web={"Ladybug"\[DirectedEdge]"Aphid","Beetle"\[DirectedEdge]"Caterpillar","Towhee"\[DirectedEdge]"Caterpillar","Towhee"\[DirectedEdge]"Grasshopper","Towhee"\[DirectedEdge]"Ladybug","Dragonfly"\[DirectedEdge]"Mosquito","Towhee"\[DirectedEdge]"Mosquito","Aphid"\[DirectedEdge]"Sunflower","Caterpillar"\[DirectedEdge]"Sunflower","Grasshopper"\[DirectedEdge]"Sunflower","Louse"\[DirectedEdge]"Sunflower","Owl"\[DirectedEdge]"Towhee"};

shapes = {"Sunflower"->,"Aphid"->,"Ladybug"->,"Towhee"->,"Owl"->,"Grasshopper"->,"Louse"->,"Caterpillar"->,"Beetle"->,"Mosquito"->,"Dragonfly"->};

style ={ VertexSize->.7,EdgeStyle->Directive[Arrowheads[{{.05,.6}}],Hue[.4,1,.3]],VertexShape->shapes};

Graph[web,style]