Transcript the diversity

Community Ecology –
Descriptive and functional approches
Distinction between Population a
Community Ecology is rather
fuzzy
• “Papuan” counting (one, two, three, many)
• Community – when I am not able to study
each population separately (~ many)
• Classical trade-off – I can either study very
limited number of populations, each in
detail, or study many populations together,
but some details must be neglected
Community ecology
vs. [Pflanzen]sociologie, =
Phytocoenologia = Phytosociology
• Community ecology (functional approach):
e.g. Mechanisms of (many) species
coexistence, interspecific interactions in
community context
• Phytosociology – description and
classification of plant communities in
landscape, vegetation maps, Z-M community
classification
Legacy of phytosociology
• Databases of phytosociological relevés
• Contain broad-scale patterns of species
composition
• Use with caution (non-random/intentional
selection of locations to record), but they
contain incredibly large (100 000+ in Czech
phytosociological database) number of
compositional records
Pattern and process
• Observation and manipulative experiment
• The goal of ecology is to explain observed
patters by mechanisms (processes); so the
good description of pattern is the first step
• Temporal and spatial scales for observation
and experiment
• Selection of model communities:
species poor – easier to study
species rich – more interesting
Methodological constrains
• Ability to identify (and subsequently
quantify abundance of) species; compare:
vascular plants in temperate zone [well
know], tropical insects [much worse
known], soil bacteria [difficult to identify,
quantification problematic]
• Species names are only labels – knowledge
of life history of species, species traits
Community Ecology – complex
of causal relationships, causal
chains
British imperium saved by old maids
Removal of seed eating rodent increased other abundance
of other seedeaters, but not of insectivors
Rodent removal in Sonoran
desert
Both, ants and rodents eat seeds
(ants prefer smaller seeds), but
partial overlap
The higher density
of Erodium, the
higher is percented
of plants infected
by fungus – in
fact, the fungus
and rodents
compete for a
plant (plant is their
common resource)
Removal of rodents
– increase of largeseeded plants, but
on the expense of
decrease of smallseeded plants,
which are
suppressed by
competition.
Net effect of
rodents on ants
depends also on the
time scale
Community as a biotic
component of ecosystem
• Composed of individual populations
• We are never able to study all the species =>
inclusion criteria
• Functional (community of faeces decomposers) –
compare with “guild”
• Spatial…
• Taxonomic (plant community - usually means
vascular plants / and sometimes bryophytes)
„Species assemblage“ - not necessarily functional relationships (species
assemblages from light traps) – ?rather terminological problem
The big one
Diversity
(Species diversity, Richness,
Biodiversity)
Ecologists are fascinated by
diversity. Questions:
• Why they are so many (so few) species
• What is diversity determined by (local ecological
interactions vs. historical factors)
• Changes of diversity along environmental
gradients (what are diversity determinants)
• Effect of diversity on community functioning
To be abe to provide answer to any of these
(and many other) question about diversity
We must be able to define and
subsequently measure the
diversity
How to characterize the population
structure (which species are there
and how are they represented) of a
community?
• Number of species (=species richness)
• Diversity, reflecting not only number, but
also relative representation of species
populations
• Eveness, Equitability as o component of
diversity
• Spatial aspects of diversity
Species-area (Species - no of individuals)
relationship – often SAR
Number of species
Area (or number of individuals)
The same
equations are used
for within
community species
area, and for the
dependence in
archipelago
Methodological
note – independent
quadrats, or
„collectors curve“
(nested quadrats)
Causes of SAR – with increasing
spatial scale
• Increased number of individuals
• Environmental heterogeneity (at various
spatial scales, from, e.g. small scale
heterogeneity within a meadow, up to
heterogeneity among habitats on a
landscape scale)
• Biogepgraphical divides, evolutionary
differences
Tow most often used equations
Pover curve (Arrhenius)
S=c.Az , fitted usually as log S = log c + z log A
assumption: by increasing area two times, species number will
increase 2z times – usually z ~ 0.2 to 0.35]
[Semi]Logarithmic curve (Gleason)
S=a+b.log(A)
assumption: by increasing area two times, species number will
increase by b.log(2) species Negative for small A
Similar relationship also for dependence on number of sampled
individuals
Area increases faster than no. of
species
• Typical conservationist’s slogan: Our island
comprises only 5% of land of the Earth, but
hosts 20% of all vascular plants
• You can say similarly: the rubbish dump
comprises only 0.1% area of the whole
Ceske Budejovice, but hosts 10% of all its
species (say 70 out of 700)
Concept of minimal area
(historically used in plant ecology)
Attempt to find an upper asymptote (which, in
my view does not exist), and identify Area (=
minimal area of a community) when it is
“nearly reached” (sometimes, more
sophisticated methods, looking for decrease in
heterogeneity, e.g. Moravec – today mostly of
historical relevance)
Comparing “samples” of varying size (i.e. varying no. of individuals)
(compare meaning of sample in statistics and community ecology)
Rarefaction – estimates expected number of species in a sample of
reduced size:
E(S) – expected no. of species
  N  Ni  

