ELSEVIER Available online at www.sciencedirect.com *?#' ScienceDirect Deep-Sea Research I 54 (2007) 1641-1654 DEEP-SKA RESEARCH PART I www.elsevier.com/locate/dsri Biodiversity and community structure of deep-sea foraminifera around New Zealand Martin A. Buzas'''*, Lee-Ann C. Hayek'', B.W. Hayward^, Hugh R. Grenfell'', Ashwaq T. Sabaa^ '^Smithsonian Institution, Washington, DC 20560-0121, USA Geoinarine Research, 49 Swainston Rd., St. Johns, Auckland, New Zecdand Received 16 May 2006; received in revised form 16 May 2007; accepted 18 May 2007 Available online 29 May 2007 Abstract The biodiversity and community structure of benthic foraminifera were estimated from 217 stations distributed in four geographic regions (north, south, east, west) around New Zealand. An analytical method accumulating sample values of species richness (S), the information function (//) and evenness (?") with increasing number of individuals (A^) called SHE analysis was used to estabhsh 16 foraminiferal communities and their community structure at shelf (0-200 m), bathyal (200-2000 m) and abyssal ( > 2000 m) depths. A decrease in S, H and E occurs from north to south and this latitudinal gradient extends to abyssal depths. An increase in S and H with depth occurs in the northern and southern areas. For In S, H and In E against In N, regression lines on values obtained from SHE analysis at shelf, bathyal and abyssal depths all diverge in the southern area. Each of the other areas exhibits crossing of regression lines so that establishing the rank order of S, H or E with depth within an area requires consideration of A^. For a log series pattern, // is a constant proportional to a, the parameter of the log series, and, based on the decomposition equation \nS = H + \nE, a. regression of In S against [nE yields a regression coefficient of ?1 and an intercept of H. At depths of less than 1000 m, 2 of 8 communities have regression coefficient confidence intervals that include ?1. At depths of greater than 1000 m, 7 of 8 communities intervals include ?1. Thus, overall, the majority of cases, but especially those at depths greater than 1000 m, have a log series pattern. Published by Elsevier Ltd. Keywords: Biodiversity; Community structure; Foraminifera; New Zealand 1. Introduction A fundamental component of biodiversity studies is the relative species abundance vector (RSAV). The RSAV is the column of numbers composed of each species proportion at a site(s). The number of entries or rows in the column is called the rank of *Corresponding author. E-mail address: buzasm@si.edu (M.A. Buzas). the vector which in turn is called the species richness (S). Formally, we have, then, the species proportion p?^ where ; = (1,2,..., S) and p = Pi,p2,... ,Ps- The statistical distribution of p or the RSAV is referred to as community structure (Buzas and Hayek, 2005). In this sense a community is simply a group of organisms, usually a taxonomic entity, of interest to the researcher. Thus, we may have a bivalve community, foraminiferal community and so forth. For the purposes of this paper, community, 0967-0637/$ - see front matter Published by Elsevier Ltd. doi:10.1016/j.dsr.2007.05.008 1642 M.A. Buzas et al. / Deep-Sea Research 154 (2007) 1641-1654 biofacies, assemblage and faunal zone are synon- ymous. Recently, because of renewed theoretical interest, a renaissance in research on species abundance has occurred (Hubbell, 1997, 2001; Volkov et al., 2003; Magurran, 2005; McGill, 2006; Shipley et al., 2006). The approach for the evaluation of