vol. 171, no. 5 the american naturalist may 2008 Complex Positive Connections between Functional Groups Are Revealed by Neural Network Analysis of Ecological Time Series Simon F. Thrush,* Giovanni Coco,† and Judi E. Hewitt‡ National Institute of Water and Atmospheric Research, P.O. Box 11-115, Hamilton, New Zealand Submitted September 18, 2007; Accepted December 27, 2007; Electronically published March 14, 2008 Online enhancements: appendixes. abstract: The relationships between functional linkages within communities and community dynamics are fundamental to biodiversity-stability relationships. By teasing apart the hidden layers within artificial neural networks (ANNs), we developed webs defining how functional groups influence each other’s temporal dynamics. ANNs were based on 15 years of bimonthly monitoring of macrobenthic communities on three intertidal sandflats in Manukau Harbor (New Zealand). Sites differed in web topology and diversity, with the site dominated by one functional group exhibiting only a few strong links, the lowest a-, b-, and g-diversity, and the highest temporal stability in a-diversity. However, positive interactions between functional groups, nonconcordant with harborwide or sitespecific environmental variables, always dominated the interaction webs. The increased number of links we observed with increased temporal variation of species richness within functional groups and overall diversity supports the insurance hypothesis. While our findings suggest that there may be no consistent model characterizing the topology of temporal interactions between functional groups, decreasing diversity is likely to decouple interactions between functional groups and decrease ecosystem functionality. Keywords: temporal dynamics, diversity-stability, functional groups, artificial neural networks, time-series analyses, macrofauna. Despite their theoretical, empirical, and applied applications to ecology, the relationships between biodiversity and the stability, resilience, and functionality of communities * Corresponding author; e-mail: [email protected]. † E-mail: [email protected]. ‡ E-mail: [email protected]. Am. Nat. 2008. Vol. 171, pp. 669–677. 䉷 2008 by The University of Chicago. 0003-0147/2008/17105-42737$15.00. All rights reserved. DOI: 10.1086/587069 have been hard to define (Goodman 1975; Huston 1994; Carpenter et al. 2001; Loreau et al. 2001; Ives and Carpenter 2007). Debate on the strength and functional form of such relationships has had a long history (Elton 1958; Whittaker 1975; Raffaelli 2006; Houlahan et al. 2007). Recent syntheses haves indicated that communities tend to be numerically dominated by weak interactions, with stability dependent on species or functional groups capable of providing differential responses to changes in species composition or environmental factors and delivering different elements of ecosystem function (McCann 2000; Wootton and Emmerson 2005; Hector and Bagchi 2007). Empirical support for these relationships between biodiversity and stability/function across different ecological systems is often limited, in part because of the practical limitations of empirical studies in encompassing long-term community dynamics. This leads to disparities between empirical and theoretical investigations. Over temporal scales relevant to community stability, resource management, and conservation, scaling issues often cloud the debate on biodiversity-stability and biodiversityfunction relationships. One problem is that rigorous experimental tests are rarely conducted over sufficient space and timescale to reflect broadscale emergent patterns. Moreover, few studies have addressed how diversity relates to functional linkages within communities (Cottingham et al. 2001). Time-series data are needed both to describe the temporal dynamics of populations and communities and to provide insight into the interactions between species and environmental factors that influence community stability and resilience (Gaston and McArdle 1994; Ives et al. 2003). Temporal information on the dynamics of populations, functional groups, and communities is also important in defining the magnitude of ecological response of anthropogenic stressors. Thus, time-series data may be especially useful in elucidating relationships between diversity and functional interactions within communities, even though the increased temporal replication typically limits spatial replication in such data sets. Interaction webs describing the nature, pathway, and strength of links between species have been developed 670 The American Naturalist from experimental manipulations (Paine 1980; Wootton 1994; Menge 1995). The description of links between community members has provided important insights into community function and spatial heterogeneity (Menge et al. 2004). However, the direction and strength of effects and the importance of direct and indirect interactions are often sensitive to the duration of experiments (Menge 1997; Tegner et al. 1997; Dayton et al. 1999). Thus, techniques that enable us to define the links between community members over time would provide a new perspective. With sufficient temporal data, relationships within sites could be used to contrast sites with different community dynamics, diversity, or levels of environmental forcing. But to do this we need to develop techniques to characterize the strength of interactions between populations, functional groups, or other