Behavioural Processes, 3 (1978) @ Elsevier Scientific Publishing

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COMPARATIVE ETHOMETRICS: CONGRUENCE OF DIFFERENT MULTIVARIATE ANALYSES APPLIED TO THE SAME ETHOLOGICAL DATA

WAYNE

P. ASPEY

and JAMES

E. BLANKENSHIP

Division of Comparative Neurobiology and Behavior, The Marine Biomedical Institute and Department of Physiology and Biophysics, The University of Texas Medical Branch, Galveston, Texas 77550 (U.S.A.) (Received

7 June

1977;

revised 21 November

1977)

ABSTRACT Aspey, W.P. and Blankenship, J.E., 1978. Comparative ethometrics: congruence of different multivariate analyses applied to the same ethological data. Behav. Processes, 3: 173-195. Five statistically appropriate multivariate analyses were applied to the same data on burrowing in the sea hare Aplysia brasiliano to: (1) identify homogeneous subject-related subgroups within a heterogeneous sample, and (2) compare the extent of congruency among the analyses in terms of the number of extracted subgroups and each subject’s placement within the subgroups. Raw scores from 32 subjects on ten burrowing parameters were origin-corrected, standardized to z-scores, and normalized in order to facilitate comparisons among the analyses. One to five identified subgroups were extracted which indicated sensitivity differences to sampling variability among the methods. These results suggested that selecting a biologically interpretable analysis represents the subjective aspect of quantitative data treatment. Q-factor analysis (three subgroups) and linear typal analysis (four subgroups) yielded the most biologically interpretable subgroups for these data. Multidimensional scaling (one group) and principal-components analysis (two subgroups) tended to “lump” subjects, while simple distance-function cluster analysis (five subgroups) tended to “split” subjects into additional groups. As a diagonistic tool, multivariate analyses provide insight into underlying dimensions of individual variation and help generate testable hypotheses for guiding future research.

INTRODUCTION

Ethometry is the application of analytically descriptive and inferential statistics to ethological data, as demonstrated by Brothers and Michener (1974), Aspey and Blankenship (1976 a), and Aspey (1977 a and b), and is not just the quantitative measurement of behavioural responses (Block and Bell, 1974). Whereas experimentally-oriented behavioural research focuses on a single dependent variable and attempts to gain precision by holding extrinsic sources of variation constant, ethological data tend to be multidimensional, widely variable, scaled in arbitrary units, and frequently include interacting variables.

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Thus, control over important sources of variation is often impossible, especially when: (1) animals selected for observation are sampled from a population composed of several distinct subpopulations (e.g., dominant and subordinate animals), and (2) numerous behavioural measurements are recorded for each subject (e.g., frequency of behaviours exhibited during agonistic interactions). When observations are made on numerous variables, certain modal patterns recur frequently and the assumption is inferred that these patterns represent homogeneous subgroups. Since understanding relationships among numerous variables requires treatment more comprehensive than afforded by traditional parametric and/or nonparametric statistics, multivariate statistics provide potentially useful alternatives (Morrison, 196’7; Cooley and Lohnes, 1971; Overall and Klett, 1972; Atchley and Bryant, 1975 a and b; Bishop et al., 1975). Typically, such empirical classification typologies are derived from internal relationships among the subjects without reference to any pre-existing classification system. Thus, for the organization, analysis, and interpretation of complex data, multivariate techniques minimize the number of variables by classifying individuals and/or examining similarities and differences among them in terms of multiple measurements. Additionally, multivariate analyses allow the visualization of numerous variables simultaneously through numeric, geometric, and graphic expression (Rohlf, 1968). Multivariate analyses have been widely used in ecology (Cassie and Michael, 1968; Cassie, 1969; James, 1971), systematic zoology (Rohlf and Sokal, 1958; Rohlf, 1968,1971; Leamy, 1975), and psychology (Thurstone, 1947; Royce et al., 1973; Ekehammar et al., 1975), but their application to animal behaviour is relatively novel (Dudzinski and Norris, 1970; Morgan et al., 1975). Although Wiepkema (1961) introduced factor analysis to ethology, animal behaviourists have only recently begun to apply multivariate techniques. To illustrate, studies demonstrating the power of multivariate analysis for establishing homogeneous subgroups from naturallysampled heterogeneous populations, and for identifying relationships among the extracted subgroups include: the behavioural genetics of human twins (Eaves, 1972), social signals in squirrel monkeys (Maurus and Pruscha, 1973), marmot social organization (Svendsen and Armitage, 1973), bee colony interactions (Brothers and Michener, 1974), canid behavioural taxonomy (Bekoff et al., 1975), newt sexual behaviour (Halliday, 1976), territorial aggression in sticklebacks (Huntingford, 1976 a and b), cat neuroethology (Schwartz et al., 1976), wolf spider sociobiology (Aspey, 1977 a and b), and fiddler crab behaviourd ecology (Aspey, 19’77 c). As in other analytical efforts, a diversity of approach is desirable to produce the most complete understanding of a system’s dynamics. To this extent we compared the congruence, in terms of the number of extracted subgroups and their biological interpretability, of five different multivariate techniques when applied to the same data. The ethological data on burrowing in the sea hare Aplysiu brasiliana (Aspey and Blankenship, 1976 a and b) served as the refer-

