parameters to differ between species (I, III – VI). .8 / !"##$%& In the system described by eqn. (1), the community equilibrium can be found as (May 1974): N* = A !1K . (2) 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). >1;1 E.#-,&5-8/)$-'&8&$. 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 , (3) 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): !N i bij = !N j =" N* # ij ri N *j Ki , i$ j. (4) 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). U-P-V !"##$%& >1>1 E*,"<%-:9&5/ -#4/ *#7&%"#,*#$-8/ where " is the correlation coefficient between )$"59-)$&5&$. all pairs of environmental time series and " is the autocorrelation coefficient. Setting " < 0 ?+#3F%$)(15-"95+%*$19*& 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 rounding errors. 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 D$%1$*139 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 variance (VII). 1+ %2 ( ) (5) %= 1# ' ' J-,*35($,*15-53##"91*&-#3:+= Environmental variation in population models is often assumed to affect all individuals U-GH-V !"##$%& 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 $ ( 1 K i " S ) ! ij N j ,t &( exp #$) i ,t &' , (7.a) ' j =1 x t +1 = Bx t + ! t , (8) 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 & Benton 2005): ( )( Vec (C ) = I ! " 2B # B I ! " 2I # B or * $ 1 N i ,t +1 = N i ,t exp , ri & , &% K i 1 + ! i ,t + ( ) 'S " N # 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. 1998): !1 (I ! " B # I) (I ! B # B) ) !1 !1 • , (9) 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. U-GG-V !"##$%& 3-8C:4-96! 66D8C/-4 81,54467,89:-0; E:4;,:B/;:5065F6,-45/,1-4 81,54467,89:-0; ?97- # <-0;,- @8A <8,,2:07618=81:;2>66 ! " Fig. 4. Environmental variation affecting population carrying capacities across a resource gradient. Environmental fluctuations are either filtered through species-specific environmental tolerances (a), or affect population carrying capacities directly (b). ! @BA ( w = 0.2 # " ! ! !$#) !$) !$*) 3-45/,1-67,89:-0; # " ! " ! %!! '!! ! #!! %!! +,-./-012 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 varied ! !$# is!$% !$&along !$' 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). >1=1 @#-8.)*) 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- U-GT-V !"##$%& 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 1977): J=! 1 S " p ln pi , ln S i=1 i (8) 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*): T ER = S !! N i ,t < N iE t =1 i=1 ST . (9) 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 & Legendre 1998): ij SSteinhaus = 2W , A+B (10) 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). U-GW-V !"##$%& =1 H*)(8$)/-#4/E&)5())&"# “I try to think but nothing happens” drift processes for community organisation and dynamics (VI). — Esa Ranta Although the models investigated here are relatively simple, the response of these model communities becomes rather complex when environmental stochasticity is introduced in different ways. Therefore it is not necessarily easy to derive general patterns from the results presented. Therefore, the following results and discussion do not strictly follow those in the thesis chapters, but rather intend towards a clearer synthesis of my thesis. The main results are: (1) Environmental correlation (i.e., correlation between species responses to environmental variation) is an important characteristic of competitive communities, affecting the persistence (I, II) diversity (III) and temporal stability (IV) of these communities. Environmental correlation influences the community response to variation both in the magnitude and temporal autocorrelation of environmental fluctuations. Qualitative predictions regarding species diversity are maintained between simple, diffuse communities (II) and hierarchically structured communities (III). (2) Reddened environmental stochasticity and ecological drift processes (such as demographic stochasticity and dispersal limitation) have important implications for patterns in species relative abundances (V, VI) and community dynamics over time and space (VI). Our understanding of patterns in biodiversity at local and global scale can be enhanced by considering the relevance of different (3) The underlying process generating fluctuations in environmental conditions does not qualitatively (nor quantitatively) affect the results presented here (VII). =101 !",,(#&$./ %*):"#)*)/ $"/ *#7&V %"#,*#$-8/ %*44*#&#</ I@JK/ -)/ )&,V :8*/-)/&$/<*$) 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 U-GX-V !"