Logical synthesis of environment of King Penguin, Aptenodytes patagonicus

Ecological Modelling, 56 (1991) 291-311 Elsevier Science Publishers B.V., Amsterdam

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Logical synthesis of environment of King Penguin,

Aptenodytes patagonicus B.S. Niven and D.E. Abel Division of Science and Technology, Griffith University, Nathan, Qld. 4111, Australia (Accepted 13 November 1990)

ABSTRACT Niven, B.S. and Abel, D.E., 1991. Logical synthesis of environment of King Penguin, Aptenodytes patagonicus. Ecol. Modelling, 56: 291-311. The environment of the King penguin, Aptenodytes patagonicus, is classified according to a mathematical definition of the animal environment. A semi-formalizedlogical 'sentence' is used to justify the inclusion of each object in the environment. The envirogram, a stylized diagram derived from the mathematical definition, shows each object in its logical place in the penguin's environment.

INTRODUCTION Research presently being carried out on formalized theory of ecology is aimed at developing new pure mathematics to act as a basis for an integrated science of ecology, including plant, animal and h u m a n ecology, Some of this research necessarily involves the construction of mathematical definitions of various ecological concepts. The environment definition is one of these. By a happy coincidence an early formulation of this definition was given to the biologists Andrewartha and Birch just in time for them to incorporate it into the updated version of their well-known 1954 book, i.e. their 1984 book The Ecological Web. More on the Distribution and Abundance of Animals, and to derive a useful diagram called an 'envirogram' from the definition (see below). Part of the formal requirements for such a branch of pure mathematics is the development of precise mathematical definitions of various ecological concepts (Niven, 1982, 1989). Precise definitions were strongly called for by Haskell (1940) who com0304-3800/91/$03.50

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plained of the prevalence in ecology papers of "non-orderable, operationally inconsistent categories" and wrote that " . . . i t is no more possible to make present ecological theory produce accurate predictions than to make a wild cherry tree produce fancy dessert cherries." A mathematical definition of an individual animal's environment was published in 1980, followed by a more elegant version in 1982. However, it became clear that the relatively high level of mathematical sophistication required in order to obtain a correct classification of objects in the environment militated against the wide use of the method given in these two papers, particularly its use by undergraduates. For this reason a new formulation aimed at teaching undergraduate zoology students was developed in 1987. In order to provide examples of the use of the method the new formulation was applied immediately to studying the environments of the freshwater sponge, Spongilla lacustris, the rat tapeworm, Hymenolepis diminuta, the common octopus, Octopus vulgaris, the cane toad, Bufo marinus and the chimpanzee, Pan troglodytes. The original (1980) formulation was checked against a wide range of animals, including the King penguin (Niven and Stewart, 1981). In the present paper this work is updated, using the 1987 formulation of the environment definition. THE KING PENGUIN EXAMPLE The King penguin, Aptenodytes patagonicus, is the second-largest of the penguins, second only to the Emperor penguin A. forsteri. The average weight of an adult King penguin is about 15 kg and it stands about 90 cm high. Complex agonistic behavioral patterns have been observed (Jouventin, 1982) but the Kings have been described by Pettingill (1975) as "gentle and sedate, rarely given to hurried or ungraceful movements". They are easily distinguished from other penguins by their vivid orange-yellow ear patches (Fullagar, 1970). "The Kings breed well to the north of Antarctica, on sub-antarctic and cold temperate islands, in a large circle from Tierra del Fuego through the Falklands, South Georgia, South Sandwich, Marion, Crozet, Kerguelen and Heard Islands and clear round to Macquarie Island. They occupy low, often marshy places near the shores, and there incubate a single egg.., male and female take turns incubating the egg and feeding the chick" (Simpson, 1976). The breeding site of Crozet Island lies at latitude 46 °S which gives some indication of a northern limit of their range. In more southerly latitudes they are replaced by the Emperor penguin. Regular vagrant Kings have been observed, since 1969, in Tasmania (Rounsevell, 1984). No nest is constructed. The eggs are laid almost any time from November to March. The

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time from one egg to the next for any given breeder is 14 to 16 months, so an early breeder one year could be a late breeder the next year but could not breed successfully in the third year. The net result is that there are on average two breeding cycles in three calendar years. The Kings do not commence breeding until they are several years old and inexperienced breeders have poor success, frequently abandoning their nesting sites. Adult Kings, unlike the Emperors, do not huddle to keep warm in winter, however, the chicks have been observed to huddle. For further details of the general biology of the Kings see Stonehouse (1975). At one time the Kings were hunted for their oil; since this has been stopped massive increases in population sizes have been reported. Rounseveil and Copson (1982) report an increase at Lusitania Bay, Macquarie Island, from 3400 birds in 1930 to 218 000 in 1980. There were, in 1980, at least 70 000 breeding pairs. Lewis Smith and Tallowin (1980) reported 22 000 breeding pairs on South Georgia. Adams (1987) estimated the traveling speed through water to be 3.4-10 k m h -1. There was no relationship with size. (See note 6 below for foraging range.) K o o y m a n (1975) estimated the traveling speed to be 7 - 1 0 k m h -1. Clark and Bemis (1979) reported details of the swimming abilities of Kings and other penguins. TH E E N V I R O N M E N T D E F I N I T I O N

