Detecting compensatory dynamics in competitive communities under environmental forcing

Transcription

1 Oikos 000: , 2008 doi: /j x # The authors. Journal compilation # Oikos 2008 Subject Editor: Tim Benton. Accepted 18 March 2008 Detecting compensatory dynamics in competitive communities under environmental forcing Esa Ranta, Veijo Kaitala, Mike S. Fowler, Jouni Laakso, Lasse Ruokolainen and Robert O Hara E. Ranta (esa.ranta@helsinki.fi), V. Kaitala, M. S. Fowler, J. Laakso and L. Ruokolainen, Integrative Ecology Unit, Dept of Biological and Environmental Sciences, PO Box 65 (Viikinkaari 1), FI00014 University of Helsinki, Finland. R. O Hara, Dept of Mathematics and Statistics, PO Box 68 (Gustaf Hällströmin katu 2b), FI00014 University of Helsinki, Finland. Competition is assumed to generate compensatory dynamics where an increase in one species is compensated by a decrease in others. Recently, using a community covariance technique, Houlahan et al. found that compensatory dynamics are only visible in 2530% of natural communities studied. The study was based on scoring the sum of covariances of population densities. In contrast to the theory, and as a cautionary reminder to the interpretation of natural time series data, we show that negative community covariance can be absent even in strongly competitive communities and can be found present in communities without competitive interactions. Precise knowledge of various features of the underlying species biology and characteristics of the environmental variation is required before community covariance can be correctly interpreted as a proxy for the importance of competition or environmental forcing in driving community fluctuations. Other tools may therefore be more appropriate, e.g. explicit modelling of competition using modern time series analytical tools. Disentangling agents of population fluctuations remains at the core of contemporary ecological research. Contrasting schools have long existed to account for the causes of population fluctuations. The mainstream view (Lack 1954, MacArthur 1972, Diamond 1975, May 1981) builds on the theory that density-dependent processes regulate fluctuations and that interspecific competition is a mechanism causing population variability. An alternative is that density-independent environmental forcing mechanisms (e.g. climate) are responsible for population fluctuations (Andrewartha and Birch 1954, Murray 1979, Turchin 1999). The latter view has gained increasing foothold due to recent concern of climate change and its impact on ecological systems (Walther et al. 2002). Competition theory suggests that populations in communities of ecologically similar species (guilds) fluctuate in a compensatory way, i.e. increases in the abundance of one species are accompanied by decreases of other ecologically equivalent species (Tilman 1988, Ives 1995, Klug et al. 2000, Fischer et al. 2001). Indeed, the unified neutral theory of biogeography (Hubbell 2001) builds on the assumption that interspecific dynamics in ecological communities is a stochastic zero-sum game: an increase in the abundance of one species is compensated by a decrease in the total abundance of all other species. Based on the above arguments, if competitive interactions are important for community dynamics, they should be visible in the community fluctuations. Otherwise it can be assumed that environmental forcing rules. Therefore a tool is required that can differentiate between these different mechanisms. For this purpose the negative community covariance method has been frequently applied (Ives 1995, Klug et al. 2000, Fischer et al. 2001, Houlahan et al. 2007). In this note we highlight that in many cases this method is not the most appropriate tool, as it often dismisses importance of competition in driving community dynamics though it is heavily involved. We show that the type of environmental autocorrelation, correlation in species responses to the environment, and the underlying density dependence (growth rate) strongly modulate community covariance. Assuming that community covariance can be used to distinguish between the importance of competitive or environmental factors in regulating community dynamics represents an oversimplified dichotomy that may lead to erroneous interpretations from time-series data. Methods A straightforward approach to various kinds of community dynamics is to attempt to split fluctuations into their component parts (Ives 1995, Klug et al. 2000, Fischer et al. 2001), and to assess whether the signature of compensatory dynamics is visible. Therefore, consider an S-species community where X i denotes the time series of the population density of the ith species. The variance of the sum of all population densities (or community biomass) over time is given as (Box et al. 1978): Early View (EV): 1-EV

