A comparison between two GAM models in quantifying relationships of environmental variables with fish richness and diversity indices

Various regression methods can be used to quantify the relationships between fish populations and their environment. Strong correlations often existing between environmental variables, however, can cause multicollinearity, resulting in overfitting in modeling. This study compares the performance of a regular generalized additive model (GAM) with raw environmental variables as explanatory variables (regular GAM) and a GAM based on principal component analysis (PCA-based GAM) in modeling the relationship between fish richness and diversity indices and environmental variables. The PCA-based GAM tended to perform better than the regular GAM in cross-validation tests, showing a higher prediction precision. The variables identified being significant in modeling differed between the two models, and differences between the two models were also found in the scope and range of predicted richness and diversity indices for demersal fish community. This implies that choices between these two statistical modeling approaches can lead to different ecological interpretations of the relationships between fish communities and their habitats. This study suggests that the PCA-based GAM is a better approach than the original GAM in quantifying the relationship between fish richness and diversity indices and environmental variables if the environmental variables are highly correlated.

[1]  Karim Erzini,et al.  Fish assemblages of shallow intertidal habitats of the Ria Formosa lagoon (South Portugal): influence of habitat and season. , 2012 .

[2]  C. Monteiro-Neto,et al.  Patterns of fish and crustacean community structure in a coastal lagoon system, Rio de Janeiro, Brazil , 2014 .

[3]  D. M. Nelson,et al.  Biologically-based estuarine salinity zones derived from a multivariate analysis , 1993 .

[4]  M. Burrows.  Influences of wave fetch, tidal flow and ocean colour on subtidal rocky communities , 2012 .

[5]  R. Tibshirani,et al.  Generalized Additive Models , 1991 .

[6]  M. Steele.  Effects of predators on reef fishes: separating cage artifacts from effects of predation , 1996 .

[7]  F. G. Araújo,et al.  Environmental influences on the demersal fish assemblages in the Sepetiba Bay, Brazil , 2002 .

[8]  A. Lehmann,et al.  Improving generalized regression analysis for the spatial prediction of forest communities , 2006 .

[9]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[10]  Pieter M. Kroonenberg,et al.  Non‐linear principal components analysis: an alternative method for finding patterns in environmental data , 2006 .

[11]  L. Buisson,et al.  Modelling stream fish species distribution in a river network: the relative effects of temperature versus physical factors , 2008 .

[12]  A. Friedlander.  Essential Fish Habitat and the Effective Design of Marine Reserves: Application for Marine Ornamental Fishes , 2001 .

[13]  Serkan B. Bozkurt,et al.  Forecasting the evolution of seismicity in southern California : Animations built on earthquake stress transfer : Stress transfer, earthquake triggering, and time-dependent seismic hazard , 2005 .

[14]  F. F. Pérèz,et al.  Mixing analysis of nutrients, oxygen and dissolved inorganic carbon in the upper and middle North Atlantic ocean east of the Azores , 1998 .

[15]  P. Goethals,et al.  Use of fish distribution modelling for river management , 2012 .

[16]  Christopher D. Wilson,et al.  Climate–ocean variability and Pacific hake: A geostatistical modeling approach , 2008 .

[17]  B. MacKenzie,et al.  Larval fish feeding and turbulence: A case for the downside , 2000 .

[18]  Michael Elliott,et al.  Environmental Influences on the Fish Assemblage of the Humber Estuary, U.K. , 1998 .

[19]  H. Hämäläinen,et al.  The importance of sedimenting organic matter, relative to oxygen and temperature, in structuring lake profundal macroinvertebrate assemblages , 2013, Hydrobiologia.

[20]  J. Maes,et al.  Modelling the migration opportunities of diadromous fish species along a gradient of dissolved oxygen concentration in a European tidal watershed , 2007 .

[21]  William J. Emery,et al.  Data Analysis Methods in Physical Oceanography , 1998 .

