Fixing legend in ggplot

I am plotting a scatter plot with 4 geom_ablines. The current plot looks like below:

I want to make two changes in the legend of this plot.

Removing the dot points on lines in the legend.
Making the lines in the legend horizontal instead of tilted. Is it possible because the lines have been drawn using geom_abline.

The code is:

fig <- ggplot(scalingdata, aes(x=Re, y=Sw, color=Size)) + 
  geom_point(size=3) +
  theme_minimal() +
  theme(panel.background = element_rect(fill = "#f0f4f5",
                                        size = 0.5, linetype = "solid"),
        panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.border = element_rect(color = "black",fill = NA,size = 1),
        plot.title = element_text(size = 25, face = "italic"),
        axis.title.y = element_text(size=17.5),
        axis.text.y = element_text(size=15, face="bold"),
        axis.title.x = element_blank(),
        axis.text.x = element_blank())+
  scale_x_log10(limits = c(1,10^8), breaks = trans_breaks("log10", function(x) 10^x),
                labels = trans_format("log10", math_format(10^.x))) + 
  scale_y_log10(limits = c(1,10^8), breaks = trans_breaks("log10", function(x) 10^x),
                labels = trans_format("log10", math_format(10^.x))) + annotation_logticks()

lines <- data.frame(name = c("Sw ~ Re^13/15", "Sw ~ Re^9/10", "Sw ~ Re^2/3", "Sw ~ Re^3/4"),
                    intercept = c(1, 0.79, 1.35, 1.1),
                    slope = c(13/15, 9/10, 2/3, 3/4))

fig + geom_abline(data = lines, aes(intercept=intercept, slope=slope, color=name, size=name, linetype=name))+ # color=name, size=name, linetype=name)+
  scale_color_manual(name='Size',
                     values=c("Sw ~ Re^13/15" ='Blue', "Sw ~ Re^9/10" ='Blue',
                              "Sw ~ Re^2/3" ='Red', "Sw ~ Re^3/4" ='Red',
                              'Fish' = 'Blue', 'Larvae' = 'Red'),
                     breaks=lines$name) +
  scale_size_manual(name='Size',
                    values=c("Sw ~ Re^13/15" =1, "Sw ~ Re^9/10" =1.25, "Sw ~ Re^2/3" =1, "Sw ~ Re^3/4" = 1.25)) +
  scale_linetype_manual(name='Size',
                        values=c("Sw ~ Re^13/15" ='solid', "Sw ~ Re^9/10" ='dashed',
                                 "Sw ~ Re^2/3" ='solid', "Sw ~ Re^3/4" ='dashed'))

And MRE is:

structure(list(X = 400:585, Sw = c(762000, 781000, 794000, 823000, 
846000, 849000, 853000, 882000, 887000, 898000, 941000, 979000, 
1030000, 1060000, 1070000, 1080000, 1090000, 1140000, 1170000, 
6469900, 7584900, 7914000, 7995300, 8139300, 8254100, 8482100, 
8485600, 8557900, 8642000, 8730800, 8734400, 8779000, 8812900, 
8869100, 8902600, 8914600, 8975200, 9075000, 9203000, 9269900, 
9481200, 9565700, 9656200, 9664300, 9821400, 9825700, 9989900, 
10410400, 10552900, 10820800, 10959400, 11449900, 11855900, 41766.8, 
44815, 46421, 51017, 52530, 54453, 55151, 60703, 60748, 61022, 
61850, 62083, 64308, 65524, 66017, 66115, 66963, 69001, 70887, 
74872, 74928, 76174, 85619, 85940, 300720, 349790, 414460, 507870, 
538620, 540430, 570270, 595730, 617120, 667810, 687150, 697620, 
704690, 717830, 741100, 754920, 760010, 769000, 825210, 875180, 
899020, 1042220, 1665250, 1687780, 1930520, 2071620, 1484730, 
1560040, 2205640, 3198090, 3225130, 4840500, 73.698, 91.148, 
91.843, 126.687, 130.467, 155.199, 232.717, 602.22, 615.05, 619.05, 
626.62, 655.73, 677.34, 747.73, 768.65, 778.66, 816.82, 859.61, 
885.06, 906.12, 925.43, 975.49, 1020.79, 1024.12, 1091.84, 1094.5, 
1114.2, 1122.36, 1165.94, 1290.31, 1291.33, 1302.88, 1361.19, 
1477.34, 1543.46, 1564.86, 1609.89, 1679.22, 1720.21, 1748.66, 
1769.04, 1778.18, 1804.09, 1816.32, 1842.21, 1861.27, 1861.88, 
1875.09, 1957.71, 1975.41, 2028.23, 2049.21, 2193.15, 2214.41, 
2320.91, 190.301, 213.437, 215.963, 217.451, 226.594, 227.932, 
243.172, 244.607, 292.403, 297.318, 308.91, 310.428, 319.697, 
332.16, 339.738, 345.449, 363.165, 388.971, 399.016, 414.572, 
415.794, 453.714), Re = c(401000, 343000, 537000, 414000, 595000, 
392000, 448000, 421000, 633000, 496000, 633000, 466000, 648000, 
524000, 729000, 516000, 504000, 795000, 802000, 4114000, 3809200, 
4687400, 4130800, 4228400, 4891300, 3757100, 3974800, 4798000, 
4516600, 4074300, 4310400, 4479500, 3904400, 4358000, 6464600, 
3851100, 4824400, 4412200, 5069000, 4642300, 4316300, 6473400, 
4096700, 4572600, 5340600, 5041200, 5224500, 5429300, 5481800, 
5952800, 7097300, 7165900, 7781600, 25778, 29630, 20784, 28523, 
38410, 36744, 33414, 56160, 41702, 49165, 30384, 42771, 33623, 
46439, 47329, 24810, 38161, 56150, 51390, 47929, 54400, 56860, 
59810, 67890, 303110, 236540, 282380, 354240, 408170, 391180, 
377560, 408170, 391180, 402420, 526760, 435040, 411070, 585800, 
508420, 450730, 497730, 463680, 477010, 745400, 553540, 846800, 
889800, 935100, 1047300, 1148400, 553800, 723800, 746600, 1720200, 
2939400, 2374500, 10.115, 10.11, 12.227, 29.025, 20.106, 10.165, 
17.613, 83.12, 105.2, 123.1, 148.64, 113.79, 111.14, 333.77, 
120.21, 283, 206.68, 287.45, 341.67, 318.34, 291.98, 366.66, 
456.8, 296.57, 467.7, 439.2, 415.7, 390.39, 456.8, 308.38, 478.8, 
671.2, 606, 587.2, 542.8, 749, 760.9, 692.4, 659.3, 667.6, 643, 
560.6, 777.7, 686.5, 735.2, 856.6, 690.8, 870, 710.4, 894.7, 
730.6, 825, 817.3, 920.1, 880.8, 25.031, 32.901, 29.787, 27.193, 
23.62, 29.056, 30.791, 23.425, 30.537, 36.339, 50.199, 58.272, 
52.758, 54.085, 68.21, 27.193, 71.09, 50.617, 48.967, 44.702, 
73.49, 73.49), Species = c("Dace, Trout, and Goldfish", "Dace, Trout, and Goldfish", 
"Dace, Trout, and Goldfish", "Dace, Trout, and Goldfish", "Dace, Trout, and Goldfish", 
"Dace, Trout, and Goldfish", "Dace, Trout, and Goldfish", "Dace, Trout, and Goldfish", 
"Dace, Trout, and Goldfish", "Dace, Trout, and Goldfish", "Dace, Trout, and Goldfish", 
"Dace, Trout, and Goldfish", "Dace, Trout, and Goldfish", "Dace, Trout, and Goldfish", 
"Dace, Trout, and Goldfish", "Dace, Trout, and Goldfish", "Dace, Trout, and Goldfish", 
"Dace, Trout, and Goldfish", "Dace, Trout, and Goldfish", "Giant Bluefin Tuna", 
"Giant Bluefin Tuna", "Giant Bluefin Tuna", "Giant Bluefin Tuna", 
"Giant Bluefin Tuna", "Giant Bluefin Tuna", "Giant Bluefin Tuna", 
"Giant Bluefin Tuna", "Giant Bluefin Tuna", "Giant Bluefin Tuna", 
"Giant Bluefin Tuna", "Giant Bluefin Tuna", "Giant Bluefin Tuna", 
"Giant Bluefin Tuna", "Giant Bluefin Tuna", "Giant Bluefin Tuna", 
"Giant Bluefin Tuna", "Giant Bluefin Tuna", "Giant Bluefin Tuna", 