aggregate community variables over time. Disentangling the effects of diversity, community composition, and species interactions on temporal dynamics requires robust statistical techniques (Ives et al. 2003). To examine relationships between community members, we took the novel approach of teasing apart the hidden layers, or “neurons,” within artificial neural networks (ANNs). ANNs enable models to be built that link explanatory and dependent variables (Bishop 1995; Bose and Liang 1996), and they have become popular in species-environment applications because of their ability to encompass nonlinearities and complex interactions (Olden et al. 2006; Ozesmi et al. 2006). But their internal complexity has meant that in most ecological applications, ANNs are treated as a black box, where input variables are simply used to make a prediction irrespective of the nature of the relationships between input variables and hidden layers. However, techniques have been developed to disentangle the ANN and estimate the role of each input variable (Vaughn 1996; Benı́tez et al. 1997; Dimopoulos et al. 1999; Musick et al. 2000; Olden and Jackson 2002). Here, we couple two of these techniques to define the nature and strength of relationships between community members. We built ANNs from data sets derived from 15 years of bimonthly monitoring of macrobenthic communities on three intertidal sandflats in Manukau Harbor, New Zealand. The different communities at each site reflect community dynamics, with a range of starting conditions but from similar habitats, and integrate across trophic levels (Pridmore et al. 1990; Turner et al. 1995). We were interested in identifying general patterns that link diversity to function, and we consequently focused on functional groups. Functional groups are commonly used in ecology; in benthic ecology the shared traits are generally related to feeding, mobility, and interactions with the sediment or sediment-water interface (see, e.g., Bremner et al. 2006a, 2006b). The use of functional groups also allowed us to compare across the three sites, despite species composition varying between sites, by averaging over species-specific effects (Doak et al. 1998). In biodiversity-ecosystem function relations, the manipulation of functional groups has been recommended (Balvanera et al. 2006), although their role has not been thoroughly investigated in theoretical studies (Wootton and Emmerson 2005). In our analyses, we provide new insight into the temporal dynamics of functional groups in relation to diversity both within and across groups. Thus our study provides a novel long-term assessment of the functional links within three different diverse, multitrophic communities. In this article, we examine the topology of the interaction web between functional groups, derived from the ANNs, to determine the relationship between diversity and the degree of connectivity between functional groups. Both negative (Rhoads and Young 1970; Black and Peterson 1988; Wilson 1991; Olafsson et al. 1994) and positive (Gallagher et al. 1983; Thrush et al. 1992, 1996; Norkko et al. 2006) interactions have been described in soft-sediment communities. However, Houlahan et al. (2007) demonstrated that compensatory dynamics were rare in ecological time series. Moreover, positive effects tend to become more apparent with increasing scale of observation (Bruno and Bertness 2001). Thus we predicted that positive interactions would dominate. Defining the potential for positive interactions in community dynamics is important, especially in broadscale data sets, because many community theories are driven by negative interactions (predations and competition; e.g., McCann 2000). We also predicted that increasing evenness in the distribution of individuals among species within functional groups would lead to many connections between groups and that community dominance by one functional group would produce few, but strong, connections. Furthermore, we expected that the topology of the functional group interaction web, derived from ANNs, would provide a new way to assess longterm functional links within multitrophic communities. Methods Time-series data were collected from three sites (Auckland Airport [AA], Cape Horn [CH], and Clarks Beach [CB]) located near the three main channels draining Manukau Harbor, North Island, New Zealand (Pridmore et al. 1990). This harbor is a large (340 km2), shallow inlet with intertidal sandflats making up about 40% of the area. The three sites (each 9,000 m2) were all located in the midlow tide level and were chosen for their similarity in overall physical appearance and predominance of fine sand sediments. Data on macrofaunal communities were collected every 2 months (October 1987–February 2005), with the exception of October and December 1988 at all three sites Complex Positive Connections between Functional Groups 671 and February 1997–February 2000 at CH. Each site was divided into 12 equal sectors (each 25 m # 30 m), and on each sampling occasion, one core sample (13 cm in diameter, 15 cm deep) was taken from each sector (Hewitt et al. 1993; Thrush et al. 1994a). After collection, samples were sieved (500 mm) and preserved in either 5% formalin or 70% isopropyl alcohol. All the macrofauna were sorted, identified to the lowest practical level, and counted. For each site, we calculated the total (across all times) species richness (g-diversity), the temporal average species