1
Electronic supplementary material
2
Field estimates of calf-cow ratios
3
On Wyoming elk winter ranges (Clarks Fork, Cody, and Jackson herds), classification
4
surveys were conducted over 1-2 days via helicopter and ground observation, during late January
5
and February. One or more observers counted the number of calves (< 1 y), adult females (> 1
6
y), yearling bulls (1-2 y, spike-antlered), and adult bulls (>2 y, branch-antlered). The ratio of
7
calves per 100 adult females is used by agencies and in our work as an index of calf recruitment.
8
Though some studies have questioned the value of age ratios, they are considered comparatively
9
reliable in the open habitats characteristic of our study area (1); moreover, a recent modeling
10
study based on the life history of an elk population of the Greater Yellowstone Ecosystem (GY)
11
indicated that changes in elk calf survival explained 93% of the variation in calf-cow ratios (2).
12
On the winter range of the northern Yellowstone herd, which spans the boundary of Yellowstone
13
National Park (YNP) including areas in both Wyoming and Montana, surveys are typically
14
conducted in mid-March across a subset of 68 units that are stratified among four elevation
15
sectors (see [3] for detailed survey methods). Where possible (Clarks Fork, Cody, and Jackson
16
herds), we used a subset of the survey data taken from winter range where GPS collar
17
information indicated elk were largely or entirely migratory (e.g., 4).
18
To assess the timing of calf losses, we assembled calf-cow ratios conducted while the
19
migratory elk subpopulations surveyed during winter were located on their high-elevation
20
summer ranges inside YNP. The Clarks Fork herd was sampled by helicopter between
21
September 14-22, 2007-2010 (n = 250-835) (4). The Cody herd was sampled by helicopter on
22
August 13-14, 2011 (n = 1,376). Elk from the Jackson herd that summer inside YNP were
23
sampled in August 1991, 2001, 2005, and 2010 (n = 713-1,311). Elk in the Dome Mountain
24
herd, which comprises a major portion of the northern Yellowstone herd, were sampled in July
25
and August 2007-2008 (n = 1,060) (5). Calf-cow ratios are prone to observation error and can be
26
influenced by mixing of subpopulations in partially-migratory GYE elk, thus we present these
27
data primarily to illuminate general patterns rather than to explore fine-scale inter-annual or
28
inter-population variation. We assume that when summer ratios are similar to winter ratios in a
29
given population, the majority of annual mortalities (due to all causes) have already occurred.
30
Could historical predation rates have been biased low?
31
It is possible that historical studies of grizzly bear foraging ecology underestimated the
32
rate of elk calf predation, which could lead us to overestimate the dietary shift. An earlier study
33
that tracked grizzly bears using VHF collars (6) may have had a lower probability of detecting
34
elk calf predation events. Other past studies involving visual observations of grizzly bear activity
35
described bouts of calf predation by individual bears in some localized areas, suggesting that calf
36
predation might be more common (e.g., 7). However, the VHF-based study (6) used more
37
systematic sampling involving a larger sample size of marked individual bears, over a larger
38
geographic area and a longer study period – and ultimately the author applied a correction factor
39
based on the amount of time grizzly bears spent at carcasses of varying size. Moreover, the
40
apparent increase in grizzly bear predation on elk calves spans a period of steadily declining elk
41
numbers (8), suggesting increasing selection for elk calves by grizzly bears.
42
Simulated elk population growth rates and calf-cow ratios
43
We explored the potential influence of changes in grizzly bear diets and elk calf predation
44
rates on elk calf recruitment and population growth by generating a series of stochastic age-
45
structured female-only population projection matrices. We assumed elk had five age classes (9):
46
calves (0-1 y), yearlings (1-2 y), prime age adults (3-9 y), post-prime age adults (9-15 y) and old
47
age adults (15+ y). We used a post-breeding census model (10), where elk in the 15+ age class
48
continued to survive and reproduce. Each age class had different mean pregnancy and survival
49
rates, and associated process variances (9) (Table 1). We assumed vital rates were beta
50
distributed and constrained between 0.0 and maximum values (9) (Table 1).