In this article we use some standard symbols used in symbolic logic. They are: - The existential quantifier '3' so '3 fish' means " t h e r e is at least one fish, such t h a t . . . " The negation ' - ', meaning "it is not the case that," so ' - (3 fish)' means "it is not the case that there is at least one fish, such t h a t . . . " We also use the 'hard' conditional '1', meaning "given that". This is the symbol used by statisticians for conditional events and conditional probabilities (Feller, 1959). By 'penguin will eat fish Ipenguin can find fish' we mean " t h e penguin will eat a (particular) fish given that the penguin can find that same fish". There are three primitive (undefined) terms used in this paper. They are: (1) ' Offspring'. (2) The survival and reproduction primitive ' H ' , which is a number. (3) The directed interaction primitive '~' which ensures that the system is totally interactive. In the mathematical system the word 'animal' is also specifically used as a primitive term. In this paper we assume that readers will have no difficulty -

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in interpreting such words as 'penguin' 'squid', 'fish' etc. A h u m a n being, for the purposes of this paper, is treated as though it were simply another animal, so that the primitive term ' H ' applies (see note 12). The interpretations of the three primitive terms follow: (1) 'Offspring' is used as in ordinary English; its meaning is the usual semantic definition. (2) The survival-and-reproduction primitive Ht(a) is a positive real n u m b e r which is a non-decreasing function of: (a) the expectation of life of the individual animal ' a ' at birth or on entering its present stage of the life cycle, and (b) the probability that ' a ' will have offspring. (3) The directed interaction primitive ~txy means that an interaction occurs between the object ' x ' and the object ' y ' which evokes immediately in ' y ' some physical, physiological or behavioral response or a change of position and no other object (other than 'x') reduces or enhances this effect of ' x ' on ' y ' , i.e. ' x ' affects 'y' directly. The objects ' x ' and ' y ' must be elements of the universe of discourse; in particular they may be animals, including the animal 'a '. Judgement as to whether the response is significant is to be made by the ecologist. The second primitive term H will be familiar to students of A n d r e w a r t h a and Birch (1954). It is their "animal's chance to survive and multiply". In the mathematical definition H is important not only as a c o m p o n e n t but also because the provision of all possible variations of H, both of subject and object, results in a complete coverage of all possible objects in the environment, in terms of H. An object which is such that no change results in the H of the subject animal does not belong to the centrum (see below); it is not interacting directly with the subject animal. In this sense, the mathematical definition of an animal's environment is complete; when both centrum and web are taken into account no objects are left out. The universe of discourse referred to in (3) is the set of all substantive objects i.e. such things as animals, plants, quantities of soil, water, air, also quantities of energy. In particular quantities of thermal energy or kinetic energy such as wind or sound are all important energy objects in the environment of the King. The environment of an individual animal is defined to be a structured set of objects. There are two subsets called the 'direct' environment or 'centrum' and the 'indirect' environment or 'web'. Full details are given in Niven (1987). The words centrum and web were introduced into the literature by Andrewartha and Birch (1984) and have largely replaced the earlier terms used by Niven (1980); we shall use centrum and web in this article. The centrum consists of four subsets called resources, mates, predators and malentities. They contain objects which interact directly with the subject

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animal. Notes 1, 4, 9 and 3, respectively, give semi-formalized sentences derived from the mathematical definitions of the four subsets which justify the classification of those objects in the environment of a subject King penguin, adult, chick or egg. The web is a structured set of objects called modifiers. First-order modifiers modify objects in the centrum. Second-order modifiers modify objects which are first-order modifiers, third-order modifiers modify second order and so on. A connected set of modifiers is called a modifier chain. Since any one particular object may simultaneously occur in a subject penguin's environment in more than one logical position the mathematical definition yields a complex network. For further information on this point see Niven (1989) where a good example of complexity is given from a study of the three-spined stickleback, Gasterosteus aculeatus. Notice that the use of the conditional in all the semi-formalized sentences implies that objects classified as resources etc would be referred to in everyday-English as potential resources, potential mates, potential predators, potential malentities, or potential modifiers. That is to say, if we want to apply the environment definition to the observations as a particular location or time, we expect that not all of the elements of the relationships will apply; that some of the elements of the relationships will not occur. For example, although the sea lion is a potential modifier of the food resources of the King penguin a study done at say, South Georgia will not encounter an instance of this relationship simply because the sea lion does not occur in this area. Hence, the actual instances of relationships encountered in any one field study will always be a subset of the potential relationships shown in the full envirogram. This study presents a model (in the ordinary sense of a mathematical model) which applies the new mathematics being developed for ecology to the environment of the King penguin. This kind of study serves to sharpen ideas and clarify them via the process of abstraction. In this fashion we construct a 'macro-model', that is, a model from which other models (such as computer simulation models) can be engendered. It might form the basis for several different lower level models. In systems language we would say that this is a 'generic' model from which any number of 'instantiations' of specific models can be formed. Such generic models are not unusual and are widely used. Consider for example the relationship for insects between development rate and day-degrees. Now when modelling for a specific insect this relationship is instantiated by finding appropriate values to use for the coefficients in the relationship. Nevertheless the generic abstraction of the model can be (and is) discussed without necessarily referring to any specific insect. As such it allows us to generalize and understand the conceptual notion of development for all insects.

