June 1 - 3 , 1978 - University of Hawaii at Manoa

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A MATHEMATICAL MODEL OF 'OHI'A DIEBACK AS A NATURAL PHENOMENON William E. Evenson* Department of Botany University of Hawaii at Manoa Honolulu. Hawaii 96822 INTRODUCTION By means of a very general model system, the possibility of interdependent dying, as contrasted to individual, random dying, in large areas of forest is investigated. In particular, insight is provided into the possible roles of natural mechanisms in pro- ducing such interdependent collapse behavior and what the proper- ties of such mechanisms must be. In this study, mechanisms of change in the forest are characterized as "natural" if they nave been part of the forest environment over an evolutionary time scale. Otherwise, they are characterized as "introduced." This model is applied to the ~roblem of dieback in the native 'ohira (~etrosideros collina kubsp. polymorpha) forests of Hawai'i. The focus of the model is on the "trigger" of the dieback. That is, we look only at the transition of trees from a healthy to a declining state (or vice versa). Mechanisms at work in thesubsequent death or reinvigoration of trees are beyond the scope of this model. The model allows separate examination of the effects of interaction between trees, external factors affecting growth, and physiological factors. Thus, it gives insight into the relative importance of various features of the 'ohi'a dieback phenomenon. It is of especial interest for 'ohi'a dieback to know whether natural factors could produce interdependent decline or whether an "introduced" epidemic (e.g . , disease or insects or some combination of introduced factors) is necessary to explain the field observations. The model presented here, while very general, deals with the plausibility of these various types of mechanisms for interdependent dieback. Before discussing the model considered in this paper and its application to 'ohi'a dieback, the value of such models from physias in biological problems and the kind of information they * Permanent address: Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602
can be expected to provide will be considered (Weidlich 1971; Callen & Shapero 1974). Problems of the sort considered here concern the behavior of "incompletely-specified systems." That is, they deal with systems (e.g., a forest) for which there is either insufficient data to predict the behavior of each individual or incomplete knowl- edge of the laws which govern individual and system behavior, or both. In fact, these systems are intrinsically incompletely specified since we are not really interested in predicting the detailed behavior of each individual and since the data necessary for that task is impossibly extensive. Incompletely specified systems are probabilistic systems by their nature. The sub- discipline of statistical mechanics in physics is directed at such problems in Hamiltopian systems (Hobson 19711, and both models and methods originally developed in physics may be appli- cable to problems of incompletely-specified systems arising in other contexts. In particular, while the causes of interdependent behavior among atomic spins in magnets and interdependent behavior among 'ohi'a trees in a dying forest are obviously rather different, the statistical behavior of these two systems does show interesting similarities. The most serious objection to the approach taken in this paper is that models from physics, like the one discussed below, are such an oversimplification of reality that their results can- not be relied upon. While this is always a danger, such diffi- culties can be minimized by focusing attention on features which are insensitive to specific details of the model. It is argued that the collapse behavior in the present study is such a fea- ture. In addition, if detailed simulation is desired, it is often possible to add specifics to such models and successively improve the simulation of reality. DESCRIPTION OF THE MODEL Imagine a forest of - N uniform-age, essentially identical trees. Let each tree be in one of two states: healthy or declining. (The effect of modifying this model to include individual differences in trees and continuous variation in vigor w i l l be discussed below.) This simple, very general model shows the important features of transition from healthy to declining in a manner which is qualitatively the model. same as a more realistic The forest of identical trees in two possible states can be modelled as a spin-+ classical magnet in two dimensions--the Ising model in statistical mechanics (Weidlich 1971; Callen & Shapero 1974). We use this analogy to analyze the behavior of our model forest. There are three important classes of variables in this problem:
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COOPERATIVE NATIONAL PARK RESOURCES
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PREFACE TABLE OF CONTENTS Apple, Ru
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Gon, Samuel M., 111 ALTITUDINAL EFF
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Stemmermann, Lani HALEAKALA NATIONA
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ROOF RAT DEPREDATIONS ON HIBISCADEL
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Feeding upon seed pods Immature see
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NENE REINTRODUCTION PROGRAM AND RES
