A multispecies perspective on ecological impacts of climatic forcing

Authors

  • Crispin M. Mutshinda,

    Corresponding author
    1. Department of Mathematics and Statistics, University of Helsinki, PO Box 68 (Gustaf Hällströmin katu 2b), FIN-00014, Finland
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  • Robert B. O’Hara,

    1. Department of Mathematics and Statistics, University of Helsinki, PO Box 68 (Gustaf Hällströmin katu 2b), FIN-00014, Finland
    2. Biodiversity and Climate Research Centre, Senckenberganlage 25, D-60325 Frankfurt am Main, German
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  • Ian P. Woiwod

    1. Plant and Invertebrate Ecology Department, Rothamsted Research, Harpenden, Herts AL5 2JQ, UK
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Correspondence author. E-mail: crispin.mutshindamwanza@helsinki.fi

Summary

1. In the prevailing context of concerns over climate change and its potential impacts on ecosystems, evaluating ecological consequences of climatic forcing has become a critical issue.

2. Historical data on the abundance of organisms have been extensively used to characterize the ecological effects of climatic forcing through specific weather and/or climatic variables, with most of the studies confined to single population models.

3. However, population responses to environmental fluctuations typically depend upon positive and negative feedbacks induced by interactions with other species. It is therefore important to integrate the insights gained from single population approaches into a multispecies perspective.

4. Here we combine the hierarchical Bayesian modelling approach with the state-space formulation to extend the scope of previously proposed models of population dynamics under climatic forcing to multi-species systems.

5. We use our model to analyse long-term macro-moth (Lepidoptera) community data from the Rothamsted Insect Survey network in the UK, using winter rainfall and winter temperature as environmental covariates.

6. The effects of the two weather variables were consistent across species, being negative for winter rainfall and positive for winter temperature. The two weather variables jointly explained 15–40% of the total environmental variation affecting the dynamics of individual species, and could explain up to 90% of covariances in species dynamics.

7. The contribution of interspecific interactions to community-level variation was found to be weak compared to the contributions of environmental forcing and intraspecific interactions.

Introduction

Evaluating population dynamical consequences of climatic forcing has become a critical contemporary issue in ecology with the rising concerns over climate change progress and its potential ecological impacts (Woiwod 1997; Harrington, Woiwod & Sparks 1999; Hughes 2000; McCarthy 2001; Hill et al. 2002; Walther et al. 2002; Parmesan & Yohe 2003; Root et al. 2003). Historical data on the abundance of organisms have been extensively used for attempting to characterize the ecological impacts of climatic forcing through specific weather variables such as temperature, rainfall, snow cover etc., or large-scale climatic indices like the North Atlantic oscillation (NAO) or the El Niño/Southern Oscillation (ENSO). For example, Saether et al. (2000) investigated population dynamical consequences of climate change for a small songbird, using winter temperature and precipitation as environmental covariates. Stenseth et al. (2004) examined the effects of fluctuations in the North Atlantic Oscillation (NAO) index on variation in Soay sheep counts. Henderson & Seaby (2005) analysed the role of fluctuations in winter NAO index and water temperature in determining temporal variation in abundance, recruitment and growth of Solea solea at Bridgwater Bay in the Bristol Channel, England. Westgarth-Smith et al. (2007) investigated the association between temporal variations in English populations of a forest insect pest, the green spruce aphid (Elatobium abietinum) and the NAO index.

However, most studies concerned with ecological impacts of climatic forcing have been confined to single population models, even though population responses to environmental fluctuations typically depend upon positive and negative feedbacks induced by interactions with other species (Ives 1995; Kilpatrick & Ives 2003). The next stage is to integrate the insights gained from single population approaches into a multispecies perspective so we can understand the mechanisms underlying fluctuations in species abundances and community structure.

