Presentation on theme: "Introduction to Demography"— Presentation transcript:
1Introduction to Demography We now move from the logistic model, that does not consider structure within a population, to ways to include aspects of sex, age, and/or size that will make it possible to better describe the dynamics of populations.In quantitative dynamics the usual tool is the life table,however for simple life histories a lot can be learned fromwhat are termed diagrammatic models. That’s where we’llstart.
2What kinds of simple life histories are amenable to study using diagrammatic models?Simple ones with the following sorts of stages:A simple plant life history animal life history(a holometabolous insect)seed eggseedling larvaimmature plant pupamature (reproductive) plant adultIn addition, we have to know whether generations overlap(parents survive through a significant part of their offsprings’ lifespan, and may reproduce again) or do not overlap.
3Case I – Non-overlapping generations First, the dynamics of a simple, annual, higher plantpopulation; one in which adults and offspring do not coexist.We'll begin with the specific, i.e. an annual plant, thenconsider the more general model.What happens to adult plants each year? They have someprobability of surviving from time t to time t+1. Now if wemake our count just prior to the annual reproductive effort,Then essentially all Nt alive at the start of our cycle reproduce, with an average fecundity of f seeds/individual.
4Of the total Nt x f seeds produced, only a fraction g germinate Of the total Nt x f seeds produced, only a fraction g germinate. For simplicity we'll assume the others die, but more complicated models could include a seed bank. Finally, of the Nt x f x g germinating seeds, only a portion e successfully become established. Establishment is a time of relatively high mortality in most plant populations.The number (in theory) in the population is made up ofsurvivors and newborns, i.e.Nt+1 = Nt + Nt x fgeSince this is a model of non-overlapping generations, forannual plants and other similar species, the Nt adults do notcarry over; the Nt term = 0.
6We could construct the same sort of diagram for an insect with a simple sequence of life stages, for example agrasshopper.
7When reproduction occurs repeatedly at different ages, the usual approach is the life table. However, it is possible to use a diagrammatic approach. Here’s an example for the English great tit, Parus major:Note that in this diagramsome adults (0.5) surviveto year t+1 after reproducingIn year t.
8What Happens If a Semelparous Species Reproduces at Varying Ages?This would mean we can’t simply diagram a life cycle frombirth to reproduction; things are happening at different times to different individuals.One useful approach has been size or stage-based models.Among the best examples are studies of teasal (Dipsacussylvestris) and mullein (Verbascum thapsus). Both are biennials. Theoretically, such plants should germinate and grow one year, then continue growth, flower, set seed and die in a second growing season.
9In these two species, a rosette of leaves grows (without any extended stem) in the year of establishment, and continuesgrowing the following year. If this rosette reaches sufficientsize, a flowering stalk is sent up in that second year, followedby reproduction and death of the adult.If, however, environmental conditions (population density,shading by taller plants of other species) slows rosette growth, the key size of the rosette for flowering is not reached, and the supposed biennial may survive additional years, until that critical size for flowering is achieved.This presents a complication for simple, age-based modeling.However, a size-stage model can easily represent this life cycle.
10The stage classifications for the teasel life history are: 1) seeds,2) seeds which remain dormant in the first spring, rather thangerminating,3) seeds which remain dormant through 2 cycles ofgermination4) small rosettes < 2.5 cm in diameter,5) medium rosettes between 2.5 and 18.9 cm in diameter,6) large rosettes greater than 19 cm in diameter, and7) flowering plants.Here is the diagram that represents this life history for one ofeight fields studied by Werner and Caswell (1977):
12If this were a perfect model (no errors, lost plants, etc. resulting from the field situation) then the sum of allTransitions (arrows leaving a box) should add up to 1.0, i.e.Something identifiable happens to each individual in the population, but note that the transitions indicated do not include mortality.We assume that the difference between the sums of indicated transitions and 1.0 is the fraction dying while in that stage.This population of teasel is growing at a growth rate/unit time, , of 1.26, or equivalently (=er) an 'r' of Those results come not from the diagram, but from the use of a stage-based matrix and its analysis. That comes later…
13Case 2: Populations With Overlapping Generations When generations are overlapping (the reproductive pattern is called iteroparity, the more usual approach is to use a life table.A few ‘rules’ about life tables:1)Traditionally, life tables give values for females only. Males are either assumed to have identical survivorship (they don’t bear young) or are tabled separately.2)At this stage we consider age-dependent birth and deathrates to be invariant with population density (and anymeasure of environmental variation, as well).
