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Forest insect defoliators often have a "scramble" competition. If larvae can find foliage they still survive, but when all foliage is destroyed then mortality increases very rapidly. This is because these insects have seasonally-synchronized life cycles. If food is exhausted before they can pupate, then none of them pupates.

Mechanisms of competition:

1. Simultaneous resource utilization. Examples: forest defoliators, dung insects

2. Direct interaction. Examples: aggression, cannibalism, territoriality

Simultaneous resource utilization is usually associated with threshold-type relationships between resource abundance and population growth rate; in some cases "scramble" competition happens.

Direct interaction among organisms makes competition balanced and usually results in a gradual decline of population growth rate with the decrease in the amount of resources.

11.2. Competition between Species

Competition among ecologically similar species is the major factor that determines the structure of animal and plant communities. The main question is, can competing species coexist or not, and what are the major factors that affect coexistence. This topic is a bridge between population ecology and community ecology.

Major problems:

1. In conservation ecology: to prevent extinction of particular species; predict potential losses in species composition after introduction of competitors; to reduce competition effects.

2. In biocontrol: to find an exotic natural enemy which will successfully fit into the community of existent natural enemies; to find exotic non-pest competitors that may oust the pest species.

In the logistic model, population density converges to the carrying capacity K, as it is shown below:

Now, we will introduce the second (competing) species. As a result, the figure becomes two-dimensional:

In this example, species #1 becomes extinct as a result of its competition with species #2.

Competitive exclusion principle was first formulated by Grinnell (1904) who wrote:

"Two species of approximately the same food habits are not likely to remain long evenly balanced in numbers in the same region. One will crowd out the other; the one longest exposed to local conditions, and hence best fitted, though ever so slightly, will survive, to the exclusion of any less favored would-be invader."

If competing species are ecologically identical (use the same resource), then interspecific competition is equivalent to intra-specific competition. Each organism competes with all organisms of both populations. As a result, population growth rate of each population is determined by the sum of numbers of both populations:

'Excel spreadsheet "lotkcomp.xls"

In this case, both isoclines are parallel and have a slope of 45° (see figures above). The species that have a higher carrying capacity (K) always wins. Higher carrying capacity means that the species can endure more crowding than the other species (e.g., due to more effective search for resources). Competitive exclusion is called K-selection because it always go in the direction of increasing K.

If competing species are sufficiently different then intra-specific competition is stronger than inter-specific competition. Organisms of another species are not considered as "full" competitors. As a result, the numbers of inter-specific competitors is multiplied by a weight wi<1:

If «fans intersect, Inn inn is a ataHa *qu Arium -al wdndi ipwH GMUHl.

If naAnss donl ntaract, Ihon ons ipntt h «dudad by anolhv spsön

If naAnss donl ntaract, Ihon ons ipntt h «dudad by anolhv spsön

Theoretically it is possible that weights wi>1. This means that organisms of another species are stronger competitors than organisms in the same population. I don't know any example of this sort. But this situation is always discussed in ecological textbooks. If wi>1 and isoclines intersect, then one species will oust the second one, but what species will be excluded depends on initial conditions (initial numbers of both populations):

This system has an unstable equilibrium which separates 2 areas of attraction: (1) where the first species ousts the second one and (2) where the second species ousts the first one.

''Excel spreadsheet "compet.xls"

Thus, species coexistence is possible if intraspecific competition is stronger than interspecific competition. This occurs if competing species have different preferences in resource usage.

When the principle of competitive exclusion became widely known among ecologists, it seemed to contradict with some well known facts and this contradiction was formulated as "paradoxes". For example, "plankton paradox" focused on the variability of plankton organisms which all seemed to use the same resources. All plankton algae use solar energy and minerals dissolved in the water. There are not so many mineral components as compared to a large variability in plankton algae species.

There is no final solution for this paradox. However, it became clear that coexistence of species that use the same resource is a common phenomenon. Mathematical models described above are correct, but they are oversimplified; thus it is difficult to apply them to real species. More complicated and more realistic models indicate that species coexistence is possible. For example, plankton algae have distinct seasonality in their abundance which is ignored in the simple Lotka-Volterra model. Cyclical dynamic regime allows species to coexist even if they cannot coexist in stable systems. Another important factor is spatial heterogeneity which effect is substantial even in such homogeneous systems as the ocean.

11.3. Ecological Niche

The ecological niche is not a notion of quantitative population ecology despite of several attempts to define it quantitatively. There were numerous definitions of ecological niche. Grinnell (1917) defined it as all the sites where organisms of a species can live (where conditions are suitable for life). Elton (1927) described the niche as the function performed by the species in the community of which it is a member. The first definition emphasized the "address" of the species and the second one emphasized its "profession" (Miller 1967).

