6.1. Collaborative Index

Collaborative Index (CI) is the number of authors per paper, as first given by Lawani (1980). Let the collection A be the research papers published in a discipline or in a journal during a certain period of interest. In the following, we write

Where,

As a measure of mean number of authors, although CI is easily computable, it is not easily interpretable as a degree. Moreover, it gives a non-zero weight to single authored papers, which refers to no collaboration (Karpagam et al., 2012).

6.2. Degree of Collaboration

Degree of Collaboration (DC) is a measure of proportion of multiple authored papers derived by Subramanyam (1983) as,

Where,

6.3. Collaborative Coefficient

DC does not differentiate among levels of multiple authorships. Collaborative Coefficient (CC) was designed to remove the above shortcomings pertaining to CI and DC by Ajiferuke et al. (1988). CC is used to measure the extent and strength of collaboration among the selected three ecology journals. It can be expressed mathematically as:

Where,

6.4. Lotka’s Law

Lotka (1926) published his pioneering study on the frequency distribution of scientific productivity. Lotka’s law is one among the three classic laws of bibliometrics, used to test the regularity in the publication activity of authors of scientific literature.

It states that, “the number (of authors) making n contributions is about 1/n2 of those making one; and the proportion of all contributors that make a single contribution is about 60 percent”, which means that out of all the authors in a given field, 60% will have only one publication, 15% will have two publications, and 7% of authors will have 3 publication and so on (Rowlands, 2005). In other words, within a particular topic, for every 100 authors whose contribution is single article, there will be 25 authors with two articles, 11 authors with three articles, etc. The generalized form of Lotka’s law can be expressed as

Where y is the frequency of authors making n contributions each and k is a constant.

According to Pao (1985), the following procedure should be followed in studying the application of fit of Lotka’s law to a given data sample.

Estimation of parameter ‘n’

The first step in the application of Lotka’s law is to determine the value of ‘n’ which is to be determined either by using the Linear Least Square (LLS) regression method or one of its equivalent forms given by the following formula:

Where,

Estimation of parameter ‘k’

The value of k, which is the theoretical number of authors with a single article, is determined from the following formula:

Here p is assumed to be 20 and n is the experimentally computed value of the exponent from the observed distribution. Once the value of n and k is determined, then, the number of authors writing 1, 2, 3…x articles is determined.

7.1. Growth of Ecology Literature

Table 1 presents the results of cumulative publications of the three journals. It was observed that the growth trend was linear. Fluctuations in publication patterns of ecology literature were noticed throughout the period of study. However, the highest number of publications was recorded in 2003 while the lowest was in 2007. The reason could be the frequency of journals, as there is an inconsistency in the number of issues published (Table 2). Another possible reason could be the shift in research focus from the field of pure ecology to applied specific research areas. Such changes in priority areas are discussed later in the paper.

Table 1.

Cumulative distribution of ecology literature for the three selected journals

Cum. – Cumulative; % - Percentage; TLCS - Total Local Citation Score; TGCS - Total Global Citation Score

Table 2.

Year-wise distribution of articles in the three selected ecology journals

EL - Ecology Letters; TEE - Trends in Ecology & Evolution; AREES - Annual Review of Ecology Evolution and Systematics

HistCite™ calculates the total local citation score (TLCS) and the total global citation score (TGCS). TLCS is the number of times a paper is cited by other papers in the local collection, which in the study is the citation scored by the collection of 2946 papers in the three journals. TGCS is the number of times a paper is included in the collection cited in WoS.

The journal-wise total research productivity of ecology journals for the years 2003-2012 is presented in Table 2. It was observed that Ecology Letters (vol. 6, 2003 to vol. 15, 2012) ranked first in order, followed by Trends in Ecology Evolution (vol. 18, 2003 to vol. 27, 2012) and then Annual Review of Ecology Evolution and Systematics (vol. 34, 2003 to vol. 43, 2012). Ecology Letters and Trends in Ecology Evolution had a periodicity of 12 issues per annum recording a higher percentage of articles published. At the same time Annual Review of Ecology Evolution and Systematics is annual.

Analysis of collected data showed that the literature on the subject ‘ecology’ was published in nine different forms i.e. Articles, Letters, Reviews, Editorial Materials, Corrections, Article; Proceedings Papers, Biographical-Items and Review; Book Chapters. It was observed that in the cumulative source-wise distribution of the three journals, articles stood first with 1,223 (41.51%) records, followed by Review with 773 (26.24%) records, Letters with 548 (18.60%) records, Review; Book chapters with 207 (7.03%) records, Editorial Materials with 151 (5.13%) records, Corrections with 40 (1.36%) records, Article; Proceedings Papers with 2 (0.07%), records and Biographical items with 2 (0.07%) records.

