Calculating maximum sustainable yield
MSY = Nr
r = rate of natural increase
N = average number of individuals present throughout the year
If N = 10000 and r = 0.14
MSY = 10000 x 0.14 = 1400 (constant rate of harvesting throughout the year
If 10% natural mortality occurs then MSY = 9000 x 0.14 = 1260 (taking into account
natural mortality)
Why do we have over-fishing?
Failure to account for:
Herbivory
Page 100-102, chapter 8 (Townsend, Begon and Harper)
How do plants deal with herbivory?
chemical and mechanical (morphological) defenses
What is the response of herbivores?
strongly influenced by plant defenses, and the amount of nitrogen in the plant
Herbivore response
1. remove 15-18% of terrestrial plant biomass; over 50% in aquatic systems
2. change plant communities by preferentially eating dominant plant species
Examples of Plant Defenses: secondary chemicals
Nitrogen compounds
Alkaloids e.g. nicotine, caffeine
Carbon compounds
Mustard oils
Terpenoids e.g. peppermint
Phenylpropanes e.g cinnamons, cloves
Quantitative defenses
e.g. Tannins, problem digesting food
Qualitative defenses
Atropine deadly poison
•
•
•
Trees (e.g. Oak) use quantitative defenses (digestive problems for the herbivore)
Weeds use qualitative defenses
Firs contain insect hormones (prevent metamorphosis of insect juveniles if
ingested)
Mathematical models predict polyphagous herbivores have a greater effect on plants
than monophagous herbivores
Model by Mick Crawley 1997 for a monophagous herbivore:
For the plant (equation to the right) for the herbivore (equation to the left)
In the absence of the herbivore the plant populations grows logistically
In the presence of the herbivore plant populations decline by bNV (where b is the
feeding rate of the herbivore.
For the herbivore population, c is the herbivore numerical response, cNV is the
efficiency of the herbivore to convert food into offspring, d is the death rate of the
herbivore.
At equilibrium,
=0
0
0
V* = d/c
Plant equilibrium abundance depends on herbivore death rates. The higher the death
rate of the herbivore the higher the plant abundance. The higher the efficiency to turn
food into offspring the lower plant abundance
Model for polyphagous vertebrates
• Constant level of herbivory = h, Herbivore densities are not tied to any one plant
At equilibrium plant biomass
aK r2K2 - 4rhK
V* =
2r