In this paper we combine the hierarchical Bayesian modelling approach (Berlinier 1996; Gelman et al. 2003; Clark 2005; Wikle & Hooten 2006) with the state-space formulation (de Valpine & Hastings 2002; Buckland et al. 2004; Clark & Bjørnstad 2004; Rivot et al. 2004; Gimenez et al. 2007), to extend the scope of previously proposed models of population dynamics under climatic forcing to multi-species systems. We demonstrate the implementation of our model with long-term macro-moth (Lepidoptera) light-trapping data from the Rothamsted Insect Survey network in the UK, using two weather variables, namely winter (December–February) rainfall and winter temperature as environmental covariates. We also evaluate the proportion of variation attributable to different factors in the dynamics of individual species, as well as the proportion of environmental variance and covariance explained by the included environmental covariates.

Materials and methods

Description of data

We use replicated time series of yearly light-trapping catches for 12 most abundant noctuid (Noctuidae) macro-moths (Lepidoptera) from the Rothamsted Insect Survey (RIS) network in the United Kingdom (Woiwod & Harrington 1994). The data involve replicates from two different sampling stations: Geescroft I and II, in woodland on Rothamsted Farm in Hertfordshire, UK (Woiwod & Gould 2008). The data cover the period 1973–2003 for Geescroft I and 1973–1998 for Geescroft II. The scientific and common names of the study species are given in Table 1, and time plots of observed species abundances (on a natural logarithmic scale) are shown in Fig. 1. Note that Mesapamea secalis is in fact a two species complex (secalis/didyma). These two species can only be separated on genitalia and were not recognized as separate when the sampling started so they are kept as one for consistency. We used winter (December–February) rainfall (F) in mm and winter temperature (T) in degrees Celsius as climatic covariates. The two variables were standardized to have zero-mean and unit variance. No significant correlation was observed between these two climatic variables (ρ = 0·07) at Rothamsted, in line with the suggestion of Westgarth-Smith et al. (2007). This implies that the two variables can enter the model additively without inducing multicollinearity issues which may lead to flawed inferences (Silvey 1969; Graham 2003). Time plots of standardized scores of the two environmental variables are shown in Fig. 2.

Table 1.   Scientific and common names of the study moth species. All species belong to the noctuid (Noctuidae) family
Scientific nameCommon name
Agrostis exclamationisHeart & Dart
Diarsia mendicaIngrailed Clay
Xestia xanthographaSquare-spot Rustic
Noctua pronubaLarge Yellow Underwing
Orthosia gothicaHebrew Character
Hoplodrina alsinesThe Uncertain
Mesapamea secalis/didymaCommon Rustic
Cosmia trapezinaThe Dun-bar
Agrochola macilentaYellow-line Quaker
Conistra vacciniThe Chestnut
Hypena proboscidalisThe Snout
Hermina grisealisSmall Fan-foot
Figure 1.

 Time plots of observed species abundances on the natural logarithmic scale. Open circles represent catches from Geescroft I over the period 1973–2003, and solid triangles represent catches from Geescroft II over the period 1973–1998.

Figure 2.

 Time plots of (a) mean winter rainfall (in mm) and (b) mean winter temperatures (in degrees Celsius) over the period 1978–2003 in Hertfordshire UK, standardized to have zero mean and unit variance.

Model specification

The model is developed and fitted with a hierarchical Bayesian approach (Berlinier 1996; Gelman et al. 2003; Wikle & Hooten 2006). A state-space formulation (de Valpine & Hastings 2002; Buckland et al. 2004; Clark & Bjørnstad 2004; Rivot et al. 2004; Gimenez et al. 2007) is used to distinguish between the process model describing the actual dynamics of the study system by conditional Markovian transitions between successive states, and the observation model intended to map the observed data to the actual states of the process.

The process model

We assume a Gompertz kernel for the underlying population dynamics. The Gompertz model has been widely used in modelling population and community dynamics (e.g. Saitoh, Stenseth & Bjonstad 1997; Jacobson et al. 2004; Dennis et al. 2006; Mutshinda, O’Hara & Woiwod 2009), and has the advantage of being linear on a logarithmic scale. The model includes intra- and interspecific interactions, as well as linear terms measuring the dynamical effects of climatic variables on the growth rates of the study populations, and is designed to accommodate species covariations in response to latent environmental factors.

