An experiment in predator-prey dynamics was conducted using Chaoborus, a predato

ID: 3230733 • Letter: A

Question

An experiment in predator-prey dynamics was conducted using Chaoborus, a predatory fly larvae, and its favored prey. Daphnia, a tiny crustacean. Daphnia were exposed to increasing densities of Chaoborus. The experiment was done in laboratory microcosms (10 gallon tanks) with a standard density of phytoplankton as food for the Daphnia. 80 Daphnia were added to each tank and the Chaoborus were given a day to attack the Daphnia and then the density of Daphnia in each tank was measured. The mean Daphnia density at each of 4 levels of Chaoborus, the number of tanks at each density, and the standard deviation at each density are given below. a) What are H_0 and H_a for this experiment? b) Given mat SS_(error) = 2815.12 and SS_(treatment) = 867.56, construct an ANOVA table and evaluate the overall effect of the treatment at an alpha of 0.05.

Explanation / Answer

Solution

Back-up Theory

Let xij = # Daphnia in the jth tank with Chaoborus Density i, where j = 1,2, ….., 13 (number of tanks per Chaoborus Density) and i = 1, 2, 3, 4 (number of treatments i.e., Chaoborus Density level 0, 2, 4, 8).

The ANOVA for this is ‘0ne-way with multiple, but equal number of observations per cell’

Model: xij = µ + i + ij, where µ = common effect, i = effect of ith treatment, and ij is the error component which is assumed to be Normally Distributed with mean 0 and variance 2.

Now, to work out the solution,

Given 13 tanks per Chaoborus Density, total number of observations, N = 4 x 13 = 52.

Number of treatments, r = 4 (4 levels of Chaoborus Density).

Also given are: SSerror (SSE) = 2815.12; SStreatment (SSR) = 867.58; = 0.05

ANOVA TABLE [explanatory notes are given below the table]

Source

Fcal

Fcrit

Significance

Treatment

r – 1 = 3

867.58

289.193

4.931

F3, 48, 0.05

= 2.80

Significant

Error

51 – 3 = 48

2815.12

58.649

Total

N – 1 = 51

SSR + SSE

= 3682.70

Explanatory Notes: MS = SS/DF; Fcal = MStreatment/MSerror; Fcrit = upper 5% () point of F3, 48. Since Fcal > Fcrit, the difference in treatment means is significant.

Conclusion: there is enough statistical evidence to suggest that the Chaoborus Density affects ## Daphnia.

DONE