Chapters 15 & 16 Community Metrics
Harned Hall 301	(615) 963 - 5782
Above: A Cardon (Pachycereus pringlei) in Baja California Sur, Mexico

Sections

• Community characteristics
• Species Richness
  • Latitudinal Gradient
  • Biotic Explanations
  • Abiotic Explanations
  • Rapoport's Rule
• Community Structure
  • Guild structure
  • Is Richness important?
• Measuring Diversity
  • Biases
  • Species-Area relationship
  • Sample size-Richness relationship
  • Rarefaction
• Diversity indices
  • Dominance approaches
  • Information approach
  • Ordinal indices
• Rank Abundance
• Community similarity indices
• Terms

Community characteristics

How can we compare communities?

• We compare things by enumerating the characteristics held in common and those not shared

So what community characteristics are there?  What are the emergent properties?

• We want some characteristics found in all communities
  • Community composition
    • We can't simply list species, as then we could only compare communities with some species in common
    • However, all communities will have species, although the number and abundance will vary
    • Species diversity is a measure of the number (richness) and abundance (in the sense of number of individuals/species) of species in a community
  • Community dynamics
    • How does the community's diversity change through time?
    • Some communities have large swings in diversity, others seem more stable (less change)
    • Community Stability is a measure of the change in community in response to some disturbance (more on the definition later)

Species Richness

Species Richness - The number of species in a community

Patterns in Richness

• Latitudinal Gradient
  • Gradient: continuous change in some characteristic over space or time
  • Richness, in general, increases as one approaches the equator
  • Examples from book: Birds, Reptiles, Ants, Molluscs, Crustaceans, Mammals
  • Since this pattern is so widespread, there are many ideas about why it occurs (keep in mind that one, all or none of these theories might apply to a particular situation):
    • Biotic Explanations -- change in richness depends on change in the interactions between organisms as one changes latitude
      • Spatial Heterogeneity Theory -- more plants in tropics mean more places for insects and vertebrates to live (notice no explanation for why there are more plants in the tropics in this theory). Also hard to explain why marine richness gradients occur with this theory
      • Competition Theory -- as you go north, abiotic conditions become more stressful and species are r-selected. In the tropics, species are K-selected and compete more. Competition reduces niche breadth for each species so that resources support more species.
      • Predation Theory -- The number of predators and parasites increases in low latitudes. Predators can prevent the competitive elimination of species by superior competitors if they depress the size of the population of the dominant competitor. A predator that acts to increase the number of species in the community is called a Keystone Predator (a keystone is the central stone in the arch which seems to hold the other stones in the arch in place - remove the keystone and the arch collapses, remove the keystone predator and the diversity of the community collapses
      • Pollinators Theory -- the lack of sustained winds in the tropics increases the importance of animal pollination. Coevolution between pollinator and plant species leads to specialization and an overall increase in the number of plant and pollinator species
    • Abiotic Explanations -- looks for relationship between individuals and abiotic characteristics of environment for explanation of latitudinal gradient
      • Time Theory -- Time leads to the evolution of greater richness. The tropics have not been subject to glaciation and so have had a constant environment for longer than temperate and polar regions and so more species are found there due to evolution of new species. Some evidence that glaciated lakes have fewer species than non-glaciated lakes (when both are at the same latitude).
      • Productivity Theory -- Greater productivity (by autotrophs) means more energy is available to support more species. Productivity is greater in tropical terrestrial systems in general (longer growing seasons). This does not seem to apply as well as to some aquatic communities, especially when productivity is very great (Eutrophic lakes are those that have very high productivity of algae but they usually have low richness of algal types and of the invertebrate and vertebrate communities supported by the algae)
      • Area Theory -- It is well established that large areas have more species than do small areas. The book applies this to the latitudinal gradient, but you instructor thinks that there is no evidence that the tropics represent a larger areas of similar habitat than do some of the desert, forest, or grasslands found in the temperate zone.
      • Evolutionary Speed-- Greater species richness is the result of a greater rate of evolution in southern latitudes. This increased rate is due to increased temperature that lead to:
        • shot generation times
        • higher mutation rates (unclear if this means on a per unit time basis or on a per replication basis)
        • higher selection pressures (one of the basic tenets of evolutionary theory is that the rate of evolution is linked to selection pressure)
    • Rapoport's Rule -- Northern species have wider ranges than tropical species (wider in terms of the degrees of latitude each species occupies). Rapoport felt that, if there were no differences in the dispersal of species, then individuals of northern species would find it easier to survive in more southern habitats, even if they could not permanently invade the south. Thus, tropical richness would be increased by the temperate species occurring there. There is little evidence that this phenomenon occurs outside of some very specific situations in which temperate species are found in tropical areas. The author, who resides in Florida, has ignored a significant counterexample from his own state. Dade County (where Miami is located) and the county to the south of Dade, have more species of trees than do all of the rest of North America (excluding Mexico). Why? Many tropical species live there after dispersing from the Caribbean area (although many do not successfully reproduce). Thus, Dade is a northern area enriched by dispersal from a southern area, just the opposite of Rapoport's Rule.

