Ecology: biology of interaction. 4.03. Demographic tables, pyramids and survival curves
Demographic tables are convenient for monitoring the dynamics of birth and death rates across different age and/or sex groups. One of the methods of constructing them involves tracking the fate of a specific cohort of individuals born within a short time interval and recording their age at...
4.03. Demographic Tables, Pyramids, and Survivorship Curves
4.04. Exponential and Logistic Population Growth
4.03. Demographic tables, pyramids and survival curves As we have noted, the most important static characteristics of a population are its sex composition (ratio of individuals of different sexes) and age composition (ratio of individuals of different ages). These parameters are traditionally described using demographic tables. The first such table was constructed by the founder of demography, John Grant, in the 17th century on the basis of mortality data of London residents that parish churches collected in order to detect the onset of plague epidemics in time. Demographic tables are convenient for monitoring the dynamics of birth and death rates in different age and/or sex groups. One way of constructing them (Table 4.3.1) is to follow the fate of a defined cohort of individuals born within a short time interval and to record the age at death of all cohort members. Table 4.3.1. Demographic table of the population of the marine acorn barnacle (Balanus glandula) – a member of the sessile crustaceans (Connell, 1970 as cited in Gilyarov, 1987)
Age, years
Number of live individuals at the time of counting
Proportion of individuals that survived to the beginning of the age interval
Number of individuals that died during the interval
0
Life expectancy of surviving individuals, years
0
142
1000
80
0,563
1,58
1
62
0,437
28
0,452
1,97
2
34
0,239
14
0,412
2,18
3
20
0,141
4,5
0,225
2,35
4
15,5*
0,109
4,5
0,290
1,89
5
11
0,077
4,5
0,409
1,45
6
6,5*
0,046
4,5
0,692
1,12
7
2
0,014
0
0,000
1,50
8
2
0,014
2
1,000
0,50
9
0
0,0
-
-
-
* No accounting was carried out in these years. These data represent average estimates of the preceding and following years. More often, demographers use another method: determining mortality in different age groups over a certain observation period (Table 4.3.2). Knowing the size of each group, mortality for each age can be calculated. This method allows assessment of mortality and survivorship in long‑lived species even when only statistical data for a short time span are available. Table 4.3.2. Demographic table of the female population of Canada in 1980 (Krebs, 1985, as cited in Gilyarov, 1987)
Number of deaths in each age group
Mortality per 1,000 persons
0‑1
1000
0-1
173 400
1 651
9,52
1-4
685 900
340
0,5
5-9
876 600
218
0,25
10-14
980 300
234
0,24
15-19
1 164 100
568
0,49
20-24
1 136 100
619
0,54
25-29
1 029 300
578
0,56
30-34
933 000
662
0,71
35-39
739 200
818
1,11
40-44
627 000
1 039
1,66
45-49
622 400
1 664
2,67
50-54
615 100
2 574
4,18
55-59
596 000
3 878
6,51
60-64
481 200
4 853
10,09
65-69
413 400
6 803
16,07
70-74
325 600
8 421
25,86
75-79
235 100
10 029
42,66
80-84
149 300
10 824
72,5
85 and over
119 200
18 085
151,7
35‑39 739 200 818 1.11 40‑44 627 000 1 039 1.66 45‑49 622 400 1 664 2.67 50‑54 615 100 2 574 4.18 55‑59 596 000 3 878 6.51 60‑64 481 200 4 853 10.09 65‑69 413 400 6 803 16.07 70‑74 325 600 8 421 25.86 75‑79 235 100 10 029 42.66 80‑84 149 300 10 824 72.5 85 and over 119 200 18 085 151.7 Demographic tables can be even simpler, containing only the numbers of specific sex‑age categories. Demographic pyramids are built on the basis of these tables. On the vertical axis the age intervals are plotted; on the left side, as a bar diagram, the number of males (in human pyramids – men), on the right side – females (women). This makes the difference in mortality between age categories and sexes visually apparent. For example, data for constructing a demographic pyramid of Ukraine are given in Table 4.3.3 (source). Table 4.3.3. Demographic table of the population of Ukraine as of 1 January 2016 (excluding territories occupied by Russia and terrorist organizations supported by Russia)
