-
Notifications
You must be signed in to change notification settings - Fork 1
/
SahulHumanSpreadGithub.SingleScenarioAvg.R
1302 lines (1118 loc) · 63.1 KB
/
SahulHumanSpreadGithub.SingleScenarioAvg.R
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
###################################################################
## Cellular automaton model of human spread through Sahul ##
## SINGLE-SCENARIO AVERAGES (ITERATED) ##
## March 2020 ##
## Corey JA Bradshaw, Flinders University ##
## [email protected] ##
## http:https://GlobalEcologyFlinders.com ##
## http:https://github.com/cjabradshaw ##
###################################################################
## remove everything
rm(list = ls())
## libraries
library(sp)
library(rgdal)
library(raster)
#library(Scale)
library(oceanmap)
library(insol)
library(OceanView)
library(abind)
library(pracma)
library(binford)
library(rgl)
library(scatterplot3d)
library(spatstat)
library(spatialEco)
library(SpatialPack)
library(foreach)
library(doSNOW)
## functions
# gradient function for immigration
# pI ~ a / (1 + (b * exp(-c * Rk)))
aI <- 0.95; bI <- 5000; cI <- 3
pI.func <- function(Rk) {
pI <- aI / (1 + (bI * exp(-cI * Rk)))
return(pI)}
pI.func(4)
xI <- seq(1,10,0.01)
yI <- pI.func(xI)
plot(xI,yI,type="l",xlab="Rk",ylab="pI")
# gradient function for emigration
aE <- 1; bE <- -3.2
pE.func <- function(Rk) {
pE <- aE * exp(bE * Rk)
return(pE)}
pE.func(0.5)
xE <- seq(0.01,1,0.01)
yE <- pE.func(xE)
plot(xE,yE,type="l",xlab="Rk",ylab="pE")
pE.out <- data.frame(xE,yE)
setwd("~/Documents/Papers/Palaeo/Sahul/Aus human spread/out/output data/")
write.table(pE.out,file="pE.csv",sep=",", row.names = F, col.names = T)
# stochastic beta sampler (single sample)
stoch.beta.func <- function(mu, var) {
Sx <- rbeta(length(mu), (((1 - mu) / var - 1 / mu) * mu ^ 2), ((((1 - mu) / var - 1 / mu) * mu ^ 2)*(1 / mu - 1)))
return(params=Sx)
}
# stochastic beta sampler (n samples)
stoch.n.beta.func <- function(n, mu, var) {
Sx <- rbeta(n, (((1 - mu) / var - 1 / mu) * mu ^ 2), ((((1 - mu) / var - 1 / mu) * mu ^ 2)*(1 / mu - 1)))
return(params=Sx)
}
# dynamics model function
Nproj.func <- function(Nt, rm, K) {
Nt1 <- round(Nt * exp(rm*(1-(Nt/K))), 0)
return(Nt1)
}
# rescale a range
rscale <- function (x, nx1, nx2, minx, maxx) {
nx = nx1 + (nx2 - nx1) * (x - minx)/(maxx - minx)
return(nx)
}
# matrix rotation
rot.mat <- function(x) t(apply(x, 2, rev))
# matrix poisson resampler
rpois.fun <- function(x,y,M) {
rpois(1,M[x,y])
}
rpois.vec.fun <- Vectorize(rpois.fun,vectorize.args = c('x','y'))
####################################################
## set grids
####################################################
## relative density, carrying capacity & feedbacks
## NPP (LOVECLIM)
npp <- read.table("NppSahul(0-140ka).csv", header=T, sep=",") # 0.5 deg lat resolution
head(npp[,1:3])
not.na <- which(is.na(npp[,3:dim(npp)[2]]) == F, arr.ind=T)
upper.row <- as.numeric(not.na[1,1])
lower.row <- as.numeric(not.na[dim(not.na)[1],1])
min.lat <- max(npp[not.na[,1], 1])
max.lat <- min(npp[not.na[,1], 1])
min.lon <- min(npp[not.na[,1], 2])
max.lon <- max(npp[not.na[,1], 2])
sahul.sub <- rep(0, dim(npp)[1])
for (n in 1:dim(npp)[1]) {
sahul.sub[n] <- ifelse(npp[n,1] <= min.lat & npp[n,1] >= max.lat & npp[n,2] >= min.lon & npp[n,2] <= max.lon, 1, 0)
}
sah.keep <- which(sahul.sub == 1)
npp.sah <- npp[sah.keep,]
head(npp.sah[,1:3])
## import sea level & palaeo-lakes layer (1 = land; 2 = palaeo-lake)
sll <- read.table("SeaLevelSahul(0-140ka)&LakeC.csv", header=T, sep=",") # 0.5 deg lat resolution
sll.sah <- sll[sah.keep,]
head(sll.sah)
range(sll.sah[,3:dim(sll.sah)[2]], na.rm=T)
## import ruggedness (average elevational slope) per cell
rug <- read.table("RuggednessSahul(0-140ka).csv", header=T, sep=",") # 0.5 deg lat resolution
sah.keep <- which(sahul.sub == 1)
rug.sah <- rug[sah.keep,]
head(rug.sah)
range(rug.sah[,3:dim(rug.sah)[2]], na.rm=T)
## set base human Leslie matrix from Bradshaw et al. (2014; PNAS)
source("~/Documents/Papers/Other/Global human population/ms/PNAS/R1/matrixOperators.r")
# Siler hazard h(x) (Gurven et al. 2007)
# average hunter-gatherer
a1 <- 0.422 # initial infant mortality rate (also known as αt)
b1 <- 1.131 # rate of mortality decline (also known as bt)
a2 <- 0.013 # age-independent mortality (exogenous mortality due to environment); also known as ct
a3 <- 1.47e-04 # initial adult mortality rate (also known as βt)
b3 <- 0.086 # rate of mortality increase
longev <- 80
x <- seq(0,longev,1) # age vector
h.x <- a1 * exp(-b1*x) + a2 + a3 * exp(b3 * x) # Siler's hazard model
l.x <- exp((-a1/b1) * (1 - exp(-b1*x))) * exp(-a2 * x) * exp(a3/b3 * (1 - exp(b3 * x))) # Siler's survival (proportion surviving) model
l.inf <- exp(-a1/b1) # survival at infinite time
T.m <- 1/b1 # time constant at which maturity is approached
h.m <- a2 # hazard for mature animals
l.m <- exp(-a2*x) # survival
h.s <- a3*exp(b3*x) # hazard for senescence
l.s <- exp((a3/b3)*(1 - exp(b3*x))) # survival for senescence
f.x <- a3*exp(b3*x)*exp((a3/b3)/(1-exp(b3*x))) # probability density function