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R. C. L. Perkins (1903) also believ
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Although Nene in HAVO pens are expo
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irds have been forced to mate with
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TABLE 1. Individual results of 6nl
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TABLE 2. Combined results of NEnS b
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therefore be of interest to review
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wasp was found to parasitize the la
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In line with this thinking, immedia
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aIal 5 ." U) 0 a, U u C 0 4 w rlw r
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BIOLOGICAL CONTROL OF WILDLAND WEED
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15 species of introduced insects es
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HALEAKALA NATIONAL PARK CRATER DIST
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areas include the planthoppers (Del
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HAWAII IBP SYNTHESIS : 5. SHORT-TER
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We in the Forest Service are excite
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shrubby Dubautia and numerous hybri
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TABLE 1. Dubautia and Argyroxiphium
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SOME ASPECTS OF A SHELL DISEASE IN
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Induction of Lesions To induce lesi
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lesions. Or they may be part of the
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LITERATURE CITED Akin, D. E., and H
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TABLE 3. Isolation of chitinoclasti
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FOREST BIRD POPULATIONS ON O'AHU Ma
Page 61 and 62: LEK BEHAVIOR AND ECOLOGY OF TWO HOM
Page 63 and 64: either species) after an encounter
Page 65 and 66: HAWAII IBP SYNTHESIS : 3. THE KILAU
Page 67 and 68: RESULTS AND DISCUSSION Fifteen exot
Page 69 and 70: One exotic bird not found but previ
Page 71 and 72: TABLE 1. A list of the birds in the
Page 73 and 74: TABLE 2. Densities (birds/4O ha) of
Page 75 and 76: FIGURE 1. A map showing the locatio
Page 77 and 78: FIGURE 3. A map showinq native fore
Page 79 and 80: Several patterns in avian distribut
Page 81 and 82: LITERATURE CITED Eden, J. T. 1971.
Page 83 and 84: TABLE 1--Continued . Scientific Nam
Page 85 and 86: The objective of this paper is to a
Page 87 and 88: Selective field hybridizations yiel
Page 89 and 90: Corn, C. A. 1979. Variation in Hawa
Page 91 and 92: POLY MORPHA ---- NO SEED - SEED PRO
Page 93 and 94: THE RARE AND THREATENED PLANTS IN T
Page 95 and 96: open ideas for consideration and to
Page 97 and 98: Presence-absence trait analysis fur
Page 99 and 100: small clearings of soil-humus depos
Page 101 and 102: LITERATURE CITED Barrau, J. 1961. S
Page 103 and 104: WIDTH OF LARGEST WALL (cm) TOTAL AR
Page 105 and 106: ESTABLISHMENT OF SOME RECENT IMMIGR
Page 107 and 108: An egg parasite*, Trissolcus sp., w
Page 109 and 110: caterpillars were found on young nu
Page 111: 'IRBLE 1. Sunnnq of sm recent imniq
Page 115 and 116: Dombois 1977). Of course the trees
Page 117 and 118: We see from the two figures that in
Page 119 and 120: Ole HEALTHY, h FIGURE 1. Probabilit
Page 121 and 122: EVALUATION OF A NEW TECHNIQUE FOR H
Page 123 and 124: in the vial cap and was immersed in
Page 125 and 126: usually requiring only a few minute
Page 127 and 128: FACTORS CONTROLLING THE DISTRIBUTIO
Page 129 and 130: With respect to the distribution of
Page 131 and 132: native rain forest. However, the se
Page 133 and 134: mites are parasitic forms which hav
Page 135 and 136: LITERATURE CITED Atyeo, W. T., and
Page 137 and 138: TABLE 2. Feather mites recovered £
Page 140 and 141: Hirstionyssidae Rhinonyssidae (Rode
Page 142 and 143: STUDY SITE The ahupua'a of Manuka,
Page 144 and 145: DISCUSSION The trend of increasing
Page 146 and 147: litter habitats at lower and higher
Page 148 and 149: plant species diversity. The more d
Page 150 and 151: vegetational situation, and habitat
Page 152 and 153: TABLE 1. mmber of families encounte
Page 154 and 155: KEY: Nmhr of families colleded fran
Page 157 and 158: HALEAKALA NATIONAL PARK CRATER DIST
Page 159 and 160: Isopterygium Plagiothecium cavifoli
Page 161 and 162: TABLE 1. Phytogeographic relationsh
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In Hawai'i rain water percolates ra
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Most continental troglobites are co
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(5) Caves are fragile ecosystems an
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the current onslaught. It is true t
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Maciolek, J. A., and R. E. Brock. 1
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In the fallowing paper, a quick sum
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have been identified which include,
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LLTERATURE CITED Htmda, N., and J.