Age
Men
Women
Age
Men
Women
0
211 339
197 833
51
268 174
312 280
1
238 053
224 436
52
282 787
334 969
2
242 884
228 566
53
286 276
343 840
3
251 286
236 070
54
295 213
356 263
4
242 525
228 012
55
302 282
369 718
5
239 790
225 895
56
283 130
354 777
6
247 658
232 081
57
276 830
352 682
7
246 292
231 359
58
260 318
338 471
8
226 677
214 535
59
254 431
337 497
9
220 970
210 041
60
232 462
315 462
10
205 415
193 481
61
233 782
324 457
11
205 494
194 605
62
208 379
296 363
12
196 088
185 961
63
212 821
309 520
13
188 378
177 020
64
208 929
306 173
14
180 933
170 616
65
202 140
302 258
15
186 068
175 950
66
201 406
312 895
16
188 132
178 596
67
164 310
259 283
17
199 667
191 300
68
140 031
229 249
18
209 887
199 416
69
129 849
222 131
19
228 717
216 345
70
81 538
146 446
20
239 365
225 479
71
89 398
168 292
21
249 004
234 132
72
77 468
149 507
22
262 351
248 210
73
95 195
189 839
23
281 119
266 380
74
122 876
245 425
24
299 627
284 254
75
119 964
245 102
25
313 751
298 618
76
118 369
258 565
26
326 933
312 701
77
116 399
261 038
27
346 300
332 604
78
113 614
254 250
28
357 229
343 228
79
87 444
195 204
29
377 924
365 398
80
66 546
151 397
30
365 389
355 317
81
46 057
105 479
31
373 599
363 325
82
35 102
84 951
32
377 596
368 473
83
39 273
103 169
33
343 652
334 841
84
37 704
97 200
34
329 211
327 713
85
41 419
110 758
35
336 112
334 930
86
27 468
84 095
36
316 073
316 770
87
25 154
80 296
37
311 492
316 567
88
20 900
63 381
38
299 213
307 561
89
15 911
52 720
39
314 648
324 098
90
11 919
41 260
40
305 622
319 800
91
8 390
31 390
41
296 250
312 008
92
5 399
19 405
42
288 153
304 467
93
3 881
13 776
43
295 105
315 155
94
3 580
10 578
44
292 515
311 807
95
3 562
9 192
45
288 882
309 322
96
1 038
2 675
46
262 769
286 474
97
998
2 995
47
265 315
291 439
98
859
1 852
48
259 160
289 260
99
345
821
49
264 886
298 893
100 and older
1 848
50
259 215
297 676
Age Men Women Age Men Women 0 211 339 197 833 51 268 174 312 280 1 238 053 224 436 52 282 787 334 969 2 242 884 228 566 53 286 276 343 840 3 251 286 236 070 54 295 213 356 263 4 242 525 228 012 55 302 282 369 718 5 239 790 225 895 56 283 130 354 777 6 247 658 232 081 57 276 830 352 682 7 246 292 231 359 58 260 318 338 471 8 226 677 214 535 59 254 431 337 497 9 220 970 210 041 60 232 462 315 462 10 205 415 193 481 61 233 782 324 457 11 205 494 194 605 62 208 379 296 363 12 196 088 185 961 63 212 821 309 520 13 188 378 177 020 64 208 929 306 173 14 180 933 170 616 65 202 140 302 258 15 186 068 175 950 66 201 406 312 895 16 188 132 178 596 67 164 310 259 283 17 199 667 191 300 68 140 031 229 249 18 209 887 199 416 69 129 849 222 131 19 228 717 216 345 70 81 538 146 446 20 239 365 225 479 71 89 398 168 292 21 249 004 234 132 72 77 468 149 507 22 262 351 248 210 73 95 195 189 839 23 281 119 266 380 74 122 876 245 425 24 299 627 284 254 75 119 964 245 102 25 313 751 298 618 76 118 369 258 565 26 326 933 312 701 77 116 399 261 038 27 346 300 332 604 78 113 614 254 250 28 357 229 343 228 79 87 444 195 204 29 377 924 365 398 80 66 546 151 397 30 365 389 355 317 81 46 057 105 479 31 373 599 363 325 82 35 102 84 951 32 377 596 368 473 83 39 273 103 169 33 343 652 334 841 84 37 704 97 200 34 329 211 327 713 85 41 419 110 758 35 336 112 334 930 86 27 468 84 095 36 316 073 316 770 87 25 154 80 296 37 311 492 316 567 88 20 900 63 381 38 299 213 307 561 89 15 911 52 720 39 314 648 324 098 90 11 919 41 260 40 305 622 319 800 91 8 390 31 390 41 296 250 312 008 92 5 399 19 405 42 288 153 304 467 93 3 881 13 776 43 295 105 315 155 94 3 580 10 578 44 292 515 311 807 95 3 562 9 192 45 288 882 309 322 96 1 038 2 675 46 262 769 286 474 97 998 2 995 47 265 315 291 439 98 859 1 852 48 259 160 289 260 99 345 821 