(log(a3) - log(a1)) / a3
T.s <- (1/b3) # modal survival time
## survival
init.pop <- 10000
lx <- round(init.pop*l.x,0)
len.lx <- length(lx)
dx <- lx[1:(len.lx-1)]-lx[2:len.lx]
qx <- dx/lx[1:(length(lx)-1)]
Sx <- 1 - qx
sx <- lx[2:len.lx]/lx[1:(len.lx-1)]
mx <- 1 - sx
Lx <- (lx[1:(len.lx-1)] + lx[2:len.lx])/2
ex <- rev(cumsum(rev(Lx)))/lx[-len.lx]
ex.avg <- ex + x[-len.lx]
# set SD for Sx
Sx.sd <- 0.05 # can set to any value
# fertility (Walker et al. 2006)
primiparity.walker <- c(17.7,18.7,19.5,18.5,18.5,18.7,25.7,19,20.5,18.8,17.8,18.6,22.2,17,16.2,18.4)
prim.mean <- round(mean(primiparity.walker),0)
prim.lo <- round(quantile(primiparity.walker,probs=0.025),0)
prim.hi <- round(quantile(primiparity.walker,probs=0.975),0)
print(c(prim.lo, prim.mean, prim.hi))
dat.world13 <- read.table("world2013lifetable.csv", header=T, sep=",")
fert.world13 <- dat.world13$m.f
fert.trunc <- fert.world13[1:(longev+1)]
pfert.trunc <- fert.trunc/sum(fert.trunc)
fert.bentley <- 4.69/2 # Bentley 1985 for !Kung
fert.vec <- fert.bentley * pfert.trunc
## construct matrix
stages <- len.lx
popmat <- matrix(0,nrow=stages,ncol=stages)
colnames(popmat) <- x
rownames(popmat) <- x
## populate matrix
popmat[1,] <- fert.vec
diag(popmat[2:stages,]) <- Sx
popmat[stages,stages] <- 0 # Sx[stages-1]
popmat.orig <- popmat ## save original matrix
## matrix properties
max.lambda(popmat) ## 1-yr lambda
r.ann <- max.r(popmat) # rate of population change, 1-yr
r.ann
#stable.stage.dist(popmat) ## stable stage distribution
R.val(popmat,stages) # reproductive value
gen.l <- G.val(popmat,stages) # mean generation length
## for r.max (set Sx=1)
Sx.1 <- Sx
Sx.1[] <- 1
popmat.max <- popmat.orig
diag(popmat.max[2:stages,]) <- Sx.1
popmat.max[stages,stages] <- 0 # Sx[stages-1]
max.lambda(popmat.max) ## 1-yr lambda
rm.ann <- max.r(popmat.max) # rate of population change, 1-yr
rm.ann
#stable.stage.dist(popmat) ## stable stage distribution
R.val(popmat,stages) # reproductive value
gen.l <- G.val(popmat,stages) # mean generation length
### population dynamics parameters
# dynamical model
# Nt+1 = Nt * exp(rm*(1-(Nt/K))) - (E - I)
lambda.ann <- exp(r.ann) # annual lambda
r.max.NEE <- 2 * log(lambda.ann^gen.l) # human rmax at generational scale (arbitrarily double)
lambda.max.ann <- exp(rm.ann)
rm.max.NEE <- log(lambda.max.ann^gen.l) # human rmax at generational scale (from Sx=1 Leslie matrix)
# Cole's allometric calculation (high)
alpha.Ab <- 15
a.Cole <- -0.16
a.lo.Cole <- -0.41
a.up.Cole <- 0.10
a.sd.Cole <- mean(c((a.Cole - a.lo.Cole)/1.96, (a.up.Cole - a.Cole)/1.96))
b.lo.Cole <- -1.2
b.up.Cole <- -0.79
b.Cole <- -0.99
b.sd.Cole <- mean(c((b.Cole - b.lo.Cole)/1.96, (b.up.Cole - b.Cole)/1.96))
r.max.Cole <- 10^(a.Cole + b.Cole*log10(alpha.Ab)) # from Hone et al. 2003-JApplEcol
r.max.Cole
r.max.lo.Cole <- 10^(a.lo.Cole + b.lo.Cole*log10(alpha.Ab))
r.max.lo.Cole
r.max.up.Cole <- 10^(a.up.Cole + b.up.Cole*log10(alpha.Ab))
r.max.up.Cole
r.max.up.gen.Cole <- log((exp(r.max.up.Cole))^gen.l)
r.max.gen.Cole <- log((exp(r.max.Cole))^gen.l)
r.max.lo.gen.Cole <- log((exp(r.max.lo.Cole))^gen.l)
print(c(r.max.up.gen.Cole, r.max.gen.Cole, r.max.lo.gen.Cole))
r.max.gen.Cole.sd <- mean(c((r.max.gen.Cole - r.max.lo.gen.Cole)/1.96, (r.max.up.gen.Cole - r.max.gen.Cole)/1.96))
## dispersal calculations
# natal dispersal distance function (from Sutherland et al. 2000 Conserv Biol)
# median
a.mid <- 1.45
b.mid <- 0.54
a.lo <- a.mid - 1.05
a.up <- a.mid + 1.05
b.lo <- b.mid - 0.01
b.up <- b.mid + 0.01
M <- 50 # average mass of hunter-gatherer adult
D.med.lo <- a.lo*M^b.lo
D.med.up <- a.up*M^b.up
D.vec <- 1:round((10*111/2), 0)
Pr.Dmed.lo <- exp(-D.vec/D.med.lo)
Pr.Dmed.up <- exp(-D.vec/D.med.up)
# max
A.mid <- 3.31
B.mid <- 0.65
A.lo <- A.mid - 1.17
A.up <- A.mid + 1.17
B.lo <- B.mid - 0.05
B.up <- B.mid + 0.05
D.max.lo <- A.lo*M^B.lo
D.max.up <- A.up*M^B.up
Pr.Dmx.lo <- exp(-D.vec/D.max.lo)
Pr.Dmx.up <- exp(-D.vec/D.max.up)
par(mfrow=c(2,2))
plot(D.vec, Pr.Dmed.up, type="l", xlab="distance (km)", ylab="Pr(D)")
lines(D.vec, Pr.Dmed.lo)
lines(D.vec, Pr.Dmx.lo, col="red")
lines(D.vec, Pr.Dmx.up, col="red")
plot(log10(D.vec), Pr.Dmed.up, type="l", xlab="log10 distance (km)", ylab="Pr(D)")
lines(log10(D.vec), Pr.Dmed.lo)
lines(log10(D.vec), Pr.Dmx.lo, col="red")
lines(log10(D.vec), Pr.Dmx.up, col="red")
cellD <- D.vec/(111/2)
plot(cellD, Pr.Dmed.up, type="l", xlab="distance (0.5-deg cells)", ylab="Pr(D)")
lines(cellD, Pr.Dmed.lo)
lines(cellD, Pr.Dmx.lo, col="red")
lines(cellD, Pr.Dmx.up, col="red")
plot(log10(cellD), Pr.Dmed.up, type="l", xlab="log10 distance (0.5-deg cells)", ylab="Pr(D)")
lines(log10(cellD), Pr.Dmed.lo)
lines(log10(cellD), Pr.Dmx.lo, col="red")
lines(log10(cellD), Pr.Dmx.up, col="red")
par(mfrow=c(1,1))
disp.max.out <- data.frame(cellD,Pr.Dmx.lo,Pr.Dmx.up)
## Hiscock rainfall-territory size relationsip (2008)
terr.rain <- read.table("territory.rainfall.Hiscock.csv", header=T, sep=",")
plot(terr.rain$annrainmm, terr.rain$terrkm2, pch=19)