 
SO 
n


E ( S )   1 
N 
i 1 
  

n 

SO – no of species in original
sample
N – no of individuals in original
sample (each species represented
by Ni individuals)
n – number of individuals in
reduced sample
Take care!
Everything is calculated under the
assumption that the reduced sample is
random selection of individuals from the
larger sample. It is usually not the case.
The no. of species is so (slightly)
overestimated in comparison with samples
taken in the field.
Comparing species richness of
area of different size
• Compare species richness of protected areas
under different management (but these are
of different size) / take care of another
problem – protected areas are usually
selected because they are species rich
• Compare number of species on islands with
and without an invasive species (again, take
care about causality)
In each comparison
• The dependence of species number on the
area must be taken into account
• Various possibilities how to statistically
filter out the effect of area
• You will either work with residuals on the
species area curve or will use area as
covariate
Diversity (taking into account
species proportions)
Higher here
Diversity indices – attempt to reflect both, number of
species and their relative proportions
Pi – relative species representation - Usually, Pi = Ni/N , N=Σni
Simpson dominance index
S
Sim pson(dom)   Pi
i 1
S
H ´   Pi . ln Pi
i 1
2
(Diversity=1/Simpson or
Diversity = 1-Simpson, i.e.
probability that two randomly
drawn individuals will belong to
different species) – assumption –
P is proportion of individuals in
infinitely large community
Shannon diversity index
Simpson
Usually, Pi = Ni/N , N=Σni
And then Pi2 = Ni2/N2 - i.e. probability that two
randomly drawn individuals will belong to species i
With number of individuals [and finite sample],
Simpson index uses
Pi2 = Ni (Ni-1))/(N (N-1))
i.e. random draw without replacement
otherwise Pi routinely calculated from biomass,
cover, etc.
Do not subtract 1 there!
Free software available at:
http://folk.uio.no/ohammer/past/index.html
Shannon formula (based on information theory,
sometimes Shannon - Weaver, Shannon - Wiener
[complicated history of various papers]
S
H ´   Pi . ln Pi
i 1
Various log are used, originally log2.
It is useful to use antilog, i.e. eH´ (for ln) 2H´(for log2) or 10H´ for
log10 – the values are the same (meaning – number of species
forming the same diversity when equally represented
General formula for diversity (Hill notation), series of
increasing importance of representation of dominants with
increasing a
1 /(1a )

