Author productivity is a foundation of scientometric research, providing valuable insights into the dynamics of scientific contributions and shaping the global knowledge systems. Research collaboration commonly known as sharing knowledge of each other, sharing of resources with one institution to another institution and working together to reach the goal (Melin G and Persson O., 1996). It is believed that collaborative research improves the impact of publications in relationship with citation (Priti Kumaria and Rajeev Kumarb., 2023). The citation performance of coauthored papers was significantly higher than papers with a single author (Gazni A and Didegah F., 2011). Researchers found that publications with international collaboration obtained additional citations than those of nationally and institutionally collaborated paper (Ibanez A, Bielza C and Larranaga P., 2013). The trend of collaboration in the field of Artificial Intelligence (AI) is to some extent negative when comparing the relationship between the number of authors and their citation (Fan L.et al., 2020). LIS productivity revealed that most of the samples differ based on their size and breadth of source than those in Lotka’s study. Based on such observations Lotka’s law in LIS and other fields recommended that the studies testing the appropriateness of Lotka’s formula should be conducted in order to attain valid outcomes (Pao M L., 1885).

Several studies in different disciplines explained the co-authorship trends and the application of Lotka’s Law. Zehra Taşkın and Arsev U. Aydinoglu explored the bibliometric investigation of the NASA Astrobiology Institute (NAI) funded research published between 2008 and 2012 and concluded that there are prominent scholars in the NASA Astrobiology Institute (NAI) belongs to the co-author network but none dominates astrobiology (Taşkın, Z and Aydinoglu, A.U., 2015). Santhakumar, examined that astrobiology research field by conducting a bibliometric analysis with 1,848 publications between 2012 and 2021 from the Web of Science database and the findings showed that Cockell, C S is the most influential author in the field of Astrobiology (Santhakumar, R., 2023). Luca Tonietti et al., quantitatively reviewed the global literature on astrobiology, with a focus on biomining and bioleaching through bibliometric network analysis, investigating patterns and trends in its development and concluded that the research is currently addressing the recognition of network analysis and temporal analyses found that the biotechnological applications are expected to play a crucial role in long-term human space exploration (Tonietti, L., 2023). Vinay Kumar Dattempted to quantify the research publications on Astrobiology and the data collected from Web of Science (WoS) database and the study found that the growth of literature was gradual. Charles S. Cockell was the most prolific author whereas Manasvi Lingam was the most promising author for recent years (Vinay Kumar D, Arun Kumar T. and Santhosh Kumar T. S., 2023). Christophe Malaterre and Francis Lareau illustrated that author networks are not from citation analyses but from topic similarity based on a topic-model of published documents and found that the underlying communities of authors by measuring author correlations in terms of topic distributions (Malaterre, C and Lareau, F., 2024). Michael Gowanlock and Rich Gazan combines bibliometric techniques with a machine learning algorithm, the sequential information bottleneck and conclude that the majority of the UHNAI team is engaged in interdisciplinary research (Gowanlock, M. and Gazan, R., 2013). Kent A. Peacock applied Lotk’s Law, that the number of survivors isa very small fraction of the species that evolve on various planets (Kent A. Peacock, 2018). Mario Coccia analysed that recent studies in monograph productivity recommend that Lotka’s law might reflect an underlying pattern in people who produce publications when the time period covered is ten years or more showing that the author productivity approximates the frequency distribution (Coccia, Mario, 2018). Mason Youngblood and David Lahti revealed an increase in productivity and collaboration over time, although a higher difference in author productivity than expected (Youngblood, M. and Lahti, D., 2018).

• To analyse the authorship pattern.
• To examine the collaborative measures.
• To evaluate the application of Lotka’s Law.

The data consisted of 11523 papers were published in the field of Astrobiology during 1991 to 2023 from Web of Science Citation database downloaded in plaintext format and the analysis was done with the help of the Bibexcel software and the data was exported in Excel for further calculations. Out of the total publications, only 11520 papers were taken for consideration due to the lack of year and one paper was listed in the year 2024 (Hemavathy. C. and C. Baskaran., 2024). The Collaborative Coefficient (CC) has been measured by the method suggested by Ajiferuke (1988). The degree of collaboration is determined according to the formula given by Subramanyam (1983). In Lotka’s Law, xⁿy = c, the parameters n and c are calculated as per the steps followed by Pao (1985).

Table 1 and Figure 1 depicts the authorship pattern for the period of 1991-2023. The analysis of the table shows that the single author contribution is 1870, two-author share and three author shares are 1583 and 1558 respectively. More than ten authors contributions are 1121. It shows that multiple author research articles have made major contributions in the field of Astrobiology literature.

Figure 1:
Authorship Pattern of Astrobiology Literature.

Table 1 shows the Authorship Pattern in the Astrobiology Literature. Neelamma G and Gavisiddappa Anandhalli find authorship pattern in the crystallography literature from 1989 to 2013 (Neelamma G. and Gavisiddappa Anandhalli., 2018). They done Collaborative index, Degree of Collaboration, Collaborative Co-efficient and applied Lotka’s Law. The following is one of the earliest methods to find the degree of Collaboration given by Lawani (1980).