More specifically, let inline image denote the actual number of individuals of species i in the community in year t (S species in total), and let Ft and Tt designate respectively the averaged winter (December–February) rainfall (in mm) and winter temperature (in degrees Celsius) in year t, standardized as indicated above. The number of individuals of species i at time t in the community is described by

image(eqn1)

where inline image and ki are the intrinsic growth rate and the natural logarithm of the carrying capacity of species i respectively; inline image is the interaction coefficient quantifying the effect of species j on the growth of species i (interspecific interaction), with all coefficients of intraspecific interactions, inline image, set to 1 (Loreau & de Mazancourt 2008; Mutshinda, O’Hara & Woiwod 2009); βi,1 and βi,2 quantify the effects of winter rainfall and winter temperature on the growth rate of species i, respectively. The random shocks, inline image, representing the variability resulting from demographic stochasticity and un-modelled (latent) environmental factors are assumed to be serially independent and normally distributed with mean zero, but are allowed to covary across species at a specific time as discussed below. The normality assumption allows us to separately model the mean and covariance structures (Ripa & Ives 2003; Mutshinda, O’Hara & Woiwod 2009). On the natural logarithmic scale, equation 1 becomes

image(eqn2)

where inline image denotes the natural logarithm of inline image. Equation 2 can be compactly written in matrix form as

image(eqn3)

where inline image is the S-dimensional vector of log-transformed abundances of the S species at time t, R is a S-by-S diagonal matrix with inline image, and 1S is the S-dimensional vector with all elements equal to 1; inline image, inline image, B is a n × 2 matrix with (βi1, βi2) as ith row, and inline image is the vector of process disturbances affecting the community dynamics at time t, with one element by species. The serially independent vectors inline image are assumed to be multivariate normally distributed around the zero-vector, with a covariance matrix denoted by inline image i.e. inline image. The covariance matrix inline image is further decomposed into its environmental and demographic components as

image(eqn4)

The covariance matrix C represents the variability not explained by intrinsic dynamics or by the included environmental covariates, including the effect of interactions with un-modelled species at the same trophic level as well as species at other trophic levels. The matrix C is henceforth referred to as the environmental covariance matrix. Species are also allowed to covary in their response to latent (un-modelled) environmental factors by assuming that the elements, inline image, ;]>on the main diagonal of C and the off-diagonal elements, Ci,j (i ≠ j), represent species-specific and joint responses to latent environmental factors, respectively. inline image, where inline image denotes the (population-level) demographic variance affecting the dynamics of species i from time t−1 to t, which is scaled inversely with the population size (Saether et al. 2000; Bjørnstad & Grinfell 2001; Lande, Engen & Saether 2003). It is in fact the dependence of demographic variance on the population size that makes the demographic and environmental components of the process variance involved in equation 4 statistically identifiable.

Following Saether et al. (2000), the total environmental variance, Ei, affecting the dynamics of species i can be split into a component, inline image, attributable to the included environmental variables, and a residual environmental variance, Ci,i, quantifying the variability not accounted for by the included variables. That is,

image(eqn5)

In particular, if the covariates F and T are standardized to unit variance as is the case here, then equation 5 takes the simple form inline image ;]>so that inline image represents the proportion of environmental variation attributable to the included weather variables. Additionally, the environmental covariance between the dynamics of species i and j is given by

image(eqn6)

which is simply inline image with standardized covariates. Moreover, if inline image and the effects of the two covariates on the dynamics of species i and j turn out to be of identical signs, then the proportion of environmental covariance between species i and j that is explained by the covariates is given by