plot(log10(terr.rain$annrainmm), log10(terr.rain$terrkm2), pch=19)
fit.terr.rain <- lm(log10(terr.rain$terrkm2) ~ log10(terr.rain$annrainmm))
abline(fit.terr.rain, lty=2)
range(terr.rain$terrkm2)
median(terr.rain$terrkm2)
plot(log10(terr.rain$annrainmm), log10(terr.rain$terr.rkm), pch=19, ylim=c(-0.1,2), xlab="log10 annual rainfall (mm)", ylab="log10 territory radius (km)")
fit.dispkm.rain <- lm(log10(terr.rain$terr.rkm) ~ log10(terr.rain$annrainmm))
abline(fit.dispkm.rain, lty=2)
abline(h=log10(D.max.lo), lty=2, col="dark red")
abline(h=log10(D.max.up), lty=2, col="dark red")
abline(h=log10(D.med.lo), lty=3, col="red")
abline(h=log10(D.med.up), lty=3, col="red")
## make rainfall relative to minimum
hist(terr.rain$annrainmm/min(terr.rain$annrainmm), main="")
plot(log10(terr.rain$annrainmm/min(terr.rain$annrainmm)), log10(terr.rain$terr.rkm), pch=19, xlim=c(-1,1.6), ylim=c(-0.1,2), xlab="log10 relative annual rainfall", ylab="log10 territory radius (km)")
fit.dispkm.rain <- lm(log10(terr.rain$terr.rkm) ~ log10(terr.rain$annrainmm/min(terr.rain$annrainmm)))
abline(fit.dispkm.rain, lty=2)
abline(v=0, lty=2, col="black")
yDmaxup <- (log10(D.max.up) - as.numeric(coef(fit.dispkm.rain)[1]))/as.numeric(coef(fit.dispkm.rain)[2])
yDminlo <- (log10(D.med.lo) - as.numeric(coef(fit.dispkm.rain)[1]))/as.numeric(coef(fit.dispkm.rain)[2])
abline(v=yDmaxup, lty=2, col="black")
abline(h=log10(D.max.lo), lty=2, col="dark red")
abline(h=log10(D.max.up), lty=2, col="dark red")
abline(h=log10(D.med.lo), lty=3, col="red")
abline(h=log10(D.med.up), lty=3, col="red")
hiscock.out <- data.frame(terr.rain$annrainmm/min(terr.rain$annrainmm), log10(terr.rain$terr.rkm))
## Binford's environmental and hunter-gatherer frames of reference (Binford 2001)
## to estimate effect of rugosity on dispersal
binforddat = NULL
binforddat$annual_move <- LRB$dismov
binforddat$annual_rain <- LRB$bio.12
binforddat$ID <- seq(1:length(binforddat$annual_rain))
binford.dat <- as.data.frame(binforddat)
binford.dat$altitude_max <- LRB$h25
binford.dat$altitude_min <- LRB$l25
binford.dat$altitude_dif <- binford.dat$altitude_max - binford.dat$altitude_min
binford.dat <- binford.dat[complete.cases(binford.dat),]
binford.dat <- binford.dat [binford.dat$altitude_dif>0,] # remove the one case with negative altitude difference
plot(binford.dat$altitude_dif, binford.dat$annual_move, pch=19, xlab="altitude difference", ylab="annual movement")
# cube root
binford.dat$annual_move_tr <- binford.dat$annual_move^(1/3)
binford.dat$annual_rain_tr <- binford.dat$annual_rain^(1/3)
binford.dat$altitude_dif_tr <- binford.dat$altitude_dif^(1/3)
res <- lm(annual_move_tr ~ + annual_rain + altitude_dif_tr, data = binford.dat)
summary(res)
#plot(res)
# 3D scatterplot with droplines
s3d <- scatterplot3d(binford.dat$annual_rain, binford.dat$altitude_dif_tr, binford.dat$annual_move_tr, pch=16, highlight.3d=F,
type="h", main="", angle=210, asp=4, grid=T,
xlab="annual rainfall (mm)", ylab="cube root altitude difference (Δm)", zlab="cube root annual movement (km)")
s3d$plane3d(res, draw_polygon = T)
altdiff.vec <- seq(from=range(binford.dat$altitude_dif)[1], to=range(binford.dat$altitude_dif)[2], by=1)
altdiff.st <- altdiff.vec / max(altdiff.vec)
annmov.pred <- (coef(res)[1] + (altdiff.vec^(1/3) * coef(res)[3]^3) + (mean(binford.dat$annual_rain, na.rm=T) * coef(res)[2]))^3
annmov.st <- annmov.pred / max(annmov.pred)
plot(altdiff.vec, annmov.pred, type="l", xlab="altitude difference (m)", ylab="predicted annual movement (km)")
plot(altdiff.st, annmov.st, type="l", xlab="standardised altitude difference (m)", ylab="standardised predicted annual movement (km)")
altmov.dat <- data.frame(altdiff.st, annmov.st)
# exponential decay function fit
# y=a+b(x)^(1/3)
param.init <- c(1, -0.01)
fit.expd <- nls(annmov.st ~ a + b*(altdiff.st)^(1/3),
data = altmov.dat,
algorithm = "port",
start = c(a = param.init[1], b = param.init[2]),
trace = TRUE,
nls.control(maxiter = 1000, tol = 1e-05, minFactor = 1/1024))
plot(altdiff.st, annmov.st, pch=19, cex=0.001, xlab="standardised altitude difference (m)", ylab="standardised predicted annual movement (km)", ylim=c(0.98,1))
altdiff.st.vec <- seq(0,1,0.01)
pred.annmov.st <- as.numeric(coef(fit.expd)[1]) + as.numeric(coef(fit.expd)[2]) * (altdiff.st.vec)^(1/3)
range(pred.annmov.st)
lines(altdiff.st.vec, pred.annmov.st, lty=2, lwd=3, col="red")
## distance to water (based on modern-day water distribution; Damien O'grady)
dir.tmp <- getwd()
rastlist <- list.files(path = dir.tmp, pattern='.tif$', all.files=TRUE, full.names=FALSE)
allrasters <- lapply(rastlist, raster)
allrasters
allrasters[[1]]
plot(allrasters[[1]], col=(topo.colors(50, 0.9)))
d2w <- read.table("Distance2Freshwater.csv", header=T, sep=",") # 0.5 deg lat resolution / units in dd
d2w.sah <- d2w[sah.keep,]
head(d2w.sah)
range(d2w.sah[,3:dim(d2w.sah)[2]], na.rm=T)
## data from Fagan & Holmes to estimate > mortality rate < MVP size
max.r.decl <- c(-3.24, -1.09, -1.96, -2.28, -0.69, -0.68, -1.88, -1.76, -2.05)
max.lam.decl <- exp(max.r.decl)
1-mean(max.lam.decl)