##$%& 8/; *+,-./01+234/51/61.107389:; !"$# $"( $ !"$ !"!# ! 33w33A3!"!# %!"& %!"' !"' !"& $") $"' !") $"( !"' $ 33 w33A3!"# %!"& %!"' !"& ! 8?; $"& !"& !"( ! 86; " A3!"B ! A3!"# ! A3! !"' !"& 33w 33A3!"B %!"& %!"' ! !"' !"& <2415+2=>20/.3/-0+?+55>./01+2@33! 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 *139 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 species 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- U-GA-V !"##$%& *+,--!--.-! 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. */,-- !--.-' 0123452364-786/+/3932: ' !"& !"% !"$ ! .---!"A " .---! " .-@!"A !"# ! ' # ( $ ) ' # ( $ ) ;/<4=+45>-8+4? 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 dynamFigure 5. 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 U-GE-V !"##$%& disturbance within a community play a considerable role in affecting the extinction risk of community members, with potential implications to population management, such as harvesting (e.g., Enberg et al. 2006). In addition, species position in an abundance hierarchy influences their population dynamics (colour and variability) and extinction probability, confirming that abundance rank can provide a useful proxy for relative competitive ability (Fowler 2005). I+9+%$=-)$**+%9,-3%-,)+51C15-%+,"=*,L The results presented above (I, II) assume that environmental variation can be modelled as a stationary autoregressive (AR) process. However, as previous work using autoregressive (Petchey et al. 1997; Ripa & Heino 1999; Schwager et al. 2006) and sinusoidal 1/f noise (Cuddington & Yodzis 1999; Morales 1999) have reported differing predictions regarding population extinction risk with environmental reddening, it is worth asking how general our results are? In chapter VII we compare population variability when forced either by AR or 1/f noise, while controlling for the variance in the environmental time series. The results show clearly that there are no qualitative difference in population variability when subjected to forcing by different noise generating processes. Even the quantitative differences are minor while considering population extinction risk in association with environmental reddening. This finding allows us to better compare results between different studies and generalise the reported relationships between environmental autocorrelation and population dynamics (e.g., Ruokolainen et al. 2009 and references therein). =1;1 !",,(#&$./ %*):"#)*)/ $"/ *#7&V %"#,*#$-8/ %*44*#&#</ ILJK/ <*$$&#</ ,"%*/5",:8*? 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. N3K-1#)3%*$9*-1,-,)+51+,-,1#1=$%1*&L 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- U-GM-V ! // / ! !"##$%& 34+1'+5/+&+%%+55 CHAPTER III !"< >-? !"; !": !"9 !"8 !"7 34+1'+5/('16%+55 ! ! D/! ! D/!"B ! D/EF 8! >@? 7; 7! ; =!"# =!": ! !": !"# $%&'()%*+%,-./-0,)1)((+.-,')%2//! 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 = 20. 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; >1? 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 !"B !"# !"A !"< & 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 conditions. 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- !"; U-GZ-V !": =!"# =!": ! !": !"# Figure 7. !"##$%& 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). '3##"91*&-:1D+%,1*&-$9:-,*$O1=1*& 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 :")&$&"#/&#/%*):"#)*/$"/4%&C$ Q3-*3-R+#+%F+9*-9+"*%$=1*&S In chapter V, I studied community dynamics in a system where fluctuating availability of limited resources affected species vital rates (K’s, r’s and !’s). In this model environmental variation changes the availability of different resources along a resource gradient. In the absence of resource limitation (and environmental variation) this model framework has been shown to generate aggregated species abundance distributions along the resource gradient (Scheffer & van Nes 2006; Pigolotti et al. 2007), with pronounced gaps between the species clusters that are maintained by competition. Such nearly neutral patterns have also been reported for other systems with host-parasite (Bonsall & Mangel 2004) and spatial (Gravel et al. 2006) dynamics. This ‘emergent neutrality’ arises because small differences in species traits lead to extremely long times for competitive exclusion to occur (Holt 2006) and it is increasingly likely to occur with increasing species richness (Purves & Pacala 2005; Holt 2006). Previous models reporting ‘emergent neutrality’ in the form of species aggregates along ecological gradients have assumed constant environmental conditions. However, when linking these predictions to the real world, this assumption is no longer valid, since biological systems are constantly buffeted by fluctuations in ambient conditions. U-GP-V !"