Conceptos Básicos en Ecología Cuantitativa

7/25/2019 Conceptos Bsicos en Ecologa Cuantitativa

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Basic Species Diversity Concepts

Species Richness

Diversity Indices- Simpson's Index

- Shannon-Weiner Index

- Brillouin Index

Species Abundance Models

Describing Communities

There are two important

descriptors of a community:

1) itsphysiognomy

(physical structure), as

described in the previous

lecture, and

2) the number of species

present and thei r relative

abundances (species

richness and diversity).

Species Diversity

By far, species diversity has received the greatest amount of

attention in community ecology. Diversity is an emergent

proper ty of the community .

Current emphasis on biodiversity and conservation has

accelerated interest in this topic, both theoretically and

practically. Biodiversity often involves the inclusion of

genetic and ecosystem diversity as well. But, the focus for

many conservation efforts has remained on species.

Thus, we will devote considerable time to the development of

concepts in diversity.

Species Richness

The simplest way to describe a community is to list the

species in it.

Species richness (S) is the number of species on that list,

and is most often used as the first pass estimate of diversity

for a community. Term coined by McIntosh (1967).

How would one generate such a list? A simple and widely

used method is to define the boundaries of the community

and then walk through it seasonally, noting all the speciesyou encounter. This is what we call a flora.

Species Richness

Some communities are simple enough to permit a complete

count of the numbers of species presentthis is the oldes t and

simplest measure of species richness.

Complete counts of species can often be done in very extreme

environments (certain deserts, polar regions, etc.); however,

this approach can rarely be taken in most mesic environments.

Estimating the totalspecies richness of a community can be a

bit difficult and will be the subject of the subsequent lecture.

For now, lets continue to think about observed richness (Sobs)

from a community sample.

Species Richness

While many studies include Sas a descriptive factor

associated with the community, it is largely

uninformative in as much as it does not reflect relativeabundance.

Example: suppose two communities (1 & 2) each contain

100 individuals distributed among five species (A-E):

EDCBA

111196Comm-2

2020202020Comm-1

Are these two communities equivalent?


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Diversity Indices

In most instances, in order to have an effective measure of

diversity, we need to account for both species richness

and the evenness with which individuals are distributedamong species.

One way to do this is through the use of a proportional

abundance index. There are two major forms of these

indices: dominance indices and information indices.

While more than 60 indices have been described, we will

look at the three most widely used in the ecological

literature: Simpson's, Shannon-Weiner, and Brillouin.

Simpson's Index

Simpson's Index is considered a dominance index because

it weights towards the abundance of the most common

species.

Simpson's Index gives the probability of any two

individuals drawn at random from an infinitely large

community belonging to different species.

For example, the probability of two trees, picked at random

from a tropical rainforest being of the same species would

be relatively low, whereas in boreal forest in Canada it

would be relatively high.

Simpson's Index

( )( )

( )( )i

S

1

n 1D

N N 1

Si

i

n

=

=

The bias corrected form of Simpson's Index is:

where n i is the number of individuals in the ith species.

SinceDs and diversity are negatively related, Simpson'sindex is usually expressed as either reciprocal or

complementary forms (1/D or 1 -D) so that as the index

goes up, so does diversity.

Simpson's Index

A worked

example for

201 trees of 5

species

assessed in

several

quadrats:

201Total

1E

20D

30C

50B

100A

No.Individuals

Treespp.

662.0196.2338.0/1/1

338.020020101...

2002014950

20020199100

===

= + + =

DorD

DS

Shannon-Weiner Index

The Shannon-Weiner Indexbelongs to a subset ofindices that maintain that diversity can be measured much

like the information contained in a code or message

(hence the name information index).

The rationale is that if we know a letter in a message, we

can know the uncertainty of the next letter in a coded

message (i.e., the next species to be found in a

community).

The uncertainty is measured asH', the Shannon Index. A

message coded bbbbbb has lo w uncertainty (H' = 0).


The Shannon Index assumes that all species arerepresented in a sample and that the sample was obtained

randomly:S

i i

i = 1

H' = - p ln p

wherep i is the proportion of individuals found in the ithspecies and ln is the natural logarithm.


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A worked example from a community containing 100

trees distributed among 5 species:

-1.2011.001005Total

-0.0460.011E

-0.2170.099D

-0.2300.110C

-0.3610.330B

-0.3470.550A

pilnpipiAbundSpecies

H'= 1.201


The most important source of errorin this index is

failing to include all species from the community in thesample (important assumption, though rarely met).

Thus, a plant community ecologist must carefully

evaluate how well their community has been sampled.

We will look at various ways to do this later.

Values of the Shannon diversity index for real

communities typically fall between 1.5 and 3.5.


The Shannon index is affected by both the number of

species and their equitability, or evenness.

A greater number of species and a more even distribution

BOTH increase diversity as measured byH'.

The maximum diversity (Hmax) of a sample is found when

all species are equally abundant.Hmax = lnS, where Sis the

total number of species.

Evenness

We can compare the actual diversity value to the maximum

possible divers ity by using a measure called evenness .

The evenness of the sample is obtained from the formula:

Evenness =H'/Hmax =H'/lnS

By definition,Eis constrained between 0 and 1.0. As with

H', evenness assumes that all species are represented within

the sample.

Brillouin Index

When the randomness of a sample cannot be guaranteed,

the Brillouin IndexHB is preferable to theH':

i

B

lnN! - ln n !H =

whereNis the total number of individuals and ni is the

number of individuals in the ith species.

A worked example follows...

Brillouin Index

= 23.95N= 25S = 54.7955

4.7954

4.7953

4.7952

4.7951

ln ni!No. IndividualsSpecies

i

B

lnN! - ln n ! ln 25! - 23.95H 1.362

25= = =


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Evenness

Evenness for the Brillouin Index is estimated as:

B

Bmax

HE =H

whereHBmax represents the maximum possible Brillouin

diversity, that is, a completely equitable distribution of

individuals between species.

In our example, we had complete equitability, therefore,HBmax =HB\ E = 1.0.

Diversity Indices

As you have probably figured out, the choice of a

particular index is chosen with respect to the goals of the

study (emphasis on abundant vs. rare species ) and to whatextent sampling can be assured to be random.

There are other factors that come in to play, but these are

the three most widely used measures of diversity that

incorporate both richness and evenness into the

determination.

Note: There is generally NO relat ionship between one

index and another.


One of the earliest observations made by plant ecologists

was that species are not equally common in a given

community. Some were very abundant, other were

uncommon.

A graphical way was sought to describe this pattern, and so

arose species abundance models.

These models are strongly advocated among some ecologists

because they emphasize abundance while util izing speciesrichness information and therefore provide the most

complete mathematical description of the data.


A species abundance model is genera ted by graphing the

abundance of each species against its rank order abundance

from 1 = highest toN= lowest.

One of four distributions usually arise:

Log normal distribution

Geometric series

Logarithmic series

McArthur's broken stick model

Species Abundance Models(Whittaker Plots)

Species Abundance Models(Changes through succession - Bazzaz 1975)


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There are a variety of mathematical methods used to fit

these models, but that will be deferred to a subsequent

lecture.

The ability to model the data permits one to determine

how close the abundance model fits the data and

whether one community differs from another in its

adherence to a particular distribution model.

For now, be able to construct a species abundance plot

and interpret the findings in a general fashion.

Conceptos Básicos en Ecología Cuantitativa

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