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THE ENVIROGRAM The mathematical definition of environment yields a complex network of objects which are directly or indirectly functionally related to the subject penguin. In the stylized diagram called an 'envirogram' which was introduced into the literature by Andrewartha and Birch (1984), the network is opened out and projected on to a flat surface. Results from field or laboratory work on m a n y animals of the same species are superimposed. The diagram displays the four subsets of the centrum in a vertical column. The subject animal is named on the extreme right, with arrows linking it to elements of the centrum. First-order modifiers are in a vertical column to the left of the centrum, followed by second-order modifiers left of first-order and so on. The modifier chains are shown by connecting the elements from the highest order modifier on the diagram through to the subject animal. Thus the diagram presents a useful and compact summary of information about the subject animal. The diagram by itself however, acts only as a guide to the classification of the base data found in the literature and the precise logical 'sentences' which abstract the relationships described in the literaKing

ENVIROGRAM FOR WEB

I

2

penguin

l

I

I

CENTRUM I RESOURCES

sea l i a r , ? subject

)[ f o o d ] 6 pengu i n t--~squ Jd 1 fish

Royal ( s u b j e c t ¢h i ck ) 8--~($ong)

adult

penguin s

)(parent) (sheathb i I I ) e

app.

2

) f o o d "s ~-~(regurg.

( p a r e n t ) 13

D(thermal

(parent) 1

) (squ i d) 1

sex~song

)adult

food) 0 e n e r g y } 13 ~J

udult penguin {chick) {{egg))

MATES app. sex 4

PREDRTORS virus

s t a t e 12

((wind}} ~

11

I e o p a r d sea I 10 ) Ieg i s I a t i on ) human 12 t h e r m a I e n e r g y 14-~ [ b o o t e r i a ]14 (parent} 9 ~ ( p e t r e I )9 human 6 ) ( (parent} }

I I A L E N T I T I ES )oi I 6 ) ( (therma I energy} }

Fig. 1. Envirograms for King penguin. The chick and egg envirograms have been superimposed on the adult envirogram. Objects in the chick envirogram are indicated by "(... }". Objects in the egg envirogram are indicated by "{(... }}". The complex network of the mathematical definition is opened out and projected on to a flat surface. The numbers refer to the notes in the text.

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ture. As such the diagram and the set of supporting notes form one document and must be read in conjunction. Unfortunately an envirogram does not easily display the complex cross-linkages implicit in the mathematical definition. Nevertheless it is a useful diagram and has been used here (Fig. 1) to display the environments of the adult King, chick and egg, distinguished by curly brackets for the chick and pairs of curly brackets for the egg. The numbers on the envirogram refer to the notes in the following section 'Analysis of the environment' in which semi-formalized sentences are given which justify the classification, also a brief description of the literature and references. Until recently all envirograms were drawn by hand. However, work by Abel et al. (1989) has provided computer software for drawing envirograms. The King penguin envirogram of this paper was drawn on a Macintosh computer with the aid of the new software. ANALYSIS OF THE E N V I R O N M E N T

In early work, in which the mathematical definition was used informally for the classification of objects in an animal's environment, it was found that mistakes in classification were commonly made, even by experienced logicians. It is largely for this reason that is now seems necessary to justify the classification with a semiformalized sentence for every kind of object which is considered. An analogous situation occurs in taxonomy; it is often necessary, when delimiting species, to provide precise measurements of anatomical features. Without this precision it is all too easy for even experienced biologists to make mistakes. There is, however, a further advantage to be gained from the effort to write down these semi-formalized sentences. Some situations appear so complex that at first sight it is difficult to know where to begin. This may be so particularly when dealing with the modifiers; without hard copy, second- and third-order modifiers, say, can easily be confused. In the following the numbers of the notes refer to the envirogram. The justification for classifying a squid as a resource in the environment of the King penguin is the following semi-formalized sentence: H(penguin) is increased and H(squid) is decreased [~ (squid)(penguin). The imprecise natural-language equivalent of the strict mathematical sentence (not given here) is: 'The survival or reproductive ability of the subject penguin at a particular time is greater than its survival or reproductive ability just before that particular time, also the survival or reproductive ability of a particular squid at that same instant of time is less than its survival or reproductive Note 1.