##$%& /+ .+ -+ "0010.+ ,+ ,+ + + /+ @%"A#");9 .+ !0010-+ -+ <;= 2+ !"#$%&' /+ !0010-+ -+ "0010,+ -+ ,+ + 3+ <>= ! 0010-+ " 0010,++ !()*)"#$%&' .+ G7:D"%:&'0%&$" /+ # 0010+43+ <B= C&)>:;&D"0:7E" 3+ # 0010+4+, <&= 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. + 5+ <"= /+ 2+ !0010,+ .+ " 0010.+ -+ <?= ! 0010,++ " 0010.+ /+ -+ ,+ + F(88#)7$90:7E" 3+ + + +43 , + +43 , 6787'&%7$90:;(%" 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. B(+-Q15(+-,*%12+,-O$52 Reddened environmental stochasticity, in particular, can increase drift in community composition, compared to static conditions (V), which may give a false impression of the unimportance of species-specific differences for community dynamics, i.e., neutrality (Bell 2001; Hubbell 2001). In chapter VI, I investigate the importance of ecological drift (both in deterministic and variable environmental conditions) on the similarity of replicated community samples that are generated using either neural or niche-based commu- U-TH-V !"##$%& 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- M1 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). N($(%*/59-88*#<*)/O/@/#*P/9":*Q While stochastic population and community models incorporating environmental variation have been analysed for over a decade, there still remains many important questions left unanswered (Ruokolainen et al. 2009). Here I will briefly go through a couple of topics I personally find worth pursuing in the future. The work presented in this thesis only scratches the surface of community responses to environmental variation. I have investigated relatively simple systems that U-TG-V !"##$%& 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 R1 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. @5S#"P8*4<*,*#$) I dedicate this thesis to my supervisor and friend, Esa Ranta. A lot was left undone after Esa’s unexpected death in August of 2008. I especially miss our discussions, flavoured with French culture and classical music. With joy I remember our excursion to Beijing in 2007, with all the medicinal cognac (due to heavy jetlag), funny coincidences with taxi drivers not really knowing where they should take us, great culinary experiences at down town (our hotel was situated in the middle of nowhere in the countryside and it took nearly an hour to transport to the city centre), and not so great wine (despite the great name; Great Wall). I also had the greatest time in Scheffield in 2008, when our group made a trip there to visit local peers. Again, unforgettable gastronomic experiences, excellent ‘refreshments’ and magnificent company. Esa, you really made my stay at IKP memorable, interesting and exciting. What comes to my thesis, I have a lot to thank Mike for. He was there for my when I desperately needed help and he also took the effort to teach me valuable things about presentation, writing and modelling. Most importantly, Mike cheered me up after those endless rejection letters, telling me that the comments I thought were fatal could be easily handled. I really enjoyed our collaboration and I hope we will continue doing so (unless I’ll end up delivering newspapers). I would also like to thank Veijo, who took over the responsibility of my supervision after Esa. I could always trust in the help of Veijo when I had mathematical problems reaching beyond my capabilities. Every time we had meeting, the conversation might start on scientific matters, it always ended up on more down-to-earth subjects. Academic work is mentally extremely challenging. Thus, it was very kind and thoughtful of Annukka to let me have my weekly escape from reality in form of floorball (given that my legs were OK, none of the children were sick, there we no more im- U-TT-V !"##$%& 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. 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