The Resource Ratio Hypothesis

|Lecture topics| Background | One resource | Two resources | Optimal foraging | Consume | Two species | Examples |


  1. General background: the need for a mechanistic explanation of competition in plants

    1. Predictions from prevailing theory (e.g., Lotka-Volterra)
      1. Plants should compete strongly due to similarities in resource requirements
      2. Competitive exclusion should be commonly observed

    2. Competitive interactions have been experimentally demonstrated over and over

    3. A mechanistic theory of competition in plants has been lacking

    4. A suitable explanation of how competition operates needs to be consistent with observed patterns

      1. More species coexist in areas of intermediate resource availability
        1. Stress limits at low resource levels
        2. Competition limits at high resource levels

      2. Experimental observation -- Rothamstead results
        1. Species diversity declines in plots with nutrient addition
        2. Species diversity changes little in plots with no nutrient addition

    5. Potential Mechanistic Explanation: Tilman's Resource Ratio Hypothesis

      David Tilman proposed a mechanistic explanation of competitive interactions in plants that was based on resource utilization. He calls this the Resource Ratio Hypothesis. Although the explanation he provides is not perfect, it has opened the way to developing a better understanding of how competitive interactions between plant species occurs. It also makes predictions that are reasonally consistent with a number of observations made within natural ecological systems.

 


|Lecture topics| Background | One resource | Two resources | Optimal foraging | Consume | Two species | Examples |
  1. Tilman's model for consumption of one resource

    1. Growth curves and mortality

    Growth rates (curve A) are a function of resource levels. The higher the resource, the more growth is exhibited by a population.

    Mortality rates (mA) are, for simplicity, considered to be independent of resource levels.

    1. Dynamics of resource uptake and population growth (by the numbers)

      Change in resource levels over time occurs because of incorporation of resources into the biomass of the plant population. (1) The population starts at a high resource level. Growth by the population results in the uptake of resources which are incorporated into standing biomass. This in turn results in the (2) decrease of available resources in the enviroment. This process continues until there is a (3) dynamic balance between resource uptake due to growth and resource release due to mortality. Essentially b=d and the population size remains fairly constant and resource levels are held at the level of R*, the minimum resource level for the maintenance of the population.


    1. Two species competing for one resource

     

    If two species are competing for the same resource, the species that can grow at the lowest resource levels will be able to drive the other species out of the system. Species B above will outcompete species A, since it can exist at lower resource levels.

     


|Lecture topics| Background | One resource | Two resources | Optimal foraging | Consume | Two species | Examples |
  1. A graphical model for one species and two resources

    1. Growth in response to two essential resources

      1. One resource

    The R* value for the first resource divides the world into two regions. At lower resource levels the population declines in size (i.e., dN/dt<0). At higher levels the population increases in size.
    The R* value for the second resource divides the world into two regions. At lower resource levels the population declines in size (i.e., dN/dt<0). At higher levels the population increases in size.

      1. ZNGI

        When the both resources are considered together, two areas of the resource plane are defined. One area to the upper right of the combined R* values represents resource conditions that will produce positive growth rates for the population. The line defined by the combined effects of the R* values for the two resources is known as the Zero Net Growth Isocline or ZNGI. This represents the resource condtions that will result in zero net growth because the rate of growth is balanced by the rate of mortality.
    1. The notion of optimal foraging in plants

      1. Definition

        Optimal foraging in plants

        Plants should consume essential resources in such a way that the resources are equally limiting.

      2. Optimal ratio for consumption

        R*2 : R*1

            The optimal consumption ratio can be determined from the ZNGIs for a pair of essential nutrients, since the optimal consumption ratio should be equal to the ratio of the nutrient concentrations at which each nutrient is limiting to further population growth, i.e, the R* values.

      3. Deriving the general relationship

        Step 1

         R2 / R1 =  R*2 / R*1 The optimal ratio of resource availabilites should always be equal to the ratio of the R* values.
        Step 2 R2 =  R*2 / R*1 x R1 For a graph depicting the relationship between resource availabilities for two essential resources, all possible values for resource availabilites where the two resources are equally limiting is given by the equation to the left. (This equation produces the line shown in the figure associated with step 3.)
        Step 3 For resource ratios not lying on the line in step 2, one of the two resources is more limiting.

|Lecture topics| Background | One resource | Two resources | Optimal foraging | Consume | Two species | Examples |

    1. Resource consumption under optimal foraging

      1. Graphical representation

      1.     Consumption under optimal foraging can be depicted grahically, as shown to the left. The blue circle represents the current availabilities of the two resources. The arrow is a vector representing the rate of consumption (length of the vector) and the consumption ratio (dirction of vector). The consumption ratio, under optimal foraging, will always parallel the optimal foraging line defined in step 3 above.

         

        The more resources that are available, the greater the rate of consumption will be.


    1. End result of consumption by one species

        Consumption will continue unitl the resources available coincide with theZNGI. Here, resources are released at the same rate that they are taken. This results in an equilibrium, where the overall biomass of the population does not change over time.

     


|Lecture topics| Background | One resource | Two resources | Optimal foraging | Consume | Two species | Examples |
  1. The two species model

(See slide in pdf file for lecture to view the figures for the 4 cases)

      1. A-wins — This occurs when the ZNGI of A falls completely below the ZNGI for B. A can thus survive at lower resource levels of both resources.

      2. B-wins — This occurs when the ZNGI of B falls completely below the ZNGI for A. B can thus survive at lower resource levels of both resources.

      3. Stable coexistence— This occurs when the ZNGI curves for A and B intersect at one point, which represents equilibrium conditions where both species are in a dynamic balance and are neither increasing or decreasing in size. This point represents a stable equilibrium if both species are most limited by the resource that they are consuming at the greatest rate. This condition represents a situation where intraspecific competition is greater than interspecific competition, the same requirement for stable coexistence found in more theoretcial treatments of competition theory.

      4. Unstable equilibrium— This occurs when the ZNGI curves for A and B intersect at one point, which represents equilibrium conditions where both species are in a dynamic balance and are neither increasing or decreasing in size. This point represents a unstable equilibrium if both species are most limited by the resource that their competitior is consuming at the greatest rate.This condition represents a situation where interspecific competition is greater than intraspecific competition, the same requirement for stable coexistence found in more theoretcial treatments of competition theory. Under these circumstances, any slight perturbation away from the equilibrium point will most likely result in one of the two species outcompeting the other. Generally, the outcome of competition for the relationships leading to an unstable equilibrium depends entirely on the initial conditions of the system, i.e., the initial resource availabilities.



|Lecture topics| Background | One resource | Two resources | Optimal foraging | Consume | Two species | Examples |
  1. Model predictions and real systems (see class handout)

    1. Experimental evidence -- the n-fixer study
    2. Prediction: ecological gradients
    3. Prediction: impact of nutrient additions
    4. Prediction: spatial heterogeneity


|Lecture topics| Background | One resource | Two resources | Optimal foraging | Consume | Two species | Examples |

© kmoloney@iastate.edu ---19 March 2001