Stoichiometry, herbivory and competition for nutrients: Simple models based on planktonic ecosystems

Models are examined in which two prey species compete for two nutrient resources, and are preyed upon by a predator that recycles both nutrients. Two factors determine the effective relative supply of the nutrients, hence competitive outcomes: the external nutrient supply ratio, and the relative recycling of the two nutrients within the system. This second factor is governed by predator stoichiometry - its relative requirements for nutrients in its own biomass. A model with nutrient resources that are essential for the competing prey is detailed. Criteria are given to identify the limiting nutrient for a food chain of one competitor with the predator. Increased supply of this limiting nutrient increases predator density and concentration of this nutrient at equilibrium, while decreasing the concentration of a non-limiting nutrient. Changes in supply or recycling of a non-limiting nutrient affect only the concentration of that nutrient. Criteria for the invasion of a second prey competitor are presented. When different nutrients limit growth of the resident prey and the invader, increased supply or recycling of the invader's limiting nutrient assists invasion, while increased supply or recycling of the resident's limiting nutrient hinders invasion. If the same nutrient limits both resident and invader, then changes in supply and recycling have complex effects on invasion, depending on species properties. In a parameterized model of a planktonic ecosystem, green algae and cyanobacteria coexist over a wide range of nitrogen: phosphorus supply ratios, without predators. When the herbivore Daphnia is added, coexistence is eliminated or greatly restricted, and green algae dominate over a wide range of supply conditions, because the effective supply of P is greatly reduced as Daphnia rapidly recycles N.