The dynamic matrix predicts population response to long-term experimental forest fragmentation

Context
 
Earth's forests are fragmented. Species' long-term persistence depends on their conservation in fragmented landscapes with remnants embedded in a matrix of human land use. This matrix influences species' persistence in fragments by determining their degree of isolation and the extent to which edge effects alter habitat. Matrix habitat is often dynamic, so its impact on persistence of remnant species changes over time.
 
Objectives
 
Previous research showed that the abundance response of predatory beetle species to matrix habitat predicted their response in fragments with a log-response ratio of about 0.5. When abundance declined in the matrix, there was a smaller but predictable decline in fragments. However, the predictive utility of a fragment:matrix log-response ratio needs testing with functionally different species, more detailed data, and a focus on mechanism.
 
Methods
 
In the Wog Wog habitat fragmentation experiment, we follow a detritivorous amphipod 27 years after ..., Invertebrates were sampled four times per year from 1985 to 1998, once during each season, November (spring), February (summer), May (autumn), and June (winter), and three times per year from 2009 to 2014 (each season excluding winter). Pitfall traps were opened for seven days during each sampling period. Traps were 8.5 cm diameter, 475 ml plastic cups filled with a 150 ml solution of 75% ethanol (95%), and 25% glycol. Samples for the two traps at each monitoring site were pooled. Amphipods were identified and counted in the laboratory., , \"Amphipod yr 3-29 by year.csv\" all data by year

# Site: 1-188 (pitfall traps are located at sites, unit at which samples are taken)

#rep: 1-6 (spatial random effect: replicates of the experiment)
#size: 1=small, 2=medium, 3=large, 4=control, NA=matrix (fragment size)
#edge: 1=core, 2=edge, 3=control, NA=matrix (proximity to fragment edge)
#topo: 1=slope, 2=drain (topography which determines vegetation communities)
#treat: 1=frag, 2=control, 3=matrix (the experimental treatment fragmentation)
#patch: 1-30 (spatial random effect: fragment/patch-level)
BeforeFrag\_abun: Amphipod abundance before fragmenation (abundances summed for first two years of the experiment before the treatment was applied)
LnBefFrag+1: Ln(amphipod abundance +1) before fragmenation
#yr3 amphipod abundance in year 3
#yr4 amphipod abundance in year 4
#yr5 amphipod abundance in year 5
#yr6 amphipod abundance in year 6
#yr7 amphipod abundance in year 7
#yr8 amphipod abundance in year 8
#yr9 amphipod abundan...