2 X S VAR X i XS [VAR(X i )]2 XS X j1 COV(X i X j ); where VAR is the variance and COV is the covariance. The first term (on the right hand side) is the sum of variances of abundance of each of the individual species, while the second term is the sum of covariance of the S species excluding species-specific covariance (which is the variance, accounted for in the first term). A notable feature attributed to Eq. 1 is that when compensatory dynamics dominate, the sum of the pairwise covariances is negative (Ives 1995, Klug et al. 2000, Fischer et al. 2001, Houlahan et al. 2007). When the species densities vary in synchrony the term is positive, and when their densities vary independently the term is zero. We utilise a population renewal model for an S-species competitive community by taking Ricker dynamics as the kernel of the renewal process: X i;t1 X i;t exp ri 1 P S j1 a ij X j;t K i (1) m i;t h i;t : (2) Here X, i and S are defined as above, t refers to discrete time steps (years), r is the intrinsic population growth rate, K is the carrying capacity and a ij indicates the strength of competition (how much species j reduces renewal of species i). As all a ij values are positive (and a ii 1), we are dealing with single-trophic level LotkaVolterra competitive communities under the impact of environmental forcing. The a ij terms are those that can induce compensatory dynamics. The two final terms in Eq. 2 refer to external forcing, m, common (but not necessarily exactly the same) for all species and to species-specific demographic stochasticity, h. Since Moran (1953) it is well known (reviewed by Ranta et al. 2006, 2007) that synchronous dynamics can be induced by m i,t. The interspecific interactions in pairs, a ij, between the S species in Eq. 2 make the off-diagonal elements in the interaction matrix, A (the diagonal elements, the intraspecific interaction terms, of this S S matrix are standardized to unity). Equilibrium population densities X* (a column vector of length S) for the S species (Eq. 2) were derived after May (1973): X*A 1 K. When all elements in X* are positive, the community is feasible. We also tested A for permanence, i.e. the long-term persistence of all community members. If the two criteria were fulfilled, the populations for the S species were initialised with X* for our replicated simulations of Eq. 1. Hence, extinctions do not occur in our system. The intensity of competition was generated from min(a ij ) to max(a ij ) so that max(a ij )min(a ij )0.1; with min(a ij ) varied from 0 with a step of 0.1 up to 0.9. In search of the determinants of community covariance we selected population growth rates from three differing growth rate regimes (r[a,b] denotes a regime where the growth rate for each species is drawn from random numbers uniformly distributed between a and b: r[1,2], which in single-species systems gives stable dynamics for all species when not disturbed (by external forcing and/or filtering through A), r[1,2.6] in single-species systems (a ij 0, i"j) giving stable to periodic dynamics, and r[1, 3.5] which yields stable to complex dynamics in single-species systems). Community size was varied from S2 to S20 (but had little effect on the general results). m i,t was drawn from a bell-shaped distribution (mode at 1.0) with range of 1-w, 1w (w 0.5, unless stated otherwise), and temporal autocorrelation between m i,t and m i,t-1, k, was varied between -1 and 1 (Ranta et al. 2006). The different species experienced m i,t values that were generated across the range of either being uncorrelated to perfectly correlated among species. We refer to the correlation of species responses to the environmental fluctuations as equivalence, E, ranging from 0 to 1, while, k is the same for all species. Noise variance is scaled to asymptotic variance, which makes noise variance invariant to the autocorrelation structure. The species-specific noise terms (demographic stochasticity), h i,t, are independent but identically distributed species-specific random numbers drawn from a uniform distribution with limits [19s w ]; s w 0.01 here. Demographic stochasticity was considered necessary, as we were interested in assessing the impact of the global disturbance strength on the frequency of detecting negative sums of covariance: in the growth rate regime r[1,2] population dynamics completely stabilize if there is no external disturbance, thus hampering the variance-covariance calculations. The system, Eq. 2, was initiated at X* 9o, where o represents a vector of random numbers selected from a normal distribution with mean 0 and variance Equation 2 was then iterated over 200 time steps, of which the final 100 steps were used for scoring the sign (positive/ negative) of the sum of community covariance [last term in Eq. 1] to assess presence/absence of compensatory population fluctuations. We present our results as the proportion of 1000 replicated runs that have a negative sign for community covariance (the third term in Eq. 1), for each parameter combination. Results With Eq. 2 it is possible to manage various species, community and environmental properties (intensity of competition, community size, growth rate, autocorrelation structure of the environmental forcing and degree of equivalency how different species experience the forcing) that are not often controlled for in data from natural communities (Ranta et al. 2006, 2007). Note that competition is always present in the model when a ij 0, but some factors (e.g. emergent second order interactions in the renewal, synchronization due to filtration of dynamics through a ij ) may mask the visibility of the compensatory mechanisms in the community. Compensatory dynamics, i.e. a negative sum of covariances among population densities, can be detected in communities with no interactions or common external forcing, simply because of sampling error (Fig. 1A). This result arises regardless of the distribution of intrinsic growth rates. However, even as the noise equivalence increases, the probability of finding a negative sum of covariances remains high over the two wider distributions of the growth rates 2-EV