175

ence data matrix on which the following multivariate statistics were applied: (1) multidimensional scaling; (2) principal-components analysis; (3) Q-type orthogonal powered-vector factor analysis; (4) linear typal analysis; and (5) simple distance-function cluster analysis. Our results indicate that selecting the most biologically/psychologically interpretable analysis comprises a qualitative aspect of treating data quantitatively. Furthermore, since both scientist and layman are accustomed to thinking in terms of classification concepts, efforts to use multivariate analysis as a diagnostic tool should: (1) result in meaningful data reduction; (2) provide insight into underlying dimensions of individual variation; (3) suggest the most biologically/psychologically interpretable analyses; and (4) provide a framework for hypothesis-seeking and guiding future research when the underlying biological basis of individual variation was unknown initially. A preliminary report of these findings has been published in abstract form (Aspey and Blankenship, 1976 c). METHODS

Subjects and apparatus

The subjects were 32 sea hares (Aplysia brasiEiana Rang), hermaphroditic marine gastropod molluscs, collected during the late summer along the southern coast of Texas in the Gulf of Mexico at Port Isabel, Texas. The animals were maintained in 950 litre circular, sand-filled holding tanks with recirculating artificial sea water (HW Marinemix sea salts, Hawaiian Marine Imports, Inc., Houston, Texas) maintained at 22°C 30°/oo salinity, filtered through charcoal, aerated, and buffered with crushed oyster-shell gravel. All animals were exposed to a 12-h light/dark cycle and fed daily with approximately 1 g of dried laver (Porphyra) seaweed (Vega Trading Co., Inc., New York). Three different aquaria maintained at the same temperature, salinity, and water conditions as the holding tanks were used during data collection. Further details concerning these aquaria are discussed in Aspey and Blankenship (1976 a). Data acquisition and transformations

Scores from ten parameters descriptive of burrowing, operationally defined in Aspey and Blankenship (1976 a), were recorded during 76 bouts of burrowing over 3 months in which each subject was observed at least 6 to 7 h in one of the testing chambers. Additional details on experimental procedures are provided in Aspey and Blankenship (1976 a). Since the scaling or measurement of ethological data is frequently arbitrary, various data transformations were used to eliminate such arbitrary and/or disparate units of measurement. Table I shows that the data of this study, for example, were “mixed” in that quantification of the burrowing parameters ranged from. direct measurements in different units (e.g., Weight in grams, Latency in minutes, Time Burrowed in days) to scales of varying

1 2 3 4 5 6 7 8 9 10 11 12 13 14 16 16 17 18 19 20 21 22 23 24 26 26 27 28 29 30 31 32

Subjects

15 73 28 101 93 86 110 76 78 80 66 120 68 74 88 76 63 52 89 107 193 180 117 64 208 156 133 247 222 59 168 98

(g)

Weight

2.60 3.75 5.92 3.50 7.96 2.63 1.73 2.85 5.70 7.35 1.02 8.60 7.23 2.38 3.98 5.67 6.60 6.92 3.06 4.88 10.20 4.68 4.42 2.28 14.60 16.67 17.26 19.17 28.87 15.60 25.53 20.00

Latency (min)

6.70 6.63 10.23 3.73 5.42 6.30 6.00 4.98 4.70 5.25 3.17 9.83 12.50 7.25 6.50 6.18 9.70 9.47 4.60 6.73 8.22 3.08 7.83 6.55 15.27 25.03 27.17 31.08 33.23 26.22 29.48 24.33

Burrowing time‘ (min) 1.33 1.00 1.67 2.00 0.67 0.33 2.00 2.33 2.00 1.00 3.00 2.67 3.33 0.67 2.00 3.67 4.00 1.00 0.33 0.17 0.67 0.04 0.33 0.33 3.33 5.83 7.33 10.67 15.33 14.00 5.30 6.00

(days)

Time burrowed

1

6 6 5 5 6 6 6 5 5 6 6 1

1 1

1 3 4 4 4 4 3 2 4 4 3 5 3 6 3 6 5 3 3

4 2 4 4 4 2 4 4 4 4

4

5

Direction (1;s)

bmsiliana

6 6

Coverage (l-6)

Burrowing parameters and unite of quentiflcation

Raw score data matrix on ten burrowing parameten from 32 Aplysia

TABLE I

3 4 4 3

1 2 2 3

3 3 2 2 1 2 1 1 1 1 1 1 1 2 1 1

4 4 4 2 2 4 4 1 1 1 1 3 1 2 1 1

4 4 4

5 3 5

2 2 3

4 2 4 4

0 0 0 0 0 1 0 1 0 3 0 0 3 0

2 3

1 6 5 3

2 3 3 1

4 4 4 4

5 6 2 6 6

(O-6)

Emergence

2 3 3 3 2

(l-3)

Inking

4 4 4 4 3

(l-4)

Vigor

2

2 2 1

1

3 3 3 3 2 2 2 3 3 3 2 3

(l-3)