"Giant Bluefin Tuna", "Giant Bluefin Tuna", "Giant Bluefin Tuna", 
"Giant Bluefin Tuna", "Giant Bluefin Tuna", "Giant Bluefin Tuna", 
"Giant Bluefin Tuna", "Giant Bluefin Tuna", "Giant Bluefin Tuna", 
"Giant Bluefin Tuna", "Giant Bluefin Tuna", "Giant Bluefin Tuna", 
"Giant Bluefin Tuna", "Giant Bluefin Tuna", "Giant Bluefin Tuna", 
"Stingrays", "Stingrays", "Stingrays", "Stingrays", "Stingrays", 
"Stingrays", "Stingrays", "Stingrays", "Stingrays", "Stingrays", 
"Stingrays", "Stingrays", "Stingrays", "Stingrays", "Stingrays", 
"Stingrays", "Stingrays", "Stingrays", "Stingrays", "Stingrays", 
"Stingrays", "Stingrays", "Stingrays", "Stingrays", "Saithe and Mackerel", 
"Saithe and Mackerel", "Saithe and Mackerel", "Saithe and Mackerel", 
"Saithe and Mackerel", "Saithe and Mackerel", "Saithe and Mackerel", 
"Saithe and Mackerel", "Saithe and Mackerel", "Saithe and Mackerel", 
"Saithe and Mackerel", "Saithe and Mackerel", "Saithe and Mackerel", 
"Saithe and Mackerel", "Saithe and Mackerel", "Saithe and Mackerel", 
"Saithe and Mackerel", "Saithe and Mackerel", "Saithe and Mackerel", 
"Saithe and Mackerel", "Saithe and Mackerel", "Saithe and Mackerel", 
"Saithe and Mackerel", "Saithe and Mackerel", "Saithe and Mackerel", 
"Saithe and Mackerel", "Sharks", "Sharks", "Sharks", "Sharks", 
"Sharks", "Sharks", "Ascidian Larvae", "Ascidian Larvae", "Ascidian Larvae", 
"Ascidian Larvae", "Ascidian Larvae", "Ascidian Larvae", "Ascidian Larvae", 
"Larval Zebrafish40", "Larval Zebrafish40", "Larval Zebrafish40", 
"Larval Zebrafish40", "Larval Zebrafish40", "Larval Zebrafish40", 
"Larval Zebrafish40", "Larval Zebrafish40", "Larval Zebrafish40", 
"Larval Zebrafish40", "Larval Zebrafish40", "Larval Zebrafish40", 
"Larval Zebrafish40", "Larval Zebrafish40", "Larval Zebrafish40", 
"Larval Zebrafish40", "Larval Zebrafish40", "Larval Zebrafish40", 
"Larval Zebrafish40", "Larval Zebrafish40", "Larval Zebrafish40", 
"Larval Zebrafish40", "Larval Zebrafish40", "Larval Zebrafish40", 
"Larval Zebrafish40", "Larval Zebrafish40", "Larval Zebrafish40", 
"Larval Zebrafish40", "Larval Zebrafish40", "Larval Zebrafish40", 
"Larval Zebrafish40", "Larval Zebrafish40", "Larval Zebrafish40", 
"Larval Zebrafish40", "Larval Zebrafish40", "Larval Zebrafish40", 
"Larval Zebrafish40", "Larval Zebrafish40", "Larval Zebrafish40", 
"Larval Zebrafish40", "Larval Zebrafish40", "Larval Zebrafish40", 
"Larval Zebrafish40", "Larval Zebrafish40", "Larval Zebrafish40", 
"Larval Zebrafish40", "Larval Zebrafish40", "Larval Zebrafish40", 
"Larval Zebrafish61", "Larval Zebrafish61", "Larval Zebrafish61", 
"Larval Zebrafish61", "Larval Zebrafish61", "Larval Zebrafish61", 
"Larval Zebrafish61", "Larval Zebrafish61", "Larval Zebrafish61", 
"Larval Zebrafish61", "Larval Zebrafish61", "Larval Zebrafish61", 
"Larval Zebrafish61", "Larval Zebrafish61", "Larval Zebrafish61", 
"Larval Zebrafish61", "Larval Zebrafish61", "Larval Zebrafish61", 
"Larval Zebrafish61", "Larval Zebrafish61", "Larval Zebrafish61", 
"Larval Zebrafish61"), Size = c("Fish", "Fish", "Fish", "Fish", 
"Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", 
"Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", 
"Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", 
"Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", 
"Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", 
"Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", 
"Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", 
"Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", 
"Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", 
"Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", 
"Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", 
"Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", 
"Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", "Fish", 
"Fish", "Larvae", "Larvae", "Larvae", "Larvae", "Larvae", "Larvae", 
"Larvae", "Larvae", "Larvae", "Larvae", "Larvae", "Larvae", "Larvae", 
"Larvae", "Larvae", "Larvae", "Larvae", "Larvae", "Larvae", "Larvae", 
"Larvae", "Larvae", "Larvae", "Larvae", "Larvae", "Larvae", "Larvae", 