[22]  M. Graham.  CONFRONTING MULTICOLLINEARITY IN ECOLOGICAL MULTIPLE REGRESSION , 2003 .

[23]  Wang Kai,et al.  马鞍列岛岩礁生境鱼类群落生态学. I . 种类组成和多样性 , 2012 .

[24]  Michael H. Kutner.  Applied Linear Statistical Models , 1974 .

[25]  J. Grabowski,et al.  Estimating spatial distribution of American lobster Homarus americanus using habitat variables , 2010 .

[26]  S. Altekruse,et al.  A Model To Estimate the Optimal Sample Size for Microbiological Surveys , 2003, Applied and Environmental Microbiology.

[27]  P. Annoni,et al.  A multivariate model to relate hydrological, chemical and biological parameters to salmonid biomass in Italian Alpine rivers , 1997 .

[28]  S. Wood.  Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models , 2011 .

[29]  J. Kohut,et al.  Improving habitat models by incorporating pelagic measurements from coastal ocean observatories , 2012 .

[30]  Yong Chen,et al.  Identification of ecological structure and species relationships along an oceanographic gradient in the Gulf of Maine using multivariate analysis with bootstrapping , 2010 .

[31]  F. Velasco,et al.  Resource partitioning amongst five coexisting species of gurnards (Scorpaeniforme: Triglidae): Role of trophic and habitat segregation , 2011 .

[32]  Lin Jun.  Constitution of fish assemblages in three nearshore habitats and the effect of benthic macroalgae on fish assemblages in Gouqi Island , 2011 .

[33]  J. Aboal,et al.  Determination of the optimal size of area to be sampled by use of the moss biomonitoring technique , 2010 .

[34]  S. Dray,et al.  Assessing species and community functional responses to environmental gradients: which multivariate methods? , 2012 .

[35]  Bertram Ostendorf,et al.  A review of methods for analysing spatial and temporal patterns in coastal water quality , 2011 .

[36]  J. Muelbert,et al.  Small-scale spatial and temporal variability of larval fish assemblages at an isolated oceanic island , 2012 .

[37]  Martin Saraceno,et al.  On the relationship between satellite‐retrieved surface temperature fronts and chlorophyll a in the western South Atlantic , 2005 .

[38]  V. Barnett,et al.  Applied Linear Statistical Models , 1975 .

[39]  T. Hastie,et al.  Comparative performance of generalized additive models and multivariate adaptive regression splines for statistical modelling of species distributions , 2006 .

[40]  J. Helešic,et al.  Temporal and spatial macroinvertebrate variance compared: crucial role of CPOM in a headwater stream , 2012, Hydrobiologia.

[41]  L. Carvalho,et al.  Quantitative responses of lake phytoplankton to eutrophication in Northern Europe , 2008, Aquatic Ecology.

[42]  V. Clark,et al.  Computer-aided multivariate analysis , 1991 .

[43]  T. Terawaki,et al.  Ecology and restoration techniques for Sargassum beds in the Seto Inland Sea, Japan. , 2003, Marine pollution bulletin.

[44]  Mario Uchimiya,et al.  Seasonality and environmental drivers of biological productivity on the western Hokkaido coast, Ishikari Bay, Japan , 2013 .

[45]  K. Winemiller,et al.  Local and regional determinants of stream fish assemblage structure: inferences based on taxonomic vs. functional groups , 2007 .

[46]  J. Link,et al.  Guidelines for incorporating fish distribution shifts into a fisheries management context , 2011 .

[47]  J. Leathwick,et al.  Predictive models of small fish presence and abundance in northern New Zealand harbours , 2005 .

[48]  A. Rieser.  Essential fish habitat as a basis for marine protected areas in the U.S. exclusive economic zone , 2000 .

[49]  Bernard Bobée,et al.  A review of statistical methods for the evaluation of aquatic habitat suitability for instream flow assessment , 2006 .