########################################################
########################################################
########################################################
## start diffusion model - iterate for average output ##
########################################################
########################################################
########################################################
### date of first colonisation?
entry.date <- 50000
### how many generations to run?
gen.run <- 300 # number of generations to run
round(gen.run*gen.l, 0) # how many years is that?
entry.date-round(gen.run*gen.l,0) # this means will run until year ...
### choose linear relationship between NPP and K, or 180 deg-rotated parabolic relationship
#K.NPP <- "linear"
#K.NPP <- "rotated parabolic"
K.NPP <- "rotated quadratic yield density"
## K reduction scalar
#modify.K <- "yes"
modify.K <- "no"
if (modify.K == "yes") {
Kreduce <- 0.75 # if yes, by how much?
}
### for unknown SDs, choose % of mean (i.e., for M.cat.sd, pmov.sd, rm.max.NEE.sd)
#SD.prop.xbar <- 0.05 # 5%
SD.prop.xbar <- 0.10 # 10%
# impose higher extinction probability below MVP size
small.pop.ext <- "yes"
#small.pop.ext <- "no"
MVP.thresh <- 100 # increase mortality in cells with N < MVP.thresh
ltMVP.red <- 0.2 # mean (beta resampled) additional mortality expected for cells meeting criteria
### choose low (2*NEE estimate) or high (generationally scaled Cole's estimate from alpha) rmax
rmax.sel <- "low" # more defensible
#rmax.sel <- "high" # seems unrealistically high
### if a lake is present, how much to reduce K in that grid (0 = 0 K; 1 = full K)?
lake.red <- 0.01 # cannot be zero
### max long-distance dispersal modifier
ldp.mult <- 1 # modify to deviate from theoretical expectations (0 - ∞)
## modifier of maximum ruggedness effect on movement
rugmov.mod <- 1
## set resistance of landscape for distance-to-water function
watmovresist <- 3 # from Saltré et al. 2009 Ecol Model
### apply catastrophe function (Reed et al. 2005)?
catastrophe <- "yes"
#catastrophe <- "no"
pop.adjacency <- 0 # to account for 'population' area of influence, in incrementing neighbourhood (1 = immediate neighbours; 2 = 2 cells away in every direction, ...)
cat.pr <- 0.14/((2*pop.adjacency+1)^2) # probability of catastrophe per generation (Reed et al. 2003) = 0.14, modified by adjacency from above
M.cat <- 0.75 # mean mortality during a catastrophe event
M.cat.sd <- SD.prop.xbar*M.cat # sd mortality during a catastrophe event
### are catastrophe's spatially clustered?
spatial.cluster <- "yes"
#spatial.cluster <- "no"
# generate a random point pattern (Thomas cluster process)
rpp.scale <- 0.015 # controls intensity of clustering (lower values = more clustering)
kappa.mod <- 1 # modifies Thomas cluster process kappa upward or downward; ~ simulates changes to Pr(catastrophe)
### print each iteration's map (progression)?
#print.map <- "yes"
print.map <- "no"
### save each iteration's map as a jpg?
save.map <- "no"
#save.map <- "yes"
# save output images?
#save.outputs <- "yes"
save.outputs <- "no"
### pick entry cell
#start.col1 <- 45; start.row1 <- 1 # north of Bird's head, N Guinea
#start.col1 <- 40; start.row1 <- 4 # west of Bird's head, N Guinea
#start.col1 <- 38; start.row1 <- 21 # N Sahul shelf
start.col1 <- 31; start.row1 <- 27 # S Sahul shelf
#start.col1 <- 8; start.row1 <- 58 # SWA
#start.col1 <- 87; start.row1 <- 59 # SNSW
if (entry.date > 75000 & start.col1 == 31) {
start.col1 <- 32}
### add secondary colonisation event?
second.col <- "no"
#second.col <- "yes"
### lag between first and second colonisation events
lag.l <- 1000 # lag (between 1st & 2nd colonisation events) length?
lag.n <- 2 # how many lag increments?
start.time2 <- ifelse((lag.n * round(lag.l/gen.l)) == 0, 1, (lag.n * round(lag.l/gen.l))) # generations after first colonisation event (increments of ~ lag years)
if (second.col == "yes") {
#start.col2 <- 38; start.row2 <- 21 # N Sahul shelf
#start.col2 <- 31; start.row2 <- 27 # S Sahul shelf
start.col2 <- 40; start.row2 <- 4 # west of Bird's head, N Guinea
}
if (entry.date > 75000 & start.col2 == 31) {
start.col2 <- 32}
# add this to jpg file names for scenario description
name.add <- paste(entry.date/1000, "ka.", gen.run, "gen.", ifelse(K.NPP=="rotated quadratic yield density", "rqydK", ifelse(K.NPP=="linear", "linK", "parK")), ".rmax", ifelse(rmax.sel == "low","-lo","-hi"), ifelse(ldp.mult != 1, paste(".ldispmod", ldp.mult, sep=""), ""), ifelse(catastrophe=="yes",".CAT", ".NOCAT"), M.cat*100, ifelse(spatial.cluster=="yes",paste("cl",rpp.scale,sep=""),""), ".neigh-adj", pop.adjacency, ".", "intro", ifelse(second.col=="no",1,2), ifelse(start.row1==1, "nBH", ifelse(start.row1==4, "wBH", "SSh")), ifelse(second.col=="yes", ifelse(second.col=="yes" & start.row2==21,"-SSh", ifelse(start.row2==4, "-wBH", "-nBH")), ""), ifelse(second.col=="yes", paste("-lag", round(lag.l*lag.n/gen.l), "g", sep=""), ""), sep="")