Community Structure

• Studies of plant communities in similar habitats in different parts of the world demonstrated that plant morphology in a habitat often remained constant, even though the individual species might be different
  • Deserts favor a reduction in leaves, storage of water in stems or roots, and photosynthesis by the plant's stem
    • In north America, Cacti have these characteristics
    • In Africa, Euphorbs (a different family of plants, unrelated to cacti) have these characteristics
    • Many lay persons can not tell the difference between cacti and euphorbs, because their morphologies have Converged due to adaptations to similar conditions
  • Animal species seem also to do this
    • Marsupials of Australia seem to be similar to placental species in Europe and North America
      • Marsupial mice, wolves, squirrels, etc.
    • Many ungulates in Africa are similar in size and shape to Rodents in South America
• Lead to investigations of plant and animal communities to see if they have become similar in similar habitats (like individual plants have)
  • Patterns in specie richness and diversity have not been found, rather, differences appear to be significant
    • Reptiles in all habitats are more diverse (rich) in Australia than in North America
  • To explain the pattern, Whittaker subdivided diversity into a hierarchy
    • (alpha) diversity -- difference between diversity within habitats between two regions
    • (beta) diversity -- difference between the diversity in different habitats within a region
    • (gamma) diversity -- difference in diversity between two regions
    • the relationship between these diversity differences (or richness differences) is then:

  

• Guild structure
  • Guild - a group of species that are exploiting the same resource in the same way
  • Lawton and friends have investigated the herbivore guilds on bracken fern (a widely dispersed species) by separating guilds by feeding method
    • found that number of species overall depended on area
    • found that many guilds were empty in particular places
    • found no pattern in community structure
• Estimating the total species richness of the Earth
  • almost impossible to do, but we are sure that there are many more species out there than we now know of
  • rate of discovery of new species is accelerating, not declining
  • Stiling makes the assumption that most speciose (greatest number of species) group is the insects but there are many who would disagree
    • nematodes are little known
    • many bacterial habitats are not well sampled
  • no really good estimates are available
• Conservation of Species Richness
  • Natural ecosystems provide very important services and are important resources
    • ecosystems help degrade pollution
    • ecosystems produce valuable products (most fish are caught from the wild, most wood is harvested from natural ecosystems, many nutrients that are deposited by rain onto crops come from productive natural systems)
    • ecosystems ameliorate environmental extremes
    • ecosystems are the source of most new pharmaceuticals
  • species richness may be linked to ecosystem function, so that we imperil our own existence if we reduce richness to the point that ecosystem services are degraded

• • Ecotron (fancy environmental chambers) experiments have shown that productivity increases with richness (richness across all trophic levels, not just plant richness)
    • since the only difference between replicates was species richness, it showed that productivity will increase even if the amount of nutrients does not
  • Species rich grasslands recover from drought faster (and are less damaged by drought)
    • experiment planted communities of prairie plants (1, 2, 4, 6, 8, 12, or 24) and measured nutrients in the soil, cover, productivity (all increased with richness)
    • however, the change between 12 to 24 was less than the change from 1 to 2, so that there comes a point where increasing richness increases the measured outcomes very little
  • Since most species are tropical, conservation must focus there as well as locally
    • There are richness "hotspots" (like Madagascar) which should be also conserved
    • Studies of hotspots for different kinds of organisms show that a hotspot for one is likely to be a hotspot for others, which allows concentration of conservation efforts
    • Although the tropics are most rich, many wish to conserve some of all habitat types

Is Richness important?