biodiversity and community structure is a method of analysis developed by Buzas and Hayek (1996, 2005) that offers researchers a new tool for this renaissance. This methodology math- ematically links accumulated values of density (A^), species richness (5), information {H) and evenness (??). The entire procedure uses the acronym SHE analysis (Hayek and Buzas, 1997). The variables {S,H,E and N) are displayed on a single graph called a biodiversity-gram (BDG) (Hayek and Buzas, 2006). The benthic foraminifera are and have been ubiquitous, abundant and speciose in the world of oceans for milhons of years. In the modern environment as well as in the fossil record, thousands of species are described, and their distribution is well documented in space and time (Culver and Buzas, 1998). For studies of marine biogeography and biodiversity, in small and large amounts of space and time, they are ideal organ- isms. Like most other organisms, they exhibit a pattern of increasing species richness with decreas- ing latitude and often show an increase in species richness with depth (Gibson and Buzas, 1973; Murray, 1973, 2006). The benthic foraminifera can provide the ideal organisms to examine the biodiversity and commu- nity structure of the deep-sea. However, much of the earher work was conducted for taxonomic and biogeographic purposes and is not suitable for careful analysis. In the deep-sea around New Zealand, the surveys of Hay ward et al. (2001, 2002, 2003, 2006, 2007) from shelf to abyssal depths have remedied this situation. Exact locations of the stations and data are given in the Hay ward et al. contributions. The purpose of this paper is to analyze this vast and unique New Zealand data set by SHE analysis for trends in biodiversity and community structure. We will do so by depth as weh as by geographic area. 2. Methods All samples used in this study come from the seafloor of the New Zealand region in the southwest Pacific between latitudes 33?S and 56?S (Fig. 1) and ^ "^?'^V * NORTH N ?35s? ?? ?^'.;' S WEST vi ?ftx ?>...,--- " . .?? ?i ^^^'?'^-yf / ?\:^k\'t North /..- ?",'.'?' r Islap^'' *? ? ^^ / . ?1' m A; / /'^ ) yjiJ' EAST ?'- / /"/ j^ : ,-"" j^ r ~'? ? ? "' ?*? ?*?-.. ?X Jsi" ' ? Chatham Rise .. ? /^SoutbKT^ vr.,...,. . ^.,.,:' ? 45S? / Island ,..'^ '?-???? * ?; ?.??-....*,....? - ,-^, i/f?^?. il ? . st?w?i??i;../' '? r..."*'.'*".-^*-^ Island \ .? , . . '??????:\ ??"?> ? ? -' ? '. ? . : ?. . ? . ? ??:.. . _ . ? ?...? SOUTH ?: '' ?. ?t .? ? ? ; '.." ? ..???*"????? ? 55s? ;?' . 165E?.' 175E? 175W? Fig. 1. Locations of benthic foraminiferal seafloor samples around New Zealand in the south-west Pacific. They have been grouped into four regions?north, west, east and south for comparitive analysis. The 1000 m depth contour is shown. at mid-shelf to abyssal depths, between 50 and 5000 m (Table 1). The samples are grouped into four areas, located off the north, west, east and south coasts of the two main islands (North and South Islands) of New Zealand (Fig. 1). The sediment samples were obtained mostly from the archives held by the National Institute for Water and Atmospheric Research (NIWA), Wellington, sup- plemented by core top samples from several Ocean Drilhng Program (ODP) sites. Except for the ODP sites, the samples analyzed were taken from the top few centimeters of gravity and piston cores or from surficial grab or dredge samples. Faunal sUdes (prefixed by F202) are housed in the collections of the Institute of Geological and Nuclear Sciences, Lower Hutt. Consequently, there was no opportu- nity