### minimum viable population size to consider a cell 'colonised' (for first-appearance map)
min.pop.size <- 100
### start founding population in 1 cell
N.found.mod <- 1
N.found.lo <- 1300*N.found.mod; N.found.up <- 1500*N.found.mod
## estimate SD of rmax according to SD proportions et above
rm.max.NEE.sd <- SD.prop.xbar * rm.max.NEE
### dispersal parameters
pmov.mean <- 1/3 # mu for beta function indicating proportion of people immigrating/emigrating
pmov.sd <- SD.prop.xbar*pmov.mean # sd for beta function
NK.emig.min <- 0.3; NK.emig.max <- 0.7 # N/K when pmov.mean emigrates
# update ruggedness movement function with rugmov.mod
rugmovmod.func <- function(x) {
rugmovmod <- as.numeric(coef(fit.expd)[1]) + rugmov.mod*as.numeric(coef(fit.expd)[2]) * (x)^(1/3)
return(rugmovmod=rugmovmod)
}
# npp @ entry date ka
sub.entry <- which(colnames(npp.sah) == paste("X",entry.date,sep=""))
npp.sah.entry <- npp.sah[,c(1,2,sub.entry)]
head(npp.sah.entry)
# plot raster
coordinates(npp.sah.entry) = ~ Lon + Lat
proj4string(npp.sah.entry)=CRS("+proj=longlat +datum=WGS84") # set it to lat-long
gridded(npp.sah.entry) = TRUE
npp.entry = raster(npp.sah.entry)
lim.exts <- 5
plot(npp.entry, xlab="longitude", ylab="latitude", xlim=c(min.lon-lim.exts, max.lon+lim.exts), ylim=c(max.lat-lim.exts, min.lat+lim.exts))
# transform to array
lz <- dim(npp.sah)[2] - 2
npp.array <- array(data=NA, dim=c(dim(raster2matrix(npp.entry)),lz))
for (k in 3:(lz+2)) {
npp.sah.k <- npp.sah[,c(1,2,k)]
coordinates(npp.sah.k) = ~ Lon + Lat
proj4string(npp.sah.k)=CRS("+proj=longlat +datum=WGS84") # set it to lat-long
gridded(npp.sah.k) = TRUE
npp.k = raster(npp.sah.k)
npp.array[,,k-2] <- raster2matrix(npp.k)
image(npp.array[,,k-2], col=rev(grey(1:100/100)))
print(k-2)
}
# example plots (entry & another)
image(npp.array[,,sub.entry-3],col=rev(grey(1:100/100)))
image(npp.array[,,12],col=rev(grey(1:100/100)))
## calculate all Ks as relative to current
npp.sah.rel <- npp.array
for (z in 1:lz) {
npp.sah.rel[,,z] <- npp.array[,,z] / npp.array[,,3]
}
npp.sah.rel[,,3] <- npp.array[,,1]
# npp to K
hum.dens.med <- 6.022271e-02
hum.dens.lq <- 3.213640e-02
hum.dens.uq <- 1.439484e-01
hum.dens.max <- 1.152206e+00
hum.dens.min <- 1.751882e-02
cell.area <- (111.12/2)*(111.12/2) # km2
# create vector of K reduction scalars for projection interval
if (modify.K == "yes") {
Kreduce.vec <- stoch.n.beta.func(lz, Kreduce, 0.05*Kreduce)
}
if (modify.K == "no") {
Kreduce <- rep(1,lz)
}
# modify underlying K magnitude by modifying NPP across the board
K.array <- npp.sah.rel
for (z in 1:lz) {
K.array[,,z] <- rscale(npp.array[,,z], round(hum.dens.min*cell.area, 0), round(hum.dens.max*cell.area, 0), min(npp.array[,,z], na.rm=T), max(npp.array[,,z], na.rm=T))
}
image(K.array[,,13], col=rev(grey(1:100/100)))
# 180-deg rotated parabola
# y = a(x - h)^2 + k
# h = median NPP; k = max K; a = negative for 180 flipped
k.Kmax <- max(K.array, na.rm=T)/2
h.NPPmed <- mean(npp.array, na.rm=T)
h.NPPmed <- mean(range(npp.array, na.rm=T))
Kmin <- min(K.array, na.rm=T)
NPP.seq <- seq(min(npp.array, na.rm=T), max(npp.array, na.rm=T), 0.01)
K.parab.pred <- (-3 * (NPP.seq - h.NPPmed)^2) + k.Kmax
K.parab.pred.rescale <- rscale(K.parab.pred, round(hum.dens.min*cell.area, 0), 0.5*round(hum.dens.max*cell.area, 0), min(K.parab.pred), max(K.parab.pred))
plot(NPP.seq, K.parab.pred.rescale, type="l", xlab="NPP", ylab="K")
# slow exponential increase combined with peak
# reciprocal quadratic yield density
# y = x/(a + b*x + c*x^2)
# y = K, x = NPP
a.rqyd <- 200; b.rqyd <- 0.60; c.rqyd <- 0.2
K.rqyd.pred <- a.rqyd * exp(-(NPP.seq-b.rqyd)^2/(2*c.rqyd^2))
K.rqyd.pred.rescale <- rscale(K.rqyd.pred, round(hum.dens.min*cell.area, 0), 0.5*round(hum.dens.max*cell.area, 0), min(K.rqyd.pred), max(K.rqyd.pred))
plot(NPP.seq, K.rqyd.pred.rescale, type="l", xlab="NPP", ylab="K")
K.lin.x <- c(min(npp.array, na.rm=T), max(npp.array, na.rm=T))
K.lin.y <- c(min(K.array, na.rm=T), max(K.array, na.rm=T))
plot(K.lin.x, K.lin.y, xlab="NPP", ylab="K", pch=19)
fit.K.lin <- lm(K.lin.y ~ K.lin.x)
abline(fit.K.lin, lty=2)
K.lin.pred <- as.numeric(coef(fit.K.lin)[1]) + as.numeric(coef(fit.K.lin)[2])*NPP.seq
plot(NPP.seq, K.lin.pred, type="l", lty=2, xlab="NPP", ylab="K", pch=19)
lines(NPP.seq, K.parab.pred.rescale, lty=2)
lines(NPP.seq, K.rqyd.pred.rescale, lty=2)
abline(h=0.5*max(K.array, na.rm=T), lty=3)
# rotated parabolic
K.array.parab <- (-3 * (npp.array - h.NPPmed)^2) + k.Kmax
K.array.parab.rescale <- K.array.parab
for (z in 1:lz) {
K.array.parab.rescale[,,z] <- rscale(K.array.parab[,,z], round(hum.dens.min*cell.area, 0), round(hum.dens.max*cell.area, 0), min(K.array.parab[,,z], na.rm=T), max(K.array.parab[,,z], na.rm=T))
}
