Interaction terms in GLM I a trying to determine whether or not fertilizer decreases biodiversity, and if additional light can mitigate the loss of biodiversity. My data look like this:

I created an initial plot to look at the data, and here is that plot:

Based on this plot, it seems clear to me that without additional light, fertilizer does lead to a decrease in diversity. But light mitigates the effect. I ran a GLM like so, with an interaction effect between Fertilizer and Light. I'm not sure if this is the best way to go about it. I'm skeptical of the results because the model is saying there's only a significant effect for fertilizer, but it seems pretty clear that light is having an impact. Should I be looking at this another way?
> summary(plant_glm)

Call:
glm(formula = Diversity ~ Fertilizer * Light, family = poisson, 
    data = plant)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-0.92920  -0.24454   0.04186   0.38080   0.91640  

Coefficients:
                     Estimate Std. Error z value Pr(>|z|)    
(Intercept)            1.9981     0.1302  15.348   <2e-16 ***
FertilizerF+          -0.4940     0.2115  -2.336   0.0195 *  
LightL+                0.1851     0.1762   1.051   0.2933    
FertilizerF+:LightL+   0.4798     0.2704   1.775   0.0759 .  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for poisson family taken to be 1)

    Null deviance: 21.2770  on 31  degrees of freedom
Residual deviance:  6.6221  on 28  degrees of freedom
AIC: 136.61

Number of Fisher Scoring iterations: 4


Using the Poisson family GLM means (among other things) that you assume that in the population, the variance of the response conditional on your independent variables is equal to the mean of your response conditional on your independent variables.
You are seeing a clear effect in your plot, while the model suggests that you don't have enough data to draw a conclusion. The reason for the discrepancy is that part of what makes the effect look so obvious is how bunched up the data are. The response variance in the sample is lower than the mean.
One way to analyze the data is to say, we have some measure of sample variance, which we use to estimate population variance. The difference in sample mean between your groups is high relative to that estimated variance, and so your results are significant.
Another approach, which you have chosen, is to say we don't need any estimate of population variance other than the mean, because we know that the population variance exactly equals the population mean, since the data are Poisson. If we believe this, then the difference in mean response between your groups is not so big. Basically, we must believe that the close grouping of your data is a fluke.
So anyway it all comes down to: what is "Diversity", and do you have a strong reason to believe that it's Poisson distributed. If you use the gaussian family or quasipoisson family, you will get much lower p-values. But if you really do have strong reason to believe your response is Poisson distributed, don't do that.
Call:
glm(formula = Diversity ~ Fertilizer * Light, family = quasipoisson, 
    data = plant)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-0.92920  -0.24454   0.04186   0.38080   0.91640  

Coefficients:
                     Estimate Std. Error t value Pr(>|t|)    
(Intercept)           1.99810    0.06330  31.564  < 2e-16 ***
FertilizerF+         -0.49402    0.10283  -4.804 4.74e-05 ***
LightL+               0.18514    0.08566   2.161  0.03936 *  
FertilizerF+:LightL+  0.47983    0.13146   3.650  0.00106 ** 
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for quasipoisson family taken to be 0.2364279)

    Null deviance: 21.2770  on 31  degrees of freedom
Residual deviance:  6.6221  on 28  degrees of freedom
AIC: NA

Number of Fisher Scoring iterations: 4
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