51
Because of uncertainty in the size of the elk population exposed to grizzly bear predation
52
and in their vital rates over time, our goal in this analysis was to illustrate the potential
53
magnitude of the demographic impact of increased grizzly bear predation on elk, not to simulate
54
the specific dynamics of the elk population nor to account for all sources of demographic
55
variation. Thus, we assumed that the only difference in elk vital rates before and after the
56
cutthroat trout decline involved lower elk calf survival due to grizzly bear mortality. We
57
assumed that calf mortality was a product of non-grizzly-related mortality (M) and grizzly
58
predation (Pbt) prior to cutthroat trout decline, so that calf survival equaled:
59
60
61
𝐶
𝑆𝑏𝑡
= (1 − 𝑃𝑏𝑡 )(1 − 𝑀),
eq. S1
For each matrix, we calculated the non-grizzly mortality (M) by rearranging Equation S1,
𝑆𝐶
𝑏𝑡
𝑀 = 1 − 1−𝑃
,
𝑏𝑡
eq. S2
62
𝐶
where 𝑆𝑏𝑡
was the total (randomly drawn) calf survival rate. We calculated Pbt (calf mortality
63
due to grizzly bears before cutthroat trout decline, i.e., “before trout”) as the number of calves
64
eaten by grizzly bears per year over the total number of calves born. The total number of calves
65
born equaled the starting population of calves (male and female) under a stable age distribution
66
from a matrix of mean vital rate values. Both P and M were constrained so that they were
67
between 0.0 and 1.0. The total population size (reported in Figure 4) including bulls was
68
calculated assuming a 50:50 sex ratio of calves and yearlings, and a bull:cow ratio of 0.25
69
(equivalent to the approximate mean bull:cow ratio across Wyoming elk herds; Wyoming Game
70
and Fish Department, unpublished data).
71
The calculation of the non-grizzly-related mortality (M) component of calf survival
72
allowed us to estimate calf survival rate after the cutthroat trout decline by substituting the “post
73
decline” predation rate (Pat) back into Equation 1 and calculating a new calf survival rate. This
74
approach assumes that non-grizzly bear-related calf mortality rates were the same before and
75
after the cutthroat trout decline. In other words (as discussed in the main text), we assumed that
76
grizzly bear-related mortality was additive, and that calf mortality from other factors (i.e., other
77
predators, malnutrition, etc.) did not change before and after the cutthroat trout decline. Grizzly
78
bear predation is one of the only mortality factors that has been inferred to be largely additive in
79
our study area (11).
80
We examined two combinations of “pre-decline” and “post-decline” grizzly predation
81
rates. One combination used a 1:1 nutritional equivalency of the cutthroat trout biomass lost
82
from the diet with the elk calf biomass inferred to have replaced it (12; see main text for details),
83
with a pre-decline predation estimate of 245 elk calves and a post-decline predation estimate of
84
542 calves. Additionally, we calculated an estimate based on studies of grizzly bear kill rates
85
(see main text) of 245 calves pre-trout-decline and 476 calves post-trout-decline. We calculated
86
population growth rates for each matrix (pre- and post-decline) by taking the asymptotic lambda
87
value (eigenvalue). We found the change in lambda by subtracting the pre-decline lambda value
88
from the post-decline lambda value.
89
To calculate the changes in expected calf-cow ratios across population sizes, we
90
projected the population (at stable age distribution) eight months into the future, so that calves
91
were eight months old, reflecting the approximate date (February 15th) when winter calf-cow
92
ratios are collected in the field. We assumed that calf survival to eight months was a product of
93
bear-related mortality and half of the annual non-bear-related mortality. For each iteration, we
94
calculated the change in calf-cow ratios between the before and after trout declines.
95
For each population size, we iterated the above procedure 1,000 times, using a different
96
random set of vital rates for each run and we report the mean and 95% confidence intervals for
97
the change in population growth rates and change in calf-cow ratios (Figure 4). All simulations
98
were generated in program R (13). Beta values and eignevalues were simulated using the
99
“popbio” package (14).
100
References
101
1. Bonenfant C, Gaillard JM, Klein F, & Hamann JL (2005) Can we use the young: female ratio
102
to infer ungulate population dynamics? An empirical test using red deer Cervus elaphus as a
103
model. J Appl Ecol 42(2):361-370.
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
2. Harris NC, Kauffman MJ, & Mills LS (2008) Inferences about ungulate population dynamics
derived from age ratios. J Wildlife Manage 72(5):1143-1151.