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ability just before that instant, given that at the same instant the squid has a significant effect on the penguin, evoking immediately a response in the physiological state of the penguin.' Notice that the time constraint, an important feature of the precise mathematical definition (Niven, 1987), is not given and is to be understood in the semi-formalized sentence. By diving for a squid the subject penguin acts as a first-order modifier in its own environment. The justification for this classification is: (3 squid)[(squid)Res(penguin) I ~(penguin)(penguin) & (squid)Res(penguin) I - ~(penguin)(penguin)]. The imprecise natural-language equivalent is: 'At some particular time there is at least one squid such that the squid is a resource of the subject penguin given that the penguin interacts significantly with itself by diving, thus causing a change in the penguin's position and it is not the case that that same squid is a resource of the penguin given that the subject penguin does not interact with itself to cause a change in position.' Notice that the important time constraint in the precise mathematical definition also applies here. The relation between squid and King penguin is well covered in the literature. Various species of squid are important items of diet. Croxall and Prince (1980) estimated that at South Georgia 90% of the diet by weight consisted of squid (for spp. see note 6). At Marion Island Adams and Klages (1987) reported that approximately 24% by numbers and 12% by wet mass were squid. In contrast Hindell (1987) at Macquarie Island found that the diet consisted largely of fish (see note 2). Measurements of their beaks suggest that the squid taken probably weigh about 150-200 g. Therefore, during one trip, some 50 to 90 squid need to be caught to sustain the adult and feed the chick. The method of capture is a pursuit dive (Croxall and Prince, 1980). Kooyman et al. (1982) measured diving depths, metabolism and food consumption for three adult King penguins. They found that the birds frequently dived to more than 100 m, but rarely deeper than 240 m. Only about 10% of dives resulted in prey capture. During 4 - 8 days at sea the number of dives recorded were 1217 (4 days), 488 (6 days) and 890 (8 days), for three birds. The most frequently logged depth was 5-50 m. The deepest dives, of more than 240 m, are considerably deeper than those recorded for any aquatic bird except the Emperor penguin, which dives to at least 265 m. Croxall and Prince (1983) write " . . . in work with Kooyman and D a v i d . . . we found that on four-to-eight-day feeding trips, King penguins rearing chicks each made 500 to 1200 dives. More than half the dives we observed exceeded 50 metres, and two reached 235 metres... Despite all this diving activity the -

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average daily energy cost of these trips was only about twice that of incubation - testimony to the superb hydrodynamic design of penguins." Note 2. The semi-formalized sentence justifying a fish as a resource of a subject penguin is: H(penguin) is increased and H(fish) is decreased 14 (fish)(penguin). See note 1 for the natural-language equivalent. Hindell (1987) found that the diet of King penguins on Macquarie Island consisted largely of myctophid lantern fish of species Electrona Carlsbergi and Krefftichthys anderssoni. Juvenile fish of both species were eaten from December to July, and adults in August and September. Cephalopods were relatively unimportant (see note 1 and note 6). Adams and Klages (1987), working at Marion Island found that the diet consisted of fish to the extent of 87% by wet mass, 75% by numbers. Three species of myctophid fish predominated: K. anderssoni, E. carlsbergi and Protomyctophum tenisoni (see note 6). Note 3. When formally classifying environment it is necessary, in order to avoid confusion, to refer to some substantive object described as a particular quantity of thermal energy, rather than referring in loose terms to 'the influence of temperature' on the subject animal. The justification for classifying some particular amount of thermal energy as a malentity in the environment of a subject egg is: H(egg) is decreased [4 (thermal energy)(egg). The imprecise natural-language equivalent is: 'The survival or reproductive ability of the subject egg at a particular time is less than its survival or reproductive ability just before that time, given that at that same instant the thermal energy has a significant effect on the egg, evoking immediately a response in the physiological state of the egg.' The parent is classified as a first-order modifier, since we may write: (3 thermal energy)[(thermal energy)Mal(egg) I - 4(parent)(egg) & (thermal energy)Mal(egg) ] 4(parent)(egg)]. Cold, gusty wind acts as a second-order modifier, since we may write: (3 parent)[(parent)Modl(egg)] - 4 (wind)(parent)& (parent)Modl(egg) 14 (wind)(parent)]. For the natural-language equivalent see note 1. The effect of the wind is to change the position of the parent. King penguins have no nest. The parent birds carry a single egg on their feet, taking it in turns (Simpson, 1976). Yeates (1975) remarks that penguins in general tend to avoid places where the winds are gusty and variable. -

-

Note 4. The justification for classifying an adult King penguin of opposite sex as a mate of a subject penguin is the semi-formalized sentence:

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An offspring of both individuals will be produced with probability greater than zero l~ (adult opp.sex)(subject penguin). The natural-language equivalent of the mathematical definition is: 'The probability is greater than zero that at a future specified time and offspring of both individuals will be born, given that an interaction occurs between the two individuals at the present instant of time which will evoke immediately a significant response in the physiology of the subject penguin.' The gestation time is thus built in to the mathematical definition. There is vocal dimorphism between the sexes and efficient recognition of the partner's call (Derenne et al., 1979). King penguins moult into adult plumage at the end of their second year but probably do not attain full sexual maturity for at least two more years. "The earliest breeders commence their prenuptial moult in mid-September, and lay their single egg in late November... A peculiarity of King penguins is that the mating season extends over nearly half the year, and so all kinds of breeding activities may be seen at the same time" (Budd, 1975). The following passage is from Croxall and Prince (1980): "At South Georgia Stonehouse (1960) found that the breeding King penguins usually follow a sequence of early breeding (laying in NovemberDecember, chick fledging following November), late breeding (laying February-April, chick fledging January-February) and non-breeding in three successive seasons, raising, at best, two chicks in this period. At Iles Crozet a somewhat similar situation prevails, although it appears that birds there may only breed successfully in alternate seasons (Barrat, 1976)". Detailed observations of 31 widely separated breeding sites on South Georgia are given by Lewis Smith and Tallowin (1979) who discuss rookery fluctuations in relation to the irregular 3-year breeding cycle. The total population was estimated to be 39 000 (including chicks). According to Jouventin (1982) mates "are faithful all through the reproductive cycle and know each other personally by their long songs. Solitary birds on the beach searching for a mate indicate their sex by short songs." Jouventin gives very full details of the King penguin song in his 1982 monograph (see also Derenne et al., 1979). Pairs avoid singing unless strictly necessary. Newly-formed pairs rarely sing. Mates can sing simultaneously within a short distance. Even well-acquainted partners do not recognize each other visually; the territory acts as a rendezvous area and singing serves as confirmation. The justification for classifying a song as a first-order modifier in the environment of subject female is: (3 male penguin)[(male penguin)Mat(subject female) l~ (song)(subject female) & (male penguin)Mat(subject female) I - ~ (song)(subject female)]. -