7.2. Authorship Pattern and Collaborative Measures in Ecology Literature

Collaborative research can be effectively measured from the number of authors in papers. Such studies can be conducted to understand global trends, national trends, or trends in different subjects. However, the extent of collaboration may not be revealed from the citations. Efforts in this direction have been made by Ajiferuke et al. (1988) who attempted to define ‘good collaboration’ measurers. With a view to identifying the extent of research conducted by individuals in collaboration with each other, the number of authors mentioned in the papers was counted and analysed. Table 3 gives the distribution of articles on the basis of authorship pattern (cumulative) of the three journals. Multiple authorship was dominant in the present study (Saravanan et al., 2012) which indicates that researchers normally prefer co-operative and collaborative works (Parker, 2013). The other factors such as nature of the project, magnitude of instrumentation, popularity, and the rate of expansion of the area of science may also affect this tendency. It was found that two authored papers (30.31%) were followed by three authored papers (19.89%), while the contribution of sole-authored papers (15.61%) was low. In essence, this shows a clear trend towards multi-authored papers (84.39%). This proves that our second hypothesis of “Multiple authors are predominant over single authors” is valid.

Table 3.

Authorship pattern (cumulative) of the three ecology journals

NA – Number of authors; TA – Total authors; % - Percentage; AP – Authorship pattern; TMA – Total Multi authors; DC – Degree of Collaboration; CC - Collaborative Co-efficient ; CI – Collaborative index

The Degree of Collaboration (DC) was almost uniform through the years studied (standard deviation <0.05) while the Collaborative Coefficient (CC) (average 0.56) and the Collaborative Index (CI) (average 3.65) were more variable as evident in Table 3. The average DC 0.84 indicates that collaboration was high among the authors in the journals under study. The CC is increasing year to year which shows the increase in the productivity of multi-authored papers.

The role of funding agencies was also assessed as this may significantly affect the course and discipline of research. The National Science Foundation, USA had funded many of the research works that were carried out in the journals during the study period.

7.3. Most Productive Authors and Lotka’s Inverse Square Law (Cumulative of Three Ecology Journals)

Author productivity is a measure for ranking authors according to their publication output. From 2003 to 2012, 2,946 papers were published by 6,697 authors in the three selected journals. Table 4 shows the top 15 most productive authors during 2003-2012. Among the top 15 authors who contributed to the three journals, 8 were from the USA, 3 from Australia and one each from the Netherlands, Germany, Finland, and Canada. The highest records were for H.P. Possingham with 22 (0.20%, 35 TLCS and 1214 TGCS). The other most productive authors, in decreasing order, are also provided in Table 4.

Table 4.

Top productive authors vs. citations (first 15 authors)

TLCS - Total Local Citation Score; TGCS - Total Global Citation Score

The productivity of the paper contribution of the selected three ecology journals was verified to find the conformity with Lotka’s inverse square law using Pao’s (1985) method. This was done using equations (4-5) to know the values of ‘n’ and ‘k’.

Here ‘n’ is substituted with the value 2.94 and ‘k’ is calculated as 0.82 using the equation (6), while ‘p’ is assumed to be 20. By replacing the values of ‘n’ and ‘k’ in the above table the difference is calculated. Here the D is minimum and hence Lotka’s law is confirmed to the present data set. From Table 5 it is clear that the maximum absolute difference value D_max which represents the maximum deviation is identified as 0.006. The table value or critical value of D in K-S test at 0.05 level of significance is 0.0166. When the calculated value of D, i.e. 0.006, is less compared to the table value 0.328, it is clear that the calculated value of D comes within the critical value of D. Thus the distribution of author productivity of the present data set confirms Lotka’s law in Table 5.

Table 5.

K-S test on observed and theoretical distribution of authors (cumulative of three ecology journals)

7.4. Subject-wise Contribution of Ecology Literature

The purpose of subject wise analysis is to identify the performance of researchers in various subject headings in ecology and its sub-fields. We have used Library of Congress Subject Headings along with three of our domain experts in ecology, and grouped the subject ecology in to 25 disciplines during the study period. The subject-wise analysis was carried out in accordance with Budilova et al. (1997).