• ecosystem importance- How does species richness affect the entire living system
  • Ecotron experiments link total system productivity to richness (probably because resources include lots of different things [sunlight, different minerals] and the entire spectrum of resources are more efficiently used by a group of species, each most efficient with a particular resource)
  • There may be a link between richness (diversity) and the stability of ecosystems (this is a complex area discussed in a chapter we have not yet covered)
  • Rich, diverse systems may be less susceptible to invasion by foreign species
    • diversity may reduce the total amount of unused resources, preventing a new species from gaining a foothold
  • Diverse communities may be less susceptible to changes brought about through disease
    • rich communities have lower average species density, so many species may be below their threshold density of susceptibles, preventing disease from establishing itself
• importance to us
  • Many individual species provide benefits to us, and the argument is that we do not know what is out there, but we do know that losing a species is the loss of potential human benefit
  • aesthetic considerations (not to be discounted in the face of short-term economic benefit)
  • ecosystems provide many services (fresh water, cleaning the air, etc. - see chapter 1 for a discussion), and there may be a link between the diversity of an ecosystem and its ability to provide those systems (here, more diversity means better services)

Measuring Diversity

There are two components to species diversity

• Richness - number of species present
• Evenness - how evenly is each species represented - is the sample basically a few numerous species with some rare species present or are all species equally represented

Biases to avoid when comparing species richness among different samples

• Species-Area relationship
  • Larger the area, the richer the species found
  • Result is that you cannot directly compare two samples taken from areas of different size because the larger area should have more species
• Sample size-Richness relationship
  • samples with more individuals will usually have more species, so that if one compares samples of different total size from the same area then the one with more individuals should have more species (even though the richness is the same -after all, they are samples from the same area!)
  • because the relationship between the number of species in a sample and the size of a sample is not linear, you can't just reduce the number of species in a sample proportionately (halve the sample size, halve the number of species won't work)
• Rarefaction
  • Correction for bias in species number due to sample size by standardization to the number of species expected in a sample if it had the same total size as the smallest sample
    • very similar to the idea behind Effective Population Size for comparing genetic drift in two populations with different mating systems or different histories
  • Say you had two samples, A with 100 individuals total and those 100 individuals distributed among 9 species and sample B with 25 individuals distributed among 4 species.
    • Rarefaction answers the question "How many species would I expect in sample A if I had caught only 25 individuals in all instead of 100?"
  • N = total number of individuals in rarefied sample (100 in the sample above)
  • N_i = number of individuals in the i^th species
  • n = size of the smaller sample (25 in the example above).
  • We want to calculate E(S), which is the expected number of species in the sample IF THE SAMPLE WERE OF THE SMALLER SIZE (n).

  

  • Look at this expression and simplify it in your mind. Each term that you sum is 1 minus a fraction, so each term you sum is less than 1. You are summing up S (= number of species in the sample) terms, so the sum will have to be less than S (since each term is less than one and there are S terms). Therefore, the expected number of species will be less than the actual number of species
    • This is because you would expect to capture fewer species in a smaller sample
  • The expressions within the inner most parentheses are not fractions, they are combinations (note that there is no horizontal bar). These combinations are defined as:

  

  • and

  

  • remember that the fraction on the left of the = sign is not a fraction (note: no horizontal bar), and the fraction on the right is one. The ! means that the expression is a factorial. The expression on the left is called a combination because it gives you the number of ways to take N objects n at a time. For instance, there are three ways (= 3!/2!1!) to group 3 objects 2 at a time (1&2, 1&3, 2&3). Factorials (indicated by !) are gotten by multiplying the number times one less times two less times ...

  Without rarefaction, one can not compare samples that have different number of individuals in each sample

  For more on this, refer to the document "Rarefaction" by clicking on the blue link

Diversity indices

How are we to compare two communities?

• Need a way to measure diversity
  • Example - two lakes in North America with one in Argentina
    • Both have similar abiotic characteristics
    • Can differ in the number of species present
    • Can differ in the evenness of the species present
  • Which of the below is the most diverse community??
    • Notice that the overlap in species differs quite a lot, as the Argentine lake shares no species with those in North America

• Not so easy to decide is it?