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The male penguin which produces the song, in this case, is a second-order modifier in the environment of the subject female: (3 song)[(song)Modl(subject female) It (male penguin)(subject female) & (song)Modl(subject female) I - ~ (male penguin)(subject female)]. For natural-language equivalents of these semi-formalized modifier sentences see note 1. -

The justification for classifying some other penguin species, say the Royal penguin, as a first-order modifier of some particular item of food, say a squid (i.e. by competing for the food item) is: (3 squid)[(squid)Res(penguin) ] - ~ (Royal penguin)(squid) & (squid)Res(penguin) ]~ (Royal penguin)(squid)]. See note 1 for a natural-language equivalent. Croxall (personal communication, 1984) writes that there is little likelihood of dietary competition with Gentoo and Macaroni penguins during summer; there is a slightly greater chance in winter. There is, however, some possibility that a particular Royal penguin (on Macquarie Island) might compete with a subject King penguin for some food object (Stonehouse, personal communication, 1982). We have therefore tentatively included a Royal penguin on the envirogram. Note 5.

-

Any item of food is classified as a resource. See note 1 and note 2 for a semi-formalized sentence. "Analysis of the highly digested stomach samples recovered from King penguins introduces a number of biases due to differential digestion rates of both hard and soft part remains... Chitinous squid beaks are also more resistant to digestion than the calcium carbonate of fish otoliths" (Adams and Klages, 1987). These biases may account for reports prior to 1987 that the King penguin's diet consisted mainly of squid. However in that year both Hindell and Adams and Klages (see note 2) reported a predominantly fish diet; the latter authors write".., fish account for more than 70% of the diet for a least 10 months of the year and nearly 100% of the diet from November-December to January-February". Adams and Klages' paper is particularly useful in supplying data in detail which is not always (but should be) available in other works. Their table (Table 1) has an excellent and detailed summary of prey items occurring in stomach samples taken from King Penguins an Marion Island. Stonehouse (1960) estimated that a meal size would be about 200 g (13% of adult weight). Croxall and Prince (1980), working at South Georgia, found that the chick-feeding frequency was about 5-6 days and that the foraging range was about 500 km at an average flight speed of 1.9 m s - 1 Adams (1987) estimated the foraging range at Marion Island to be from 75 Note 6.

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TABLE 1 Numbers and frequency of occurrence of prey items identified from King penguin stomach samples from Marion Island Prey Item Fish Myctophidae

Krefftichthys anderssoni Protomyctophum tenisoni Electrona carlsbergi Myctophid A

Protomvctophum normani Gymnoscopelus sp. (?bolini) Paralepis coregonoides Protomyctophum bolini Protomyctophum sp. Unidentified fish

Notothenia squamifrons N. rnagellanica

Numbers

% of total

Frequency of occurrence (%)

13 385 12 234

34.75 31.76

83.3 85.0

5 068 557 379 90 64 46 45 24 8 6

13.16 1.45 0.98 0.23 0.17 0.12 0.12 0.06 0.02 0.02

70.0 70.8 28.3 3.3 30.0 9.2 6.7 10.0 2.5 1.7

4 609 750 637 253 198 36 30 20 19 9 8 3 1

11.96 1.95 1.65 0.66 0.51 0.09 0.08 0.05 0.05 0.02 0.02 0.01 < 0.01

86.7 60.8 29.2 35.0 34.2 14.2 10.0 11.7 5.0 7.5 1.7 0.8 0.8

25 9 3 3 3

0.06 0.02 0.01 0.01 0.01

6.7 4.2 1.7 1.7 1.7

38 522

100.00

Squid

Kondakovia longimana Onychoteuthidae < 2 mm LRL Onychoteuthidae > 2 mm LRL Unidentified decapod squids < 1 mm LRL Unidentified decapod squids > 1 mm LRL Oegopsid A Histioteuthis sp. Alluroteuthis sp, Moroteuthis sp. Martialia hyadesi a

•Gonatus antareticus Galiteuthis glacialis Brachioteuthis sp. Crustaceans Amphipoda

Nauticarus marionis Euphausiacea Decapoda, Natantia Unidentified crustaceans Total

~ Martialia hyadesi has been much confused with Todorodes aff. sagittatus. However, our identification has been confirmed by G.J.B. Ross (personal communication) and tentatively confirmed by M.R. Clarke (in litt.) From Adams and Klages (1987).