image(K.array.parab.rescale[,,13], col=rev(grey(1:100/100)))
# reciprocal quadratic yield density
K.array.rqyd <- a.rqyd * exp(-(npp.array - b.rqyd)^2 / (2*c.rqyd^2))
K.array.rqyd.rescale <- K.array.rqyd
for (z in 1:lz) {
K.array.rqyd.rescale[,,z] <- rscale(K.array.rqyd[,,z], round(hum.dens.min*cell.area, 0), round(hum.dens.max*cell.area, 0), min(K.array.rqyd[,,z], na.rm=T), max(K.array.rqyd[,,z], na.rm=T))
}
image(K.array.rqyd.rescale[,,13], col=rev(grey(1:100/100)))
# rescale so that parabolic total K = linear total K
hist.K.array <- hist(K.array, br=12)
hist.K.array.dat <- data.frame(hist.K.array$mids, hist.K.array$density)
sum(K.array, na.rm=T)
hist(K.array.parab.rescale, br=12)
sum(K.array.parab.rescale, na.rm=T)
sum(K.array.parab.rescale, na.rm=T)/sum(K.array, na.rm=T)
# rescale K.array.parab.rescale to same sum as K.array (distribution of Ks = same total)
K.array.parab.rescale2 <- K.array.parab.rescale / (sum(K.array.parab.rescale, na.rm=T)/sum(K.array, na.rm=T))
sum(K.array.parab.rescale2, na.rm=T)
K.parab.pred.rescale2 <- K.parab.pred.rescale / (sum(K.array.parab.rescale, na.rm=T)/sum(K.array, na.rm=T))
hist.K.parab.pred.rescale2 <- hist(K.parab.pred.rescale2,br=12)
hist.K.parab.pred.rescale2.dat <- data.frame(hist.K.parab.pred.rescale2$mids, hist.K.parab.pred.rescale2$density)
# rescale so that rotated quadratic yield density total K = linear total K
hist(K.array.rqyd.rescale, br=12)
sum(K.array.rqyd.rescale, na.rm=T)
sum(K.array.rqyd.rescale, na.rm=T)/sum(K.array, na.rm=T)
# rescale K.array.parab.rescale to same sum as K.array (distribution of Ks = same total)
K.array.rqyd.rescale2 <- K.array.rqyd.rescale / (sum(K.array.rqyd.rescale, na.rm=T)/sum(K.array, na.rm=T))
sum(K.array.rqyd.rescale2, na.rm=T)
K.rqyd.pred.rescale2 <- K.rqyd.pred.rescale / (sum(K.array.rqyd.rescale, na.rm=T)/sum(K.array, na.rm=T))
hist.K.rqyd.pred.rescale2 <- hist(K.rqyd.pred.rescale2,br=12)
hist.K.rqyd.pred.rescale2.dat <- data.frame(hist.K.rqyd.pred.rescale2$mids, hist.K.rqyd.pred.rescale2$density)
plot(NPP.seq, K.lin.pred, type="l", lty=2, xlab="NPP", ylab="K", pch=19)
lines(NPP.seq, K.parab.pred.rescale2, lty=2)
lines(NPP.seq, K.rqyd.pred.rescale2, lty=2)
abline(h=0.5*max(K.array, na.rm=T), lty=3)
NPP.K.out <- data.frame(NPP.seq,K.lin.pred,K.parab.pred.rescale2,K.rqyd.pred.rescale2)
colnames(NPP.K.out) <- c("NPP","K.lin","K.para","K.rqyd")
write.table(NPP.K.out,file="NPP.K.csv",sep=",", row.names = F, col.names = T)
write.table(hist.K.rqyd.pred.rescale2.dat,file="hist.K.rqyd.pred.rescale2.csv",sep=",", row.names = F, col.names = T)
# rotate matrix -90 & renumber from oldest to youngest
if (K.NPP == "linear") {
K.array.use <- K.array
}
if (K.NPP == "rotated parabolic") {
K.array.use <- K.array.parab.rescale
}
if (K.NPP == "rotated quadratic yield density") {
K.array.use <- K.array.rqyd.rescale
}
K.rot.array <- array(data=NA, c(dim(K.array.use)[2], dim(K.array.use)[1], lz))
for (z in 1:lz) {
K.rot.array[,,z] <- apply(t(K.array.use[,,142-z]),2,rev)
}
range(K.rot.array[,,1], na.rm=T)
image(rot.mat(K.rot.array[,,81]), col=rev(grey(1:100/100)))
if (modify.K == "yes") {
for (z in 1:lz) {
K.rot.array[,,z] <- K.rot.array[,,z] * Kreduce.vec[z]
}
}
## block out Indonesia & never-connected islands (make NA)
K.rot.array[1:20, 1:39, ] <- NA
K.rot.array[6:20, 40:44, ] <- NA
K.rot.array[9:17, 45:46, ] <- NA
K.rot.array[21:22, 24:33, ] <- NA
K.rot.array[27:28, 24:26, ] <- NA
K.rot.array[34:35, 77:83, ] <- NA
K.rot.array[22:23, 85:87, ] <- NA
K.rot.array[18, 84:85, ] <- NA
K.rot.array[9:12, 77:86, ] <- NA
K.rot.array[2:6, 70:87, ] <- NA
K.rot.array[20, 71, ] <- NA
K.rot.array[2, 52, ] <- NA
# block passage to Tasmania (70 to 67K; 60 to 46K; 43-42K cannot cross)
# K.rot.array[80, 68:70, c(71:74, 81:95, 98:99)] <- NA
# K.rot.array[79, 74:77, c(71:74, 81:95, 98:99)] <- NA
K.rot.array[80, 68:77, c(71:101)] <- NA
K.rot.array[79, 68:77, c(71:101)] <- NA
image(rot.mat(K.rot.array[,,96]), col=rev(grey(1:100/100)))
# interpolate between 1000-year NPP intervals per human generation
# interpolate Ks at gen.l intervals between 1000-yr slices
mill.gen.div <- round(1000/gen.l, 0)
subtentry <- dim(K.rot.array)[3] - (entry.date/1000)
Kentry.array <- K.rot.array[,,subtentry:(dim(K.rot.array)[3])]
image(rot.mat(Kentry.array[,,11]),col=rev(grey(1:100/100)))
K.start <- entry.date
K.end <- 0
yr.proj.vec <- seq(K.start, K.end, -round((1000/mill.gen.div),0))
Kentry.interp.array <- array(data=0, dim=c(dim(Kentry.array[,,1])[1],dim(Kentry.array[,,1])[2],length(yr.proj.vec)))
mill.vec <- seq(K.start,K.end,-1000)
for (i in 1:dim(Kentry.array)[1]) {
for (j in 1:dim(Kentry.array)[2]) {
if (length(which(is.na(Kentry.array[i,j,]))==T) < (dim(Kentry.array)[3]-1))
Kentry.interp.array[i,j,] <- approx(mill.vec, Kentry.array[i,j,], xout=yr.proj.vec, method="linear")$y
else {