3. Coughenour MB & Singer FJ (1996) Elk population processes in Yellowstone National Park
under the policy of natural regulation. Ecol Appl 6(2):573-593.
4. Middleton AD, et al. (In press) Animal migration amid shifting patterns of phenology and
predation: lessons from a Yellowstone elk herd. Ecology.
5. Cunningham JA, Hamlin KL, & Lemke TO (2008) Northern Yellowstone elk (HD313)
annual report. (Montana Fish, Wildlife, and Parks, Bozeman, MT).
6. Mattson DJ (1997) Use of ungulates by Yellowstone grizzly bears (Ursus arctos). Biol
Conserv 81(1-2):161-177.
7. Gunther KA & Renkin RA (1990) Grizzly bear predation on elk calves and other fauna of
Yellowstone National Park. In Bears: their biology and management (pp. 329-334).
8. Eberhardt LL, White PJ, Garrott RA, & Houston DB (2007) A seventy-year history of trends
in Yellowstone's northern elk herd. J Wildlife Manage 71(2):594-602.
9. Raithel JD, Kauffman MJ, & Pletscher DH (2007) Impact of spatial and temporal variation in
calf survival on the growth of elk populations. J Wildlife Manage 71(3):795-803.
10. Caswell H (2001) In Matrix population models: construction, analysis, and interpretation
(Sunderland, MA, USA, Sinauer Associates.
122
123
124
125
126
127
128
129
11. Griffin KA, et al. (2011) Neonatal mortality of elk driven by climate, predator phenology and
predator community composition. J Anim Ecol 80(6):1246-1257.
12. Fortin JK, et al. (2013) Dietary adaptability of grizzly bears and American black bears in
Yellowstone National Park. J Wildlife Manage 77(2):270-281.
13. R Development Core Team (2011) R: a language and environment for statistical computing.
(Vienna, Austria, R Foundation for Statistical Computing.
14.Stubben C & Milligan B (2007) Estimating and analyzing demographic models using the
popbio package in R. J Stat Softw 22(11), 1-23.
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
R code
## Although this program has been used by the U.S. Geological Survey (USGS), no warranty, expressed or implied,
is made by the USGS or the U.S. Government as to the accuracy and functioning of the program and
related program material nor shall the fact of distribution constitute any such warranty, and no
responsibility is assumed by the USGS in connection therewith.
##This code is same as lambda analysis, except the lambdas for pre- and post-decline are calculated as (Nt+1)/Nt,
## where Nt is a population in SAD and Nt+1 is a population following a stochastic draw of vital rates, for both preand post-decline populations.
## All A matrices are post-breeding pulse models
rm(list=ls(all=TRUE))
library(MASS)
library(VGAM)
library(shape)
library(popbio)
##Thomas A. Morrison, Wyoming Cooperative Fish and Wildlife Research Unit, University of Wyoming
##02.08.2012
##This routine generates a set of random elk population projection matrices before and after a decline in calf
##survival.
setwd()
#set.seed(11982)
reps = 1000
#number of runs per population size
pop = c(1350,2000, 2650, 3300, 3950)#, 4600, 5250) #2400,3000,3600,4200,4800,5400,6000)
#1200,1800,2400,3600,4200,female population sizes
sexratio = 0.5
#proportion of calves that are female
BCratio = 0.25
#ratio of adult cows (2+ y) to adult bulls (2+ y)
maxage = 15
#max age of elk
pred.mort1 = c(245,245) #245 estimated number of calves killed by grizzlies pre-decline based on median kill rate
from Mattson (1997)
pred.mort2 = c(542, 542) #estimated number of calves killed by grizzlies post-decline based on kill rate from
Fortin et al. (2013)
pred.mort3 = c(476)
#estimated number of calves killed by grizzlies after based on trout:calf biomass
equivalency calculations.