Where, j = the number authors in an article i.e. 1, 2, 3 ……

fj = the number of j authored articles.

N = the total number of articles published in a year.

A = the total number of authors per article.

Eg.: CI for the year 1995 is,

Table 2 shows the Collaborative Index (CI) in the Astrobiology Literature over 33 years from 1991 to 2023. The Collaborative index is 6 in the year 1991 and has been decreased in the following year1992 as 1.6667 and increased gradually up to the year 2016 as 4.0858, again from 2017 onwards decreasing happens in the calculation of Collaborative Index (CI). On the whole, the Collaborative Index (CI) is fluctuating in the field of Astrobiology publications.

Table 3 reveals the Degree of Collaboration (DC) during the period of study. It can be defined as the number of multiple author publications in the discipline published during a year as against the total number of papers (multi author and single author) published in the same year. An indicator known as the Degree of Collaboration has been used nowadays and was proposed by Subramanyam, K (1983).

Where, Nm = number of multi authors during a specific period in a discipline.

Ns = number of single authors publication in a discipline during a given period of time.

Eg.: DC for the year 1995 is,

The analysis of the Degree of Collaboration shows that in 1991 it was 1 and it has decreased to 0.2222 in the year 1997. The overall Degree of Collaboration in Astrobiology shows fluctuating trend. After the year 1991 the Degree of Collaboration reached high in the year 2023 as 0.9290.

Table 4 gives a clear understanding of the collaboration coefficient during the study period. if a publication has a single author, the author receives one credit; if a publications has a single author the authors receives one credit; if two, each receives ½ credit and in general, if we have ‘n’ authors each receives 1/n credits.

The Collaboration Coefficient (CC) counted by using the following formula suggested by Ajiferuke (1988).

Where, j=the number of authors in an article i.e.1,2,3…..

fj=the number of j authored articles.

N=the total number of articles published in a year, and

A= the total number of authors per articles.

Eg.: CC for the year 1996 is,

The highest collaboration coefficient is found in 1991as 0.8333, and it has been decreased in the following year and gradually increased from 1998 onwards and again got decreased in the year 2006 and increased in the following years. In general, the Collaborative Co-efficient in Astrobiology literature shows fluctuating trend.

Table 5 shows modified collaboration coefficient during the study period. The main purpose of MCC is to quantify how collaborative a research output is, and by analysing the contributions of multiple authors. It regulates the situations where a few authors might dominate or contribute disproportionately. Modified Collaborative Coefficient (MCC) is calculated by using the following formula suggested by Savanur and Srikanth, (2010).

Eg.: MCC for the year 1996 is,

The highest modified collaboration is counted in the year 1991and decreased in the following years up to 1997 and starts increased from 1998 onwards and much decreased in the year 2006. From 2007 onwards, slight increase and decreases take place. Finally, Astrobiology literature shows instability during the study period.

In 1926 Alfred J. Lotka tested the frequency distribution of scientific productivity from chemical abstracts between 1907 and 1916 (Lotka, A.J., 1926). Lotka concluded that the number of authors making n contributions is about 1/n² of those making one and the proportion of all contributors. The main concept of this law is that a “maximum number of articles are produced by a minimum number of authors” (A. Thirumagal¸ A. Vanitha and M. Mani, 2017).

Where, x is the number of publications of interest (1,2,3…),

y is the expected percentage of authors with frequency x of publications and,

c is a constant.

To determine the value of n,

To determine the value of c,

To determine the value of critical value (c.v.),

Kolmogorov-Smirnov (K-S) test and Chi-Square test are frequently applied to find out the goodness of fit. In this study, from Table 6 K-S test used to verify Lotka’s law. This test is carried out by calculating the theoretical and observed cumulative frequency distribution of authors. The difference at each level of cumulative frequency distribution is counted. The maximum difference is observed and compared with the critical value. In the difference, if it shows less than the critical value, it has been accepted; otherwise rejected (Chaturbhuj S B and Sadik Batcha M., 2020).

The difference (D_max) from the table value is more than the critical value. It can be affirmed that the K-S test reveals that the present data set does not fit Lotka’s Law. Hence, the authors in the field of Astrobiology have expected to produce more research papers to fix the data for Lotka’s Law application.

The maximum deviation between cumulative of observed and expected distributions of author’s productivity as per Lotkas’s law.

Where,

In this case with Lotka’s inverse square law, the D_max = 0.4663 from Table 7 is more than the critical value 0.0186. It shows Lotka’s inverse square law is also not fixing for the Astrobiology field. In both cases the data does not fit for the application of Lotka’s Law. Hence, the authors in the field are expected to publish more research papers in the field of Astrobiology.

In the present study, the maximum number of papers has contributed based on collaboration. Collaboration patterns offer advantages to the funding agency, policymakers, the scientific community, and researchers by providing insights for the development of research. It would also motivate other researchers to carry out further research in other disciplines. This study provided perceptions into the authorship trend of published literature in the Astrobiology field. Authorship pattern is nowadays considered one of the main aspects of scientometric studies. It includes analysis of types of authors, their collaboration pattern, and the number of authors, etc. The Lotka’s Inverse Square law does not conform to the study.