How to interpret repeated measures ANOVA results? how could the study have been designed differently so that a repeated measures ANOVA could have been avoided?

Background info: this data represents an experiment of ten small-mammal trapping grids that were established in order to study the effect of food addition on population densities. Five of the grids received food supplements while the others were not manipulated. The population levels on each grid were monitored 3 times at monthly intervals following the food addition.

Column 1: Food. Where: 1 = no addition; 2 = food added

Column 2: Grid. Grids 1 - 10

Column 3 - 5: Population density in June, July, and August.

treat	grid	denjun	denjul	denaug
1	1	9.089	12.308	12.128
1	2	13.405	11.846	7.69
1	3	12.645	10.816	17.427
1	4	18.27	9.131	14.538
1	5	15.837	11.931	10.077
2	6	6.58	12.418	16.239
2	7	10.466	9.322	20.156
2	8	12.008	14.323	17.689
2	9	7.77	15.943	16.302
2	10	9.373	16.809	22.052

The repeated measures ANOVA results (in R-code):

Univariate Type II Repeated-Measures ANOVA Assuming Sphericity

Sum Sq num Df Error SS den Df F value Pr(>F) (Intercept) 5190.0 1 54.47 8 762.2559 3.195e-09 *** ftreat 13.8 1 54.47 8 2.0198 0.193041 dentype 82.2 2 137.69 16 4.7751 0.023648 * ftreat:dentype 149.2 2 137.69 16 8.6699 0.002814 ** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Mauchly Tests for Sphericity

Test statistic p-value dentype 0.99263 0.97445 ftreat:dentype 0.99263 0.97445

Greenhouse-Geisser and Huynh-Feldt Corrections for Departure from Sphericity

GG eps Pr(>F[GG]) dentype 0.99269 0.023970 * ftreat:dentype 0.99269 0.002891 ** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

HF eps Pr(>F[HF]) dentype 1.319145 0.023647929 ftreat:dentype 1.319145 0.002813563