to distinguish living from dead tests, and census counts are of total (living plus dead) faunas. We would, of course, have preferred to analyze five, dead and total populations separately. Horton and Murray (2006) discuss the advantages and disad- vantages of using each of these populations. Ideally, observation of the living population over a M. A. Buzas et al. / Deep-Sea Research 154 (2007) 1641-1654 1643 Table 1 Results of SHE analysis from South of New Zealand Biofacies Stations depth N H ?i Confidence limits 1 S6-S15 Outer shelf 143-188m ??= 169m Regression equations: In S = 1.27 + 0.39 \nN,p = 0.00, R} \nE = 2.25 - 0.54 In iV, p = 0.00, R 200 28 2.72 0.55 400 36 2.62 0.37 1000 52 2.49 0.23 1300 58 2.44 0.20 10 :0.97; // = 3.52-0.151nAf,/7 = 0.00, A" = 0.89 = 0.99; In S = 2.89 - 0.72 In E, /7 = 0.00, R^ = 0.98 2 S20-S27 Upper bathyal 435-565 m ?1 = 519m Regression equations: In 5 = 1.23 + 0.39 lnN,p = 0.00, R^ -- \nE= 1.33-0.351niV,/i = 0.00, R^ -? 3 S42-S47 Lower bathyal 960-1244 m fi= 1076m Regression equations: \nS= 1.31+0.401n7Vr,/7 = 0.00, R InE = 1.07 - 0.31 IniV, p = 0.00, R^ 200 400 1000 1300 27 35 52 56 2.78 2.81 2.83 2.88 0.58 0.46 0.33 0.31 0.98; H = 2.57 + 0.04 In Af, p = 0.22, R- = 0.48 :0.99; lnS' = 2.70- 1.121nE,/7 = 0.00, R^ 200 400 1000 1300 31 41 58 65 2.91 2.98 3.04 3.10 :0.98 0.57 0.46 0.35 0.32 ?2 - 0.99; H = 2.38 + O.lOlnAf, p = 0.98; In S = 2.76- l.26lnE,p 0.05, R- = 0.82 = 0.00, R^ = 0.98 4 S63-S68 Abyssal 3452-5000 m /I = 4352m Regression equations: lnS'= 1.11 + 0.46In7Vr,/7 = 0.00, R^ -- InE = 1.52 - 0.39IniV, p = 0.00, R^ -? 200 400 1000 1300 35 48 73 82 3.00 3.05 3.10 3.13 0.58 0.44 0.30 0.28 0.99; H = 2.63 - 0.07 In Af, p = :0.95; ^5 = 3.01 - 1.06InE,/7 0.38, R- = 0.44 = 0.00, R^ = 0.94 -0.72 -0.84 2000 m. As outlined in Section 2 SHE analysis has two facets: SHEBI and SHECSI. For an analysis with SHEBI we constructed a Hnear plot of In E vs. In A^, which was then used to delineate communities. The communities so identified were then analyzed for community structure by SHECSI. Only biofacies or communities defined by more than 4 stations were M. A. Buzas et al. / Deep-Sea Research 154 (2007) 1641-1654 1645 included in the regression analysis, and results for select values of A^ are given in the tables. In the southern area of New Zealand, we analyzed S = 214 species distributed among n = 68 stations. About half of the stations (44%) were grouped into 4 communities or biofacies. Table 1 and the BDG shown in Fig. 2 indicate that except for the outer shelf, H plots as a nearly straight hne. Although we provide regression equations for ah three measures (\nS,H,lnE) against InA^, the decomposition equation explains that only two of the three are necessary. For example, the slope for H vs. In N equals the difference between the slopes for In 5* vs. In A^ and In E vs. In N. The intercept in H vs. In A'^ equals the sum of the two intercepts for In S vs. InA^ and InE vs. InA^. The regression of In5 with InE as weh as the predicted values of S, H and E at the given values of N are approximately equivalent across the outer shelf and at upper bathyal depths (Table 1, Fig. 2). At lower bathyal and abyssal depths, however, species richness increases so that there is a decrease from abyssal-lower bathyal to upper bathyal-outer shelf (Fig. 2, Table 1). The patterns of results for the information function, H, are not so orderly. For the outer shelf biofacies, the slope for the equation for H vs. In A^ is negative resulting in increasingly smaller values for South NewZealand -X? Outer