a
N a    pi 
 i 1 
S
According to a value, we get
N0 – number of species
N1 - eH´ (asymptotic)
N2 - 1/Simpson dominance
Ninfinity - 1/relative representation of the most abundant species
(rel. repres of most abundant =Berger-Parker index)
Evenness, equitability, = vyrovnanost
Pielou (ratio of actual diversity to maximum diversity with
given number of species)
Ep = H´/ H'max = H´/ ln S;
Partially problematic
In my view better
Buzas and Gibson's evenness = eH/S
Graphical representation
of community population
structure
Diversity - dominance curves
1
Control fertilised
Removal non-fertilised
Removal fertilised
Species proportion
0.1
0.01
Control non-fertilised
0.001
0.0001
0.00001
Species sequence
Modely distribuce druhových
četností
Good web page is
http://www.columbia.edu/itc/cerc/danoff-burg/MBD%203.ppt
Four basic models Geometric Series – each species x% of previous (e.g. half,
then 80, 40, 20, 10, 5,….)
Biological explanation – niche pre-emption –
Log Series – number of species with 1, 2, 3 individuals
are αx, αx2/2, αx3/3, αx4/4 [α and x parameters, α
sometimes considered good index of diversity – useful for
numbers of individuals]
Log-Normal Series – see figure
Broken-Stick Model (a stick is broken in random S-1
points)
Dominance-diversity curves pro
4 modely
100
10
from
DonoffBurg
Broken Stick Model
1
Relative
abundance
(plotted at 0.1
log scale]
Log-Normal Series
0.01
Log Series
0.001
Geometric Series
10
20
Rank
30
40
With log-normal distribution, this graphical representation gives
normal curve
Preston - octaves
Left truncarted – Species with low abundance are missing on the left side
(less than 1 individual, so that they are actually not found).
16
Number
of
species
14
12
10
8
6
from
DonoffBurg
4
2
Less
than
2
4
8
16
32
64
128
256
512
0
Number of individuals of a species
Functional and phylogenetic
diversity
• Representation of life forms
• Diveristy of genera, families etc.
• Example: community composed of 37 species of dandelions
Taraxacum officinale will have lower phylogenetic and functional
diversity of community composed of “normal” species.
• Functional diversity should not be affected by the
ability of “splitters taxonomists” to distinguish
several functionally identical species
First posibility – Functional
groups
• Problem – how to define functional group,
what to do with hierarchical classifications,
relevance of traits used for functional
classification
• jak definovat funkční skupiny, co když je ta klasifikace hierarchická
(phanerophyty mohou být dále děleny do několika podskupin), co když
zrovna dané znaky nejsou úplně relevantní (schopnost fixovat dusík
není vázaná na žádnou životní formu, ale může být funkčně velmi
důležitá)
Rao index Shimatani 2001
• Shimatani K 2001: On the measurement of
species diversity incorporating species
differences OIKOS 93: 135-147
• Functional (or phylogenetic) diversity
reflect the dissimilarity of two randomly
selected individuals from the community
S 1
S
FD    qi , j pi p j
i 1 j i 1
• qi,j – dissimilarity of two species
• pi – relative representation of a species
• If qi,j = 1 for all species pairs, FD equals to
Simpson diversity, i.e.. 1-Simpson
dominance
Macro na http://botanika.bf.jcu.cz/suspa/FunctDiv.php
See also: Leps J., de Bello F., Lavorel S., Berman S. (2006): Quantifying and interpreting functional
diversity of natural communities: practical considerations matter. Preslia 78: 481-501.
Usually [but not necessarily]
• Two functionally identical species: q=0
• Two completely different species: q=1
• Acceptable dissimilarity measure
[qualitative traits]
• 1-(no. of identical traits/no. of all traits)
• Similar scaling useful also for taxonomic
dissimilarity
Alpha a beta and gamma diversity
• Diversity in space (compare with speciesarea relationship)
• Alpha – diversity of single habitat, of singe
quadrat, etc.
• Beta diversity – variability among the basic
units in space
• Total diversity of an area, landscape –
gamma diversity
Relationship between alpha, beta,
gamma
• Both forms were used:
• Gamma = alpha + beta
• Gamma = alpha  (beta+1)
• E.g. Whittaker
• beta = S/a – 1, where S is the total number of species in the
habitat complex studied (called sometimes γ diversity) and
a is the a-diversity, expressed as the mean number of
species per fixed sample size
• Problems with estimate of S
Characteristics of beta-diversity
• Average dissimilarity of basic units (should
not be dependent on the number of basic
units)
• Special methods when the units are on a
gradient – use of multivariate methods (e.g.
ordinations) and estimation of length of the
gradient (as in DCA)
Functional beta diversity
• Measure of trait convergence – divergence
• Use of null models in community ecology
Recommended reading:
• Maguran A.E. 2004. Measuring biological
diversity. Blackwell.
• Rosenzweig M.L. 1995. Species diversity in space
and time. Cambridge Univ. Press
• Huston M. A. 1997. Biological Diversity: The
Coexistence of Species. Cambridge Univ. Press
• My chapter in van der Maarel (2004) Vegetation
Ecology. Blackwell.