An inclusive mathematical representation for biodiversity

Biodiversity- the variety of life forms on the Earth underpins ecosystem services. Future
of mankind is inseparably linked to biological diversity. However, human activities act as
pressure points and strain other living organisms. Holistic understanding of biological
diversity and their dynamics across time is important to plan and implement conservation
measures.
Whilst strategic plan for biodiversity 2011-2020 and its Aichi targets have been recognized as
an integral component in Sustainable Development Goals, possibly due to paradox of plenty,
the global indicator frameworks of biodiversity within SDGs is yet to identify any Tier I or II
indicator for biodiversity assessment. It has become a convention to narrow down biological
diversity measures to diversity indices. Most of the diversity indices proposed over years are
probability functions and convey information about a single level. This report proposes a new
inclusive representation of biodiversity and introduces Nair’s Measure of Biodiversity (NMB).
A study was carried out within 11 sacred groves Pulikottukonam Nagar Kavu (PNK), Kavil
Shree Maheswarashramam (KSMA), Erumakkavu (EK), Shree Bhadrakali Temple (SBT),
Dharmasastha kavu (DK), Edayilekkadu kavu (EK), Poonkottukavu (PK),
Muchukunnukottah (MK), Vallikkattukavu (VK), Iringole kavu (IK) and Amaramkavu Devi
Temple (ADT) in Kerala during January – February 2018 to collect field data. The study was
limited to tree species. Representative hemispherical photographs of the groves were also
taken. Historical data of these groves (1993 and 2015) were also used for the study.
Parameters from multiple levels have been effectively utilized to represent the diversity with
more information content.
The diversity within each grove was initially estimated using the traditional diversity indices
over two periods. True diversity, expressed as effective number of species obtained from the
Shannon index was different from Simpson index for all groves. The Present data shows that
grove KSMA was most diverse and EK was least diverse. The groves EDK, MK, VK and
ADT show similar diversity of 13 equally common species from Shannon index and groves
EDK, MK and ADT show a similar true diversity of 9 equally common species from the
Simpson index.
The diversity observed across the groves using the old data was different from the current
results. Similar to present results grove KSMA was most diverse and EK was least diverse for
both the indices. But the diversity of these groves was higher than the present data. The
groves IK and SBT shows similar true diversity from Shannon index and groves PK and VK
show a similar true diversity from Simpson index. The grove EK and KSMA shows a
maximum decrease of effective number of species for Shannon index
and Simpson index
respectively for the two periods.
NMB takes into account the conservation
status of species. The grove data obtained were
classified as per IUCN conservation status and modified to new measures using mathematical
transformations. Observed values were reduced to a single variable depicted by the solid
angle (in Steradian) subtended by it on a plane. This ensured that there was no loss of
information. This facilitates a reader to work back to arrive at the species composition within
each site.
The mean canopy openness calculated from the groves shows that grove ADT is most dense.
Groves DK and MK show high canopy openness. But the standard errors associated with all
groves are different. This clearly indicates the uneven distributions of species across the
groves.
The biodiversity representation introduced here includes multilevel diversity parameters such
as effective number of species derived from the Shannon entropy (H' (en)), NMB, mean canopy
openness at each location (μ(CO)) and total number of species (NS) with time stamp (in ordinal
date (OD); YYYY-DDD). The representation takes the general form [H'(en)
; NMB; μ(CO); NS;
OD] and conveys more information than conventional diversity indices. Shannon effective
number of species describes the stability of the ecosystem. NMB adds information at species
level and mean canopy openness paints a picture of the thickness of stand. The time stamp
renders inclusiveness and facilitates comparative studies.

MPhil EI 2017-2018 INT Dr. R. Jaishanker