Shelf - -a - Lower Bathyal ? o- ? Upper Bathyal - - -t- - - Abyssal Fig. 2. Biodiversitygram (BDG) for area south of New Zealand. In S is the natural log of the number of species, H is the information function. Ini; is the evenness defined as lnE = H-lnS. H as the number of individuals increases (Fig. 2, Table 1). At deeper biofacies, the slope of i/vs. InA^ is close to zero, making the plotted Hne essentially parallel to the In A^ axis. As with species richness the deeper biofacies exhibit larger values o? H as N increases and regression Hnes diverge. As with the information function, the plot for evenness clearly differentiates the outer shelf from the other deeper biofacies that have higher values for evenness (Fig. 2). The regression hnes for evenness also diverge as N increases. For higher densities the biofacies are more easily differentiated. Overall, Fig. 2 shows an outward spread of data lines as A^ increases; at lower values of A^ there is less discrimination of S, H and E than at higher values. Examination of Table 1 indicates that at A^ = 400, the change in 5* from outer shelf to abyssal depths is 12 species; for H the change is 0.43 and for E, 0.07. However, at A^ = 1300, the changes are 24, 0.69 and 0.08, respectively. The con?dence intervals for the slope in each equation for In S vs. InE, except that for the outer shelf, include the value ? 1, the theoretical constant from the log series distribution. In the area north of the North island of New Zealand, 238 species distributed in 56 samples were analyzed by SHEET The analysis placed 51 samples or 91% into 4 biofacies. The first biofacies contains ? = 33 stations and extends from mid-shelf to upper bathyal depths (50-561 m). This wide span in depth encompassing a single community is not observed elsewhere around New Zealand or from any of the other studies subjected to SHE analysis so far. The remaining 3 biofacies each contain 6 stations (Table 2). Species richness is nearly identical for shelf to mid-bathyal depths (Fig. 3). However, species richness increases at lower bathyal and abyssal depths (Table 2, Fig. 3). The regression coefficients for the equation In 5 vs. InA^ for outer shelf, upper bathyal, lower bathyal and abyssal depths are similar (Table 2). Values for H are more complicated, because the regressions for H vs. In A^ are nearly horizontal at the two deepest biofacies, but have positive slopes at the two shahowest (Table 2). Consequently, at lower densities (In A^ = 6 or A^ ?? 400) the values of H can be differentiated for all four biofacies, but as InA^ increases only the value for abyssal depths remains distinctly higher than the others (Fig. 3). As with the H values, slopes for the \nE vs. In A^ regressions at lower bathyal and abyssal depths are more similar than those at the shallower depths. 1646 M.A. Buzas et al. / Deep-Sea Research 154 (2007) 1641-1654 Table 2 Results of SHE analysis for north of New Zealand Biofacies Stations depth N H Confidence limits 1 N56-N24 Upper bathyal 50-561 m ?1 = 223 m Regression equations: In 5'= 1.52 + 0.39 In 7Vr,/7 = 0.00, R^ -- In ? = 0.99 - 0.28 \nN,p = 0.00, R^ ?? 2 N20-N15 Mid-bathyal 754-1242 m ^ = 967m Regression equations: lnS'= 1.12 + 0.451n7Vr,/7 = 0.00, R^ -- ln? = 0.23-0.191nAf,/; = 0.00, R^ ?? 3 N14-N9 Lower bathyal 1295-2036 m ?I = 1664m Regression equations: \riS= 1.74 + 0.38ln7V,p = 0.00, R In ?? = 1.43 - 0.36 In A^, ;7 = 0.00, R^ 33 200 400 1000 1300 36 47 68 75 3.09 3.18 3.28 3.30 0.61 0.50 0.39 0.36 :0.98; // = 2.51+0.111nA',/7 = 0.00, A" = 0.94 = -0.98; InS = 2.92 - \39\nE, p = 0.00, R^ = 0.99 200 400 1000 1300 33 46 69 77 2.78 2.95 3.19 3.28 0.46 0.42 0.35 0.32 0.99; H = :0.98; In S 1.35+ 0.27 In A',/7 = = 1.84-2.28 In E,/7 0.01, R- = 0.93 = 0.00, R^ = 0.94 200 400 1000 1300 43 54 77 87 ?