Understanding the Meta-analysis Model output in layman terms I am conducting a meta-analysis from a large number of studies. In each study are compared weights of two groups (fishes with and without internal parasite). I am interested if the weight can explain the presence/absence of a parasite. From forest plot it seems to be clear that in each continent (and for world as a whole)  there is a clear preference towards bigger fishes.
I have studies from all over the world, that means the term "bigger" fish is a relative. The bigger fish in Africa could be very small in comparison with smallest fish in Australia. Because of this fact I have used random-effect model. It should be a good choice according to some textbooks.
Is random-effect model appropriate for my situation?
Could you please help me with interpretation of model output? There are some things I do not understand:
P-value from model results is highly significant. So it is highly probable that the weight has something to do with parasite infestation. However, the Test for Heterogeneity is also significant. Does it means that my model do not meet the assumption for normal distribution of residuals? Similarly like a in the case of some simple regression?
And what about tau^2, tau, I^2 and H^2?
Is any of them similar to R-squared?
Please give me some guidance (in layman terms if possible).
library(metafor)
mod_weight <- rma(yi, vi, data = dat_weight); summary(mod_weight)

Random-Effects Model (k = 62; tau^2 estimator: REML)

  logLik  deviance       AIC       BIC      AICc  
-65.0051  130.0103  134.0103  138.2320  134.2172  

tau^2 (estimated amount of total heterogeneity): 0.3618 (SE = 0.0808)
tau (square root of estimated tau^2 value):      0.6015
I^2 (total heterogeneity / total variability):   86.67%
H^2 (total variability / sampling variability):  7.50

Test for Heterogeneity: 
Q(df = 61) = 395.7163, p-val < .0001

Model Results:

estimate       se     zval     pval    ci.lb    ci.ub          
  0.8007   0.0853   9.3830   <.0001   0.6334   0.9679      *** 

P.S. the fish-parasite research is a made-up story :)
 A: This is a number of questions, so I'm going to chip in a reference as well, and highly suggest you have some grounding in the subject before you do a meta-analysis. It's not a "turn the crank" kind of study, and generally speaking any statistical programming before you understand what you're doing is worrisome.
Systematic Reviews in Health Care: Meta-analysis in context by Egger, Davey Smith and Altman. The "in Health Care" bit only applies to an over fondness for clinical trials, but the general principles are solid and clear.
Onto your questions:

Is random-effect model appropriate for my situation?

Seems like it - generally, a random effect model is probably pretty appropriate unless you can really justify a fixed effect model, and it doesn't sound like you have any such justification for why "small" vs "large" fish would have a constant effect across all studies.

However, the Test for Heterogeneity is also significant. Does it means
  that my model do not meet the assumption for normal distribution of
  residuals? Similarly like a in the case of some simple regression?
And what about tau^2, tau, I^2 and H^2? Is any of them similar to
  R-squared?

No, none of these are like R^2. They are all measures of heterogeneity. Along with your test for heterogeneity being significant, these are all ways to look for heterogeneity between studies. The presence of heterogeneity suggests that meta-analytical approach may not be appropriate. Basically, that your studies don't represent random sampling variation around a single estimate, but that there's some underlying difference between the studies that makes it iffy to pool them all together.
It's possible this heterogeneity is terminal, and you cannot go beyond a systematic review. It's also possible stratifying your studies, meta-regression, etc. may solve your problems, but in that case you really need to revisit doing this without more background or someone with expertise in conducting a meta-analysis.