richness (a-diversity), and species turnover (b-diversity; b p g ⫺ a). We calculated the temporal consistency of species richness over the time series for each site and the temporal consistency of each functional group using both log standard deviation and the coefficient of variation (Cottingham et al. 2001). Because both variables revealed the same patterns between sites and groups, we present only the coefficient of variation. We also calculated average species richness and Pielou’s evenness both across species within each functional group and between functional groups at each site (Pielou 1975). We then took all of the macrofaunal species and allocated them to six functional groups: five were feeding groups, and the other we called RARE (defined as sporadically occurring taxa with a total density of !25 individuals over the entire time series). The five feeding groups were surface deposit feeders (SRDEP), subsurface deposit feeders (SBDEP), suspension feeders (SUSP), predator/ scavengers (PRED), and intermediate taxa capable of switching feeding mode between surface deposit and suspension feeding (INTER). Taxa were allocated to functional groups based on natural-history information (see Pridmore et al. 1990). We found the RARE group to be important in influencing the stability of ANN modeling. In our preliminary ANN development, we found that excluding RARE produced models with less explanatory power. Also, inclusion of RARE consistently produced ANNs with higher explanatory power than the ANNs obtained by substituting RARE with a time series of random numbers. In both terrestrial and marine systems, most species are rare, that is, represented by a small number of individuals and/or present at only a few sites or times. These rare species are theoretically important in maintaining the stability of ecosystem functioning, via the insurance hypothesis (Yachi and Loreau 1999; Pfisterer and Schmid 2002), especially in changing environments (Loreau et al. 2001). This is because, theoretically, the more diverse a community, the higher its potential for connections between species. Therefore, when species within the community decrease in fitness or abundance, other species are able to maintain the interaction web and ensure stability and resilience in function. Previous research in marine systems suggests that rare species may play a role in community resilience (Ellingsen et al. 2007) and also in community and ecosystem functioning (see Thrush and Dayton 2002 and references therein). Full details of ANN development and the determination of the strength of temporal connections between functional groups are presented in appendix A in the online edition of the American Naturalist. All input variables to the ANNs (functional types or environmental variables) were standardized to facilitate postprocessing and analysis of variable importance, irrespective of differences in the abundance of functional groups across sites. We developed ANNs with the simplest structure; two hidden nodes in one hidden layer and a single-node output layer predicted a specific functional type (INTER, SBDEP, RARE, PRED, SUSP, or SRDEP) using the same functional type at the previous time step (t⫺1), other functional types, or environmental variables. We included the previous time step in the ANN because our initial model development identified only first-order autocorrelation as important. Inclusion of previous time steps (t⫺2, t⫺3, t⫺4) did not increase the ANN explanatory power. We also investigated the role of both global and local environmental variables in affecting the time series of abundance within each functional group. Global environmental variables were the same across all sites; the variables were an index of atmospheric pressure variation across New Zealand that encapsulates the strength of the westerly wind band over New Zealand (Salenger and Mullen 1999), the Southern Oscillation index (SIO–Troup index; see http://www .bom.gov.au/climate/glossary/soi.shtml; McBride and Nicholls 1983), and annual maximum and minimum air temperatures recorded at Auckland Airport, on the shore of Manukau Harbor. Local environmental variables were derived from a water-column sampling program conducted adjacent to the benthic monitoring sites and included oxygen concentration, salinity, turbidity, and temperature (Wilcock and Martin 2003). These were the only available local-scale data collected over the entire ecological time series. Sediment grain-size data had been collected from the sites initially (Pridmore et al. 1990) and on other occasions later in the time series. While insufficient data were available for their inclusion in the ANN analysis, there were no apparent temporal trends in grain size (S. F. Thrush, G. Coco, and J. E. Hewitt, unpublished data). Results Over the 15 years encompassed by our data, the macrobenthic communities at the three sites remained different, despite some within-site variation. Appendix B in the online edition of the American Naturalist provides background information on the temporal dynamics of the functional groups at the three sites and the overall contribution 672 The American Naturalist of the functional groups to macrofaunal abundance. At site AA, SRDEP consistently dominated, while other functional groups varied in importance with no clear seasonality in abundance. The bivalve Macomona liliana was the most dominant species on all but five sampling occasions, with 18 other species