"Larvae", "Larvae", "Larvae", "Larvae", "Larvae", "Larvae", "Larvae", 
"Larvae", "Larvae", "Larvae", "Larvae", "Larvae", "Larvae", "Larvae", 
"Larvae", "Larvae", "Larvae", "Larvae", "Larvae", "Larvae", "Larvae", 
"Larvae", "Larvae", "Larvae", "Larvae", "Larvae", "Larvae", "Larvae", 
"Larvae", "Larvae", "Larvae", "Larvae", "Larvae", "Larvae", "Larvae", 
"Larvae", "Larvae", "Larvae", "Larvae", "Larvae", "Larvae", "Larvae", 
"Larvae", "Larvae", "Larvae", "Larvae", "Larvae", "Larvae", "Larvae", 
"Larvae"), St = c(0.302433374165808, 0.362389853900744, 0.235323518267981, 
0.316386985184939, 0.226293726046568, 0.344699568138944, 0.303033145076212, 
0.333430716272689, 0.223017542504579, 0.288146783640142, 0.236594709692005, 
0.334361212296077, 0.252977172911813, 0.321953903004644, 0.233601359236799, 
0.333114218203138, 0.344203337900817, 0.228221648865378, 0.232183102213908, 
0.250295128437197, 0.316909457357351, 0.268709577645423, 0.308048935041855, 
0.306358622430061, 0.268574355248053, 0.359310368633893, 0.339771064454215, 
0.283874302307228, 0.3045241557553, 0.341051647591493, 0.322503638696486, 
0.311913824779625, 0.359239145081061, 0.323900368274474, 0.219176667244061, 
0.368414047393468, 0.296087410852063, 0.327348653980426, 0.288952360656955, 
0.317805173505505, 0.349599499061661, 0.23518164782688, 0.375138127690756, 
0.336377010833042, 0.292686346632698, 0.310204924915008, 0.304323523404437, 
0.30517060120053, 0.306385178491378, 0.289305836077696, 0.245760867447159, 
0.254302170218483, 0.242484923070044, 0.257870165748749, 0.240719274240546, 
0.355471244064845, 0.2846681185215, 0.217661796677678, 0.235860109140741, 
0.262690301692974, 0.17202920082822, 0.231843122013434, 0.197537480456343, 
0.323976771042564, 0.231016184479705, 0.304402110063851, 0.224562202134299, 
0.221997238656593, 0.424123516982184, 0.279276421804133, 0.195580134425664, 
0.219536681625896, 0.248622358777944, 0.219212016357345, 0.213215622321579, 
0.227832389358595, 0.20146919759615, 0.157899648862937, 0.235354178413181, 
0.233597292524979, 0.228178161508506, 0.210019930393074, 0.219878073423756, 
0.240388487016993, 0.232288390949214, 0.251079985698921, 0.264114641433334, 
0.207614593756514, 0.255216558855981, 0.272835854188107, 0.19502547907645, 
0.231992157091137, 0.266565280053204, 0.243021448263837, 0.263953297612413, 
0.27533163553866, 0.186864632918074, 0.258487448689974, 0.195883416277148, 
0.297855865613987, 0.287261150364813, 0.293374469828208, 0.28710187409247, 
0.426691163020906, 0.343033292092993, 0.47018174096222, 0.295890385833758, 
0.17462549544427, 0.32444207224037, 1.15960193451398, 1.43487842039073, 
1.1954881211204, 0.694670633111126, 1.03274740893889, 2.42996854423028, 
2.10287709536259, 1.15310473651356, 0.930494475702483, 0.800362608672448, 
0.670946160047344, 0.917149369794335, 0.969963623056172, 0.356546865546547, 
1.01767041791117, 0.437905647321569, 0.628994758168588, 0.475946636660009, 
0.41227308378791, 0.453016082808868, 0.504440080025434, 0.423426859723028, 
0.355655416919196, 0.549594966348079, 0.371544423161221, 0.396618119014455, 
0.426581724604903, 0.457564804982094, 0.406227408970275, 0.66592753876014, 
0.429242005148684, 0.308938181405404, 0.357491106253483, 0.400417939035907, 
0.452558426733727, 0.332516184043711, 0.336734593477769, 0.385984313372426, 
0.415257522282799, 0.416877219867739, 0.437870609858534, 0.504826034458151, 
0.3692029958207, 0.421086132923672, 0.398797799365072, 0.345820252410603, 
0.428961656779362, 0.343022005040261, 0.43859585449659, 0.351397709779422, 
0.441831474644956, 0.395322591846656, 0.42707677378149, 0.383038227789757, 
0.419372655758695, 1.20999057171145, 1.0324754309382, 1.15390937655487, 
1.27269225907284, 1.52681925668428, 1.24850012592141, 1.25692362442215, 
1.66191343132771, 1.52396351968135, 1.30216898419267, 0.979390794690607, 
0.84785205830123, 0.964426984707154, 0.977438888352537, 0.792711561574157, 
2.02183603756457, 0.813045009817121, 1.22303796362965, 1.29689832478866, 
1.47601961377895, 0.900469664727307, 0.982591604164768)), row.names = 400:585, class = "data.frame")

