Regressions of Length and Width to Predict Arthropod Biomass in the Hawaiian Islands1 Daniel S. Gruner2 Abstract: Biologists in many fields use published regression equations to predict biomass from simple linear body measurements. Power functions are used with arthropods, facilitating biomass estimation of a sample when destructive tech- niques are not feasible. Resulting predictive coefficients vary widely depending on region and taxa. There are no published biomass regressions for oceanic island fauna, despite the widely accepted conclusion that their arthropod as- semblages are unusual in composition. I present a suite of general and tax- onomically and morphologically restricted regression equations developed for arthropods in the Hawaiian Islands. General regression equations were highly significant when only length was used to predict biomass, but fits were usually improved by including body width. In regressing restricted sets of taxa, the ad- dition of width did little to improve the fit of the functions. Thus, the choice of regression equations involves a trade-off in taxonomic resolution: precise bio- mass estimates will come either from (1) low taxonomic resolution measured for both length and width, or (2) high taxonomic resolution measured only for body length. These equations have a high predictive capacity for a broad range of arthropod taxa common in the Hawaiian Islands and, in the absence of locally developed equations, the arthropods of other oceanic islands. The sheer abundance and diversity of (Brown and Maurer 1986, Blackburn et al. arthropods in terrestrial ecosystems attest to 1993, Blackburn and Gaston 1997) to the their importance in ecosystem function. A availability of food resources for birds (Ho´dar number of applications require the estima- 1997) or other vertebrates (Sage 1982). Ar- tion of arthropod biomass in ecosystems, thropods can be weighed directly while fresh from testing of classic hypotheses of biomass or subsequent to freezing. However, fresh ratios in trophic groups (Hairston et al. 1960) biomass measurements are sensitive to the and description of macroecological patterns conditioning of the sample, local relative humidity, or any factor that influences the 1 Specimens were collected during research supported water content of specimens. More often, re- by NSF DGE-9355055 and DUE-9979656 to the Center searchers collect a large quantity of material for Conservation Research and Training of the Univer- in a short time and must preserve specimens sity of Hawai‘i at Ma¯noa, the John D. and Catherine T. for identification and analysis at a later date. MacArthur Foundation, the Science to Achieve Results (STAR) program of the U.S. Environmental Protection These specimens can then be dried and Agency, Sigma Xi, the Hawai‘i Audubon Society, the weighed in bulk to eliminate the variable in- ARCS Foundation, and the NSF Doctoral Dissertation fluence of body water content but at the price Improvement Granting program. Manuscript accepted of destruction of soft-bodied arthropods and 19 December 2002. any ability to identify and voucher them. 2 Department of Zoology and Ecology, Evolution and Conservation Biology Graduate Program, University of A preferred approach to biomass estima- Hawai‘i at Ma¯noa, 2538 The Mall/Edmondson Hall, tion is to use general or taxonomically re- Honolulu, Hawai‘i 96822 (phone: 808-735-3983; fax: stricted regression relationships to predict 808-956-9812; E-mail: [email protected]). arthropod biomass from easily obtained length and/or width measurements (Rogers Pacific Science (2003), vol. 57, no. 3:325–336 et al. 1976, 1977, Schoener 1980, Sage 1982, : 2003 by University of Hawai‘i Press Gowing and Recher 1984, Sample et al. 1993, All rights reserved Ho´dar 1996). Using power functions, these 325 326 PACIFIC SCIENCE . July 2003 equations reduce the effort required to esti- the biomass equations will benefit future mate biomass of a sample when destruc- work focused on Pacific island fauna. tive techniques are not feasible. But which regression coefficients to use? Significant sta- materials and methods tistical differences among compared equa- Field and Laboratory tions appear to be rare (Gowing and Recher 1984, Sample et al. 1993). However, Ho´dar I selected specimens as available within inci- (1996) compared nine published length- dental or nonquantitative collections obtained weight regression relationships and found over the course of other work in the Hawai- their performance highly variable in com- ian Islands from 1996 to 2001. With few ex- parison with the actual known biomass of ceptions, specimens were collected from the samples. Several authors emphasized the in- endemic tree Metrosideros polymorpha Gau- creased precision obtained with equations