ranking among the five most dominant species (with the dominance of individual species varying both seasonally and between years). The dominance of functional groups varied over time at site CH, with SBDEP or INTER dominating the initial part of the time series and SRDEP dominating toward the end of the time series. This reflected a shift in communities dominated by the polychaete Heteromastus filiformis (SBDEP) or Boccardia syrtis (INTER) to domination by Magelona ?dakini (SRDEP). Strong seasonality was apparent in the other dominant species, with 31 species represented in the five most dominant species recorded over the time series. Site CB showed the most variability in functional dominance, with switches mainly between the SRDEP and SBDEP groups. This reflected the variability in species that were numerically dominant (H. filiformis on 25 occasions, the bivalve Nucula hartvigiana [SRDEP] on 26 occasions, B. syrtis on 16 occasions, the polychaete Macroclymenella stewartensis [SBDEP] on 12 occasions, M. liliana on 10 occasions, and occasional dominance by the amphipods Torridoharpinia hurleyi [SRDEP] and Paracalliope novaezelandiae [SRDEP], the crab Halicarcincus whitei [PRED], and the polychaetes Euchone sp. [SUSP] and Prionospio aucklandica [SRDEP]). Thus, despite the overall similarities in habitat type, community dynamics were distinctly different at each site. Total species richness (a-diversity) and species turnover (b-diversity) were lowest at AA and similar at CH and CB (table 1). Temporal stability in species richness (CV) indicates that the most stable site was the one with the lowest diversity. Community evenness and between–functional group evenness followed the same trend, with lowest values at AA. The low between–functional group evenness at AA was driven by low evenness of the SRDEP and SUSP functional groups. The interaction webs derived from the ANNs for each site demonstrate differences in connections among functional groups; as predicted, most of the connections were positive (fig. 1). Moreover, while the strongest interactions were due to temporal autocorrelation (t⫺1) within functional groups, it was also apparent that negative connections tend to be weak. Some consistent patterns of connection across the sites emerged. When PRED interacted with rare species (RARE) or SRDEP interacted with INTER, there was always a negative connection. Conversely, when PRED interacted with SBDEP, there was always a two-way positive connection. PRED also positively affected INTER at two of the three sites. Positive and generally bidirectional connections between INTER and RARE occurred at both CH and CB. Overall, INTER tended to be more affected by other functional groups rather than being a driver of change. Both SBDEP and SUSP tended to have an equal balance in influencing, and being influenced by, other functional groups, and often their connections ran in both directions. Generally there were few strong bidirectional interactions, indicating that connectivity in the temporal dynamics of functional groups implied by the ANNs was mediated through multiple group connections. The site with the lowest diversity, species turnover, and evenness between functional groups, but with high temporal consistency, exhibited the least connectivity among functional groups. Comparisons of diversity and evenness with the number of links between functional groups at the three sites indicated that there may be a relationship with increasing diversity and evenness leading to more but weaker connections (cf. table 1 and fig. 1). This may have been simply driven by the higher dominance (low evenness) of SRDEP at AA, which exhibited a few strong connections. There was no apparent relationship between the evenness within a functional group and the number of links between functional groups (Pearson’s R p ⫺0.31, P p .200). This relationship does not support the general importance of species-specific niche differentiation within the functional group; we expected a positive relationship between the within-group evenness and links between groups if species-specific niches were generally important. Only a weak relationship between the temporal stability in the number of individuals within a functional group and number of links from that group was apparent (Spearman’s r p 0.41, P p .0907). However, the more the species richness within functional groups varied over time, the more connections existed between functional groups (Spearman’s r p 0.41, P p .0201). Our analysis of links between functional groups was based on time-series data, and thus, apparent relationships may also be driven by environmental drivers with links emerging as a result of concordant or discordant dynamics. The high frequency of positive relationships between functional groups could indicate an important role of environmental forcing on the relationships between functional groups or that net positive relationships between groups dominate interactions over time. However, none of the environmental variables available at either the local or global scale were identified by the ANNs as significant influences on the temporal variation in the density of functional groups. Complex Positive Connections between Functional Groups 673 Table 1: Summary community and functional group diversity statistics for the three sites in Manukau Harbor Parameter Community: g-diversity (all times) b-diversity (between times) a-diversity (site mean ⫹ SD) Coefficient of variation in a (all times) Overall species evenness (all times) Functional group: Within-group evenness: SBEDP INTER PRED RARE SUSP SRDEP Between-group evenness AA CH CB 95 68.7 26.3 ⫹ 3.8 14.3 .61 136 103 33 ⫹ 9.8 29.6 .71 137 98.3 38.7 ⫹ 8.4 21.6 .82 .67 .67 .77 .64 .45 .45 .61 .55 .38 .70 .49 .62 .61 .71 .54 .51 .77 .77 .73 .66 .77 Note: See “Methods” for definitions of functional group and site abbreviations. Discussion Overall, positive connections between functional groups dominated the webs derived for each site. This is an intriguing result that adds further weight to other empirical studies that emphasize the role of positive connections between community members. The dominance of positive interactions agrees with a recent analysis of ecological time series (Houlahan et al. 2007) that demonstrated that positive covariance is the norm in nature. However, based on the lack of evidence for competition, Houlahan et al. (2007) inferred that it was environmental drivers that caused positive relationships. In contrast, we explicitly tested the role of both local and regional environmental drivers and found no significant relations with temporal trends in the abundance of functional groups. While we were limited in the range of environmental variables with comparable time series we could include in our analysis, the variables used either directly or as surrogates reflect major environmental forces acting on sandflat communities. For example, the broadscale variables related to atmospheric pressure gradients drive variation in wind, waves, and rainfall, while the local-scale variables such as turbidity reflect sediment input to the harbor and resuspension; both are expected to drive variability in sediment characteristics. While there will always be the potential of missing a key environmental driver, we would expect that if environmental forcing were driving temporal dynamics in functional groups, we would have seen at least a weak effect in our ANN analysis of environmental variables; yet this was not apparent. The lack of importance of environmental drivers in influencing abundance within functional groups over time may indicate that individual species respond to en- vironmental drivers in specific ways, allowing for species substitution within the functional group as the environment changes, an important component of the insurance hypothesis. Similarly, long-term experiments on the response of grassland communities to climate change have highlighted the potential for complex interactions to ameliorate direct climate effects. This informative experiment revealed that when environmental change is sustained over years, feedbacks and species interactions dominated responses, despite short-term changes in individual species response (Suttle et al. 2007). While the positive connections identified through our ANN analysis of the temporal dynamics of functional groups do not necessarily imply causal relationships, manipulative experiments on the timescale of our time series would be difficult to maintain. Moreover, there is a growing recognition of the importance of positive interactions between community members, especially in marine benthic communities where individual species or functional groups can modify habitat structure and nutrient dynamics (Bertness and Leonard 1997; Thrush and Dayton 2002; Lohrer et al. 2004; Solan et al. 2004; Hewitt et al. 2005; Coco et al. 2006). Often, positive interactions between species are more commonly detected at broader spatial scales because they are emergent properties of processes interacting across scales (Bruno and Bertness 2001; Bruno et al. 2003). Our analyses of the 15-year time series of the macrofauna from intertidal sandflats indicated that temporally, a similar pattern may emerge that is not strongly driven by environmental drivers. Positive interactions are especially important in community dynamics because the breaking of these links can lead to hysteresis and regimeshift effects. 674 The American Naturalist Figure 1: Interaction webs derived from artificial neural network models of temporal changes in abundance within the six functional groups. Dashed arrows indicate negative correlations, and full arrows indicate positive correlations. Arrow direction indicates the influence of one group on another. Arrow thickness indicates the strength of correlation. Values next to each arrow are the product of Spearman’s rank correlation coefficient and the relative importance (%) of the weight associated with the variable. When no line is present, connections were extremely weak and nonsignificant. The importance of positive interactions was further highlighted by the absence of negative links between suspension feeders and deposit feeders, generally known to soft-sediment ecologists as the trophic group amensalism hypothesis (Rhoads and Young 1970; Aller and Dodge 1974; Myers 1977). This hypothesis was based on obser- vations of sediment destabilization by deposit feeders that increased sediment resuspension and negatively influenced adjacent suspension feeders. Overall, the small number and low strength of negative interactions between functional groups did not indicate compensatory dynamics. Intertidal flats are often disturbance-dominated habitats (Woodin 1981; Levin 1984; Thrush et al. 1996; Thrush 1999), where recovery dynamics and restrictions to communities reaching theoretical carrying capacity are important