^ -0.99; // = 3.17 + 0.021nA',/7 = 0.99; In S = 3.23- 1.041nE,/7 4 N6-N1 Abyssal 2550-3757 m /I = 3002 m Regression equations: InS = 2.34 +0.31 ln7Vr,/7 = 0.00, R^ -- In ?= 1.43 - 0.34 In Af, p = 0.00, R^ ?? 200 400 1000 1300 54 68 90 96 3.28 3.29 3.30 3.31 0.47, R- = = 0.00, R^ 3.66 3.65 3.63 3.63 0.99; H = i.ll - 0.02\aN, p = 0.1\, R^ = : 0.97; In S = 3.72 - 0.86 \nE,p = 0.01, R^ 0.62 0.48 0.35 0.32 0.37 = 0.99 0.69 0.55 0.40 0.36 0.20 = 0.93 -1.39 -1.44 ? Lower Bathyal ? InE Fig. 4. BDG for area west of New Zealand. Symbols as defined in Fig. 2. The north, west and east areas each have biofacies represented in the mid-bathyal depth range (600-1000 m). Fig. 9 shows that the regression equations predict that at lower values of N species richness is highest in the west and at higher values in the east. A prediction of similar values of In 5" occurs at about InN = 6.9 or N = 1000. For H the western values are nearly constant while the slopes for north and east are nearly identical (Fig. 9, Tables 2-A). For In E, the north and west are also nearly parallel, but the west has larger values. The east has higher values of InE at smaller N, but after about InN = 6.9 or A^ = 1000, the west is always the highest (Fig. 9). At lower bathyal depths (1000-2000 m) all four areas are represented. The northern area again has the highest species richness: however, there is considerable crossing of regression lines at about N = 1000. Both the north and west values of H are M. A. Buzas et al. / Deep-Sea Research 154 (2007) 1641-1654 1649 Table 4 Results of SHE analysis for east of New Zealand Biofacies Stations depth N H Confidence limits 1 E32, E45, E3, E46, E63, E34, E47 Upper bathyal 289-511 m ? = 394 m Regression equations: In S = -1.09 + 0.77 In iV, /I = 0.00, B? \nE = 0.47 - 0.25 \nN,p = 0.00, B? = 2 E33, E4, E26, E35, E48, E27, E12, E5, E13 Mid-bathyal 547-980 m ? = 735 m Regression equations: In S = -0.66 + 0.70 lnN,p = 0.00, B^ In ?= 1.97 - 0.44 In iV, p = 0.00, B^ = 3 E62, E36, E28, E49, E52 Lower bathyal 1003-1204 m ?= 1109m Regression equations: In S = 0.71 + 0.53 lnN,p = 0.00, B^ = lnE= 1.52 - 0.39IniV,/I = 0.01, B^ = 4 E51, E14, E7, E53, E39, E38 Lower bathyal 1462-1841 m /i= 1692m Regression equations: InS =-0.12 +0.60 IniV, 0 = 0.00, B^ 200 400 1000 1300 20 34 71 84 2.19 2.56 3.03 3.18 = 0.99; H -. 0.97; In S: -0.62 + 0.53 lnN,p = 0.00, R^ : 0.49 - 3.06InE, p = 0.00, R^ = 200 400 1000 1300 21 34 67 78 2.69 2.87 3.12 3.17 0.42 0.36 0.29 0.27 = 0.98 0.98 0.70 0.51 0.34 0.31 :0.78 = 0.98; H =1.31+ 0.26 In A?, p = 0.01, R^ 0.98; ^5 = 2.58+ -1.501nE,/7 = 0.00, R^ =0.94 200 400 1000 1300 34 49 79 91 2.97 3.07 3.19 3.23 0.58 0.36 0.31 0.28 0.99; H = 2.23 + 0.141nAf, p = 0.04, R- = 0.90 : 0.96; In S = 2.83 - 1.29 lnE,p = 0.00, R^ 200 400 1000 1300 21 32 56 66 2.40 2.56 2.77 2.80 lnE= 1.42-0.39 In iV, : 0.00, B' = 0.98; H =\.29 + 0.21 lnN,p = 0.02, R^ -. 0.99; In S = 2.08 -l.55lnE,p = 0.00, R^ = 5 E29, E54, E65, E61, E8 Abyssal 2030-2332 m /i = 2245 m Regression equations: In S = 0.96 + 0.48 \nN,p = 0.01, R^ -- In ? = 2.12 - 0.48 In iV, n = 0.00, B^ -? 200 400 1000 1300 0.96; H = :0.99; In S 3.08- = 3.05 33 46 72 82 0.0051n7Vr,/! = -0.99\nE,p-. 