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to 902 km for penguins returning between 2 and 24 days at sea. A d a m s noted that "chick-feeding frequency is more variable within individuals than between individuals and presumably reflects large variations in foraging distance due to changes in prey distribution from foraging trip to foraging trip." Kooyman et al. (1982) found that a metabolic rate for a 13-kg penguin tending a chick is 4.3 W kg -1. The average daily metabolic rate at sea was about 1.5 to 2 times that on the rookery. Adams (1984) estimated a utilization efficiency of a squid diet by the King penguin as 81.3%, using four non-breeding adults on a diet of Loligo

reynaudi. A badly-oiled King penguin was found by Copestake et al. (1983) on a beach on South Georgia and taken in for cleaning. During 3 weeks in captivity the bird became very tame and could be fed by hand. The opportunity was taken to conduct some simple experiments with krill and fish meals (squid being unavailable) and on the rate of weight loss during a short fast to obtain information on metabolic costs. On fish diets averaging 1400-1700 g d -1 weight loss between feeds was about 60 g h 1 and overall weight gains of 100-200 g d -a were recorded. During a 5-day fast, energy consumption calculated from weight loss was about 1500 kcal d -1. Croxall (1982) reviewed and discussed weight loss and energy consumption of fasting, non-moulting penguins and of moulting penguins and gives tables of comparative results from various authors. The oil is classified as a malentity and the human responsible for the oil slick as a first-order modifier since: H(penguin) is decreased 14 (oil)(penguin). (3 oil)[(oil)Mal(penguin) 14 (human)(oil) & (oil)Mal(penguin) I - 4 (human)(oil)]. -

Note 7. The justification for classifying a sea lion as a first-order modifier of an item of diet, say a squid, by acting as a competitor is: (3 squid)[(squid)Res(penguin) I - 4 (sea lion)(squid) & (squid)Res(penguin) 14 (sea lion)(squid)]. (Notice how the formalized sentence differs from that in note 1; formally speaking the subject penguin of note 1 acts as a positive first-order modifier in its own environment, whereas the sea lion is a negative first-order modifier). According to Spellerberg (1975) sea lions are not a major predator of penguins. However the diet of sea lions includes squid, fish and crustacea and they therefore enter the environment of a penguin as competitors, i.e. -

kcal d 1 according to Copestake et al. (1983).

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first-order modifiers. Croxall (personal communication, 1984) adds that " . . . m o s t marine vertebrates that co-occur with Kings eat squid, fish and crustaceans in some combination". The justification for classifying regurgitated food as a resource for a subject King penguin chick is: H(chick)is increased I~ (regurg. food)(chick). The parent, as a supplier of the regurgitated food, is a first-order modifier: (3 regurg, food)[(regurg, food)Res(chick) I~ (parent)(regurg. food) & - (regurg. food)Res(chick) I - ~ (parent)(regurg. food)]. The chick song is a second-order modifier and the chick itself, by producing the song, is a third-order modifier in its own environment: (3 parent)[(parent)Modl(chick) I ~ (song)(parent) & (parent)Modl(chick) I - ~ (song)(parent)]. Note 8.

-

(3 song)[(song)Mod2(chick) I ~ (chick)(song) & - (song)Mod2(chick) I - ~ (chick)(song)]. Sheathbills, by stealing regurgitated food just as it is about to be given to a chick (Spellerberg, 1975) act as first-order modifiers: (3 regurg, food)[(regurg, f o o d ) R e s ( c h i c k ) l - ~ (sheathbill)(regurg. food) & - ( r e g u r g . food)Res(chick) I ~ (sheathbill)(regurg. food)]. Kooyman et al. (1982) found that in February and 8-kg chick is fed about every 4 days and it gets about 3 kg of squid per visit. Adams (1987) noted that six adults feeding large chicks traveled from 52 to 107 km d -1, whereas three adults feeding small chicks traveled significantly shorter distances, 17 to 73 km d -1. The average feeding frequency for 15 chicks was from 3.2 to 5.1 d, during October-December 1984. Twenty eight adults feeding small chicks were away to sea for from 4 to 21 d. The adults spent less than 24 h ashore at the colony when returning to feed large chicks. Brood shifts were noted by Stonehouse (1960) to shorten progressively through the brooding period. "The vocal repertoire of penguin chicks is limited to one call, becoming higher-pitched and more variable when the chick is frightened" (Jouventin, 1982). The King penguin chick produces a frequency-modulated whistle lasting half a second at most, with dominant frequencies at about 2000 Hz. The frequency band extends over 1.5 kHz. A King penguin returning from the sea approaches its territory and utters its song, which attracts the correct chick. Frequent inter-parent or parent-chick duets form the basis of individual recognition. Details of experiments confirming these observations are given by Jouventin. He also gives sonagrams which show that an individual

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chick's song has only slight variations, whereas the variation among different chicks is obvious. In experiments with a recording of a chick's song it was shown that when the chick was in sight the recording was less effective; at a distance the parent tends to hesitate between the chick and the loud-speaker. Chicks of 3-4 months old can tolerate 4 - 6 months of fasting (Cherel et al., 1987; Le Ninan et al., 1988). See also note 4 and note 6.

Note 9. The justification for classifying a Giant petrel, Macronectes giganteus as a predator of a subject chick and the parent as a first-order modifier is: H(chick) is decreased and H(petrel) is increased I~ (petrel)(chick). (3 petrel)[(petrel)Pred(chick) I - 4 (parent)(petrel) & - (petrel)Pred(chick) 14 (parent)(petrel)]. The Giant petrel is probably the most important predator of King penguin chicks (Spellerberg, 1975). The petrels will attack and kill the chicks even though they do not eat the flesh of their catch but the contents of the stomach only. Weak or wounded chicks are taken more often than healthy chicks. Budd (1975) remarks that the petrels are not seen near the Kings in summer on Heard Island but they probably attack the chicks in the winter. Jouventin (1982) describes the attack posture of the parent; the penguin faces the enemy, wings raised ready to strike, neck and bill stretched out to nip.