mechanisms. Similarly, our results emphasized the importance of multiway and positive connections between functional groups over time and the need to weight positive interactions over negative ones in theoretical models of community interaction and assembly. The level of connectivity in the interaction webs emphasized the difficulty of divining cause and effect relationships. Nevertheless, the patterns common across sites can be supported mechanistically. The mainly weak interactions of PRED with RARE, INTER, and SBDEP were common to CB and CH (app. B) and may be related to the higher diversity of infaunal predators at these sites (Pridmore et al. 1990). Here, the underpinning mechanism may increase diversity, skewing consumer-resource interactions toward dominance by weak interactions (McCann 2000; Wootton and Emmerson 2005). The weak negative interactions between SRDEP and INTER may be accounted for by the abundance of bivalve Macomona liliana at AA and CB; the feeding of adult Macomona on the sediment surface can have a strong density-dependent influence on community structure (Thrush et al. 1997, 2000, 1994b). The positive, and generally two-way, interactions between INTER and RARE at CH and CB may be a consequence of the high densities that occurred over the time series of the polychaete Boccardia syrtis, which can form extensive tube mats that stabilize sediment from windwave disturbance (Thrush et al. 1996). Finally, the balanced interactions of SBDEP and SUSP with other functional groups may be linked, via the differential effects of these species on nutrient flux and the productivity of microphytobenthos (Thrush et al. 2006). The mechanistic and theoretical support for interpretation of the ANNproduced webs suggests that this technique is capable of assessing functional links over time. This technique provides not only a long-term perspective against which to view theories but also the opportunity to investigate the implications of different temporal dynamics on functional changes and community stability. The differences in web topology observed at the three sites were not due to density variation between sites because of the data scaling used in the ANNs. Instead, they seemed to be related to differences in temporal dynamics, at the species and functional group levels, and a-, b-, and g-diversity. The site that exhibited the lowest a-, b-, and Complex Positive Connections between Functional Groups 675 g-diversity (AA) had the highest temporal stability in species richness and displayed few, but strong, connections between functional groups. Overall, high temporal variability in species richness within the functional groups tended to lead to more connections. Because of statistical averaging (as a consequence of the formation of functional groups), we should expect a negative correlation between community variability and increasing species richness when species fluctuations are not perfectly synchronous (Doak et al. 1998). This was apparent in our analysis. As evenness decreased, statistical averaging in aggregate variables such as functional groups increased, leading to a weakening of the negative relationship between richness and community variability. Despite strong seasonality and variance in dominance structure at both population and functional group levels at two of the sites, all three sites exhibited persistence in community structure. This indicates that the greater number of connections existing in diverse sites could play an important role in community persistence in the face of temporal variability of populations. The stability of ecological communities has been related to interactions between three components of community structure: species composition, diversity, and species interactions (Ives et al. 2003). Stability in ecological systems is also a multifaceted concept that can be defined in terms of return to equilibrium, change in response to disturbance, or change in temporal variability (Ives and Carpenter 2007). Differences in the topology of the interaction webs we detected are important because the degrees of direct and indirect interaction within the web can profoundly affect the way communities respond to change (van Veen and Murrell 2005). This has certainly been demonstrated for food webs (Polis and Strong 1996), but the links we identified between feeding functional groups reflect more than just trophic relationships and may incorporate many types of both direct and indirect species interactions. Our analyses of the temporal dynamics of functional group interactions indicate that more connections can occur with high temporal variability in species richness, supporting the role of species substitutions in functional groups in dynamic ecosystems. Thus, declines in overall diversity will lead to a loss of intrinsic stabilizing mechanisms and accelerated simplification of multitrophic communities. To effectively manage ecosystems, we need to be able to understand the implications of different temporal dynamics and to tie temporal trends to functional changes and resilience. Long-term data can contribute to debates over fundamental ecological relationships. Resolving such issues is not purely of academic interest because relations between diversity, resilience, and ecological function can profoundly influence the direction of policy and the nature of management actions in response to environmental issues. 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