image

We used the Bayesian variable selection method known as stochastic search variable selection (SSVS) (George & McCulloch 1993; Mutshinda, O’Hara & Woiwod 2009) to constrain the coefficients of spurious inter-species interactions to be close to zero so that they do not affect the model results. The rationale of SSVS is to embed a multiple regression set-up in a hierarchical normal mixture model, and use latent indicators to identify promising sets of predictors. For each coefficient of interspecific interaction, αi,j (i ≠ j), we introduced an auxiliary indicator inline image, ;]>0 < pi,j < 1, such that γi,j = 1 when species j is included in the dynamics of species i, and γi,j = 0 otherwise. Conditionally on γi,j, we defined the prior distribution of αi,j as a mixture of two Gaussians i.e. inline image. The positive constant c1 was selected to be small and c2 to be large. This prior specification constrains αi,j to be concentrated around zero when γi,j = 0 since the ensuing prior corresponds to the spike part of the Gaussian mixture prior placed on αi,j, which is confined around zero. On the other hand, αi,j is freely estimated from the data when γi,j = 1 since the corresponding prior, the slab part of the Gaussian mixture priors placed on αi,j, is diffuse (flat).

A Gibbs sampling methodology is used to generate samples from the joint posterior of all unknowns, including the inclusion indicators γi,j. The relevance of a single interaction effect, αi,j, is evaluated through the Bayes factor inline image, which quantifies the amount by which the prior odds of including vs. not including αi,j into the model are changed into posterior odds by the data. If Bi,j is larger than 1, we say that the data provide more support in favour of including αi,j into the model than assumed a priori, and vice-versa. Bayes factors for comparing two hypotheses (or models) H1 and H2 are usually interpreted on the following scale due to Jeffreys (1961). B1,2 < 1: ‘Negative support for H1 (i.e. support for H2)’; 1 ≤ B1,2 < 3: ‘Barely worth mentioning evidence in favour of H1’; 3 ≤ B1,2 < 10: ‘Substantial support for H1’; 10 ≤ B1,2 < 100: ‘Strong support for H1’; B1,2 > 100: ‘Decisive support for H1’. For us here H1 and H2 represent the inclusion and exclusion of individual interaction coefficients into the model, respectively.

The observation model

We took advantage of the replicated feature of our data (time series from two light-traps: Geescroft I and Geescroft II on the same site) to explicitly accommodate potential discrepancies in capture efficiency across traps for different species. Our observation model was also specified with Gaussian errors.

More specifically, let Yi,t,k denote the observed number of individuals of species i at time t from trap k, and let inline image. We assume that

image(eqn7)

where the random variable inline image, intended to correct for differences in capture efficiency between species across traps, is set to zero for one of the traps (Geescroft I) to force identifiability. So we only estimate bi,2, and consider negative values of it as implying lower capture efficiency for Geescroft II compared to Geescroft I and vice-versa.

Prior specification

Fitting a Bayesian model to the data requires explicit statements of prior distributions for all unknown quantities. We placed on the covariance matrix C an inverse Wishart prior with scale matrix Ω and a number, q, of degrees of freedom set to the smallest possible number, i.e. the rank of Ω, to convey vague prior information. We then set Ω to the S-dimensional identity matrix, IS. For all species, we independently placed diffuse inline image on the log-carrying capacities and inline image on the intrinsic growth rate, where I(.) denotes the indicator function. The parameters βi,1 and βi,2 representing the effects of winter rainfall and winter temperature were independently assigned diffuse N(0, 100) priors, and all pi,j (the a priori inclusion probability of interspecific interactions) were set to 0·2. Finally, we placed Unif(0, 10) priors on the standard deviations δi, τi and σr. Gelman (2006) gives a justification for this approach to prior specification for variance parameters.

Model fitting

We used Markov chain Monte Carlo (MCMC) simulation methods (Gilks, Richardson & Spiegelhalter 1996) through OpenBUGS (Thomas et al. 2006) to sample from the joint posterior of the model parameters. We ran 80 000 iterations of three Markov chains starting from dispersed parameter values, and discarded the first 20 000 samples of each chain as burn-in, thinning the remainder to every 25th sample. The convergence was assessed visually through the mixing of the chains and the behaviour of the sample autocorrelation plots. The BUGS code for the model fitting is provided in the Appendix S1 (Supporting information).