3 Figure 1. Probability to find compensatory dynamics in communities where intensity of competition may vary. The different symbols indicate communities drawn randomly from different growth rate regimes in the Ricker renewal (k r[1, 2] yielding stable dynamics when not disturbed, m r[1,2.6] giving stable to periodic dynamics, I r[1,3.5] yields stable to complex dynamics). Panels (A), (C) and (E) represent the simulation results in the absence of species interactions, whereas panels (B), (D) and (F) include species interactions. (A) The probability of detecting compensatory dynamics in the absence of species interactions is graphed against how equivalently the environment disturbance (with k0.7) matches for the five competing species (S5, w0.5 is the strength of the common environmental disturbance, and s w 0.01 is the strength of species-specific demographic stochasticity). (B) The probability of compensatory dynamics is graphed against how well the same environment disturbance as in panel (A) matches for the five competing species (with average a ij 0.5). In (C) and (D) the autocorrelation of the environment, k, varies for communities with no interaction and with interaction, respectively (other parameter values inserted). (E) The size of the community with no species interactions ranges from S2 to S20. (F) Mean of the interspecific competition coefficients, a ij, ranges from 0.05 to tested (r[1, 2.6], r[1, 3.5]). When competitive interactions are present in the model, the probability of detecting compensatory dynamics increases considerably for r[1, 2] and r[1, 2.6] compared to uncoupled communities, but decreases for r[1, 3.5], except under high environmental equivalence (Fig. 1B). An increased probability of detecting compensatory dynamics can also be seen in positively autocorrelated environments, without and with interactions (Fig. 1CD). However, the equivalence of species responses to the environment can quickly switch from perfect visibility of compensatory dynamics to total invisibility as similarity in 3-EV

4 the environment (either over time or between species) increases, even in a case of extremely intensive competition (Fig. 1B, 1D). Interestingly enough, adding competitive interactions decreases detection of compensatory dynamics for r[1, 3.5] under high positive values of environmental autocorrelation, with the opposite effect in less dynamically complex communities (compare Fig. 1A and 1D). Community size S has only a marginal impact on the potential for detection of compensatory community dynamics, either in the absence (Fig. 1E) or in the presence (not shown) of the density dependent interactions. Finally, increasing the intensity of competition can greatly amplify the probability of detecting compensatory dynamics in the community (Fig. 1F). The factors enhancing the probability of compensatory dynamics are low population growth rate, positively autocorrelated environmental variation, low degree of environmental equivalence, and a high degree of community interaction. However, there are many parameter combinations (Fig. 1B, 1D, 1F) under which compensatory dynamics is not detected though it is present. A more striking feature (Fig. 1A, 1C, 1E) is that the probability of detecting compensatory dynamics might be high (up to 0.5) even in absence of interspecific interactions. This cautions against careless use of Eq. 1 as an omnipotent tool for scoring presence or absence of competition in natural communities. Finally, we assessed the relative importance of environmental noise and competitive interactions independently for community covariances in the three different regimes of growth rates (Fig. 2). The strength of environmental forcing has a relatively weak influence on observed community covariances. Interestingly, this effect is opposite to what may be expected: increasing noise strength increases the proportion of negative community covariances found, irrespective of the dynamical regime of population growth rates. Again, the visibility of compensating community dynamics is decreased by increasingly complex dynamics in the communities. Discussion We found that using the negative community covariance technique (Ives 1995, Klug et al. 2000, Fischer et al. 2001, Houlahan et al. 2007) detecting compensatory dynamics is possible if population growth rates of the S species come from the range of growth rates that in single-species systems yield stable equilibrium dynamics (here exemplified by the Ricker model as the kernel for population renewal for all species). Contrary to earlier suggestions (Klug et al. 2000, Fischer et al. 2001, Houlahan et al. 2007), our results show that visibility of compensatory dynamics requires external forcing that has to be highly positively autocorrelated. The ability to detect competition influencing population fluctuations with this method also improves if the equivalence of the S species experiencing the autocorrelated noisy environment is not perfect. This highlights an underlying problem with using the covariance method to detect the importance of competition in