Hutchinson (1957) defined a niche as a region (n-dimensional hypervolume) in a multidimensional space of environmental factors that affect the welfare of a species. This definition is more close to Grinnell's definition. It became popular because the range of tolerance to ecological factors can be easily measured, whereas species "profession" is hardly measurable. It is believed that the intensity of competition is proportional to the degree of niche overlapping. However, this kind of statements should be accepted with caution because: (1) measurement of niche volume is a subjective procedure, (2) some important dimensions of the niche may be not known, (3) niches change in the life-cycle, (4) niches change from one geographical region to another.

More information about niches can be found in Pielou, chapter 13.

11.4. Cooperation

Intra-specific cooperation results in increased reproduction and/or survival of organisms in groups as compared to isolated organisms. This is called group effect which was first analyzed Allee (1931) and is often called "Allee effect".

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Group effect results in the increase of population growth rate with increasing population density when density is low. There is more danger of extinction in populations with group effect because there is a minimum population density below which population declines until it is gone.

Cooperation between different species is relatively rare in nature and we will not study its models. Usually it has a form of symbiosis.

Lecture 12. Dispersal and Spatial Dynamics

12.1. Random walk

Early population studies concentrated on local population dynamics. However, spatial processes are very important in life-systems of most of the species. They may so significantly modify system behavior that local model would be unable to predict population changes.

Several ecological problems cannot be addressed without analysis of organism dispersal. Examples are: spread of invading species, epidemics, etc.

Let's take the problem of pest insect control as an example. The first question is what area to treat. If this area is too small it will be immediately colonized by immigrants. Crop rotation is often used to prevent propagation of pests, but the distance between fields with the same crop in two consecutive years should be separated further than migration distance. Finally, many insect pests are sampled using traps (pheromone-baited traps or UV-traps). To determine pest density from trap catches it is important to know dispersal abilities of the insect.

The main problem: how many organisms disperse beyond a specific distance?

Random walk is simulated here assuming that 50% individuals stay at the same place, 25% move to the left, and 25% move to the right. After several time steps the distribution of organisms becomes close to the normal distribution:

-Excel spreadsheet "diffus.xls" Normal (=gaussian) distribution corresponds to equation

Random walk can be defined in a 2-dimensional space. If organisms were released at the center of coordinates (0,0), then their distribution can be described by 2-dimensional normal distribution:

This is a 2-dimensional normal distribution:

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ZtkiiHBlanal nomul dAbücn

12.2. Diffusion Models

Advantage of diffusion models is that they can be applied to any initial distribution of organisms. The most simple diffusion model in 1-dimensional space is:

9t a

where N is population density, and D is diffusion coefficient. This equation indicates that the rate of population change is proportional to the curvature of population density. Examples below show that population increases where curvature is positive and decreases where it is negative.

Skellam (1951) combined diffusion equation in a 2-dimensional space with exponential local population growth:

Model assumptions:

all individuals simultaneously disperse and reproduce; there is no variation in dispersal abilities of individuals.

Skellam's model predicts that if a population was released at a single point, then its spatial distribution will be a 2-dimensional normal distribution:

One of the most interesting features of this model is that it predicts the asymptotic rate of expansion of population front. The rate of population expansion, V, is defined as the distance between sites with equal population densities in two successive years:

Skellam's model gives the following equation for the rate of population expansion:

■'Excel spreadsheet "skellam.xls"

Both parameters, r and D, can be estimated in independent experiments. Intrinsic rate of population increase can be determined from the life-table. Diffusion coefficient D can be estimated using mark-recapture experiments. For example, if marked animals are released within a uniform grid of traps, then diffusion coefficient is estimated as:

where M(t) is mean displacement of organisms recaptured t units time after their release (Skellam 1973).

Example:

The muskrat (Ondatra zibethica) was introduced to Europe in 1905 near Prague. Since that time its area expanded, and the front moved with the rate ranging from 0.9 to 25.4 km/yr. Intrinsic rate of population increase was estimated as 0.2-1.1 per year, and diffusion coefficient ranged from 51 to 230 sq.km/yr. Predicted spread rate (6.4-31.8 km/yr) corresponds well to actual rates of spread.

12.3. Stratified Dispersal

One of the major limitations of diffusion models is the assumption of continuous spread. In nature many organisms can move or can be transferred over large distances. If spread was continuous, then islands would never be colonized by any species. Discontinuous dispersal may result in establishment of isolated colonies far away from the source population.

Passive transportation mechanisms are most important for discontinuous dispersal. They include wind-borne transfer of small organisms (especially, spores of fungi, small insects, mites); transportation of organisms on human vehicles and boats. Discontinuous long-distance dispersal usually occurs in combination with short-distance continuous dispersal. This combination of long- and short-distance dispersal mechanisms is known as stratified dispersal (Hengeveld 1989).

Stratified dispersal includes:

• establishment of new colonies far from the moving population front;

• growth of individual colonies;

• colony coalescence that contributes to the advance of population front.

The area near the advancing population front of the pest species can be subdivided into 3 zones:

• Uninfested zone where pest species is generally absent

• Transition zone where isolated colonies become established and grow

• Infested zone where colonies coalesced

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