comp1 = 0.0161
comp2 = 0.0161
sc = 0.354; sy = 0.875; spa = 0.886; soa = 0.856; ss = 0.717 #age-class survival rates
fc = 0; fy =0.198; fpa = 0.928; foa = 0.864; fs = 0.530
#age-class fecundity rates
vrhi = c(0.729, 0.999, 0.999, 0.999, 0.900, 0.01, 0.250, 0.494, 0.475, 0.346)
#Max values allowed when
other vital rates are at best
vit.rates = cbind(c(0.354, 0.883, 0.886, 0.868, 0.724),
c(sqrt(0.02001),sqrt(0.00420),sqrt(0.002),sqrt(0.002),sqrt(0.00588)),
#Raithel et al. (2007) survival
estimates
#c(sqrt(0.03854),sqrt(0.00420),sqrt(0.00336),sqrt(0.00336),sqrt(0.00588)), #variance survival
c(0,0.198/2,0.928/2,0.864/2, 0.530/2),
#Pregnancy rates
c(0,sqrt(0.01508),sqrt(0.00126),sqrt(0.00250),sqrt(0.00647)))
#variance pregnancy
A = APre = APost1 = APost2 = matrix(0,maxage,maxage)
ran.beta1 = ran.beta2 = matrix(0,length(vit.rates[,1]),2) #"calf","yrlg","PA","OA","senes")
dater1 = dater2 = dater3 = dater4 = M.temp = M1.temp = NULL
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
# Age classes: 0-1, 1-2, 2-9, 10-14, 15+
# Post-birth pulse matrix model to establish number of calves born to calculate P ####
A[1,] =
c(0,vit.rates[2,3]*vit.rates[2,1],rep(vit.rates[3,3]*vit.rates[3,1],8),rep(vit.rates[4,3]*vit.rates[4,1],4),vit.rates
[5,3]*vit.rates[5,1]) #preg * surv
A[2,1] = vit.rates[1,1] #calf
A[3,2] = vit.rates[2,1] #Yearlings
A[4,3] = vit.rates[3,1] #Prime-age adults
A[5,4] = vit.rates[3,1]
A[6,5] = vit.rates[3,1]
A[7,6] = vit.rates[3,1]
A[8,7] = vit.rates[3,1]
A[9,8] = vit.rates[3,1]
A[10,9] = vit.rates[3,1]
A[11,10] = vit.rates[3,1]
A[12,11] = vit.rates[4,1] #Old age adults
A[13,12] = vit.rates[4,1]
A[14,13] = vit.rates[4,1]
A[15,14] = vit.rates[4,1] #Senescent adults
A[15,15] = vit.rates[5,1]
p.stable = eigen.analysis(A, zero=TRUE)
for (k in 1:length(pop)) {
pop.N = p.stable$stable.stage*pop[k]
N.calves = p.stable$stable.stage[1]*pop[k]
Nt = sum(pop.N)+sum(pop.N[1:2])+(BCratio*sum(pop.N[3:maxage]))
##########
cc.temp = cc.diff = lam.diff1 = lam.diff2 = lam.diff3 = lam.diff4 = elast1 = elast2 = NULL
Pre1 = pred.mort1[1] / (N.calves/sexratio)
get female calf predation rate
if (Pre1 > 1) Pre1 = 1
Pre2 = pred.mort1[2] / (N.calves/sexratio)
if (Pre2 > 1) Pre2 = 1
Post1 = pred.mort2[2] / (N.calves/sexratio)
if (Post1 > 1) Post1 = .99
Post2 = pred.mort3[1] / (N.calves/sexratio)
if (Post2 > 1) Post2 = .99
#pre-decline low predation rate (least conservative) -- divide by 2 to
#pre-decline high predation rate (most conservative)
#post-decline low predation rate (least conservative)
#post-decline biomass intake (most conservative)
i=0
while (i<reps) {
for (j in (1:length(vit.rates[,1]))) {
repeat
{ ran.beta1[j,1] <- betaval(vit.rates[j,1],vit.rates[j,2])
if (ran.beta1[j,1] < vrhi[j]) break
}
}
for (j in (1:length(vit.rates[,1]))) {
repeat
{ ran.beta1[j,2] <- betaval(vit.rates[j,3],vit.rates[j,4])