To analyze the changes in the focus areas of publications in ecology, we sub-divided the study period into two blocks of five years and extracted the number of publications and their percentages, journal-wise, for the three studied journals (Table 6). We observed a decrease in publications in all the three journals in the disciplines of Movement, Interactions & Behavioural Ecology, Physico-Chemical Ecology, Soil Ecology, and Biogeography, while increase in publications was observed in the disciplines of Freshwater Ecology, Arid Zone Ecology, Fire Ecology, and Forest (Plant) Ecology. The total output of 2,946 subject keywords was classified and as expected the highest contributions were in the disciplines of Biodiversity and Evolutionary Ecology in the selected three ecology journals in the 2003-2007 block, while in the 2008-2012 block the highest contributions are from Biodiversity and Movement, and Interactions & Behavioural Ecology in the selected three ecology journals.

Table 6.

Discipline-wise publications and their percentages (in parentheses), journal-wise arranged in two blocks of 5 years (2003-07 and 2008-12)

EL - Ecology Letters; TEE - Trends in Ecology & Evolution; AREES - Annual Review of Ecology Evolution and Systematics

7.5. Institution-wise Distribution of Ecology Literature

Analysis of references reveals that most of the research works in ecology were being pursued in universities and other higher educational institutions. Research institutes/laboratories were more active in the field of ecology. 2,946 papers were published in the journals during 2003-2012 with contributions from 7,536 institutions. The University Calif. Davis, USA was the topmost contributor in the list (Table 7) with 130 papers (1.73%, TLCS 561 and TGCS 12027), and remaining institution names with records are given below.

Table 7.

Institution wise distribution of contribution (Cumulative of three ecology journals) (first 15 institutions)

TLCS - Total Local Citation Score; TGCS - Total Global Citation Score

It is evident that American and British institutions contributed to 80% (12 out of 15 institutions) of the publications. It is of significance that ecologists have accepted that most of the impact of environmental and ecological damages will be felt higher in Africa and South Asia; no institutions from this region were listed in the top fifteen. In the Geographic distribution of articles (Table 8) the same trend was observed, though China occupies the 15^th position.

Table 8.

Geographical distribution of contributions (Cumulative of three ecology journals) (first 15 countries)

TLCS - Total Local Citation Score; TGCS - Total Global Citation Score

7.6. Geographical Distribution of Ecology Literature

Geographical analysis of papers revealed that during the period of study contributions from the selected three ecology journals numbered 2,946 from 82 countries (Table 8). The USA (1,551 papers, 32.05%, TLCS 4074 and TGCS 105045) has come in the top position followed by the UK. In another work by Biradar and Mathad (2000) the USA also has occupied the first position nation-wise in terms of papers. Nearly 90% of the publications have been contributed by authors from 15 countries; none of these countries is from the third world, clearly indicating the dominance of advanced countries in carrying out ecological research. We attribute this to better infrastructure, laboratory, and library facilities in the advanced countries. Language barriers do not seem to be an issue here as we can see that not all the countries in the list are English speaking (of course in many of the publications, collaborations and joint authorship would have included native English speaking persons). Though the third world countries are endowed with rich traditional knowledge, unfortunately such knowledge has not been translated into scientific outputs.

7.7. General Observations on Ecology Literature

A general picture of the selected three ecology journals from Web of Science^® is given in Table 9. A reference to a text or part of a text identifying the document in which it may be found, or the format of such a reference—which would typically include the author, title, and bibliographic description of the document—is called Citation. The method of calculating the citation rate that is followed by Web of Science^® is accomplished by counting the number of references to the cited journal, but treating duplicate references from the same source article as only a single citation link.

Table 9.

General observations on ecology literature in three ecology journals

‘h-index’ is an index that quantifies both the actual scientific productivity and the apparent scientific impact of a scientist. Hirsch (2005) postulated that “[a] scientist has an index h if h of his or her Np papers has at least h citations each and the other (Np –h) papers have less than h citations each. The value of h is equal to the number of papers (N) in the list that have N or more citations” (Dhiman, 2012; Liao & Huang, 2014).

In Table 9, Ecology Letters has an h index of 130; it means that 130 of the documents have been cited at least 130 times. The published documents with fewer citations than h, in this case less than 130, are considered but would not count in the h index. The h-index of Trends in Ecology and Evolution, and Annual Review of Ecology Evolution and Systematics, are 146 and 97, respectively.