We used posterior predictive cross-validation to check the model adequacy by omitting the last five observations from the Geescroft I data set for each species, and forecasting them from the model to determine how well the model predictions would approximate the omitted data. In all cases, the model predictions were consistent with the discarded data as illustrated by Fig. 3 where M. secalis/didyma and H. proboscidalis are used for illustration.

Figure 3.

 Posterior predictive distributions of observed population densities of Mesapamea secalis/didyma and Hypena proboscidalis over the period 1998–2003 for Geescroft I. The black diamonds represent posterior means, the error-bars show the 95% central predictive intervals, and the open squares plotted on top represent the observed values. The two species were selected to illustrate the full set of our results.

Results

The multivariate normality assumption on the residuals inline image, was corroborated by the Shapiro–Wilks multivariate normality test through the function mshapiro() from the mvnormtest R package (the R Development Core Team 2009), ruling out concerns about model misspecification.

Environmental variation was the most important driver of population dynamics in the focal community, accounting for between 45 and 75% of variation in the dynamics of individual moth species. Intraspecific interactions (i.e. the effects of density dependence) were found to be the second most important source of variation in species abundances and explained roughly 10–30% of temporal variation in species abundances. However, the contribution of interspecific interactions was minor, broadly explaining less than 10% of variation in the dynamics of individual species (Fig. 4c).

Figure 4.

 (a) Posterior means and 68% credible intervals for the parameters representing the effects of winter rainfall (grey squares) and winter temperature (black circles) on the growth of individual species; (b) Posterior means and 68% credible intervals for the variable b representing the efficiency of the Geescroft II trap relative to Geescroft I for each species, with all values corresponding to Geescroft I set to zero. Panel (c) shows barplots for the proportions of environmental variance attributable to environmental stochasticity, as well as intra-/interspecific interactions in the dynamics of individual species, whereas panel (d) shows barplots for the proportions of environmental variance explained by winter rainfall and winter temperature, both individually and collectively.

Effects of the two weather variables were consistent across species, being negative for winter rainfall and positive for winter temperature (Fig. 4a). When the environmental variance was split into contributions from the two environmental covariates and the residual (unexplained) variance, the two weather variables jointly explained 15–40% of the total environmental variation. Individually, the two variables explained 10–20% of the total environmental variation (Fig. 4d). Moreover, the two environmental variables explained up to 90% of environmental covariances between species. The highest environmental covariances are given in Table 2.

Table 2.   Proportions of covariance in species abundances explained by the environmental covariates
 X. xanthographaN. pronubaM. secalis/didymaC. trapezinaC. vaccini
N.  pronuba30% 32%58%65%
O. gothica48%67%90%80%85%
M. secalis/didyma26%32% 37%72%

The coefficients of interspecific interactions were mainly far lower than one, with Bayes factors in favour of their inclusion providing no more than a barely worth mentioning support.

The contribution of demographic stochasticity to the temporal variation in species abundances was estimated to be weak, with posterior means of inline image lying between 1·5 and 3, implying much lower population-level demographic variances, given that our data sets are limited to species occurring in high numbers.

Figure 4b shows posterior means and 68% central credible intervals for the variable b, implying slightly higher capture efficiency for the Geescroft I trap for most species.

Discussion

In this paper we developed a hierarchical Bayesian model to investigate the ecological impacts of climatic forcing from a multispecies perspective. We applied the methodology to macro-moth (Lepidoptera) light-trapping data from the Rothamsted Insect Survey network in the UK, using winter (December–February) rainfall and winter temperature as environmental covariates. The results agree with our previous analysis of the same community (Mutshinda, O’Hara & Woiwod 2009), although there are some small differences, as this analysis included two replicate sampling stations.