Kentry.interp.array[i,j,] <- rep(NA, length(yr.proj.vec))
}
}
}
image(rot.mat(Kentry.interp.array[,,400]), col=rev(grey(1:100/100)))
image(rot.mat(Kentry.interp.array[,,1]), col=rev(grey(1:100/100)))
# transform sea level & palaeo-lakes file (sll) to an array
lz <- dim(sll.sah)[2] - 2
sll.array <- array(data=NA, dim=c(dim(raster2matrix(npp.entry)),lz))
for (k in 3:(lz+2)) {
sll.sah.k <- sll.sah[,c(1,2,k)]
coordinates(sll.sah.k) = ~ Lon + Lat
proj4string(sll.sah.k)=CRS("+proj=longlat +datum=WGS84") # set it to lat-long
gridded(sll.sah.k) = TRUE
sll.k = raster(sll.sah.k)
sll.array[,,k-2] <- raster2matrix(sll.k)
image(sll.array[,,k-2], col=rev(grey(1:100/100)))
print(k-2)
}
# example plots (entry & another)
par(mfrow=c(1,2))
image(sll.array[,,sub.entry],col=rev(grey(1:100/100)))
image(sll.array[,,12],col=rev(grey(1:100/100)))
par(mfrow=c(1,1))
# rotate matrix -90 & renumber from oldest to youngest
sll.rot.array <- array(data=NA, c(dim(sll.array)[2], dim(sll.array)[1], lz))
for (z in 1:lz) {
sll.rot.array[,,z] <- apply(t(sll.array[,,142-z]),2,rev)
}
range(sll.rot.array[,,1], na.rm=T)
image(rot.mat(sll.rot.array[,,100]), col=(rainbow(2,1)))
## copy values between 1000-yr intervals
sllentry.array <- sll.rot.array[,,subtentry:(dim(sll.rot.array)[3])]
sllentry.copy.array <- array(data=0, dim=c(dim(sllentry.array[,,1])[1],dim(sllentry.array[,,1])[2],length(yr.proj.vec)))
for (i in 1:dim(sllentry.array)[1]) {
for (j in 1:dim(sllentry.array)[2]) {
if (length(which(is.na(sllentry.array[i,j,]))==T) < (dim(sllentry.array)[3]-1))
sllentry.copy.array[i,j,] <- approx(mill.vec, sllentry.array[i,j,], xout=yr.proj.vec, method="linear")$y
else {
sllentry.copy.array[i,j,] <- rep(NA, length(yr.proj.vec))
}
}
}
image(rot.mat(sllentry.copy.array[,,240]), col=(rainbow(2,1)))
hist(sllentry.copy.array)
# transform distance to water file (d2w) to an array
lz <- dim(d2w.sah)[2] - 2
d2w.array <- array(data=NA, dim=c(dim(raster2matrix(npp.entry)),lz))
for (k in 3:(lz+2)) {
d2w.sah.k <- d2w.sah[,c(1,2,k)]
coordinates(d2w.sah.k) = ~ Lon + Lat
proj4string(d2w.sah.k)=CRS("+proj=longlat +datum=WGS84") # set it to lat-long
gridded(d2w.sah.k) = TRUE
d2w.k = raster(d2w.sah.k)
d2w.array[,,k-2] <- raster2matrix(d2w.k)
image(d2w.array[,,k-2], col=rev(grey(1:100/100)))
print(k-2)
}
# just use matrix
d2w1.mat <- (as.matrix(d2w.array[,,1]))
# rotate matrix -90
d2w.mat <- matrix(data=NA, nrow=dim(d2w1.mat)[2], ncol=dim(d2w1.mat)[1])
d2w.mat <- apply(t(d2w1.mat),2,rev)
range(d2w.mat, na.rm=T)
image(rot.mat(d2w.mat), col=rev(grey(1:100/100)))
# transform ruggedness file to array
lz <- dim(rug.sah)[2] - 2
rug.array <- array(data=NA, dim=c(dim(raster2matrix(npp.entry)),lz))
for (k in 3:(lz+2)) {
rug.sah.k <- rug.sah[,c(1,2,k)]
coordinates(rug.sah.k) = ~ Lon + Lat
proj4string(rug.sah.k)=CRS("+proj=longlat +datum=WGS84") # set it to lat-long
gridded(rug.sah.k) = TRUE
rug.k = raster(rug.sah.k)
rug.array[,,k-2] <- raster2matrix(rug.k)
image(rug.array[,,k-2], col=rev(grey(1:100/100)))
print(k-2)
}
# example plots (entry & another)
par(mfrow=c(1,2))
image(rug.array[,,sub.entry],col=rev(grey(1:100/100)))
image(npp.array[,,sub.entry],col=rev(grey(1:100/100)))
par(mfrow=c(1,1))
par(mfrow=c(1,2))
image(rug.array[,,12],col=rev(grey(1:100/100)))
image(npp.array[,,12],col=rev(grey(1:100/100)))
par(mfrow=c(1,1))
# rescale rugosity from 0-1
rug.array.rescale <- rug.array
for (z in 1:lz) {
rug.array.rescale[,,z] <- rscale(rug.array[,,z], 0, 1, min(rug.array[,,z], na.rm=T), max(rug.array[,,z], na.rm=T))
}
image(rug.array.rescale[,,13], col=rev(grey(1:100/100)))
range(rug.array.rescale, na.rm=T)
# rotate matrix -90 & renumber from oldest to youngest
rug.rot.array <- array(data=NA, c(dim(rug.array.rescale)[2], dim(rug.array.rescale)[1], lz))
for (z in 1:lz) {
rug.rot.array[,,z] <- apply(t(rug.array.rescale[,,142-z]),2,rev)
}
range(rug.rot.array[,,1], na.rm=T)
image(rot.mat(rug.rot.array[,,20]), col=rev(grey(1:100/100)))
## interpolate between 1000-yr intervals
rugentry.array <- rug.rot.array[,,subtentry:(dim(rug.rot.array)[3])]
rugentry.interp.array <- array(data=0, dim=c(dim(rugentry.array[,,1])[1],dim(rugentry.array[,,1])[2],length(yr.proj.vec)))
for (i in 1:dim(rugentry.array)[1]) {
for (j in 1:dim(rugentry.array)[2]) {
if (length(which(is.na(rugentry.array[i,j,]))==T) < (dim(rugentry.array)[3]-1))
rugentry.interp.array[i,j,] <- approx(mill.vec, rugentry.array[i,j,], xout=yr.proj.vec, method="linear")$y
else {
rugentry.interp.array[i,j,] <- rep(NA, length(yr.proj.vec))
}
}
}
image(rot.mat(rugentry.interp.array[,,400]), col=rev(grey(1:100/100)))
# spatial clustering of catastraphe events controlling parameters
kappa.mult <- 0.9
cellslo <- 1
cellshi <- 3772
kappa.mult.up <- 1.2*kappa.mod
kappa.mult.lo <- 0.3*kappa.mod
kappa.rep <- seq(kappa.mult.up,kappa.mult.lo,-(kappa.mult.up-kappa.mult.lo)/cellshi)
