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scrap.txt
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taken from MT_spatial_avg.Rmd :
---------------------------------------
Intro :
\lettrine{U}{}nderstanding the mechanisms behind spatial and temporal
dynamics has been a long-standing focus in community ecology [@gibson2009; @turner1989].
Interspecies interaction in a grassland
community could be advantageous or
disadvantageous to either or both species involved,
which led to mutualism or competition
as the case might be. These inter-species response were
found to be affected by several biotic and abiotic factors
including climate, fire, soil-nutrients, pollinators, micorrhizae,
grazing and other form of disturbances
[@mcnaughton1983; @parton1995; @bardgett2008; @belsky1992;
@collins1992; @olff1998; @fry2017; @potts2003; @hudewenz2012;
@canals2003; @hallett2014].
Excessive pressure of any of those
disturbances could alter the competitive balance in the community
and could shift the species-dominance affecting overall species richness and
ecosystem-function. Most of the prior studies used, in general, the correlation
or regression based approach to understand species-variability with other
species within a community (or with environmental variables) to establish causal
relationship and thereby lacking important information embedded in their joint
distribution structure.
We chose Jasper Ridge Biological
Preserve (JRBP), a biodiversity hotspot in californian serpentine grassland, as our study system.
Long term observations in JRBP showed the serpentine grassland vary widely in its
species composition both in temporal and spatial scale [@hobbs2007; @zhu2016].
Climate change and invasion by
exotic species in JRBP had detrimental effect on native species shifting its dominance
from one species to another
and thereby posing habitat loss of their
dependent species leading to extinction [@stromberg2007].
For example, bay-checkerspot butterfly
\textit{Euphydryas editha bayensis} is now locally extinct at Jasper Ridge.
It may be due to declining abundance of its principal larval
host plant \textit{Plantago erecta}
in competition with invasive species like \textit{Bromus hordeaceus}.
Jasper Ridge has been served as an experimental model system to
study ecological hypothesis since long and proved to be effective
in decision making from conservation and management perspective.
Our objective is to find the
synchronous (for positively correlated variables)
or compensatory (for negatively correlated variables) dynamics in
the serpentine grassland of JRBP and mixed-prairie of Hays in Kansas
using "tail-dependence" feature of copula.
Using a model selection approach as well as nonparametric analysis, we try to
find is there any asymmetric tail-dependence in those grassland community and
if there is, then could this tail-dependence be explained depending on
species-environment interactions? We also suggest an alternative measure of
community variability in terms of quantifying skewness of total biomass over years.
=============================================================================================
Results : jrg
BRMO-PLER study reference
Similar finding was also observed earlier
by Hobbs et al.[@hobbs1991] where several years of above-average rainfall
led to an abundance in \textit{Bromus hordeaceus} and shifted the dominance
among native annuals from \textit{Plantago Erecta} to \textit{Lasthenia Californica}.
VUMI-LAPL_ORDE dynamics (all LTdep.)
Another multispecies interaction was native annual
\textit{Vulpia microstachys} (sp42)
found to show stronger lower tail dependence (positive correlation with
simultaneous low-abundance) with other two species \textit{Layia Platyglossa} (sp19)
and \textit{Castilleja densiflora} (sp30).
================Results including growing season ppt. effect on jrg spatial avg data====================
Interestingly, we found
that annual and perennial showed different tolerance towards total precipitation
for the growing season. For example, some extreme dry years [e.g. 2012 or 2014's
drought [@griffin2014]]
with little precipitation made annual
forb \textit{Castilleja densiflora} (sp30) uncommon whereas perennial forb
\textit{Brodiaea spp.} (sp5)
became abundant at those years (see Fig. \ref{SI-fig_spaceavg_drought}).
Earlier study [@pitt1978] showed years with "suboptimal" rainfall had relatively higher cover
of perennial forbs whereas years with "favorable" rainfall patterns promoted earlier
germination and better growth for annual grasses. Another perennial
native bunchgrass \textit{Nassella pulchra} (sp36) became rare in the community with
low average temperature (considered as sp44)
during growing season for two successive years, showing lower tail-dependence.-->
===========================================================================================================================