256:... The germs of existence contained in this spot of earth, with ample food, and ample room to expand in, would fill millions of worlds in the course of a few thousand years. Necessity, that imperious all pervading law of nature, restrains them within the prescribed bounds. The race of plants, and the race of animals shrink under this great restrictive law. And the race of man cannot, by any efforts of reason, escape from it. Among plants and animals its effects are waste of seed, sickness, and premature death. Among mankind, misery and vice. "
1129:
1117:
248:
Malthus wrote that all life forms, including humans, have a propensity to exponential population growth when resources are abundant but that actual growth is limited by available resources:
1021:
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104:
461:
406:
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410:
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1165:
457:
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2126:
959:
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344:
138:
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991:
682:
263:
37:
2136:
1864:
433:
2141:
1698:
649:
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1746:
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1905:
1158:
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1418:
943:
382:
612:
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252:"Through the animal and vegetable kingdoms, nature has scattered the seeds of life abroad with the most profuse and liberal hand.
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based on the idea of the function being proportional to the speed to which the function grows. The model is named after
1121:
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969:
875:
2446:
2166:
1370:
1267:
938:
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1989:
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1360:
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672:
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1849:
1731:
853:
642:
273:
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2102:
1954:
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964:
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677:
334:
305:
165:
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1786:
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1031:
895:
734:
299:
32:
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54:
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2009:
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741:
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293:
230:
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588:
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1934:
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1207:
1036:
974:
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724:
713:
451:
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222:
28:
2156:
2587:
2556:
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1979:
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1232:
1217:
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885:
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339:
289:
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2014:
2004:
1999:
1964:
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1607:
1408:
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1222:
1087:
1082:
868:
863:
746:
702:
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567:
523:
328:
550:
Ginzburg, Lev R. (1986). "The theory of population dynamics: I. Back to first principles".
2677:
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2151:
2019:
1925:
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1252:
1178:
1097:
858:
226:
142:
597:
from Steve McKelvey, Department of
Mathematics, Saint Olaf College, Northfield, Minnesota
591:
from Steve McKelvey, Department of
Mathematics, Saint Olaf College, Northfield, Minnesota
563:
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2481:
2434:
2364:
2359:
2254:
2121:
1994:
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1791:
1771:
1648:
1574:
1539:
1478:
1355:
1310:
1202:
1102:
501:
Turchin, P. "Complex population dynamics: a theoretical/empirical synthesis" Princeton
331:– an extension of the Malthusian model accounting for population explosions and crashes
600:
571:
2711:
2682:
1658:
1632:
1589:
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1534:
1521:
1501:
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841:
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527:
314:
296:
that adjusts growth rate based on how close it is to the maximum a system can support
130:
241:. By now, it is a widely accepted view to analogize Malthusian growth in Ecology to
2667:
2652:
2309:
2279:
2224:
2107:
2072:
1949:
1448:
890:
237:
as the founder. The exponential law is therefore also sometimes referred to as the
502:
1959:
1688:
1506:
1468:
1443:
1433:
1398:
1345:
1325:
773:
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2214:
1854:
1806:
1751:
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1627:
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1488:
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1315:
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272:
A model of population growth bounded by resource limitations was developed by
42:
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2531:
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1703:
1673:
1473:
1428:
1403:
1340:
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1305:
1297:
1242:
828:
392:
318:
309:
784:
2632:
2561:
2092:
1599:
1511:
1458:
1413:
900:
823:
363:"Malthus, An Essay on the Principle of Population: Library of Economics"
2622:
2429:
2299:
2294:
1921:
1869:
1529:
1174:
234:
276:
in 1838, after he had read
Malthus' essay. Verhulst named the model a
159:
The model can also be written in the form of a differential equation:
805:
514:
Turchin, Peter (2001). "Does population ecology have general laws?".
621:
609:
Professor of
Entomology, Alan Berryman, Washington State University
377:(A complete variorum ed.). Oxford: Oxford University Press.
1894:
1147:
631:
627:
424:
Lotka, Alfred J. (Alfred James), 1880-1949. (2013-06-29).
41:(1798), one of the earliest and most influential books on
1022:
International
Conference on Population and Development
168:
57:
607:
On principles, laws and theory of population ecology
302:– a leading proponent of the Malthusian Growth Model
2570:
2470:
2395:
2268:
2205:
2065:
1933:
1835:
1714:
1641:
1598:
1520:
1487:
1384:
1296:
1190:
1075:
1000:
952:
931:
814:
760:
711:
665:
200:
98:
540:Paul Haemig, "Laws of Population Ecology", 2005
481:Théorie analytique des associations biologiques
373:Fisher, Ronald Aylmer, Sir, 1890-1962. (1999).