THANK YOU...

Solution

Using the data you have provided + How to change angle of line in customized legend in ggplot2

library(ggplot2)
library(grid)

GeomAbline$draw_key <- function(data, params, size) 
{
  segmentsGrob(0, 0.5, 1, 0.5, gp = gpar(col = alpha(data$colour, 
                                                     data$alpha), lwd = data$size * .pt, lty = data$linetype, 
                                         lineend = "butt"))
}  
ggplot() + 
  geom_point(data = scalingdata, 
             mapping = aes(x=Re, y=Sw, color=Size), 
             size=3, 
             show.legend = F) +
  geom_abline(data = lines, 
              mapping = aes(intercept=intercept, 
                                slope=slope, 
                                color=name, 
                                size=name,
                                linetype=name))+ 
  scale_color_manual(name='Size',
                     values=c("Sw ~ Re^13/15" ='Blue', "Sw ~ Re^9/10" ='Blue',
                              "Sw ~ Re^2/3" ='Red', "Sw ~ Re^3/4" ='Red',
                              'Fish' = 'Blue', 'Larvae' = 'Red'),
                     breaks=lines$name) +
  scale_x_log10(limits = c(1,10^8), breaks = trans_breaks("log10", function(x) 10^x),
                labels = trans_format("log10", math_format(10^.x))) + 
  scale_y_log10(limits = c(1,10^8), breaks = trans_breaks("log10", function(x) 10^x),
                labels = trans_format("log10", math_format(10^.x))) + annotation_logticks() +
  scale_linetype_manual(name='Size',
                        values=c("Sw ~ Re^13/15" ='solid', "Sw ~ Re^9/10" ='dashed',
                                 "Sw ~ Re^2/3" ='solid', "Sw ~ Re^3/4" ='dashed')) +
  scale_size_manual(name='Size',
                    values=c("Sw ~ Re^13/15" =1, "Sw ~ Re^9/10" =1.25, "Sw ~ Re^2/3" =1, "Sw ~ Re^3/4" = 1.25)) +
  theme_minimal() +
  theme(panel.background = element_rect(fill = "#f0f4f5",
                                        size = 0.5, linetype = "solid"),
        panel.grid.major = element_blank(), panel.grid.minor = element_blank(),
        panel.border = element_rect(color = "black",fill = NA,size = 1),
        legend.key.size = unit(1, 'cm'),
        plot.title = element_text(size = 25, face = "italic"),
        axis.title.y = element_text(size=17.5),
        axis.text.y = element_text(size=15, face="bold"),
        axis.title.x = element_blank(),
        axis.text.x = element_blank())