if (ran.beta1[j,2] < vrhi[j+5]) break
}
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
}
for (j in (1:length(vit.rates[,1]))) {
repeat
{ ran.beta2[j,1] <- betaval(vit.rates[j,1],vit.rates[j,2])
if (ran.beta2[j,1] < vrhi[j]) break
}
}
for (j in (1:length(vit.rates[,1]))) {
repeat
{ ran.beta2[j,2] <- betaval(vit.rates[j,3],vit.rates[j,4])
if (ran.beta2[j,2] < vrhi[j+5]) break
}
}
M = 1-(ran.beta1[1,1]/(1-Pre1)) #M isolates “natural” non-bear predation rate -- least conservative Npre grizzly =
95
M1 = 1-(ran.beta1[1,1]/(1-Pre2)) #M1 isolates “natural” non-bear predation rate -- most conservative Npre grizzly
= 304
if (M < 0 ) M = 0
if (M1 < 0 ) M1 = 0
M.temp = rbind(M.temp,M)
M1.temp = rbind(M1.temp,M1)
s.post1 = ran.beta1[1,1]
s.post2 = (1-M)*(1-Post1)
s.post3 = (1-M1)*(1-Post2)
S=c(s.post1,s.post2,s.post3)
#least conservative
#most conservative
#Post-birth pulse matrix model#
APre[1,] =
c(0,(ran.beta1[2,2]*ran.beta1[2,1]),rep(ran.beta1[3,2]*ran.beta1[3,1],8),rep(ran.beta1[4,2]*ran.beta1[4,1],4
),(ran.beta1[5,2]*ran.beta1[5,1])) #calf
APre[2,1] = S[1]
#calf S
APre[3,2] = ran.beta1[2,1] #yrling
APre[4,3] = ran.beta1[3,1] #PA
APre[5,4] = ran.beta1[3,1]
APre[6,5] = ran.beta1[3,1]
APre[7,6] = ran.beta1[3,1]
APre[8,7] = ran.beta1[3,1]
APre[9,8] = ran.beta1[3,1]
APre[10,9] = ran.beta1[3,1]
APre[11,10] = ran.beta1[3,1] #OA
APre[12,11] = ran.beta1[4,1]
APre[13,12] = ran.beta1[4,1]
APre[14,13] = ran.beta1[4,1]
APre[15,14] = ran.beta1[4,1]
APre[15,15] = ran.beta1[5,1] #senes
#Post-birth pulse matrix model pred rate -- least conservative#
APost1 <- APre
APost1[2,1] = S[2]
#APost1[1,] =
c(0,(ran.beta2[2,2]*ran.beta2[2,1]),rep(ran.beta2[3,2]*ran.beta2[3,1],8),rep(ran.beta2[4,2]*ran.beta2[4,1],4
),(ran.beta2[5,2]*ran.beta2[5,1])) #calf
#APost1[2,1] = S[2]
#calf S
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
#APost1[3,2] = ran.beta2[2,1] #yrling
#APost1[4,3] = ran.beta2[3,1] #PA
#APost1[5,4] = ran.beta2[3,1]
#APost1[6,5] = ran.beta2[3,1]
#APost1[7,6] = ran.beta2[3,1]
#APost1[8,7] = ran.beta2[3,1]
#APost1[9,8] = ran.beta2[3,1]
#APost1[10,9] = ran.beta2[3,1]
#APost1[11,10] = ran.beta2[3,1] #OA
#APost1[12,11] = ran.beta2[4,1]
#APost1[13,12] = ran.beta2[4,1]
#APost1[14,13] = ran.beta2[4,1]
#APost1[15,14] = ran.beta2[4,1]
#APost1[15,15] = ran.beta2[5,1] #senes
ppost1 = eigen.analysis(APost1, zero=TRUE)
#calculates eignevalues and elasticities
Acomp1 = APost1[,]*(1+(comp1*(ppost1$elasticities[,]/max(ppost1$elasticities)))) #Increases the vital so that
lambda = 1.03
ppost1 = eigen.analysis(Acomp1, zero=TRUE)
#Post-birth pulse matrix model protein rate -- most conservative#
APost2 = APost1
APost2[2,1] = S[3]
#calf S
ppost2 = eigen.analysis(APost2, zero=TRUE)
#calculates eignevalues and elasticities
Acomp2 = APost2[,]*(1+(comp2*(ppost2$elasticities[,]/max(ppost2$elasticities)))) #Increases the vital so that