cells.rep <- seq(cellslo,cellshi, (cellshi-cellslo)/cellshi)
plot(cells.rep, kappa.rep, type="l")
kappa.fit <- lm(kappa.rep ~ cells.rep)
kappaP.func <- function(cells.occ) {
kappa.pred <- (as.numeric(coef(kappa.fit)[1])) + as.numeric(coef(kappa.fit)[2])*cells.occ
return(kappa.pred)
}
abline(h=kappaP.func(1500),lty=2,col="red")
abline(v=(1500),lty=2,col="red")
rpp.mu.mult <- 0.6 # this, with the fluctuating kappa multiplier, keeps overall mean proportion of cells experiencing catastrophic mortality ~ 0.14
proc.sim.start <- proc.time()
reps <- 100 # number of times to redo spread model to find average values
first.arrive.array <- array(data=NA, dim=c(dim(rugentry.interp.array[,,1]), reps))
sub97.vec <- rep(0,reps)
N.mat <- matrix(data=NA,nrow=reps,ncol=(gen.run+1))
##########################
## start of m reps loop ##
##########################
for (m in 1:reps) {
## parallel set-up
cores <- 12
getDoParWorkers()
getDoParName()
cl <- makeCluster(cores, type = "SOCK")
registerDoSNOW(cl)
getDoParWorkers()
getDoParName()
getDoParVersion()
# set up NA array
NA.array <- Kentry.interp.array * 0
NA.array <- NA.array[,,1:(gen.run+1)]
image(rot.mat(K.rot.array[,,subtentry]), col=rev(grey(1:100/100)))
# set direction codes
dir.vec <- c("NW", "N", "NE", "W", "E", "SW", "S", "SE")
# generations to run
gen.run * gen.l # numbers years to run
# set up N array
array.N <- Kentry.interp.array * 0
array.N <- array.N[,,1:(gen.run+1)]
# set up direction array (dominant direction of influx)
dir.array <- array.N
array.N[start.row1, start.col1, 1] <- round(runif(1, N.found.lo, N.found.up), 0)
image((rot.mat(array.N[,,1])), col=rev(grey(1:100/100)))
# log10 relative K array
Kentry.interp.lrel.array <- log10(Kentry.interp.array / min(Kentry.interp.array, na.rm=T)) # log10 relative K
## assume same slope between relative NPP and radius movement
disp.npp.slope <- as.numeric(coefficients((fit.dispkm.rain))[2])
disp.npp.int <- as.numeric(coefficients((fit.dispkm.rain))[1])
disp.npp.max.int <- 1.6646371
i.rows <- dim(array.N[,,1])[1]
j.cols <- dim(array.N[,,1])[2]
z.layers <- dim(array.N)[3]
# storage vectors
N.vec <- poparea.vec <- pc.complete <- cat.pr.est <- rep(0,z.layers)
N.vec[1] <- array.N[start.row1,start.col1,1]
if (second.col == "yes") {
N.vec[start.time2] <- array.N[start.row1,start.col1,start.time2]
}
poparea.vec[1] <- cell.area/1000
proc.start <- proc.time()
#############################
## project
for (t in 1:(z.layers-1)) {
# Poisson-resampled K matrix
Kentry.interp.poiss <- outer(1:nrow(round(Kentry.interp.array[,,t],0)), 1:ncol(round(Kentry.interp.array[,,t],0)), rpois.vec.fun, round(Kentry.interp.array[,,t],0))
# reduce Ks if lake present
Kentry.interp.pois <- Kentry.interp.poiss
for (i in 1:i.rows) { # i rows
for (j in 1:j.cols) { # j columns
Kentry.interp.pois[i,j] <- ifelse(sllentry.copy.array[i,j,t] > 1, lake.red * Kentry.interp.poiss[i,j], Kentry.interp.poiss[i,j])
}
}
# step through array in t for immigration & emigration
for (i in 1:i.rows) { # i rows
for (j in 1:j.cols) { # j columns
if (second.col == "yes") {
if (t == start.time2) {
array.N[start.row2, start.col2, start.time2] <- round(runif(1, N.found.lo, N.found.up), 0)
}
}
# set cell-cell gradients relative to focal cell
NW.RK <- ifelse(i > 1 & j > 1, (Kentry.interp.pois[i,j] / ifelse(length(Kentry.interp.pois[i-1,j-1]) > 0, Kentry.interp.pois[i-1,j-1], NA)), NA) # NW
N.RK <- ifelse(i > 1, (Kentry.interp.pois[i,j] / ifelse(length(Kentry.interp.pois[i-1,j]) > 0, Kentry.interp.pois[i-1,j], NA)), NA) # N
NE.RK <- ifelse(i > 1 & j < j.cols, (Kentry.interp.pois[i,j] / ifelse(length(Kentry.interp.pois[i-1,j+1]) > 0, Kentry.interp.pois[i-1,j+1], NA)), NA) # NE
W.RK <- ifelse(j > 1, (Kentry.interp.pois[i,j] / ifelse(length(Kentry.interp.pois[i,j-1]) > 0, Kentry.interp.pois[i,j-1], NA)), NA) # W
E.RK <- ifelse(j < j.cols, (Kentry.interp.pois[i,j] / ifelse(length(Kentry.interp.pois[i,j+1]) > 0, Kentry.interp.pois[i,j+1], NA)), NA) # E
SW.RK <- ifelse(i < i.rows & j > 1, (Kentry.interp.pois[i,j] / ifelse(length(Kentry.interp.pois[i+1,j-1]) > 0, Kentry.interp.pois[i+1,j-1], NA)), NA) # SW
S.RK <- ifelse(i < i.rows, (Kentry.interp.pois[i,j] / ifelse(length(Kentry.interp.pois[i+1,j]) > 0, Kentry.interp.pois[i+1,j], NA)), NA) # S
SE.RK <- ifelse(i < i.rows & j < j.cols, (Kentry.interp.pois[i,j] / ifelse(length(Kentry.interp.pois[i+1,j+1]) > 0, Kentry.interp.pois[i+1,j+1], NA)), NA) # SE
## current population distances from K in each cell
focal.dK1 <- array.N[i,j,t] / Kentry.interp.pois[i,j]
NW.dK1 <- ifelse(i > 1 & j > 1, array.N[i-1,j-1,t] / Kentry.interp.pois[i-1,j-1], NA)
N.dK1 <- ifelse(i > 1, array.N[i-1,j,t] / Kentry.interp.pois[i-1,j], NA)
NE.dK1 <- ifelse(i > 1 & j < j.cols, array.N[i-1,j+1,t] / Kentry.interp.pois[i-1,j+1], NA)
W.dK1 <- ifelse(j > 1, array.N[i,j-1,t] / Kentry.interp.pois[i,j-1], NA)