GatherBy first entry of data

Question

Assume I have data(sim) below. How can I extract first point on each horizontal line?

sim={{0.0123645, 10}, {0.0315618, 10}, {0.0349631, 10}, {0.0602517, 
  10}, {0.110052, 10}, {0.125536, 10}, {0.126541, 10}, {0.126872, 
  10}, {0.153006, 10}, {0.157659, 10}, {0.158335, 10}, {0.172981, 
  10}, {0.186542, 10}, {0.200192, 10}, {0.214166, 10}, {0.2161, 
  10}, {0.223926, 10}, {0.244128, 10}, {0.27395, 10}, {0.287663, 
  10}, {0.295087, 10}, {0.317831, 10}, {0.331263, 10}, {0.338285, 
  10}, {0.347775, 10}, {0.358619, 10}, {0.381334, 10}, {0.383822, 
  10}, {0.387735, 10}, {0.402114, 10}, {0.450075, 10}, {0.468865, 
  11}, {0.48508, 11}, {0.502013, 11}, {0.51136, 11}, {0.517392, 
  11}, {0.523373, 11}, {0.541651, 11}, {0.543816, 11}, {0.604502, 
  11}, {0.60608, 11}, {0.662307, 11}, {0.664964, 11}, {0.692087, 
  11}, {0.754625, 11}, {0.782756, 11}, {0.792393, 11}, {0.795388, 
  11}, {0.818549, 11}, {0.827898, 11}, {0.838457, 11}, {0.864839, 
  11}, {0.886406, 11}, {0.91586, 12}, {0.933204, 12}, {0.947947, 
  12}, {0.950653, 12}, {0.953183, 12}, {0.97591, 11}, {1.01709, 
  10}, {1.05193, 10}, {1.09514, 10}, {1.12728, 10}, {1.14659, 
  10}, {1.20052, 10}, {1.22754, 11}, {1.24561, 11}, {1.27093, 
  11}, {1.27265, 11}, {1.28367, 11}, {1.28511, 11}, {1.2877, 
  11}, {1.29041, 11}, {1.31259, 12}, {1.31415, 12}, {1.31774, 
  12}, {1.32675, 12}, {1.33307, 12}, {1.34072, 12}, {1.39716, 
  14}, {1.41142, 14}, {1.42015, 14}, {1.42476, 14}, {1.43117, 
  14}, {1.43567, 14}, {1.43754, 14}, {1.45814, 14}, {1.46465, 
  14}, {1.4666, 14}, {1.46877, 14}, {1.47267, 14}, {1.47754, 
  14}, {1.4838, 14}, {1.48614, 14}, {1.51368, 14}, {1.51374, 
  14}, {1.52088, 14}, {1.53724, 14}, {1.5483, 14}, {1.55711, 14}};


ListLinePlot[sim, Epilog -> {Red, PointSize[Small], Point[sim]}, 
 Frame -> True, PlotTheme -> "Detailed", 
 FrameLabel -> {"Time", "Population"}, ImageSize -> Large, 
 InterpolationOrder -> 0]

Answer 1

First /@ SplitBy[sim, Last]

{{0.0123645, 10}, {0.468865, 11}, {0.91586,12}, {0.97591, 11}, {1.01709, 10},{1.22754, 11}, {1.31259, 12}, {1.39716, 14}}

ListLinePlot[sim, 
 Epilog -> {Red, PointSize[Large], Point[First /@ SplitBy[sim, Last]], 
  Green, PointSize[Small], Point[sim]}, 
 Frame -> True, FrameLabel -> {"Time", "Population"}, 
 ImageSize -> Large, InterpolationOrder -> 0]