3.05 3.05 3.04 3.04 :0.98 0.52 0.36 0.28 0.25 = 0.89 0.98 0.66 0.47 0.29 0.27 0.94, B^ = 0.05 = 0.00, R^ = 0.98 -3.06 -3.70 2000 m) are found in the north, south and east. The northern area has the highest species richness, information function and evenness (Fig. 11). The S, H and E for the east and south are nearly identical throughout the range of N. All three areas have nearly zero 1650 M.A. Buzas et al. / Deep-Sea Research 154 (2007) 1641-1654 slopes for H vs. InA^, indicating that the abyssal communities exhibit a log series pattern of commu- nity structure. If we concatenate the areas and examine S, H and E with depth categories, both In S and H increase with depth (significant regression at the 0.05 level, Fig. 12). At A^ = 1000 we expect 5 = 58 at outer shelf depths and 5 = 74 at abyssal depths. Similarly, at A^ = 1000 we expect H = 2.84 at outer shelf depths and H = 3.28 at abyssal depths. Although In E also increases with depth it does so only slightly and the regression is not significant. East New Zealand ? "? "" A 0_ - ? " ? 24---? 1 0 -1 -2 ? o- ? Upper Bathyal -A- Mid-Bathyal - - + - - Abyssal ..-*?- ^jstiS-i^^- --o:5;i^--::.^..,^ -^^?=^~-^-,^J^j^.,_^ ^ InS InE New Zealand Outer Shelf 100-200m 6 5 4 3-J 2 1 0 -1 -2 -3 West-.^.- South y'-^- -?*? TTTT -?- ?.*: InS InE InN Fig. 5. BDG for area east of New Zealand. Symbols as defined in Fig. 2. InN Fig. 7. BDG for outer shelf depths (100-200 m) south and west of New Zealand. Symbols as defined in Fig. 2. North West East InN South InS = 4.391 - 0.075 Area p = 0.018, R2 = 0.338 H = 3.486-0.155 Area p = 0.006, R2 = 0.434 InE = -0.926 - 0.076 Area p = 0.028, R2= 0.300 Fig. 6. Regressions of InS, H and Ini? against areas. All depths included in each area. Values printed on graphs are from regression equations shown on the right of the graph. In S and XME were converted to numbers for ease of interpretation. M. A. Buzas et al. / Deep-Sea Research 154 (2007) 1641-1654 1651 New Zealand Upper Bathyal 200-600m 6 5 4 3 2 1 0 -1 -2 North - i East South iJ.'-"- ^?" ..: .A_-A ,Ai?A?i>?< iMi? ?gY.-^-^-^-T-T vr iMfi^A^A ?-'^--V-4^^AAiU44.,M^j^ InS InE 7 InN Fig. 8. BDG for upper bathyal (200-600m) depths north, south and east of New Zealand. Symbols as defined in Fig. 2. -?-.-- H New Zealand Lower Bathyal 1000-2000m 5 4- - -A - North -? - East -?- West --?- - South ..^..'i-^'^'"^ 3- m 2- 1 - 0- -1 - ""~^-^Ti^g?^^_^ -? InS InE InN Fig. 10. BDG for lower bathyal (1000-2000m) depths north, south, west and east of New Zealand. Symbols as defined in Fig. 2. New Zealand Mid-Bathyal 600-1000m -A- - North - ?- East - ?- - West InN Fig. 9. BDG for mid-bathyal (600-1000 m) depths north, west and east of New Zealand. Symbols as defined in Fig. 2. 4. Discussion Traditional biodiversity analysis examines each sample or station individually. Values for individual samples (a single value of N) then are analyzed for a trend, or several samples will be bundled together by a category such as depth, and the means from the New Zealand Abyssal >2000m -.j:.r---^ InS 5 4- - -A - North -? - East - T- ? South 3- ^.. _ ? ,,_... J, ...J. = 15 =y--?: - :?--.: r-. 2- 1 - 0- 1 - o ? ?