competition equations
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2006 ◽  
Vol 10 (10) ◽  
pp. 1-30 ◽  
Author(s):  
Vivek K. Arora ◽  
George J. Boer

Abstract The global distribution of vegetation is broadly determined by climate, and where bioclimatic parameters are favorable for several plant functional types (PFTs), by the competition between them. Most current dynamic global vegetation models (DGVMs) do not, however, explicitly simulate inter-PFT competition and instead determine the existence and fractional coverage of PFTs based on quasi-equilibrium climate–vegetation relationships. When competition is explicitly simulated, versions of Lotka–Volterra (LV) equations developed in the context of interaction between animal species are almost always used. These equations may, however, exhibit unrealistic behavior in some cases and do not, for example, allow the coexistence of different PFTs in equilibrium situations. Coexistence may, however, be obtained by introducing features and mechanisms such as temporal environmental variation and disturbance, among others. A generalized version of the competition equations is proposed that includes the LV equations as a special case, which successfully models competition for a range of climate and vegetation regimes and for which coexistence is a permissible equilibrium solution in the absence of additional mechanisms. The approach is tested for boreal forest, tropical forest, savanna, and temperate forest locations within the framework of the Canadian Terrestrial Ecosystem Model (CTEM) and successfully simulates the observed successional behavior and the observed near-equilibrium distribution of coexisting PFTs.


2001 ◽  
Vol 91 (8) ◽  
pp. 720-729 ◽  
Author(s):  
H. K. Ngugi ◽  
S. B. King ◽  
J. Holt ◽  
A. M. Julian

Field studies were conducted at Alupe in western Kenya in 1995 and 1996 to evaluate the efficacy of crop and species mixtures for the management of sorghum anthracnose (caused by Colletotrichum sublineolum) and leaf blight (caused by Exserohilum turcicum). The progress of these diseases developing simultaneously on a susceptible sorghum cultivar planted in inter- or intra-row mixtures of varying proportions with either maize or resistant sorghum was monitored. The effects of host type and mixture patterns on disease progress were compared by parameter estimates derived from fitted Lotka-Volterra competition equations and nonlinear logistic models. Competition coefficients were not significant and their confidence intervals included zero in most cases, suggesting that interactions between C. sublineolum and E. turcicum did not occur. Mixtures of the susceptible sorghum with either the nonhost maize or the resistant sorghum delayed the time when disease is first observed and reduced the rate of disease progress and carrying capacity for both anthracnose and leaf blight, with a more pronounced effect on the latter disease. The lower efficacy of mixtures in reducing anthracnose was attributed to an aggregated spatial pattern, coupled with higher rates of progress for this disease. Intra-row mixtures were more efficient than inter-row mixtures in reducing disease development in all years. The implications of these observations for the management of sorghum diseases under small-scale farming systems are discussed.


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