community time series. If we assume that the sign of the community covariance value gives an indication of the relative importance of environmental or competitive interactions in driving population fluctuations, we implicitly assume that any covariance values being negative indicate the presence of competition between species in a community. Setting environmental autocorrelation and/or species equivalency as the currency of importance is also complicated, since these factors, along with noise severity, are known to lead to qualitative modifications in the covariance structure of interacting populations (Greenman and Benton 2005, Ruokolainen and Fowler pers. comm.). Furthermore, positive community covariance is not necessarily an indication of environmental variation being a dominant factor. For example, in the presence of non-stable dynamics, species interactions are the cause of the high frequency of positive covariances, i.e. synchronous population fluctuations. Figure 2. Relative importance of competition and environmental forcing in affecting community covariance, under a white noise environment. The contour values indicate the proportion of negative community covariances based on 1000 replica communities. Three different regimes of population dynamics are considered in (A) population growth rates are drawn randomly from a uniform distribution with limits [1, 2], whereas in (B) the limits are [1, 2.6] and in (C) [1, 3.5]. Results are based on communities with S5, where species are independent in their responses to environmental variation (equivalency0). Intensity (y-axis) of competition represents the minimum intensity min(a ij ), where the mean interspecific interaction coefficients, a ij, range from 0.05 to EV

5 Houlahan et al. (2007) reported that compensatory dynamics were found in no more than 30% of natural animal and plant communities tested with the community covariance method. Consequently, they concluded that environmental forcing is generally more important than interspecific interactions in driving population fluctuations. Our results suggest that before negative covariance can be detected in competitive communities, the environment should be positively autocorrelated, and the autocorrelation coefficient, k, should preferably be ]0.5. An unforeseen outcome is that the autocorrelation of the environment seems to be equally important as the (non) equivalence of species responses to the noisy environment. Changes in either factor strongly influence the ability to detect compensatory dynamics. Thus, the results of Houlahan et al. (2007; see also Ives 1995, Klug et al. 2000, Fischer et al. 2001) do not necessarily mean that the relatively low frequencies of compensatory dynamics found equate to the actual proportion of communities being driven by interspecific interactions. As we have shown, communities with compensatory mechanisms show different frequencies of compensatory dynamics depending on interspecific interactions and on the interactions between species and their environment. Little, if anything is known about the kind of environmental forcing, and its equivalence for the species present, acting upon the communities studied using the negative covariance approach (Ives 1995, Klug et al. 2000, Fischer et al. 2001, Houlahan et al. 2007). Having said all this, there is also a fundamental statistical issue that questions the use of the negative covariance method. We have shown here that the degree of community covariance is extremely sensitive to factors that commonly vary between different communities. Yet, the method is based on the assumption of statistical equivalency where these factors are assumed invariable. In our simulation approach, we control many of the potentially varying factors that are required for statistical equivalency, e.g. community size (number of elements in the covariance matrix), local conditions (K-values), autocorrelation and correlation structure of environmental variation, etc. Comparing the covariance scores of different natural communities that exist in different environments (autocorrelation structure of the environmental noise terms), respond differently to noise (species equivalence), harbour different species, etc., violates the assumptions of a statistical comparison of the distribution of the derived covariance values. We conclude that the negative community covariance method (Ives 1995, Klug et al. 2000, Fischer et al. 2001, Houlahan et al. 2007) is of limited practical value when attempting to detect the presence of interspecific interactions among species in a community, or the relative importance of competition and environment in driving population fluctuations. Our results demonstrate that the sign of the community covariance depends in a complicated way on the underlying dynamics of the species in the community, on the type of external forcing, the intensity of competition between species, and the interaction between these factors. To tease apart the signature of environmental forcing from other causes of population fluctuations therefore requires methods that incorporate knowledge of the architecture that are the base of fluctuations in real populations influenced by environmental forcing. References Andrewartha, H. G. and Birch, L.C The distribution and abundance of animals. 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