250:
1906:
1159:
643:
8:
405:: CS1 maint: multiple names: authors list (
1047:United Nations world population conferences
460:) CS1 maint: multiple names: authors list (
426:Analytical theory of biological populations
48:Malthusian models have the following form:
16:Exponential growth based on a constant rate
2127:Latitudinal gradients in species diversity
1913:
1899:
1891:
1166:
1152:
1144:
960:Population and housing censuses by country
650:
636:
628:
464:) CS1 maint: numeric names: authors list (
456:: CS1 maint: location missing publisher (
409:) CS1 maint: numeric names: authors list (
375:The genetical theory of natural selection
345:The Genetical Theory of Natural Selection
169:
167:
139:The Genetical Theory of Natural Selection
135:Malthusian parameter of population growth
87:
77:
56:
2025:Predator–prey (Lotka–Volterra) equations
1664:Tritrophic interactions in plant defense
683:Estimates of historical world population
221:. It is widely regarded in the field of
2057:Random generalized Lotka–Volterra model
356:
264:An Essay on the Principle of Population
217:This model is often referred to as the
38:An Essay on the Principle of Population
1865:Herbivore adaptations to plant defense
449:
398:
7:
1880:Predator avoidance in schooling fish
1116:
613:Introduction to Social Macrodynamics
243:Newton's First Law of uniform motion
129:= the population growth rate, which
2330:Intermediate disturbance hypothesis
1052:Voluntary Human Extinction Movement
292:for the mathematical model used in
201:{\displaystyle {\frac {dP}{dt}}=rP}
123:(0) is the initial population size,
2083:Ecological effects of biodiversity
14:
1419:Generalist and specialist species
944:Population and Development Review
2142:Occupancy–abundance relationship
1128:
1127:
1115:
992:Population concern organizations
698:Projections of population growth
528:10.1034/j.1600-0706.2001.11310.x
99:{\displaystyle P(t)=P_{0}e^{rt}}
2162:Relative abundance distribution
1875:Plant defense against herbivory
1742:Competitive exclusion principle
1454:Mesopredator release hypothesis
1093:Human impact on the environment
1027:Population Action International
211:with initial condition: P(0)= P
1747:Consumer–resource interactions
1042:United Nations Population Fund
552:Journal of Theoretical Biology
67:
61:
1:
2593:Biological data visualization
2420:Environmental niche modelling
2147:Population viability analysis
572:10.1016/s0022-5193(86)80180-1
27:growth model, is essentially
2078:Density-dependent inhibition
308:– related growth model from
2547:Liebig's law of the minimum
2382:Resource selection function
1273:Metabolic theory of ecology
1067:World Population Foundation
1057:World Population Conference
970:World population milestones
2754:
2447:Niche apportionment models
2167:Relative species abundance
1371:Primary nutritional groups
1268:List of feeding behaviours
939:Population and Environment
624:Lev Ginzburg, Mark Colyvan
601:Laws Of Population Ecology
147:intrinsic rate of increase
2696:
2628:Ecosystem based fisheries
2240:Interspecific competition
2132:Minimum viable population
1990:Maximum sustainable yield
1975:Intraspecific competition
1970:Effective population size
1850:Anti-predator adaptations
1361:Photosynthetic efficiency
1111:
849:Human population planning
673:Demographics of the world
479:Lotka, Alfred J. (1934).
2738:1798 in economic history
2618:Ecological stoichiometry
2583:Alternative stable state
854:Compulsory sterilization
274:Pierre Francois Verhulst
2462:Ontogenetic niche shift
2325:Ideal free distribution
2235:Ecological facilitation
1985:Malthusian growth model
1955:Consumer-resource model
1812:Paradox of the plankton
1777:Energy systems language
1497:Chemoorganoheterotrophy
1464:Optimal foraging theory
1439:Heterotrophic nutrition
796:Malthusian growth model
589:Malthusian Growth Model
21:Malthusian growth model
2608:Ecological forecasting
2552:Marginal value theorem
2350:Landscape epidemiology
2285:Cross-boundary subsidy
2220:Biological interaction
1570:Microbial intelligence
1258:Green world hypothesis
923:Zero population growth
918:Sustainable population
842:Malthusian catastrophe
801:Overshoot (population)
678:Demographic transition
335:Malthusian catastrophe
306:Exogenous growth model
270:
261:Thomas Malthus, 1798.