49 264 886 298 893 100 and older 1 848 50 259 215 297 676 Demographic pyramids help to visually represent population history. Consider the pyramid for the population of Ukraine (Fig. 4.3.1). You can see, for instance, how it reflects the decline in births during World II. The “echo” of these events manifested even a generation later and, to a lesser extent, two generations later, when the long‑term consequences of the war were compounded by a decline in living standards caused by incompetent governance of Ukraine in the early (unfortunately, not only the first) years of its independence. The number of people who, by age, are children and grandchildren of those born during the war turns out to be smaller than the size of adjacent age groups. The reduction in newborn numbers is likely a consequence of Russian aggression and the worsening economic situation of the country. [IMG_1] Fig. 4.3.1. Demographic pyramid of the population of Ukraine (excluding occupied territories) as of 2016 (based on Table 4.3.3) In addition, demographic tables provide material for constructing survival curves. This graphical representation of the proportion of individuals still alive as a function of age in the 1920s was proposed by Robert Pearl. He distinguished three basic types of survival curves (Fig. 4.3.2). [IMG_2] Fig. 4.3.2. Three types of “ideal” mortality curves according to Pearl Type I curve (Drosophila type) has a convex shape. It describes a situation where high mortality occurs in mature ages. This is typical for Drosophila, mayflies and other insects that reproduce shortly after eclosion and then die. Survival curves of large mammals approximate the Type I curve. Type II curve (hydra type) is characteristic of organisms with a constant mortality rate at any age. On a graph this corresponds to a straight line. Such curves are typical for fish, reptiles, birds, herbaceous perennials, etc., with the single caveat that the counting starts from individuals that have already passed the most vulnerable developmental stages. Type III curve (oyster type) has a concave shape. It is characteristic of organisms that mainly die in the early stages of life. Oysters lead a sessile adult life, while their larvae are planktonic; this period is when they are most vulnerable. Individuals that successfully pass the larval stage have a greatly increased chance of survival. This type of curve is common among many highly fecund animals that provide no parental care. Real survival curves are combinations of these types. The human curve is convex, relatively close to Type I, yet it can take different shapes in different contexts (Fig. 4.3.3). [IMG_3] Fig. 4.3.3. Types of survival curves in primitive and developed societies
4.02. Population Characteristics
D. Shabanov, M. Kravchenko. Ecology: The Biology of Interaction Chapter 4. Population Ecology
4.04. Exponential and Logistic Population Growth
D. Shabanov, M. Kravchenko. Ecology: Interaction Biology Chapter 4. Population Ecology 4.04. Exponential and logistic population growth
4.04. Exponential and Logistic Population Growth Exponential and logistic population growth occurs when the number of births and deaths depends only on the population density. The growth curve has an exponential shape and is described by the equation: [IMG_N] where N is the population size, t is time, and r is the intrinsic rate of increase. However, this type of growth cannot continue indefinitely because environmental resources are limited. Therefore, a more realistic model is logistic growth, described by the equation: [IMG_N] where K is the carrying capacity of the environment, i.e., the maximum population size that the environment can sustain. BATRIMG2>BATR Logistic growth is characterized by rapid population growth in the initial stages, but as population density increases, the growth rate decreases and eventually reaches zero when the carrying capacity is reached.