dichaud-Beaupre´ (Myrtaceae). Metrosideros is specific to lower taxonomic groupings (Gow- a common genus throughout the Pacific to ing and Recher 1984, Ho´dar 1996). Even New Zealand (Mueller-Dombois and Fos- among specific groups, Schoener (1980) no- berg 1998), but it is particularly abundant and ticed differences in parameter estimates of widespread in the Hawaiian Islands (Daw- tropical versus temperate insects and sug- son and Stemmerman 1990). The arthro- gested hypotheses why there might be sys- pod fauna of this tree is particularly diverse tematic differences in the faunas to explain among Hawaiian trees (Southwood 1960), this pattern. representing a number of lineages (Stein The arthropod fauna of the Hawaiian 1983). Thus it is a reasonable first approxi- Islands is widely cited as disharmonic and mation for arthropod biomass predictions in locally depauperate relative to other tropical the Hawaiian Islands and, perhaps, Pacific is- areas as a result of its extreme isolation from lands more generally. I collected arthropods sources of colonizing lineages (Zimmerman through pyrethrum canopy fogging (Gruner 1948, Howarth 1990). The most common and Polhemus in press), branch clipping, groups in these Islands may not be well rep- vegetation beating, malaise trapping, and resented in regression equations developed hand collecting at sites on Hawai‘i, Moloka‘i, elsewhere. In addition, shifts to smaller or O‘ahu, and Kaua‘i (Appendix 1). Several texts larger forms are common in the evolution of provide detail on these collection methods endemic species on islands (Whittaker 1998). (New 1998, Southwood and Henderson It is not known to what extent these size 2000, Toda and Kitching 2002). Most collec- changes alter the allometric relations of linear tions were from intact, predominantly native measurements to body mass. Thus, it is not at forest ecosystems at elevations above 1000 m. all clear which published length-weight rela- All specimens were stored in 70% ethanol tionships are most applicable to estimation of and measured directly upon removal from arthropod biomass on tropical island ecosys- preservative. Alcohol may distort some speci- tems. Recent investigations into the diet of mens, especially in soft-bodied groups such as endangered birds required biomass equations, Lepidoptera and Araneae. Storing of speci- but equations specific to Hawai‘i were un- mens in alcohol also may result in extraction available (Peck 1993, Fretz 2000). Because of some body materials (Rogers et al. 1976). the assessment of the most appropriate pub- Ethanol is, however, the arthropod preserva- lished equations may have proven as labo- tive of choice for many practitioners in vari- rious as generating new ones, I sought to ous fields. These regressions, then, will apply remedy this lack. I present a suite of tax- to data most easily obtained and widely avail- onomically general and specific regression able. If biomass is indeed lost during ethanol equations developed through the course of storage, the regression estimates of biomass ongoing work in the Hawaiian Islands. Be- will be conservative (Gowing and Recher yond their immediate utility, it is hoped that 1984). Hawaiian Arthropod Biomass . Gruner 327 Specimens were chosen to represent a other spiders, and several families of beetles range of taxa, sexes, life stages, and sizes as and genera of Heteroptera were isolated on available in the incidental collections. As the same rationale. Following other authors noted by Ho´dar (1996), it is of greater im- (Rogers et al. 1977), I used a power model to portance to represent the full range of vari- describe the size-weight relationships. The ation in the estimation procedure than to model takes the form: randomize specimen selection. Only undam- b ¼ ð Þ aged specimens were selected. Specimens y a x were identified to species where possible. where y ¼ dry biomass; x ¼ size measure- Otherwise, specimens were assigned to Op- ment, whether length or length * width; a and erational Taxonomic Units (OTU) or ‘‘mor- b are coefficients estimated in the regression phospecies’’ within the finest taxonomic procedure. Morphometric and weight data classification obtainable. were transformed to natural logarithms for Length was measured using a dissecting analysis using linear regressions: microscope with an ocular micrometer to 0.05 mm precision. Body length included the lnð yÞ¼lnðaÞþb * lnðxÞ tip of the abdomen to the end of the head Logarithmic transformations reduced hetero- or carapace, excluding mouthparts, genitalia, scedasticity in the data in accordance with ovipositors, antennae, or spinnerets (spiders). statistical assumptions. Data were analyzed Width was measured at the widest point of with linear regressions using the Systat sta- the mesothorax.