*---a-.Jt-^-A---- InE InN Fig. 11. BDG for abyssal (> 2000 m) depths north, south and east of New Zealand. Symbols as defined in Fig. 2. categories will be compared (Ricklefs and Schl?ter, 1993; Gibson and Buzas, 1973). Instead of examining diversity values at a single value of N, SHECSI analysis examines the values of In 5, H and \nE as N accumulates (samples are added together). The results are plotted on a BDG 1652 M.A. Buzas et al. / Deep-Sea Research 154 (2007) 1641-1654 InS = 3.996 + 0.062 Depth P = 0.025,R2 = 0.311 H = 2.740+ 0.107 Depth p = 0.035, R2= 0.281 lnE =-1.255+ 0.041 Depth p = 0.185, R2 = 0.122 Outer Upper Mid Lower Abyssal Shelf Bathyal Bathyal Bathyal InN Fig. 12. Regressions of In 5, //and In/; against depths. All areas where data are available are included at each depth. Values printed on graphs are from equations shown on the right of the graph. In 5 and In/i were converted to numbers for ease of interpretation. with In S, H and In E on the F-axis and In A^ on the X-axis (Hayek and Buzas, 2006). If we examine just the In S vs. In N portion, we have a hnear regression analysis often used for rarefaction in species richness studies (Hayek and Buzas, 1997). However, SHECSI also results in linear regression equations for H and In E. The expected value for H is known for major statistical distributions and the decom- position equation provides the value for In E. As A^ accumulates, the observed pattern formed by In^" vs. InA'^ defines the statistical distribution or community structure. The observed distribution can then be compared to the theoretical. For example, if In E is constant, then H and In S must be parallel as they increase with \nN (this is identified as a broken stick distribution). If In 5 and In^" have the same value for their slopes but with different signs, then H must be constant (best described as a log series distribution). SHECSI provides for rarefaction by hnear regression of not only In 5, but also for H and \nE. More importantly, however, SHECSI provides a distribution function approach for examining community structure. Both the traditional analysis of individual sam- ples and SHE methodology indicate a trend over areas and depths around New Zealand. In general. the northern area has the highest values of S, H and E while the southern has the lowest. Thus, the weh- known latitudinal diversity gradient with highest values at lower latitudes (Huston, 1994; Rosenz- weig, 1995) is also present around New Zealand (Fig. 6), a trend noted by Hayward et al. (2006). Fig. 12 shows there is also a trend of increasing S and H with depth. This pattern is apparent in the south (Table 1, Fig. 2) and north (Table 2, Fig. 3), but not in the west or east, a trend also noted by Hayward et al. (2006). The changes in S observed with depth in New Zealand are smaller than those observed in the western North Atlantic and Gulf of Mexico (Gibson and Buzas, 1973). Higher biodiversity values at abyssal depths in the north relative to the other areas (Fig. 11) indicate the latitudinal diversity gradient is present even at depths of greater than 2000 m. This observation is in agreement with those of Gibson and Buzas (1973) and Culver and Buzas (2000) who observed the same phenomenon in the North and South Atlantic as well as in the northeastern Gulf of Mexico. Because SHE analysis examines community structure dynamically over accumulated values of A^, examination of foraminiferal communities well beyond the traditional biodiversity analysis is possible. Let us examine the insights gained. M. A. Buzas et al. / Deep-Sea Research 154 (2007) 1641-1654 1653 In the northern area, SHEBI analysis indicates that biofacies or community 1 (Table 2) extends from the mid-shelf to upper bathyal depths an accumulation of ? = 33 stations. This is the largest accumulation of stations observed thus far by the SHE technique. Cluster analysis in the same area identified 6 associations (Hayward et al., 2006). The changes in the relative abundance of the species with depth are evidently so continuous and small that the entire