Note 10. The Leopard seal (Hydrurga leptonyx) is classified as a predator, since we may write: H(penguin) is decreased and H(seal) is increased 14 (seal(penguin). Spellerberg (1975) believes that the Leopard seal is probably the most important marine predator of King penguins. Budd (1975) writes " T h e Leopard seal Hydrurga leptonyx, which is probably the main predator of the King penguin at sea, hauls out in large numbers on the beaches at Heard Island throughout the year. In winter more than 160 have been seen in a single day on the beach at Corinthian Bay (Brown, 1957) and in summer more than 50 may be seen lying together on the beach at Southwest Bay, the landing beach for the King penguin colony at Vahsel moraine". Note 11. The justification for placing viruses in the class 'predators' is: H(penguin) is decreased and H(virus) is increased ]4 (virus)(penguin). Virus infections of penguins on Macquarie Island have been studied by Morgan et al. (1978, 1981). As for other penguins, tests on the King penguin show no evidence of serum haemagglutination-inhibition antibody against influenza A virus or alphavirus. The species had antibody to PMV-IM

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paramyxovirus, also HI antibody to flaviviruses was detected but at low levels, suggesting that "either opportunity for flavivirus infection is low or that infection is often fatal and few infected birds survive". Morgan et al. (1981) suggest that the tick Ixodes uriae, which is widespread on Macquarie Island, may carry the virus, since this species of tick is commonly associated with penguins, however further information is needed on this point. For the moment it seems advisable to leave the modifier chain incomplete and record only that certain viruses are formally of the class 'predators'. Loupal (1984) found lymphoid leukosis in a captive King penguin, but gives no details of the virus. At one time King penguins were attacked by humans for their oil. A human is classified as a predator, the legislation to hinder that human is a first-order modifier and the state which enforces the legislation is a secondorder modifier: H(penguin) is decreased and H(human) is increased I~ (human)(penguin). Note 12.

(3 human)[(human)Pred(penguin) I - ~ (legislation)(human) & - (human)Pred(penguin) I~ (legislation)(human)] (3 legislation)[(legislation)Modl(penguin) [ ~ (state)(legislation) & (legislation)Modl(penguin) ] - ~ (state)(legislation)]. According to Conroy (1975) the numbers of penguins are increasing following the cessation of attacks by people. Rounsevell and Copson (1982) report a massive increase in King penguin population at Lusitania Bay, Macquarie Island, from 3400 birds in 1930 to 21 800 in 1980, at least 70000 breeding pairs. The 'legislation' to stop the killing should be interpreted as 'marks on paper' to be in accordance with the underlying universe of discourse of the mathematical system. -

Young chicks are provided with suitable quantities of thermal energy, a resource, by a parent, thus acting as a first-order modifier, since: H(chick) is increased I~ (thermal energy)(chick).

Note 13.

(3 thermal energy)[(thermal energy)Res(chick) I ~ (parent)(chick) & (thermal energy)Res(chick) I - ~ (parent)(chick)]. According to Barr6 (1978) during a period when the average air temperature was 16 °C the hatching temperature was 34.3 °C and the brooding temperature after 20 days was 39.2 ° C. -

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The classification of a set of bacteria as predators and thermal energy as a first-order modifier is put forward tentatively (see discussion below). The semi-formalized sentences, for one bacterium, are: H(penguin) is decreased and H(bacterium) is increased]~ (bacterium) (penguin). Note 14.

(3

b a c t e r i u m ) [ ( b a c t e r i u m ) P r e d ( p e n g u i n ) l - ~ (thermal energy)(bacterium) & (bacterium)Pred(penguin) L~ (thermal energy)(bacterium)]. " A n important aspect of the environment of penguins may be reflected in the virtual absence of an anti-bacterial enzyme ('lysozyme') in their eggwhite" [Manwell (personal communication); see also Baker and Manwell (1975)]. As a result of this there is a set of bacteria, represented by [bacteria] on the envirogram, which may possibly limit the home range of the King penguin. Nevertheless the picture is not at all clear. Thus Manwell and Baker (1973) concluded that ambient temperature is not a key factor when they found that the fairy penguin, which nests in warm places, is also deficient in lysozyme activity. "It remains for someone to attempt a thorough study of the entire suite of anti-bacterial egg-white proteins versus nesting habits and environmental bacterial levels" (Manwell and Baker, personal communication, 1989). -

DISCUSSION

In science classification is of fundamental importance. The precise classification of objects in an animal's environment which resulted from the work on formalized theory of animal ecology has advantages in addition to (or perhaps because of) the simplicity of the method. First, it is easy to justify the classification of objects, as has been done in this paper. Then again, ecologists are able to see immediately where their specialized observations and experiments fit into the overall research on the species. They can compare progress from one animal to another, for instance it is clear from such analyses that more is known about the cane toad or the chimpanzee than the King penguin (see Niven, 1987, 1988). The environment analysis makes it possible to combine reports from various sources, even different disciplines, in a standardized form which is then accessible to all. For example, in this study material is drawn from such diverse sources as field ecologists, ethologists, parasitologists and biochemists. Indeed, the precision of the classification and the methodology underlying the construction of the definition enables precise cross-cultural comparisons to be made and such a study, on the brachiopod Lingula, is presently

