Nonparametric Threshold Model of Zero-Inflated Spatio-Temporal Data with Application to Shifts in Jellyfish Distribution

There is increasing scientific interest in studying the spatial distribution of species abundance in relation to environmental variability. Jellyfish in particular have received considerable attention in the literature and media due to regional population increases and abrupt changes in distribution. Jellyfish distribution and abundance data, like many biological datasets, are characterized by an excess of zero counts or nonstationary processes, which hampers their analyses by standard statistical methods. Here we further develop a recently proposed statistical framework, the constrained zero-inflated generalized additive model (COZIGAM), and apply it to a spatio-temporal dataset of jellyfish biomass in the Bering Sea. Our analyses indicate systematic spatial variation in the process that causes the zero inflation. Moreover, we show strong evidence of a range expansion of jellyfish from the southeastern to the northwestern portion of the survey area beginning in 1991. The proposed methodologies could be readily applied to ecological data in which zero inflation and spatio-temporal nonstationarity are suspected, such as data describing species distribution in relation to changes of climate-driven environmental variables. Some supplemental materials including an animation of jellyfish annual biomass and web appendices are available online.

[1]  R. Brodeur,et al.  Abundance and distribution of large medusae in surface waters of the northern California Current , 2005 .

[2]  Claudia E. Mills,et al.  Evidence for a substantial increase in gelatinous zooplankton in the Bering Sea, with possible links to climate change , 1999 .

[3]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[4]  N. Stenseth,et al.  Phenological and geographical patterns of walleye pollock (Theragra chalcogramma) spawning in the western Gulf of Alaska , 2007 .

[5]  Monica Chiogna,et al.  Semiparametric zero-inflated Poisson models with application to animal abundance studies , 2007 .

[6]  Ramiro Ruiz-Cárdenas,et al.  Spatio-temporal modelling of coffee berry borer infestation patterns accounting for inflation of zeroes and missing values , 2009 .

[7]  Richard A. Kronmal,et al.  Two-Part Models for Analysis of Agatston Scores with Possible Proportionality Constraints , 2006 .

[8]  Hugh P Possingham,et al.  Zero tolerance ecology: improving ecological inference by modelling the source of zero observations. , 2005, Ecology letters.

[9]  Alan E. Gelfand,et al.  Zero-inflated models with application to spatial count data , 2002, Environmental and Ecological Statistics.

[10]  David I. Warton,et al.  Many zeros does not mean zero inflation: comparing the goodness‐of‐fit of parametric models to multivariate abundance data , 2005 .

[11]  S. Wood.  Generalized Additive Models: An Introduction with R , 2006 .

[12]  M. Youngbluth,et al.  Behavior of Nemopsis bachei L. Agassiz, 1849 medusae in the presence of physical gradients and biological thin layers , 2010, Hydrobiologia.

[13]  J. Reynolds,et al.  Climate Change and Distribution Shifts in Marine Fishes , 2005, Science.

[14]  G. Stauffer.  NOAA protocols for groundfish bottom trawl surveys of the nation's fishery resources, March 16, 2003 , 2004 .

[15]  Andrea Battisti,et al.  EXPANSION OF GEOGRAPHIC RANGE IN THE PINE PROCESSIONARY MOTH CAUSED BY INCREASED WINTER TEMPERATURES , 2005 .

[16]  N. Bond,et al.  Recent shifts in the state of the North Pacific , 2003 .

[17]  D. Lindenmayer,et al.  Modelling the abundance of rare species: statistical models for counts with extra zeros , 1996 .

[18]  David Harte,et al.  PtProcess: An R Package for Modelling Marked Point Processes Indexed by Time , 2010 .

[19]  N. Stenseth,et al.  MODELING PULSE DISTURBANCE IMPACT ON COD POPULATION DYNAMICS: THE 1988 ALGAL BLOOM OF SKAGERRAK, NORWAY , 2003 .

[20]  H. Tong.  Non-linear time series. A dynamical system approach , 1990 .

[21]  Dean Follmann,et al.  Semiparametric two‐sample changepoint model with application to human immunodeficiency virus studies , 2008 .

[22]  Steven R. Hare,et al.  Empirical evidence for North Pacific regime shifts in 1977 and 1989 , 2000 .

[23]  J. Purcell.  Climate effects on formation of jellyfish and ctenophore blooms: a review , 2005, Journal of the Marine Biological Association of the United Kingdom.

[24]  T. Gross,et al.  Predicting the distribution of the scyphomedusa Chrysaora quinquecirrha in Chesapeake Bay , 2007 .

[25]  Adrian P. Martin,et al.  Climate-driven range expansion of a critically endangered top predator in northeast Atlantic waters , 2007, Biology Letters.

[26]  H. Hirche,et al.  Abundance, distribution and prey composition of scyphomedusae in the southern North Sea , 2007 .

[27]  J. van den Broek,et al.  A score test for zero inflation in a Poisson distribution. , 1995 .

[28]  Jaromír Antoch,et al.  Permutation tests in change point analysis , 2001 .

[29]  J. Purcell.  Environmental effects on asexual reproduction rates of the scyphozoan Aurelia labiata , 2007 .

[30]  Kung-Sik Chan,et al.  Introducing COZIGAM: An R Package for Unconstrained and Constrained Zero-Inflated Generalized Additive Model Analysis , 2010 .

[31]  N. Bond,et al.  On the temporal variability of the physical environment over the south-eastern Bering Sea , 2001 .

[32]  W. Graham,et al.  In situ quantification and analysis of large jellyfish using a novel video profiler , 2003 .

[33]  R. Hopcroft,et al.  Gelatinous zooplankton of the Arctic Ocean: in situ observations under the ice , 2005, Polar Biology.

[34]  Hongsheng Bi,et al.  Modeling the pelagic habitat of salmon off the Pacific Northwest (USA) coast using logistic regression , 2007 .

[35]  N. Bond,et al.  Rise and fall of jellyfish in the eastern Bering Sea in relation to climate regime shifts , 2008 .

[36]  David B. Lindenmayer,et al.  MODELING COUNT DATA OF RARE SPECIES: SOME STATISTICAL ISSUES , 2005 .

[37]  Erhan Mutlu,et al.  Distribution and abundance of moon jellyfish (Aurelia aurita) and its zooplankton food in the Black Sea , 2001 .

[38]  G. Hunt,et al.  Increases in jellyfish biomass in the Bering Sea: implications for the ecosystem , 2002 .

[39]  D. Musolin.  Insects in a warmer world: ecological, physiological and life‐history responses of true bugs (Heteroptera) to climate change , 2007 .

[40]  S. Wood.  Thin plate regression splines , 2003 .

[41]  A. Welsh,et al.  Generalized additive modelling and zero inflated count data , 2002 .

[42]  Fox,et al.  Patterns in the spawning of cod (Gadus morhua L.), sole (Solea solea L.) and plaice (Pleuronectes platessa L.) in the Irish Sea as determined by generalized additive modelling , 2000 .

[43]  Diane Lambert,et al.  Zero-inflacted Poisson regression, with an application to defects in manufacturing , 1992 .

[44]  Richard A. Hoover,et al.  Interannual variation of strobilation by the scyphozoan Aurelia labiata in relation to polyp density, temperature, salinity, and light conditions in situ , 2009 .