topic 7 - models of interspecific comp

Question 1

what models are used? why?

Answer 1

• Lotka-Volterra (1925)
○ Builds on logistic model of population growth
○ Modified to consider interspecific competition between two species
○ Considers different patterns of resource utilization

Question 2

what equation do you start with?

Answer 2

logistic growth: dN/dt = rN ((K-N)/K)

equivalent to dN/dt= rN (1-N/K)

Question 3

what subscripts are added to the logistic growth equation for species 1? why?

Answer 3

dN1/dt=r1N1 ((K1-N1)/K1)
the N1 term decreases pop growth bc individuals of species 1 reduce resource supply = use up carry capacity
this is true if individuals of species 2 are around too so dN1/dt=r1N1

Question 4

what if species 2 individuals are twice or half as hungry as species 1?

Answer 4

convert # of individuals of species 2 into an equivalent # of species 1
dN1/dt = ((K1-N1-aN2)/k1)

Question 5

describe the variables of LV model for competition

Answer 5

wo equations, one for each competitor
○ α = conversion factor for expressing species 2 in units of species 1
§ inhibitory effect on species 1 by species 2
○ β = conversion factor for expressing species 1 in units of species 2
§ Inhibitory effect on species 2 by species 1
§ The bigger the #, the greater the inhibitory effect on that species

Question 6

what effect does a have

Answer 6

§ inhibitory effect on species 1 by species 2

Question 7

what effect does B have

Answer 7

nhibitory effect on species 2 by species 1

The bigger the #, the greater the inhibitory effect on that species

Question 8

how are the LV models also commonly written

Answer 8

○ also commonly written:
§ α = α12
§ β = α21

Question 9

two possible outcomes of competition based on LV models?

Answer 9

1. Co-existence: both species persist (at a reduced density)

2 OR - The stronger competitor drives the weaker one extinct

Question 10

when does coexist occur

Answer 10

○ Occurs when neither species has a strong effect on the other, i.e., they are limited more by intraspecific than interspecific competition

Question 11

parameters in coexistence?

Answer 11

○ K1 represents how strongly species 1 limits its own population
○ K2 represents how strongly species 2 limits its own population
○ K2/β represents how strongly species 1 limits species 2
○ K1/α represents how strongly species 2 limits species 1

Question 12

stable coexistence if?

Answer 12

K1

Question 13

what if stronger competition wins

Answer 13

The stronger competitor drives the weaker one extinct
○ Species 1 goes extinct (& species 2 persists)
○ Species 2 goes extinct (& species 1 persists)
○ Limited more by interspecific than intraspecific competition

Question 14

how can the winning species be evaluated?

Answer 14

w plane phase anlysis

Question 15

Steps of plane phase analysis

Answer 15

STEP 1
• α = conversion factor for expressing species 2 in units of species 1
• STEP 2
• Graphically evaluate changes in populations size of species 2 when competing with species 1
• β = conversion factor for expressing species 1 in units of species 2
• STEP 3
• Put ZGI for species 1 and 2 on the same figure and examine outcome of competition

Question 16

what happens at K on the phase graph

Answer 16

zero growth of species 1 - dN1/dt=0

Question 17

what happens at the ZGI line for step 1/species 1

Answer 17

resources may be used up by species 1 and 2

growth of species 1 still at zero on ZGI line - pops of species 1 below the line will increase until they reach zgi

Question 18

what happens at K and ZGI line of species 2? (step 2)

Answer 18

at K2 = all resources used up by a single spcies
at k2/B= growth of species 2 has stopped dN2/dt = 0
at zgi - pops of sp 1 below line will increase until they reach zgi

Question 19

cases for phase plane? look at graphs for each case

Answer 19

case 1 N1 wins
case 2 N2 wins
case 3 stable eq
case 4 unstable eq