Condition

177

intervals (e.g., 1 to 3 for Inking, 0 to 6 for Emergence). However, since different methods of transforming data can influence the number of subgroups that emerge, the raw data of this study were cast into a matrix of ten columns (burrowing parameters) and 32 rows (subjects) (see Table I), and transformed in the same way for all analyses. In this way, comparisons among the different analyses were facilitated while accommodating any statistical requirement(s) of a particular analysis. Although some investigators prefer raw scores for generating vector-product matrices for multivariate analyses (Nunnally, 1962; Tucker, 1968), transformed data are sometimes more practical in ethology since interest frequently lies in studying individual differences (Gollob, 1968). Common transformations of raw data include: (1) ranked scores; (2) standardized z-scores; (3) origin-corrected means; and (4) normalized data. Ranking is the transformation of choice for scaled interval data when the scale is five to seven (or more) units and a uniform range exists across behavioural variables (e.g., all variables scaled one to six). Whereas neither raw nor ranked scores are appropriate for the mixed data of this study, z-scores, origin-corrected, and normalized data are useful when subject and/or behaviour parameter variation is large (see Table I). For this study: (1) the data were standardized to z-scores across individuals; (2) behavioural profiles for each subject were corrected to zero mean; (3) a constant h was added (k = 0.5623) to obtain a better origin correction; and (4) the resulting transformed scores were normalized. The rationale and advantage for each of these points are discussed below; mechanical procedures and their theoretical bases are presented in Overall and Klett (1972). Data transformed to z-scores across individuals eliminate arbitrary and disparate units of measurements and allow more meaningful comparisons among variously scaled data. Since the zero-points for such measurement scales are frequently arbitrary, specific row and column effects must be removed in order to demonstrate meaningful pattern differences (Gollob, 1968). Thus, correcting all variables within each subject’s profile to zero mean is equivalent to subtracting a constant from all profiles (Overall and Klett, 1972). Although which corrections to use depend partially on the type of measurement, origin-corrected data help avoid cases: (1) where there results one less than the number of homogeneous subgroups actually represented in the data; or (2) where one large general factor (subgroup) emerges. Additionally, in those cases where data are transformed to z-scores as well as origincorrected, Overall and Klett (1972) recommend that a constant (k) be added to provide for an origin that maximally accounts for individual differences. Finally, the transformed scores are then normalized so that the sum of squares across all variables equals unity in the principal diagonal of the variance-covariance matrix. This transformation accounts for individual differences and not just statistical variance due to diverse units of measurements among the variables (e.g., grams, seconds, minutes, days). The Q-type matrix (i.e., where the extracted homogeneous subgroups are subject-related

178

rather than behaviour-related) obtained from these transformations was then analyzed by the multivariate statistical techniques discussed below. MULTIVARIATE

STATISTICAL

TECHNIQUES

The five multivariate statistics used to analyze the data matrix are empirical methods for deriving homogeneous groupings of individuals from multiple measurements without regard for any previously existing classification scheme. All computer programs were written in FORTRAN IV for IBM 1130/1800 digital computers with disk storage. Computation was performed at the Psychometric Laboratory of The University of Texas Medical Branch at Galveston. A computer program for the multidimensional scaling is given in Overall and Free (1972), while programs for the remaining analyses are found in Overall and Klett (1972). Data transformations were user-selected options or subroutines within each program. Multidimensional

scaiing

Multidimensional scaling involves the representation of similarities and differences among subjects or concepts in terms of distances along coordinate axes. Data to which multidimensional scaling are applicable range from subjectively judged similarities and differences (e.g., “greater than” or “lesser than” comparisons) to calculations of similarity indices from measurement profiles (Overall and Free, 1972; Morgan et al., 1975). The multidimensional scaling program developed by Overall and Free (1972) was originally used for relating clinical symptom data to models of psychotherapeutic drug action established on pre-clinical test animals. This program has numerous applications since the method scales M objects (e.g., subjects) on the basis of relationships inherent in N, measurement variables (i.e., behavioural parameters). This method can be used when scale dimensions are defined to display maximally the differences among N, primary objects (behaviours) and NZ other objects when they are subsequently located in the resulting model. This program can also be used for ordinary multidimensional scaling in which neither objects nor variables are segregated into discrete subsets, as in the present study. Overall and Free’s (1972) multidimensional scaling is essentially a principalcomponents analysis that displays relationships among all objects or variables on the basis of a preliminary analysis of one subset. Consequently, the following discussion of principal-components analysis is also applicable to multidimensional scaling. Shepard et al. (1972) provide a comprehensive treatment for both the theory and application of multidimensional scaling. Additional information from an ethological perspective and sources of computer programs for multidimensional scaling are available in Morgan et al. (1975).

179

Principal-components analysis Principal-components analysis describes differences between individuals in a heterogeneous sample in terms of a relatively few composite variables (i.e., components) To this extent, principal-components analysis reduces multiple correlated variables to a smaller set of statistically independent linear combinations which characterize individual differences (Overall and Klett, 1972). The first principal component is that weighted combination maximally accounting for the total variation (i.e., individual difference) in the complete set of original variables. The second principal component is that weighted combination of the original multiple variables, which of all possible weighted combinations uncorrelated with the first, accounts for the greatest possible proportion of the remaining variance. In order to determine the number of principal components to consider, only extracted components with eigenvalues greater than or equal to 1.0 were retained for interpretation purposes. Although principal-components analysis makes no assumptions about the distribution of the variables, if several variables have disproportionately large variance the solution will be “pulled” in the direction of accounting for these variances. Thus, for principal-components analysis to account maximally for individual differences and not just statistical variance, the variance-covariance matrix should be transformed with unity in the diagonal, as was done in this study. Accounts of the theory and techniques of principal-components analysis are provided by Hope (1968), Child (1970), and Overall and Klett (1972). Research applications of principal-components analysis to animal behaviour include studies by Brothers and Michener (1974), Halliday (1976), and Huntingford (1976 a and b). Factor analysis Factor analysis aims to understand the structure among multiple variables by showing that a relatively few factors can account for a large proportion of the variance among the original variables. As with principal-components, only eigenvalues greater than or equal to 1.0 were retained for determining the number of factors (Guttman, 1954; Kaiser, 1960; Comrey, 1973). We used Q-type orthogonal powered-vector factor analysis as a strategy for reducing large correlated categorical data to a smaller number of uncorrelated variables (i.e., factors) in order to suggest some hypothesis concerning their underlying relationship. Q-factor analysis is the preferred approach for studying natural groupings among individuals (Rummel, 1970; Overall and Klett, 1972; Aspey, 1977 a), treating the subjects with their corresponding scores on various behavioural parameters as variables and extracting subject-related groups. In contrast, R-factor analysis extracts behaviour-related factors by factoring the behaviours as variables (Rummel, 1970; Aspey, 1977 a). Orthogonal factor analysis defines statistically uncorrelated factors. Factors