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being planned in connection with work on formalized theory of h u m a n ecology. The question arises as to the place of the food-web within the context of 'environment' as defined by Niven (1987, 1988). A food-web is limited to the relations 'food-resource' or 'predator' between two organisms. It excludes (a) other resources, such as nesting-sites, (b) modifiers of resources, (c) mates and modifiers of mates (for example, a chemical which induces sterility in a potential mate), (d) modifiers of predators, (e) malentities and the modifiers of malentities. The modifier chains of environment are the functional linkages of a community [see Niven (1989) for a definition of 'community'] and should not be disregarded. Consider, as an example, animal of species A, which eats animal B, which eats C which eats D which eats E. We immediately connect these in a food-web (or environment) analysis. However there are other ways in which A and E might be functionally connected; E might, say, modify the mates, predators or malentities of A. If it is a first-order modifier then there is a very much shorter 'ecological path' between A and E than the one passing through B, C and D. We might say that this is a 'shorter ecological distance' between the two species. Clearly, the environment analysis (or an envirogram) is a much richer and more complete representation of the set of relationships between the subject animal and other objects, whereas the food-web is a representation of a subset of these relationships. Thus while it is possible to derive a food-web from an analysis of environment it is not possible to derive the environment analysis (or an envirogram) from a food-web. We could construct other structured subsets of environment, using other relations, to arrive at an analogy of a food-web, a non-food resource and its modifiers, for instance; this would provide a web-like structure which may or may not be intuitively appealing or useful to an ecologist. In everyday practice the complex network of the mathematical definition would be difficult to deal with without the simplification introduced by the highly stylized 'envirogram' of Andrewartha and Birch (1984). F r o m the penguin envirogram of this paper a n u m b e r of points are immediately apparent: (a) There is a shortage of results on interactions with other animals, both those competing for resources and those classified as predators. In particular more work is needed on the parasites, viruses and bacteria attacking the penguin. (b) There needs to be more research on the mating habits of the King penguin. Such matters as what happens to a rejected suitor, or the situation when one parent fails to return to feed a chick, need more study. (c) The part of the envirogram dealing with malentities is particularly

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sparse. Penguins, like other animals, must surely be subject to numerous accidents. There is, however, a marked scarcity of such reports in the literature. ACKNOWLEDGEMENT

We have pleasure in acknowledging our debt to the two anonymous referees of the original version of this paper, who, by their pertinent questions and constructive suggestions and criticisms, by far the most scholarly ever seen by the authors, gave us a clear idea of the difficulties of biologists faced with the mathematical subtleties of the formalization project. We have, we hope, so enlarged the original introductory parts of the paper and the discussion that the arguments are now much clearer to a trained biologist. REFERENCES Abel, D.E., Bass, K.L., Chorvat, T.A., Gavranic, A.B., Howlett, R.J., Howe, E., Niven, B.S. and Zalucki, M.P., 1989. A computer program for producing envirograms. Bull Ecol. Soc. Aust., 19: 16-17. Adams, N.J., 1984. Utilization efficiency of a squid diet by adult King penguins (Aptenodytes patagonicus). Auk, 101: 884-886. Adams, N.J., 1987. Foraging range of King penguins Aptenodytes patagonicus during summer at Marion Island. J. Zool. London, 212: 475-482. Adams, N.J. and Klages, N.T., 1987. Seasonal variation in the diet of the King penguin (Aptenodytes patagonicus) at sub-Antarctic Marion Island. J. Zool. London, 212: 303-324. Andrewartha, H.G. and Birch, L.C., 1954. The Distribution and Abundance of Animals. Chicago University Press, Chicago, IL, 782 pp. Andrewartha, H.G. and Birch, L.C., 1984. The Ecological Web. More on the Distribution and Abundance of Animals. Chicago University Press, Chicago, IL, 506 pp. Baker, C.M.A. and Manwell, C., 1975. Penguin proteins: biochemical contributions to classification and natural history. In: B. Stonehouse (Editor), The Biology of Penguins. MacMillan, London, pp. 43-56. Barrat, A., 1976. Quelques aspects de la biologie et de l'~cologie du Manchot royal (Aptenodytes patagonica) de l'ile de la Possession, archipel Crozet. Com. Nat. Fr. Rrch. Antarct., 40: 9-52. Barrr, H., 1978. Energy metabolism of the King penguin chick during growth. J. Physiol. (Paris), 74: 555-562. Brown, K.G., 1957. The Leopard Seal at Heard Island, 1951-4. Aust. Nat. Anarct. Res. Exped. Interim Rep. 16, Antarctic Division, Department of External Affairs, Melbourne, Vic., 34 pp. Budd, G.M., 1975. The King Penguin, Aptenodytes patagonica at Heard Island. In: B. Stonehouse (Editor), The Biology of Penguins. MacMillan, London, pp. 337-352. Cherel, Y., Stahl, J. and Macho, Y.L., 1987. Ecology and physiology of fasting in King penguin chicks. Auk 104: 254-262.

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