• Must include both a species richness component and a species evenness component
• There is no one way to measure diversity, so we will look at more than one

• Dominance approaches - the Simpson and Berger-Parker indices
  • In dominance indices, the most common species make the greatest contribution, and adding lots of rare species will not increase the index's value by much
  • Berger and Parker proposed a simple index which is the total number of individuals of all species divided by the number of individuals in the most common species. Adding species (which must increase the numerator) will increase the index's value

    

    • Notice that this is the RECIPROCAL of the formula presented in the textbook so that the index will increase as the diversity of the community increases
      • If one were to use the formula as presented in the book (Nmax over N), the advantage there is that the index goes from 1 (least diverse) to 0 (most diverse) and this restricted range might be useful in an index
    • In this index, the addition of more rare species does not change the denominator but will increase the numerator (in the formulation above)
  • Simpson's index is simply the inverse of the sum of the square of the species proportions (slightly modified for communities of finite size). It is an inverse because we want an index that increases as we add species or as we even out the proportions of the species
    • If there are S species and n_i is the number of individuals of the i^th species and N is the total number of individuals, then Simpson's index (which = 1 - D) is:

  

  • Notice that D will get smaller as the diversity of the community increases (if you keep N constant and increase the number of species, each ni must be smaller, on average, and so the numerators get smaller).
  • Simpson's index is normally expressed as 1/D so that the index will increase as diversity increases
  • Simpson's index uses information from each species, unlike Berger Parker, and so it is in some ways more accurate, but it is very insensitive (unchanging) to the addition of rare species to the sample

• Information approach - the Shannon and Brillouin indices
  • This is a very different approach taken from the mathematical theory of information.
  • The rationale is that information is needed to characterize a community. How much?
    • Each individual needs to be included, but it there is less information needed if they can be grouped and tagged as a group.
    • So, if all individuals are different species, you would need a tag for each one (maximum information needed) and when all are members of the same species you need only one tag for all (minimum information needed).
  • Shannon index is a measure of the amount of information needed to describe every member of the community. If p_i is the proportion of individuals (from the sample total) of species i, then diversity (H') is:

  

  • the negative out front is needed to offset the negative you get when you take the natural log of p_i (since p_i is a fraction, its log is negative)
  • as more species are included, the average p_i gets smaller and so its log get s more negative and the total value of the index increases
  • This is a useful measure because one can calculate evenness using it.
    • For any given sample size containing (N) containing S species, the value of H' will change when evenness changes. The maximum H' value (Hmax), without adding individuals or species, is attained when the numbers of individuals of every species is equal (here, the proportion would be 1/S). Evenness (E) is then the ratio of the actual H' value to the maximum value (and thus it ranges from 0 to 1)

  

  • In this index, both species richness and evenness matter.
    • When the number of species increases, H' increases.
    • When one species dominates (and evenness decreases), H' decreases.
  • However, the Shannon index is dependent on the assumption that the sample used to generate it is a random sample of the community

  • Brillouin Index
    • Useful when the randomness of the sample is suspect
    • Similar to H', but based on numbers instead of proportions

    

    • all of the symbols are as before
    • this index will increase as the total number of individuals in the sample increases, even if the number of species nor the species' proportions do not change
    • For more on the calculation of these indices, refer to the document "Diversity Index Calculation" by clicking on the blue link
• Ordinal indices
  • If an index treats all species the same, it is a cardinal index
  • If an index use some characteristic of the species (its danger of extinction, its trophic position, its value to humans) to rank or weight species, than the index is an ordinal index
    • The book gives an example, but there are as many ways to do the weighting as there are reasons for weighting species, so we will go no farther than to mention it as an alternative

Rank Abundance

A graph can provide more information than can a simple index number, so many have turned to a graphical way of describing diversity

• Rank-Abundance diagrams
  • y-axis is proportion of total individuals in a species (or total biomass, total canopy area, or total ground cover, etc.) - this data is often expressed as a logarithm or a log scale is used
  • x-axis is species, ordered (ranked - hence the name for this technique) from the species with the largest proportion to that with the smallest proportion (most common to most rare species)
  • draw a curve linking the midpoint of the columns and you have a species abundance curve
    • usefulness of this approach is that different relationships between species give different curves, so one can look for patterns produced by different ecological processes
  • Broken Stick model
    • A null hypothesis based on no relationship between species
    • Resource axis (the stick) is divided between species randomly and all at once (like dropping a glass rod and then measuring the lengths of the broken parts)
  • Geometric model
    • Results from a resource axis which is colonized by a series of species one after the other
      • Each species takes the same proportion of the resource remaining after preceding species have taken their portions
    • Most applicable to simple situations
      • Single resource exploited by community
      • One abiotic factor has very large effect on individual's success (water in a desert)
  • Log-normal model
    • This diagram is often presented a little differently
    • x-axis is the abundance of a species
      • this axis is made categorical by dividing up the number of individuals into classes of abundance
        • the scale is usually one of doublings, so each category is twice the size of the previous category
        • can be any base, so 3x or 10x scales are also used (depends on the range of species abundances)
    • y-axis is the number of species in each class
    • when large numbers of independent factors affect the number of species present, the shape of the curve should be a hump, higher in the middle than at either end
      • often there is no falling off at the low end of the x-axis, a truncated log-normal curve
      • Preston (who pioneered this approach) felt that these truncated log-normal curves resulted from the failure of small samples to capture individuals of rare species (the low end of the X-axis is where the rare species are found)
      • when larger samples are taken, the curve should be shifted to the right, revealing some or all of the truncated part of the curve
    • this shape is like the normal curve, which is why normal is part of the name "log-normal"
      • the book says that this indicates randomness, but this is not necessarily so
        • many independent factors may be indistinguishable from random
• Potential Importance of this approach
  • Attempt to match how species interact within a community with an easily measured pattern
    • If successful, one need only sample a community, do the diagram, and the interactions between species within the community is knows from the pattern
      • If log-normal, species abundances are independent of one another, no interactions
      • If broken stick or geometric, then species interact to limit one another's abundance
        • If broken stick, then species get a random fraction of total resource
        • If geometric, then some sort of colonization or dominance hierarchy determines abundance of a species
  • We are not at the point where we can simply use this approach to determine community interactions

Community similarity indices

How can one compare the diversity of two different communities or the same community but different locations?

• can simply compare the diversity indices
  • however, these are summary indices and do not make use of all of the information one collects in the sample of each community
    • this can be fine if one wants to examine species richness and evenness without reference to which species are present
    • this can be bad if one wants to compare not just the number and evenness of species but also which species are shared by different sites or communities
• similarity indices use all of the information by comparing the presence and absence of individual species in each of the areas
  • there are many indices proposed, but we will look at three only as they represent three different approaches to measuring similarity

• Jaccard Index (C_j)

  

  • here, the number of species present in both areas is divided by the total number of species present in both areas
  • avoids using d, the number of species absent from both
  • d is interesting only if you are sure that you know which species are missing, which means you must know the species pool (total number of species possible) and this knowledge is usually not available
• Matching Coefficient (C_sm)

• Similar to Jaccard, but makes use of the absence of a species as well as its presence
• if there is a species pool (say all of the species found on an island group) and you are comparing the communities on two islands, then one might argue that the absence of a species is significant and should be part of the index

• Morisita-Horn index (C_mh)
  • Horn's modification of a well-known index by Morisita

  

  • S = total number of species at both sites
  • aN = the total number of individuals of all species collected at site A
  • bN = the total number of individuals of all species collected at site B
  • an_i = the number of individuals of the i^th species collected at site A
  • bn_i = the number of individuals of the i^th species collected at site B
  • and, in the denominator, there are two terms summed that are defined as:

  and

• Uses information about the number of a species found as well as the richness (notice that the two indices above just use presence or absence)
• When applied to comparing two species instead of two communities, it is a measure of niche overlap (see competition chapter)

• Cluster analysis
  • When more than two sites are compared, then these indices will not work
  • Cluster analysis is a way to link three or more sites (or communities)
  • produces a tree (also called a dendrogram, which means a tree picture) in which each species is clustered with the most similar other species or cluster of species
  • There are many ways to cluster
  • the book only discusses methods that build up the tree by starting with a single site and adding each site to the tree one at a time
    • we will not go into the clustering methods
  • a second way of approaching this is to start with all of the sites clustered and to divide them into smaller and smaller clusters
• Ordination
  • we will not discuss ordination at this time

Terms:

Species diversity, Community Stability, Latitudinal Gradient, Gradient, Spatial Heterogeneity Theory, Competition Theory, Predation Theory, Keystone Predator, Pollinators Theory, Time Theory, Productivity Theory, Area Theory, Rapoport's Rule, a (alpha) diversity, b (beta) diversity, g (gamma) diversity, Guild, Richness, Species area relationship, Sample size - Richness relationship, Rarefaction, expected number of species E(S), diversity indices, Dominance approaches, Simpson's index, Berger and Parker index, Dominance approaches, Shannon index, evenness, Brillouin Index, cardinal index, ordinal index, Rank-Abundance diagrams, species abundance curve, Broken Stick model, Geometric model, Log-normal model, truncated log-normal curve , similarity indices , Jaccard Index (C_j), Matching Coefficient (C_sm), Morisita-Horn index(C_mh), Cluster analysis

Last updated April 10, 2006