202:
100:
2723:Mathematical modeling
2613:Ecological humanities
2512:Ecological energetics
2457:Niche differentiation
2320:Habitat fragmentation
2088:Ecological extinction
2035:Small population size
1787:Feed conversion ratio
1767:Ecological succession
1699:San Francisco Estuary
1613:Ecological efficiency
1555:Microbial cooperation
1032:Population Connection
896:Mere addition paradox
735:Physiological density
317:– related ideas from
300:Albert Allen Bartlett
203:
101:
33:Thomas Robert Malthus
23:, sometimes called a
2638:Evolutionary ecology
2603:Ecological footprint
2598:Ecological economics
2522:Ecological threshold
2517:Ecological indicator
2387:Source–sink dynamics
2340:Land change modeling
2335:Insular biogeography
2187:Species distribution
1926:Modelling ecosystems
1585:Microbial metabolism
1424:Intraguild predation
1213:Biogeochemical cycle
1179:Modelling ecosystems
1062:World Population Day
1017:Church of Euthanasia
906:Non-identity problem
881:Political demography
837:Human overpopulation
324:Human overpopulation
166:
55:
2688:Theoretical ecology
2663:Natural environment
2527:Ecosystem diversity
2497:Ecological collapse
2487:Bateman's principle
2442:Limiting similarity
2355:Landscape limnology
2177:Species homogeneity
2015:Population modeling
2010:Population dynamics
1827:Trophic state index
911:Reproductive rights
742:Population dynamics
693:Population momentum
564:1986JThBi.122..385G
294:Population dynamics
231:population dynamics
2733:Population ecology
2699:Outline of ecology
2648:Industrial ecology
2643:Functional ecology
2507:Ecological deficit
2452:Niche construction
2415:Ecosystem engineer
2192:Species–area curve
2113:Introduced species
1928:: Other components
1860:Deimatic behaviour
1762:Ecological network
1694:North Pacific Gyre
1679:hydrothermal vents
1618:Ecological pyramid
1565:Microbial food web
1376:Primary production
1321:Foundation species
1037:Population Matters
752:Population pyramid
730:Population density
725:Population decline
603:Dr. Paul D. Haemig
223:population ecology
198:
96:
29:exponential growth
25:simple exponential
2705:
2704:
2588:Balance of nature
2345:Landscape ecology
2230:Community ecology
2172:Species diversity
2108:Indicator species
2103:Gradient analysis
1980:Logistic function
1888:
1887:
1845:Animal coloration
1822:Trophic mutualism
1560:Microbial ecology
1351:Photoheterotrophs
1336:Myco-heterotrophy
1248:Ecosystem ecology
1233:Carrying capacity
1198:Abiotic component
1141:
1140:
1012:7 Billion Actions
886:Population ethics
779:Carrying capacity
688:Population growth
622:Ecological Orbits
435:978-1-4757-9176-1
340:Neo-malthusianism
290:Logistic function
278:logistic function
187:
2745:
2405:Ecological niche
2377:selection theory
2197:Umbrella species
2182:Species richness
2118:Invasive species
2098:Flagship species
2005:Population cycle
2000:Overexploitation
1965:Ecological yield
1915:
1908:
1901:
1892:
1797:Mesotrophic soil
1737:Climax community
1669:Marine food webs
1608:Biomagnification
1409:Chemoorganotroph
1263:Keystone species
1223:Biotic component
1168:
1161:
1154:
1145:
1131:
1130:
1119:
1118:
1088:Green Revolution
869:Two-child policy
864:One-child policy
787:
747:Population model
703:World population
652:
645:
638:
629:
617:Andrey Korotayev
576:
575:
547:
541:
538:
532:
531:
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492:
476:
470:
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404:
396:
370:
364:
361:
329:Irruptive growth
268:
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207:
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199:
188:
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105:
103:
102:
97:
95:
94:
82:
81:
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2746:
2744:
2743:
2742:
2708:
2707:
2706:
2701:
2692:
2678:Systems ecology
2566:
2537:Extinction debt
2502:Ecological debt
2492:Bioluminescence
2473:
2466:
2435:marine habitats
2410:Ecological trap
2391:
2271:
2264:
2207:
2201:
2157:Rapoport's rule
2152:Priority effect
2093:Endemic species
2061:
2020:Population size
1936:
1929:
1919:
1889:
1884:
1837:
1831:
1817:Trophic cascade
1727:Bioaccumulation
1710:
1637:
1594:
1516:
1483:
1380:
1292:
1253:Ecosystem model
1186:
1172:
1142:
1137:
1107:
1071:
1005:
1003:
996:
948:
927:
876:Overconsumption
859:Family planning
816:
810:
783:
767:
764:
756:
718:
715:
707:
661:
656:
585:
580:
579:
549:
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478:
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397:
385:
372:
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358:
353:
286:
269:
260:
253:
227:first principle
219:exponential law
214:
179:
171:
164:
163:
143:Alfred J. Lotka
118:
83:
73:
53:
52:
17:
12:
11:
5:
2751:
2749:
2741:
2740:
2735:
2730:
2725:
2720:
2718:Empirical laws
2710:
2709:
2703:
2702:
2697:
2694:
2693:
2691:
2690:
2685:
2680:
2675:
2670:
2665:
2660:
2658:Microecosystem
2655:
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2630:
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2620:
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2610:
2605:
2600:
2595:
2590:
2585:
2580:
2574:
2572:
2568:
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2565:
2564:
2559:
2557:Thorson's rule
2554:
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2544:
2539:
2534:
2529:
2524:
2519:
2514:
2509:
2504:
2499:
2494:
2489:
2484:
2482:Assembly rules
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2464:
2459:
2454:
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2444:
2439:
2438:
2437:
2427:
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2417:
2412:
2407:
2401:
2399:
2393:
2392:
2390:
2389:
2384:
2379:
2367:
2365:Patch dynamics
2362:
2360:Metapopulation
2357:
2352:
2347:
2342:
2337:
2332:
2327:
2322:
2317:
2312:
2307:
2302:
2297:
2292:
2287:
2282:
2276:
2274:
2266:
2265:
2263:
2262:
2257:
2255:Storage effect
2252:
2247:
2242:
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2227:
2222:
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2211:
2209:
2203:
2202:
2200:
2199:
2194:
2189:
2184:
2179:
2174:
2169:
2164:
2159:
2154:
2149:
2144:
2139:
2137:Neutral theory
2134:
2129:
2124:
2122:Native species
2115:
2110:
2105:
2100:
2095:
2090:
2085:
2080:
2075:
2069:
2067:
2063:
2062:
2060:
2059:
2054:
2053:
2052:
2047:
2037:
2032:
2027:
2022:
2017:
2012:
2007:
2002:
1997:
1995:Overpopulation
1992:
1987:
1982:
1977:
1972:
1967:
1962:
1957:
1952:
1947:
1941:
1939:
1931:
1930:
1920:
1918:
1917:
1910:
1903:
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1885:
1883:
1882:
1877:
1872:
1867:
1862:
1857:
1852:
1847:
1841:
1839:
1833:
1832:
1830:
1829:
1824:
1819:
1814:
1809:
1804:
1802:Nutrient cycle
1799:
1794:
1792:Feeding frenzy
1789:
1784:
1779:
1774:
1772:Energy quality
1769:
1764:
1759:
1754:
1749:
1744:
1739:
1734:
1732:Cascade effect
1729:
1724:
1718:
1716:
1712:
1711:
1709:
1708:
1707:
1706:
1701:
1696:
1691:
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1656:
1651:
1645:
1643:
1639:
1638:
1636:
1635:
1630:
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1620:
1615:
1610:
1604:
1602:
1596:
1595:
1593:
1592:
1587:
1582:
1577:
1575:Microbial loop
1572:
1567:
1562:
1557:
1552:
1547:
1542:
1540:Lithoautotroph
1537:
1532:
1526:
1524:
1522:Microorganisms
1518:
1517:
1515:
1514:
1509:
1504:
1499:
1493:
1491:
1485:
1484:
1482:
1481:
1479:Prey switching
1476:
1471:
1466:
1461:
1456:
1451:
1446:
1441:
1436:
1431:
1426:
1421:
1416:
1411:
1406:
1401:
1396:
1390:
1388:
1382:
1381:
1379:
1378:
1373:
1368:
1363:
1358:
1356:Photosynthesis
1353:
1348:
1343:
1338:
1333:
1328:
1323:
1318:
1313:
1311:Chemosynthesis
1308:
1302:
1300:
1294:
1293:
1291:
1290:
1285:
1280:
1275:
1270:
1265:
1260:
1255:
1250:
1245:
1240:
1235:
1230:
1225:
1220:
1215:
1210:
1205:
1203:Abiotic stress
1200:
1194:
1192:
1188:
1187:
1173:
1171:
1170:
1163:
1156:
1148:
1139:
1138:
1136:
1135:
1125:
1112:
1109:
1108:
1106:
1105:
1103:Sustainability
1100:
1095:
1090:
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131:Ronald Fisher
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26:
22:
2668:Regime shift
2653:Macroecology
2374:
2370:
2310:Edge effects
2280:Biogeography
2225:Commensalism
2073:Biodiversity
1984:
1950:Allee effect
1689:kelp forests
1642:Example webs
1507:Detritivores
1346:Organotrophs
1326:Kinetotrophs
1278:Productivity
1120:
932:Publications
891:Antinatalism
829:
806:World3 model
795:
666:Major topics
555:
551:
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519:
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428:. New York.