lambda = 1.03
ppost2 = eigen.analysis(Acomp2, zero=TRUE)
p.Pre = eigen.analysis(APre, zero=TRUE)
#calculates eignevalues and elasticities
p.Post1 = eigen.analysis(APost1, zero=TRUE) #calculates eignevalues and elasticities -- least conservative
p.Post2 = eigen.analysis(APost2, zero=TRUE) #calculates eignevalues and elasticities -- most conservative
APre.stable = eigen.analysis(APre, zero=TRUE)
NFpre = APre.stable$stable.stage*pop[k]
temp = 2*NFpre[1]*(1-Pre1)*((1-M)^(8/12))
NFpre = sqrt(APre)%*%NFpre
NFpre[1] = temp
ccpre = NFpre[1]/sum(NFpre[2:maxage])
APost1.stable = eigen.analysis(APost1, zero=TRUE) #least conservative
NFpost1 = APost1.stable$stable.stage*pop[k]
temp = 2*NFpost1[1]*(1-Post1)*((1-M)^(8/12))
NFpost1 = sqrt(APost1)%*%NFpost1
NFpost1[1] = temp
ccpost1 = NFpost1[1]/sum(NFpost1[2:maxage])
APost2.stable = eigen.analysis(APost2, zero=TRUE) #most conservative
NFpost2 = APost2.stable$stable.stage*pop[k]
temp = 2*NFpost2[1]*(1-Post2)*((1-M1)^(8/12))
NFpost2 = sqrt(APost2)%*%NFpost2
NFpost2[1] = temp
ccpost2 = NFpost2[1]/sum(NFpost2[2:maxage])
ccLeastCon = (ccpost1-ccpre)
ccMostCon = (ccpost2-ccpre)
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
#Nt1.pre = sum(NFpre)+sum(NFpre[1:2])+(BCratio*sum(NFpre[3:maxage]))
#Nt1.post1 = sum(NFpost1)+sum(NFpost1[1:2])+(BCratio*sum(NFpost1[3:maxage]))
#Nt1.post2 = sum(NFpost2)+sum(NFpost2[1:2])+(BCratio*sum(NFpost2[3:maxage]))
lam.diff1 = rbind(lam.diff1, c(1,pop[k], p.Post1$lambda-p.Pre$lambda)) # #"low pred rate, least
conservative","Least",
lam.diff2 = rbind(lam.diff2, c(2,pop[k], p.Post2$lambda-p.Pre$lambda)) # #"biomass rate, most
conservative","Most",
cc.temp = rbind(cc.temp, c(ccpre,ccpost1,ccpost2))
cc.diff = rbind(cc.diff, c(ccMostCon,ccLeastCon))
i=i+1
}
temp1 = sort(lam.diff1[,3])
L95.d1 = temp1[reps*0.05]
U95.d1 = temp1[reps*0.95]
temp2 = sort(lam.diff2[,3])
L95.d2 = temp2[reps*0.05]
U95.d2 = temp2[reps*0.95]
temp3 = sort(cc.diff[,2])
L95.d3 = temp3[reps*0.05]
U95.d3 = temp3[reps*0.95]
temp4 = sort(cc.diff[,1])
L95.d4 = temp4[reps*0.05]
U95.d4 = temp4[reps*0.95]
dater1 = rbind(dater1,c(Nt,mean(lam.diff1[,3]),L95.d1,U95.d1))
dater2 = rbind(dater2,c(Nt,mean(lam.diff2[,3]),L95.d2,U95.d2))
dater3 = rbind(dater3,c(Nt,mean(cc.diff[,2]),L95.d3,U95.d3))
dater4 = rbind(dater4,c(Nt,mean(cc.diff[,1]),L95.d4,U95.d4))
}
Table legends
Table 1. Elk vital rate means and variances used in the elk population model.
Tables
Table 1
Age Class (years)
Survival
Variance
Max Survival
Pregnancy
Variance
Max Pregnancy
Calves (0-1)
0.354
0.02001
0.729
0.000
0.00000
0.000
Yearlings (1-2)
0.875
0.00420
0.999
0.198
0.01508
0.500
Prime age adults (2-9)
0.886
0.00200
0.999
0.928
0.00126
0.988
Post-prime adults (9-15)
0.856
0.00336
0.999
0.864
0.00250
0.950
Old adults (15+)
0.717
0.00588
0.900
0.530
0.00647
0.692