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TABLE 2. Cmpnents for the tree laye
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TABLE 4. Example of a vegetation ty
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ETGLTRE 2. Location of the U. S. Fi
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The sweet potato is unique in that
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tempting to suggest that the introd
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LITERATURE CITED Brand, D. D. 1971.
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DEDICATION ADDRESS FOR HAWAII FIELD
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I want to say that I strongly disag
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We will see how far these ideas get
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While the $28,000 would not even bu
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By no means, however, do I imply th
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Due primarily to lack of personnel
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National Park Service. 1969. Dark-r
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HAWAII IBP SYNTHESIS : 7. IMPACT OF
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Management Techniques The first clu
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!IWLE 1. Summary of production at 6
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PART A: Shipnan Strain Geese (14 Ge
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WLE 4. Gn5 restoration project reco
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HUMAN PERCEPTION OF THE HAWAIIAN EN
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public opinion concerning the issue
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(Question) Variables No Bsponse TAB
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(Question) Variables 10 11 12 13 14
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This is a survey to find out how th
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THE SEPTEMBER 1977 ERUPTION OF KILA
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General Conclusions 1. Zonal (or co
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- )RIGIN - TeC - TeL - TrP - 11.000
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A SOIL FUNGUS SET I B C ZONES SET2
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The high tree species diversity of
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It is probable that ecological gene
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THE ROLE OF THE HAWAIIAN TWO-LINED
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HABITAT UTILIZATION AND NICHE COMPO
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Hawaii Field Research Center. The p
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It is understandable that there is
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To accomplish the objectives of the
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FIGURE 1. Map of the island of Hawa
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METHODS Old mamane seed pods were c
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Seedling survival Seedling survival
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TABLE 1. Comparisons of percent see
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254 Figure 2--Cumulative number of
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COMMUNICATIONS TECHNIQUES AND THE S
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In a ten-minute paper like today's,
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ut are now growing in a normal upri
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Table 1--Grafting trials of Acacia
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Table 3--Treatments applied to Acac
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Table 5--Clonal variation in rootin
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with the major distribution being i
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as size classes (height and diamete
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there were more available microhabi
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CONCLUSIONS The Devastation Study A
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TABLE 1. Habitat 5. Structure and v
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VBLC 3. Witat 5. Wantitative charac
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HABITAT PROFILE - NOS. 1.2,4,5,6 OF
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HALEAKALA NATIONAL PARKCRATER DISTR
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LITERATURE CITED Bryan, W. A. 1915.
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climates experience alternating per
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correlated with the amount and phys
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HALEAKALA NATIONAL PARK CRATER DIST
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LITERATURE CITED Degener, 0. 1930.
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TABLE 2. Potentially aggressive wee
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- Rubus rosaefolius Sn. 2 !l%e thim
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Land availability is necessary to a
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Conf irmatlon of existing informati
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A NECROPSY PROCEDURE FOR SAMPLING D
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Division, P. 0. Bos 243, Cockeysvil
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Instructions RESULTS The following
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I. External Analysis (Examine bird
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PART I1 (1) Face, legs, or feet: le
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(14) Feather, follicle, or skin par
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Examine a wet smear of intestinal c
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SUMMARY More work needs to be done
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TABLE 1. Summary of diseases in avi
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TABIE l--Continued '. Disease Patho
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TABLE 1--Continued '. Disease Patho
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' Information not our own is £ran
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the bare-root system have failed. K
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Results of the efforts on the first
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Areas for these vegetation communit
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FIGURE 1. Courses of the topographi
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2500 mm ---+ MEAN ANNUAL PRECIPITAT
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FOREST BIRD POPULATION VARIATION AS
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SPP . r Pelea sp., and Vaccinium ca
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PREHISTORIC HAWAIIAN BIRDS * Alan C
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List of Participants (Continued) De
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List of Participants (Continued) Ca
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June 1 - 3 , 1978 - University of Hawaii at Manoa

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