[50]  Graeme Newell,et al.  Species distribution modelling for conservation planning in Victoria, Australia , 2013 .

[51]  Thomas W Yee,et al.  Constrained additive ordination. , 2006, Ecology.

[52]  R. Margalef,et al.  Information theory in ecology , 1958 .

[53]  E. Lefkaditou,et al.  Influences of environmental variability on the population structure and distribution patterns of the short-fin squid Illex coindetii (Cephalopoda: Ommastrephidae) in the Eastern Ionian Sea , 2008, Hydrobiologia.

[54]  A. Millar,et al.  Key biodiversity areas as globally significant target sites for the conservation of marine biological diversity , 2008 .

[55]  G. Jenkins,et al.  The influence of habitat structure on nearshore fish assemblages in a southern Australian embayment: Comparison of shallow seagrass, reef-algal and unvegetated sand habitats, with emphasis on their importance to recruitment , 1998 .

[56]  Conrad S. Toepfer,et al.  Fish and Habitat Heterogeneity in Four Streams in the Central Oklahoma/Texas Plains Ecoregion , 1998 .

[57]  D. Weller,et al.  Species Distribution Models of Freshwater Stream Fishes in Maryland and Their Implications for Management , 2013, Environmental Modeling & Assessment.

[58]  Lei Wang,et al.  Constitution of fish assemblages in three nearshore habitats and the effect of benthic macroalgae on fish assemblages in Gouqi Island: Constitution of fish assemblages in three nearshore habitats and the effect of benthic macroalgae on fish assemblages in Gouqi Island , 2012 .

[59]  Influences of native and non-native benthivorous fishes on aquatic ecosystem degradation , 2013, Hydrobiologia.

[60]  Mark J. Kennard,et al.  Environmental, spatial and phylogenetic determinants of fish life-history traits and functional composition of Australian rivers , 2013 .

[61]  M. Sheaves,et al.  Are distributions of fishes in tropical estuaries influenced by turbidity over small spatial scales , 2007 .

[62]  W. S. Lakra,et al.  The influence of habitat on the spatial variation in fish assemblage composition in an unimpacted tropical River of Ganga basin, India , 2012, Aquatic Ecology.

[63]  S. Blaber,et al.  Factors affecting the distribution of juvenile estuarine and inshore fish , 1980 .

[64]  P. Moyle,et al.  EFFECTS OF FLOW REGIME ON FISH ASSEMBLAGES IN A REGULATED CALIFORNIA STREAM , 2001 .

[65]  Charles N. Kroll,et al.  Impact of multicollinearity on small sample hydrologic regression models , 2013 .

[66]  R. Hannesson.  Exclusive Economic Zone , 2013 .

[67]  J. Darmstadter,et al.  Species Composition and Diversity , 2015 .

[68]  R. Menni,et al.  Environmental factors structuring fish communities of the Río de la Plata estuary , 2004 .

[69]  赵静 Zhao Jing,et al.  Fish community ecology in rocky reef habitat of Ma’an Archipelago II. Spatio-temporal patterns of community structure , 2013 .

[70]  K. Winemiller,et al.  Fish assemblage structure of Koycegiz Lagoon–Estuary, Turkey: Spatial and temporal distribution patterns in relation to environmental variation , 2005 .

[71]  P. Afonso,et al.  Predictive habitat modelling of reef fishes with contrasting trophic ecologies , 2013 .

[72]  S. McClatchie,et al.  Demersal fish assemblages off southern New Zealand in relation to depth and temperature , 1998 .

[73]  E. May,et al.  Relationships Between Fish Assemblage Structure and Selected Environmental Factors in Maryland's Coastal Bays , 2007 .

[74]  R. Death,et al.  Physical and chemical differences in karst springs of Cantabria, northern Spain: do invertebrate communities correspond? , 2009, Aquatic Ecology.

[75]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .