Incidence Functions

• Concept introduced by Diamond (1975) to describe the probability of occurrence of a species with respect to ordered site characteristics, such as species number

Incidence Functions

• The x-axis is the number of species on the island and the y axis is the proportion of islands in a given size class that were occupied by the species

Incidence Functions

• “High-S” species occurred mostly on large, species-rich islands, whereas the much less common “supertramp” species showed the opposite pattern

Incidence Functions

• Gilpin and Diamond (1981) explored the connection between the incidence function and the equilibrium theory of island biogeography

• The IF represents the time that a species occupies islands of a particular size class (early succession species occur briefly…)

• Paradigm was a lack of competition with each species having a species-specific colonization and extinction rates

Incidence Functions

• The IF may also simply reflect the distribution of habitat types among islands

• For example, high-S species may be habitat specialists and those ‘specialized’ habitat may only exist on larger islands

Incidence Functions

• We can use null models to clarify what the proper interpretations of the IF should be

• Whittam and Siegel-Causey (1981) examined Alaskan seabird colonies using IF

Incidence Functions

• They found examples of both high-S species (CM) as well as supertramps (GWG)

Species Richness

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Incidence Functionsother implications

• IF analysis can be used to identify unusual minimum area requirements for particular species

• Just looking at the charts may not be enough as small islands may be missing certain species due to the small likelihood of random settlement

Incidence Functions

• Schoener and Schoener (1983) expanded Diamond’s IF idea to go beyond island area or species richness.

• One can order sites by any number of criteria, and then the occurrence of species tested against this ordering (i.e. Mann-Whitney U test; a measure of the strength of ordering)

Example

• Schoener and Schoener examined 76 species of birds on 521 small islands in the Bahamas (as well as other vertebrate groups)

• They also measured area, isolation, habitat availability and vegetation structure

• Lizards are perfectly ordered

• Resident birds are highly structured

• Migrant birds are more haphazard

Occurrence Sequence

Results

• Species occurrences were predictable, although different groups followed different assembly rule

• Lizards and resident birds were ordered with respect to island area, migrant birds were more related to island isolation

• The occurrence of both lizards and birds cold be predicted by vegetation and habitat structure

Implications

• Some checkerboards will only be detected when habitat differences among sites are measured and incorporated into the analysis

• When distributions of species are with respect to site characteristics, the less the patterns will conform to a simple checkerboard pattern

• An alternative is ‘nested’ species patterns

Competition and Invasion History

• While it is clear that competition does have the potential to strongly influence the structure of a community, it has become equally clear that random or stochastic events may also play a significant role, both in initial development of the community matrix and in the maintenance of that structure

Competition and Invasion History

• The invasion history (the sequence and timing of arrival of different colonists in a community) has a significant effect on the their chances of establishment and on the resultant community structure

Competition and Invasion History

• Perhaps the best evidence that invasion sequence does affect the pattern of community development in this way comes from the growing number of experimental analyses of community development in laboratory microcosms

Competition and Invasion History

• E.g. Robinson and Dickerson (1984, 1987) ran a series of experiments using beakers and small aquatic organisms (e.g. algae, ciliates, rotifers, flagellate)

• Species were added a in a specific sequence at two different rates

• Differences were determined to be influenced by both sequence and introduction rate

Competition and Invasion History

• However, there is also some evidence from these studies that the communities once assembled subsequently adjust to become less vulnerable to further invasion

• Some even suggest in some cases there is a ‘deterministic’ convergence on ‘end’ communities (priority effects)

Competition and Invasion History

• There are caveats that need to be considered when we extrapolate from microcosms into ‘real’ world communities that are much more complex

Competition and Invasion History

• A series of small seasonal pools on a freshwater marsh offers additional insight

• Natural colonization could occur in these identical pools… 50 former holes from concrete pillars removed (i.e. same size, depth, age, substrate)

Competition and Invasion History

• Pools were categorized based upon their isolation from source and extent of drying (tides)

• Resulting communities within similar groups converged upon very homogeneous (with a total of 79 species)

Competition and Invasion History

• A number of species were recorded on only one or two occasions in only one or two pools

• Jefferies divided species into two groups based on their relative occurrence (> or < 50% of pools)

• He concluded that ‘expected’ species occurred at 79.6% and ‘unlikely’ species (occurring solely through deterministic processes) was 10.9%

Competition and Invasion History

• Let’s take a more in-depth look at the importance of history and priority effects

Competition and Invasion History

L-V models of two competitors (N1 and N2) in which the outcome of competition is independent of initial conditions (A), or depends on initial conditions (B)

Competition and Invasion History

• Differences of only a few days in the arrival times of mycophagus Drosophila in the communities that develop in decaying mushrooms can alter the outcome of competition

Competition and Invasion History

• We have a pretty good idea of the influence of communities that are relatively ephemoral, but long-lived organisms are much harder to understand

Competition and Invasion History

• Dragonfly community structure is a result of temporal variation, habitat selection, and predator-prey effects

Competition and Invasion History

• One group breeds early and emerges synchronously while ‘later’ breeders tend to stagger the emergence throughout the remaining summer months, waiting until the early breeders have emerged. Why?

Competition and Invasion History

• Experimental results suggest early arriving species may act as predators or simply act as strong inhibitory priority effects on later arrivals (early arrival may allow for individuals to be larger and simply displace smaller individuals)

Competition and Invasion History

• Similar experiments have been conducted using Odonates (Morin), but added fish to the system (strong predator of odonate larvae)

Competition and Invasion History

Fish reduce the abundance of odonates, reducing the intensity of competition and priority effects and changing the relative abundance of surviving dragonflies

Competition and Invasion History

• Other examples: many sessile-based communities (rocky shores, coral reefs) where competition for free-space is the major force structuring communities

• Introduction of a predator into the system (predatory coral reef fish) can greatly impact subsequent community structure

Competition and Invasion History

Competition and Invasion History