The model was based on a loglinear (Gompertz) kernel and included intra- and interspecific interactions, along with linear terms measuring the effects of environmental variables, and was designed to accommodate species covariation in response to latent environmental factors.

The effects of winter rainfall and winter temperature on the dynamics of the study species were consistently negative for the former and positive for the latter (Fig. 4a). These results are in line with the suggestions of previous studies of the ecological impacts of weather on Lepidoptera (Beirne 1955; Pollard 1988; Crozier 2004).

Plausible explanations for negative effects of winter rainfall on Lepidoptera include the fact that heavy rains are usually accompanied by strong winds which might dislodge larvae from their host plants, thereby disrupting their feeding behaviour. In addition, wet weather might favour the incidence and the spread of moth fungal pathogens which may drastically affect larval and pupal survival.

The positive association between winter temperature and the growth rate of the study species agrees with the generally accepted view that warm conditions are favourable to larval survival for many Lepidoptera species (e.g. Crozier 2004).

Environmental stochasticity (not including the variation due to interspecific interactions between the included species) was the most important source of variation in species abundances as it accounted for between 45 and 75% of the total variance in the dynamics of individual species. Intraspecific interactions were of secondary relative importance and accounted between 10 and 30% of the total variance in the dynamics of individual species. The influence of interspecific interactions on community-level variation was found to be minor with contributions to total variance in the dynamics of individual species broadly less than 10%. This result corroborates the previously suggested weak contribution of interspecific interactions to explaining community-level variation (Ives, Gross & Klug 1999; Kokkoris, Troumbis & Lawton 1999; Houlahan et al. 2007; Mutshinda, O’Hara & Woiwod 2009). Moreover, the Bayes factors in favour of including inter-species interactions into the model were found to be broadly less than one, except a few of them whose values lay between 1 and 3, implying a support that is not worth more than a bare mention on the Jeffreys’ scale.

We further partitioned the total environmental variance affecting the dynamics of individual species into the contributions from the included weather variables and the unexplained (residual) variance. Winter rainfall and temperature jointly explained up to 40% of the total environmental variation in the dynamics of individual species.

The environmental covariances between species were broadly positive, and the two environmental covariates accounted for up to 90% of covariances between species. We chose environmental covariates that we suspected, a priori, would influence the community, and there are many other covariates that might also have an effect. It is thus promising that we can start to untangle the causes of these environmental correlations. The excess environmental covariation may be ascribed to other factors not included in the model such as extra-trophic interactions (e.g. predation pressure from insectivorous birds or generalists parasitoids), or indirect climatic effects. It is also well known that if two populations have the same density-dependent structure, then correlated density-independent factors can bring the population fluctuations into synchrony, the ‘Moran effect’ (Moran 1953; Royama 1992).

Synchrony in population fluctuations has implications for the community viability, with positive correlations increasing the probability of local and even global extinction. Palmquist & Lundberg (1998) pointed out that synchronously fluctuating populations face a greater risk of global extinction than do independently fluctuating populations. We have shown that we can find some of the causes of these environmental correlations, which then suggests that we can start to estimate the effects of changes in these variables (e.g. due to anthropogenic climate change) on real communities, and assess their viability.

The population-level signature of demographic variances was found to be weak. This is not surprising given the inverse scaling of the demographic variance with the population size (Lande, Engen & Saether 2003) and the fact that the data sets used here are confined to species occurring in high numbers.

Acknowledgements

We thank Otso Ovaskainen, Len Thomas and two anonymous referees for their helpful comments on the manuscript. Funding for this research was provided by the Academy of Finland (project no. 205371), and the research funding programme ‘LOEWE–Landes-Offensive zur Entwicklung Wissenschaftlich-ökonomischer Exzellenz’ of Hesse’s Ministry of Higher Education, Research and the Arts. Rothamsted Research is grant-aided by the UK Biotechnology and Biological Sciences Research Council.

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