The Resource Ratio Hypothesis
Lecture topics Background
 One resource  Two resources  Optimal
foraging  Consume  Two species
 Examples 
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. 
Growth rates (curve A) are a function of resource levels. The higher the resource, the more growth is exhibited by a population.
Mortality rates (m_{A}) are, for simplicity, considered to be independent of resource levels.
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. 
 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.


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. 
Optimal foraging in plants 
Plants should consume essential resources in such a way that the resources are equally limiting. 
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. 
Step 1 
R_{2 }/ R_{1} = R*_{2 }/ R*_{1}  The optimal ratio of resource availabilites should always be equal to the ratio of the R* values. 
Step 2  R_{2 } = R*_{2 }/ R*_{1} x R_{1}  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. 
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. 
 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.
(See slide in pdf file for lecture to view the figures for the 4 cases)