180

are considered orthogonal if the matrix of intercorrelations, or “cosines”, among the factors is an identity matrix (e.g., unity in the principal diagonal and zeroes in the off diagonals). Highly correlated factors (e.g., 0.7 or greater) should be collapsed into a single common factor for interpretation purposes (Overall and Klett, 1972). The powered-vector method of factor analysis (Overall and Porterfield, 1962; Overall, 1968) yields an orthogonal “cluster-oriented” solution in which each factor represents a distinct, homogeneous subset of variables (or subjects when using Q-factor analysis). The first factor correlates with those variables intercorrelating highly, thus forming a distinct subset relatively independent of other such subsets. The second powered-vector factor correlates with variables in a second distinct cluster orthogonal to the first factor. Additional factors are extracted until no further homogeneous subsets result. The orthogonal powered-vector method of factor analysis tends to position factors meaningfully without Kaiser’s (1958, 1959) Varimax rotation, a procedure almost always required to establish meaningful relations between factors and the original variables following principal-axis factor analysis (Overall and Klett, 1972). Although factors extracted by the principal-axis method are statistically orthogonal and account for the maximum possible variance with the fewest factors, they tend to be complex and difficult to interpret. By contrast, the powered-vector method places less emphasis on parsimony (i.e., maximum variance accounted for by a few factors) and more emphasis on biologically/psychologically meaningful factor definition. Formally, principal-components analysis and principal axis factor analysis are identical when both are applied to Pearson product-moment correlation matrices with unity in the diagonal, and differ only in vector scaling and interpretation. Theoretically, however, the emphasis of principal-components analysis and factor analysis are different. For example, whereas the primary focus of factor analysis is understanding structural relationships among multiple variables, the main concern of principal-components analysis is on the definition of composite (factor-score) variates having certain optimal or desirable statistical properties (Overall and Klett, 1972). Textbook accounts of factor analysis are given in Harman (1967), Child (1970), Rummel (1970), and Comrey (1973), while applications of factor analysis to animal behaviour are provided in Wiepkema (1961), Baerends and Van der Cingel(1962), Svendsen and Armitage (1973), Royce et al. (1973), and Aspey (1977 a). Linear typal analysis

Linear typal analysis is used to study relationships among individuals and assumes that a relatively few basic “pure-types” underlie any heterogeneous group of subjects. Linear typal analysis aims to discover the nature and number of underlying pure-types, and to determine the similarity of each individual to the hypothetical pure-types. Mechanically, linear typal analysis is similar to factor analysis except for minor scaling differences and the fact

181

that each subject is simply assigned to a particular pure-type with no factor loadings used. Overall and Klett (1972) provide a comprehensive treatment of linear typal analysis, while Aspey and Blankenship (1976 a) applied linear typal analysis in conjunction with Q-type orthogonal powered-vector factor analysis (hereafter referred to as “factor analysis”) to analyze burrowing in A. brusiliana. This study (Aspey and Blankenship, 1976 a) provides the reference data for comparing results obtained by multidimensional scaling, principal-components analysis, and simple distance-function cluster analysis in the present investigation. Cluster analysis Cluster analysis involves a systematic search to identify homogeneous clusters to which similar individuals are then added using agglomerative algorithms. Cluster analysis results in several mutually exclusive subgroups (clusters) within which individuals are relatively similar and between which individuals are relatively different. Matrices of simple distance-function coefficients (d2) provide the most frequent basis for cluster analysis, although vector-product matrices can also be used (Overall and Klett, 1972). The simplest and perhaps most generally useful index of multivariate similarity is the simple distance-function cluster analysis in which (d) is calculated as the sum of squares of differences between corresponding scores in two multivariate profiles. A cluster nucleus is first identified consisting of highly similar profiles; then other similar cluster profiles were added to the original nuclear cluster members. To calculate the matrix of distances for simple distance-function cluster analysis, scores on the original measurements were employed as Cartesian coordinates to locate each profile as a point (vector) in multidimensional space. Each original measurement variable is associated with a distinct orthogonal axis, and differences between two individuals’ scores are conceived of as differences in projections on the orthogonal reference axes. According to a generalization of the Pythagorean theorem, the square of the distance between two profiles in p-dimensional space equals the sum of squares of differences in projection on p-orthogonal coordinate axes. The interested reader is referred to Overall and Klett (1972) for a complete and detailed account of the theory of simple distance-function cluster analysis, as well as an outline of the basic steps in deriving and cluster-analyzing the d2 matrix. Cluster analysis methods are widely used in a variety of forms, often make fewer assumptions than other multivariate techniques, and are easier to understand. An additional advantage of cluster analysis is the diversity of data representations available, including numerical characterization with the d2 matrix, or visual representations using dendrograms, maximum spanning trees, and three-dimensional geometric models. Morgan et al. (1975) review four cluster analysis techniques as applied to ethological data, and recompute factor-analyzed data from Wiepkema (1961) and Baerends et al. (1970) using