area can be regarded as adhering to a single statistical distribution or, by our definition, a single community, even though analysis of species com- position indicates several associations. Around New Zealand, we identified 16 communities, and none of the others had accumulations of greater than 10 stations. These also are similar to associations determined by cluster analysis. Because the species richness, S, is a function of the number of individuals, A'^, most foraminiferal researchers realize that comparisons of species richness requires measurement at a constant N or else rarefaction to a constant value. We have extended this concept to H and \nE as well and shown how they are aU finked by a decomposition equation. Questions regarding comparisons or rank order of S, H or E with depth or area must consider not only the value of A^, but also the community structure. At abyssal depths around New Zealand (Fig. 11) /? is nearly constant, a log series pattern, so that In 5* and In ? have equal but opposite slopes. Given this community structure, as the BDG in Fig. 11 shows, S, H and E are always greater in the north regardless of N. On the other hand, at mid- bathyal depths, only the east has a relatively constant value of H (Fig. 9). Consequently, at low values of A^ a rank order is distinguishable, while at higher values of A^ (In 7) values converge. The same pattern exists for the upper bathyal (Fig. 8) and is shown most dramatically on the outer shelf (Fig. 7). On the outer shelf, the southern area has a nearly constant value for H while, in the west, H vs. InA^ has a positive slope. At lower values of A^, 5, H and E are greater in the south while at higher values of A^, they are greater in the west (BDG, Fig. 7). The complexity of these patterns would not be apparent without SHECSl analysis. The confidence intervals for the regression coefficients of 9, or 56% , of the 16 communities identified around New Zealand, include ? 1 (Tables 1-4). Because the methodology used here is relatively new, there are no studies to indicate the usefulness of the confidence belts about these values. However, it can be shown that for a log- normal distribution this slope will be closer to ?4 or -5 rather than -1 (Hayek et al., 2007). Tables 1^ show that while the slopes may be smaller or larger than ?1, they are closer to ?1 than ?4 or ?5. Most of the SHE evaluations of foraminifera from other areas outside of New Zealand, are from very shallow water where 9 of 12 communities have values close to ?1 (see Buzas, 2004, for a review). Clearly, the foraminifera have a propensity for a log series pattern. Figs. 7-11 indicate that in New Zealand the 8 communities deeper than 1000 m (lower bathyal and abyssal) most often have confidence intervals that include ?1 (7 of 8 = 88%). Communities from less than 1000 m have 2 of 8, or 25%. The only comparable data from depths greater than 1000 m come from Pleistocene sedi- ments cored in the Arctic (Hayek et al., 2007). In 7 trials of observed communities in these cores all regression slopes were close to or less than ?1. While more observations are needed, at present, it appears that benthic foraminifera in general are inclined toward a log series pattern and deep dwelhng communities (> 1000 m) are almost exclu- sively so. Acknowledgments We thank J. Jett for her help with figures and tables. Acknowledgment is made to the Donors of the American Chemical Society Petroleum Research Fund for partial support of this research. 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