Lecture

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.