182

cluster analysis. Research applications of cluster analysis in behavioural biology include investigations by Altmann (1968), Maurus and Pruscha (1973), and Schwartz et al. (1976). RESULTS

Table II and Fig. 1 summarize the wide divergence in the number of sub groups extracted (from one to five), and the extent of congruence among the different analyses with regard to subject placement. Considering only those analyses yielding more than one subgroup (multidimensional scaling simply ordered the subjects along a single continuum), Table II shows that only 47% (15/32) of the subjects were classed together in the same way; When factor analysis was deleted from consideration, still only 47% of the subjects were similarly grouped together by the remaining three analyses. However, as linear typal analysis, cluster analysis, and principal-components analysis were systematically deleted in turn one at a time, 53% (17/32), 66% (18/32), and 59% (19/32) of the subjects, respectively, were then classed the same (Table II). In comparing the congruence of subject placement between factor analysis and each of the remaining analyses, Table II indicates that factor analysis and principal-components analysis classed 66% (21/32) of subjects alike, factor analysis and cluster analysis classed 72% (23/32) alike, and factor analysis and linear typal analysis classed 91% (29/32) alike. We selected the factor analysis and linear typal analysis as the most congruent and biologically interpretable analyses (Aspey and Blankenship, 1976 a). In a subsequent study (Aspey and Blankenship, 1976 b), we demonstrated the utility of this resultant classification scheme for experimental research in animal behaviour. Our . results from the factor analysis and linear typal analysis are summarized below as a reference for comparing the other multivariate techniques in terms of: (1) the number of subgroups extracted; (2) subject placement within the identified subgroups; and (3) the biological interpretability and consequent utility of the subgroups for future research. TABLE II Comparisons

of the number of extracted

Number of extracted subgroup

Multivariate statistical techniques

2

Principal-components enelysis Q-type orthogonal factor analysis Linear typal anslysi Simple distance-function cluster analysis

3 4 5

subgroup

end subject classification

by different multivariate

analyses

Per cent of burrowing Aplysia bmsiliana (N = 32) classed together in the sane way by the indicated (X) analyses 47%

41%

53%

56%

X

X

X

X

X

X

X

X

X X

X X X

X X

X

59%

66%

72%

91%

X

X

X X

X X

183 Number of Groups and Multivariate Analyses

Original Subject Number

1

2

3

4

5

Multidimensional Scalino

PrincipalComponents Analysis

Orthogonal Factor Analysis

Linear Typal Analysis

Cluster Analysis

26 29 32 27 31 25 28 24 30 16 18 17 8 12 4 7 1 lb-l 15 2 3 11 14 5 23 19 21 6 13 20 22 9

cl I

4 4 4 4 3 4 4 5

Fig.1. A comparison of the number of extracted subgroups and subject placement within each subgroup when five different multivariate statistical analyses were applied to data on burrowing by 32 Aplysia brasiliana Congruence of subject placement within subgroups and across analyses is coded with reference to the Q-type orthogonal powered-vector factor analysis classification (stripes represent Factor I, stippling Factor II, and open area Factor III). Scores for the multidimensional scaling indicate placement by rank along a single dimension of burrowing; the checkerboard background indicates no direct congruence with the subgroups extracted by factor analysis. Scores for the principal-components analysis indicate significant positivity (+) or negativity (-) on either the first (1) or second (2) principal component. Scores for the factor analysis are factor loadings on that factor which best characterizes each subject. Scores for the linear typal analysis and cluster analysis identify each subject’s subgroup placement. Subjects comprising the fourth puretype extracted by linear typal analysis are indicated “4 *” . Subjects not classified by cluster analysis are indicated ‘I-“.

184

Factor analysis

Factor analysis yielded three factors which accounted for 80.2% of the total variance. All subjects within a factor correlate highly with the dimension represented by that factor, and each factor is relatively independent of the other two, each explaining a different source of variation. Although factor loadings on the three factors for each subject are presented in Aspey and Blankenship (1976 a), the factor loadings on that factor which best characterized each subject are summarized in Fig.1. Fig.2 graphically represents the three subject-related factors as distinct, homogeneous subsets of animals. Factor I (N = 9, larger striped circles) accounted for 36.7% of the variance and consisted of subjects having either the highest or lowest scores on all burrowing parameters, these animals being the heaviest, slowest, and least vigorous burrowers. Factor I was interpreted as “Inefficient Burrowers”, perhaps represehting old and/or unhealthy Aplysia.

Fig.2. Q-type orthogonal powered-vector factor analysis of 32 burrowing Aplysio brasiliana with the three extracted subgroups plotted in three-dimensional space. Factors I and II are plotted along the horizontal planes, while the vertical height of each subject’s projection corresponds to its loading on Factor III. The origin of the three axes falls in the center of the three-dimensional space, and labels along the edges facilitate plotting. Note, for example, that every animal has a high loading on the one factor that best characterized it, but near zero loadings on the remaining two factors. This figure modified after Fig.3 from Aspey and Blankenahip (1976 a) such that Factor I (larger striped circles) represents “Inefficient Burrowers”; Factor II (smaller stippled circles) “Efficient Burrowers”; and Factor III (triangles) “Intermediate Burrowers”.