425:
419:
374:
368:
359:
271:
267:. Chapter I.
262:
251:
247:
245:in physics.
238:
218:
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158:
152:
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134:
126:
120:
113:
108:
47:
36:
35:, who wrote
24:
20:
18:
2305:Disturbance
2208:interaction
2030:Recruitment
1960:Depensation
1752:Copiotrophs
1623:Energy flow
1545:Lithotrophy
1489:Decomposers
1469:Planktivore
1444:Insectivore
1434:Heterotroph
1399:Bacterivore
1366:Phototrophs
1316:Chemotrophs
1288:Restoration
1238:Competition
815:Society and
774:Biocapacity
483:. Hermann.
145:called the
133:called the
2728:Population
2712:Categories
2673:Sexecology
2250:Parasitism
2215:Antibiosis
2050:Resistance
2045:Resilience
1935:Population
1855:Camouflage
1807:Oligotroph
1722:Ascendency
1684:intertidal
1674:cold seeps
1628:Food chain
1429:Herbivores
1404:Carnivores
1331:Mixotrophs
1306:Autotrophs
1185:components
1002:Events and
817:population
763:Population
714:Population
659:Population
615:Professor
351:References
43:population
2578:Allometry
2532:Emergence
2260:Symbiosis
2245:Mutualism
2040:Stability
1945:Abundance
1757:Dominance
1715:Processes
1704:tide pool
1600:Food webs
1474:Predation
1459:Omnivores
1386:Consumers
1341:Mycotroph
1298:Producers
1243:Ecosystem
1208:Behaviour
1098:Migration
975:6 billion
522:: 17–26.
489:614057604
452:cite book
444:861705456
401:cite book
319:economics
310:economics
2633:Endolith
2562:Xerosere
2474:networks
2290:Ecocline
1836:Defense,
1512:Detritus
1414:Foraging
1283:Resource
1133:Category
901:Natalism
824:Eugenics
393:45308589
284:See also
259:—
2623:Ecopath
2430:Habitat
2300:Ecotype
2295:Ecotone
2272:ecology
2270:Spatial
2206:Species
2066:Species
1937:ecology
1922:Ecology
1870:Mimicry
1838:counter
1782:f-ratio
1530:Archaea
1218:Biomass
1191:General
1183:Trophic
1175:Ecology
1122:Commons
765:ecology
716:biology
560:Bibcode
235:Malthus
233:, with
225:as the
155:= time.
1654:Rivers
1550:Marine
832:genics
503:online
487:
442:
432:
391:
381:
254:
141:, and
109:where
2571:Other
2472:Other
2425:Guild
2397:Niche
1649:Lakes
953:Lists
516:Oikos
1659:Soil
485:OCLC
466:link
462:link
458:link
440:OCLC
430:ISBN
411:link
407:link
389:OCLC
379:ISBN
830:Dys
568:doi
556:122
524:doi
229:of
137:in
2714::
2120:/
1924::
1181::
1177::
566:.
554:.
520:94
518:.
454:}}
450:{{
438:.
403:}}
399:{{
387:.
280:.
119:=
45:.
19:A
2375:K
2373:/
2371:r
1914:e
1907:t
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985:8
980:7
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644:t
637:v
574:.
570::
562::
530:.
526::
491:.
468:)
446:.
413:)
395:.
213:0
196:P
193:r
190:=
184:t
181:d
176:P
173:d
153:t
149:,
127:r
121:P
117:0
114:P
92:t
89:r
85:e
79:0
75:P
71:=
68:)
65:t
62:(
59:P
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