185

This interpretation was strengthened by the observation that these subjects were dead within 10 days after the last observed bout of burrowing. Factor II (N = 15, smaller stippled circles) accounted for 24.6% of the variance and consisted of animals also characterized by extreme scores on all burrowing parameters, but in the direction opposite of Factor I. Subjects comprising this factor were the smallest, fastest, and most vigorous burrowers and were interpreted as “Efficient Burrowers”, perhaps representing young, reproductively active, and/or healthy Aplysia. This interpretation was strengthened by the observation that these animals were alive, swimming, and/or copulating 10 days after the last observed bout of burrowing. Factor III (N = 8, open triangles) accounted for 18.9% of the variance and consisted of animals exhibiting low scores on six of the ten burrowing parameters and medium scores on the remaining four. These subjects were medium-sized, active animals that burrowed rhythmically and rapidly, but remained burrowed less than 1 day. Although Factor III seemed to represent “Intermediate Burrowers”, these animals shared more characteristics with Efficient Burrowers, as illustrated spatially in Fig.2. These subjects may represent animals in transition from being Efficient Burrowers to those becoming Inefficient Burrowers since transitional states as a function of maturation and/or various physiological conditions (e.g., sex changes in Crepidula, Russell-Hunter, 1968) are common in molluscs. Linear typal analysis

Linear typal analysis classed the 32 subjects almost identically as the factor analysis with the exception of subjects Nos. 2, 5 and 14, which together formed “pure-type 4”. No biologically meaningful characterization was evident for this pure-type other than that the subjects seemed to represent one extreme of Factor II (Efficient Burrowers, refer to Fig.1). A matrix of cosines (Table III) constructed to determine the extent of independence among the four pure-types revealed that pure-types 2 and 4 were highly correlated (rS = 0.705). Therefore, these pure-types were consolidated for interpretation purposes since they were not orthogonal. Note that linear typal analysis simply assigns subjects to the extracted pure-types and does not provide a relative weighting for each subject within each subgroup (e.g., such as factor loadings in factor analysis, Fig.1). TABLE III Cosine matrix among four pure-types extracted by linear typal analysis Pure-types

1

2

3

1 2 3 4

1.000 -0.305 -0.038 -0.275

1.000 0.486 0.705

1.000 0.463

4

1.000

186

-

_. 00

$-0

-0

-a,

IA--

k.

-p1

0

-R -c;1 -0

N

187

Multidimensional

scaling

Multidimensional scaling ordered the subjects along a continuum expressed as vector scores from -1 to +1 and interpreted as a single dimension of “burrowing efficiency”. Although multidimensional scaling indicated a single group, Fig. 3 indicates a general correspondence between the subjects’ ordering by multidimensional scaling and the three factor analysis subgroups (hereafter termed FA I, FA II, and FA III). For example, subjects above the horizontal line and to the left of the origin near the -1 end of the continuum (striped circles) represented subjects comprising FA I (Inefficient Burrowers, subjects Nos. 29, 28, 26, 32, 25, 31, 27, 30). Consistent with expected results, Aplysia No. 29, with the lowest multidimensional scaling score (-1.000, rank 32 of 32), had the second highest factor loading (0.97) on FA I (also see Fig.1). Similarly, Aplysia No. 26 with the highest FA I loading (0.99) had nearly the lowest multidimensional scaling score (-0.766, rank 30 of 32). Only subject No. 24 from FA I was placed among FA II subjects by multidimensional scaling. Subjects above the horizontal line and to the right of the origin (except subject No. 12) near the +l end of the continuum (stippled circles) represented animals comprising FA II (Efficient Burrowers, subjects Nos. 1, 8,11, 2, 4, 7, 14, 10, 15, 18, 16, 3, 5, 17, 12). However, in spite of relative correspondence between subjectordering by multidimensional scaling and the three factor analysis subgroupings, inconsistencies were apparent. For example, subject No. 1 had the highest positive multidimensional scaling score (0.860, rank 1 of 32) but placed near the middle of FA II (factor loading of 0.71) instead of having the highest factor loading as expected (refer to Fig.1). Similarly, subject No. 16 with the highest FA II loading (0.91) should have had the highest multidimensional scaling score instead of 0.230 (rank 13 of 32). Finally, subjects below the horizontal line (triangles) corresponded to FA III (Intermediate Burrowers, subjects Nos. 21, 20, 22, 23, 13, 9, 19,6). Aplysia No. 23 with the highest factor loading (0.87) on FA III had a multidimensional scaling score of 0.10 (rank 21 of 32), placing it near the middle of the continuum, where expected, since FA III represented Intermediate Burrowers. Principal-components

analysis

Principal-components analysis identified only two subgroups (the two principal components are identified as +1 to -1 and +2 to -2 on Fig.1) that accounted for 71% of the total variance (Fig.4). The first principal component (striped area) accounted for 59% of the variance and generally corresponded to subjects comprising FA I (striped circles, except subject No. 24) and the second half of FA II (indicated by “-1” in Fig.1). The second principal component (stippled area) accounted for 12% of the variance and corresponded to subjects comprising the first half of FA II (indicated by “-2” in Fig.1) and FA III (indicated by “2” in Fig.1).

188

Although principal-components analysis failed to differentiate three subgroups in the same way factor analysis did, Fig.4 shows a relative grouping of FA III Aplysia (triangles) above the abscissa while the FA II animals (stippled circles) fall below the abscissa. Essentially, the two principal components of burrowing could also be interpreted along a dimension of “burrowing efficiency” with the first principal component representing Inefficient Burrowers (FA I and the second half of FA II), and the second principal component representing Efficient Burrowers (the first half of FA II and FA III). Cluster analysis

Cluster analysis identified five homogeneous clusters using simple distancefunctions (“d”, measures of dissimilarity) calculated from the d2 matrix (Table IV). The principal diagonal represents the within-cluster distance while the off diagonals represent between-cluster distances. Table IV shows homogeneous within-group clustering for all five clusters since the within-cluster distances averaged less than one-half the between-cluster distance for every cluster pair. Fig.5 represents Table IV and illustrates how within- and between-cluster distances are used to position and relate the clusters in a reduced geometric space. A satisfying cluster configuration is achieved when the mean betweencluster distances exceed the average within-cluster distances by 3 : 1 or 4 : 1 (Overall and Free, 1972). For these data, the mean within-cluster distance is 0.26, and only the between-cluster distances among the first four clusters exceed this value by three or four times. Although cluster 5 (N = 2, subjects Nos. 14 and 9) showed acceptable within-group homogeneity, this subgroup did not relate well to the other clusters geometrically (i.e., the distances between cluster 5 and t,he other four clusters were not greater than three or four times the mean within-cluster distance). Although Fig.1 suggests that clusters 1, 2 and 4 correspond to FA II, FA I, and FA III, respectively, several classification difficulties exist. For example, animals comprising cluster 3 (N = 5, subjects Nos. 30, 18, 17, 3, 13) and cluster 5 (N = 2, subjects Nos. 14 and 9) are dispersed unsystematically among the factor analysis subgroups (e.g., &‘AI has one subject from cluster 3; FA II has three animals from cluster 3 and one subject from cluster 5; and FA III has one subject each from clusters 3 and 5). Furthermore, the cluster analysis failed to classify subjects Nos. 12 and 24 within any of the five clusters. DISCUSSION

One aspect of behavioural research that arouses considerable uncertainty and apprehension is knowing which quantitative analysis to use. Faced with several statistically legitimate analyses, the researcher must select the one that yields the most biologically/psychologically meaningful interpretation. On the one hand. our study illustrates that such confusion is not entire-

189

Fig.4. Principal-components analysis of 32 burrowing Aplysia brasiliana showing two extracted subgroups. When compared to the factor analysis (see text), the first principal component (striped area) accounted for 59% of the variance and generally corresponded to FA I and the second half of FA II. The second principal component (stippled area) accounted for 12% of the variance and generally corresponded to the first half of FA II and FA III (triangles). Subjects represented by stars corresponded to pure-type 4 extracted by linear typal analysis (see text).

TABLE IV Within- and between-cluster cluster analysis Clusters

1

1

0.306

2

2

0.715

0.320

3

0.793

0.854

dZ distances

3

for five clusters extracted

4

5

0.339

4

0.762

0.819

0.913

0.288

5

0.401

0.699

0.599

0.472

0.069

by simple distance-function

190

Fig. 5. A three-dimensional geometric representation of Table IV showing five clusters extracted by simple distance-function cluster analysis from 32 burrowing Aplysia bmsiliana. Each cluster’s diameter corresponds to within-group distances (d), while distances between clusters correspond to between-group distances. Subjects comprising clusters 1, 2, and 4 generally corresponded to FA II, FA I, and FA III, respectively. Subjects comprising cluster 3 were dispersed among the three factor analysis groupings. Of the two animals comprising cluster 5, one each was from FA II and FA III. Although this figure was drawn from a scale model, some distortion of the actual within- and between-cluster distances is present due to the two-point perspective artistic representation of three-dimensions.

ly unwarrented given the wide divergence in the number of subgroups extracted by different analyses when applied to the same data. However, on the other hand, most differences in subject placement within the variety of extracted subgroups could be resolved with relatively consistent interpretations of “burrowing efficiency”. Several analyses together provide a powerful base for flexible and complete data interpretation. Furthermore, all analyses reinforced one another to some extent, while each added a subtly different perspective for suggesting possible underlying behavioural mechanisms. For example, if only the multidimensional scaling (Fig.3) results were available, conceptualizing burrowing along an efficiency continuum would probably result. However, gaining insight into the significance of the variability in any systematic way would probably be more difficult to achieve. With only the two principal component groups available (Fig.4), a likely interpretation might involve two genetically discrete groups. Such an interpretation is plausible given the wide genetic variability of mollucs; however, subsequent longitudinal data did not support this interpretation. The three factor analysis groups indicated that not only relatively distinct burrowing “types” existed, but also suggested that burrowing was a dynamic process. Multidimensional scaling and principal-components analysis

191

used in conjunction with one another would have likely led to a similar conclusion; however, the factor analysis grouping permitted this conclusion more parsimoniously. Linear typal analysis and factor analysis yielded nearly identical groupings, with pure-type 4 representing one extreme of FA II. Finally, although the cluster analysis extracted too many uninterpretable groups, this analysis was testimony to the wide variability inherent in the sample. Several advantages were gained by using multivariate analyses as diagnostic tools for data organization and hypothesis-seeking: (1) burrowing appeared to be a dynamic process which nevertheless allowed the identification of distinct subgroups; (2) testable hypotheses were generated concerning the source of variation underlying burrowing for these various subgroups (see Aspey and Blankenship, 1976 a); (3) insight was provided into the functional significance of burrowing for the different subgroups (see Aspey and Blankenship, 1976 a and b); and (4) the opportunity was afforded to perform experiments using the now-identified homogeneous animal subgroups (Aspey and Blankenship, 1976 b). To illustrate this last advantage specifically, Aspey and Blankenship (1976 b) discovered a pheromone synchronizing burrowing in Efficient Burrowers that would also induce burrowing in conspecifics having near-zero probabilities of spontaneous burrowing (e.g., large and/or older swimming Aplysia). Furthermore, burrowing seemed to be a two-process phenomenon in that: (1) a pheromone triggers the behaviour, and (2) an internal state maintains the behaviour. These findings suggested how the adaptive significance of burrowing might differ for Efficient and Inefficient Burrowers (see Aspey and Blankenship, 1976 a and b), while Intermeditae Burrowers provided the basis for hypothesizing a transitional, internal state by which Efficient Burrowers become Inefficient Burrowers. Specifically, Efficient Burrowers were probably young and/or healthy animals for whom burrowing represented an aestivation-type state or period of metabolic reorganization/maturation preparatory for subsequent bouts of reproductive activities (e.g., aggregating, copulation, egg-laying). Inefficient Burrowers were probably old and/or unhealthy animals for whom burrowing represented an energy-conserving response elicited by deteriorating health and/or lowered tolerance to adverse environmental conditions in which general physiological functioning is reduced. Finally, Intermediate Burrowers may represent animals in a transitional state of going from being Efficient Burrowers to becoming Inefficient Burrowers. A variety of transitional states are common among molluscs, and in this case such states may be due to maturation and/or health-linked processes. The identification of the three homogeneous subgroups of Aplysia now allow hypotheses to be formulated and empirically tested. The use of a variety of different analyses also revealed subjects that were consistently troublesome to classify. For example, subjects Nos. 12 and 24 were: (1) not included in any of the five cluster analysis groups; (2) inconsistently classified by principle-components analysis relative to the other

192

analyses; and (3) placed near the middle of the subjects’ ordering by multidimensional scaling. Subject No. 24’s scores were more similar to those of Efficient Burrowers on Weight, Latency, Burrowing Time, and Time Burrowed, but more similar to those of Inefficient Burrowers on the other burrowing parameters. Subject No. 12’s scores were representative of Efficient Burrowers (except for Weight and Latency), and the reason for difficulty in classifying this subject is less obvious. Regarding the problem of stability and replicability, divergence among the five analyses may be attributed partially to the “mixed” nature of the data, but the subsequent data transformations should compensate for this problem. Since different transformations on the same data within a given analysis can influence the number of resulting subgroups (Overall and Klett, 1972), using the same raw score transformations across the five analyses allowed interanalysis comparisons. Although all the multivariate analyses were statistically legitimate for the data, different empirical classification typologies for uncovering homogeneous subgroups from naturally-sampled heterogeneous groups unquestionably differed in sensitivity to sampling vagaries in the data. To this extent, our results suggest guidelines for selecting an appropriate analysis. Specifically, linear typal analysis and cluster analysis appear more sensitive to sampling variability relative to the other analyses and tend to “split” subjects into additional groups. Such analyses might be most useful with precise data measurement and minimal sampling variance. Overall and Klett (1972) have also suggested that cluster analysis methods seem especially sensitive to sampling variability because the starting point for each empirical group (i.e., cluster) depends on only a few profiles out of the total sample. Conversely, multidimensional scaling, principal-components analysis, and factor analysis take into account, to varying degrees, relationships among all subjects in the sample. As such, multidimensional scaling and principal-components analysis seem less sensitive to wide sampling variability and tend to “lump” subjects relative to the other analyses. For example, the first two principal components accounted for 71.0% of the variance while the first two factors accounted for only 61.3% of the variance (the third factor accounting for an additional 18.9%). Therefore, multidimensional scaling and principal-components analysis may be more appropriate or experimentally useful for qualitatively scaled data and/or when great heterogeneity of variance exists. As much thought and care should go into selecting an appropriate data analysis as goes into planning and executing the experiment. The researcher in animal behaviour should be aware of differences in sampling variability among analyses, and select those methods either minimally or maximally sensitive to relationships between pairs of individuals: (1) according to the type of data; (2) appropriate for the problem under consideration; and (3) yielding a reasonably biologically/psychologically meaningful interpretation.

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ACKNOWLEDGMENTS

We are grateful to Dr. Ned E. Strenth for collecting the animals used in this study; to Ms. Carol Hoecker and Ms. Nan Rothman for preparing the illustrations; to Drs. Patrick W. Colgan and B. Dennis Sustare for critically evaluating the manuscript; and to Professor John E. Overall for computer facilities, statistical programs, and helpful guidance and advice throughout all phases of the research. Portions of this work were presented by W.P.A. to the 1976 meeting of the Animal Behavior Society at the University of Colorado, Boulder, and in a symposium on “Quantitative Methods in Behavior” at the 1976 Midwestern Regional Meeting of The Animal Behavior Society, The University of Illinois at Chicago Circle, Chicago. This research was supported in part by NIH Grant NS 11255 and NIH Award NS 70613 to J.E.B.

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