14There are two ‘forms’ of life tables There are two ‘forms’ of life tables. They look the same after creation, but data are collected in different ways.A.The horizontal (or static) life table. Here we sample apopulation made up of individuals of varying ages. Forthose in each age group, measure the survivorship ofindividuals through that age and the number of youngborn, on average, to a female of that age.How would you develop a life table for a tree, say SugarMaple, Acer saccharum, in a forest?a) core trees to count tree rings and age each individual.b) calculate what fraction survive from age group x to agegroup x+1.c) count the number of maple seeds or keys (usually bysubsampling branches) produced by the average femaleof each age group.
15B. The alternate type of life table, called a vertical or cohort life table, collects the same information, but does it byfollowing a cohort (all the babies born at a given time)from their birth until the last of them has died. The wholecohort is the same age.We measure:a) what fraction of those alive at one birthday (or time)are still alive at the beginning of the next time interval,andb) how many babies the average female had during thattime.This method, for any long-lived animal or plant, takes a longtime, and may even be impractical, but it is the usualtheoretical approach.
16Caveat emptor:There are problems inherent in either approach:In collecting data for a horizontal life table, we seem to beAssuming that environmental conditions in the past haven’tmaterially affected the values we get. Is what is happening to 10 year olds now the same as what happened to 20 year olds 10 years ago? It disregards environmental history.In collecting data for a cohort life table we seem to beassuming changes in environmental conditions while we arefollowing the population don’t have significant affects on the population’s demographic variables. It disregards theimportance of what is happening currently in the environment.
17One last important caveat: There is a difference between age and age class.At birth an organism is of age 0.It belongs to the first age class, i.e. age class = 1.That difference will be important in calculations, particularlywhen we develop matrix approaches (or brute forceequivalents) to assess (predict) population growth.
18The variables in the life table: x - the age of the cohortlx - the survivorship, or the fraction of the originalcohort that has survived from birth to reach age x.Expressed as an equation survivorshiplx = N(x)/N(0)mx (or bx) - the number of female children born to anaverage female of age x.
19The first of the variables we will add to the life table is the lx. Before actually filling in values, let’s look at patterns insurvivorship. There are various ways to do that. One is bymeans of expectancy of remaining life; the demographicvariable is ex. This is the variable actuaries calculate todetermine the cost of your life insurance. Here’s interestinglife expectancy data:ex
20There are 3 categories into which survivorship patterns are usually divided: Type I survivorship - organisms well-adapted to theirenvironments (or well-buffered against them), or which live in very stable environments.In these circumstances we canexpect most organisms to liveout a very large fraction of theirgenetically programmed life-spans. Examples: humans (atleast in well-developed countries,most other mammals, manyspecies in protected, zooenvironments.
212. Type II survivorship - mortality is almost totally random, resulting from interaction with the environment, and,therefore, affects a constant proportion in each of the ageclasses. That produces a diagonal survivorship curve.Examples: perching birds and, interestingly, bats.European robin species
22Type III survivorship - the youngest age class(es) are relatively unprotected and undeveloped, thus susceptible to and suffer severe mortality. Following an initial sorting out, the death rates are much lower until the onset of senescence. Examples include many insects, weedy plants like thistles, and Atlantic or Pacific salmon.data for mackerel
23These 3 categories are pigeonholes; many species have survivorship patterns intermediate between those categories.A few examples of deviations:a) milkweed bugs – they begin like other insects with a relatively severe mortality, after that their survivorship is a nearly perfect diagonal.b) Condors – like a number of other large birds, they do not have a diagonal survivorship curve; their survivorships are closer to a typical type I curve.c) After severe initial mortality in many tree species,there is a juvenile (sapling) stage during whichmortality appears basically diagonal, then a longperiod as mature adult trees during which mortalityappears to be type I.
26California condors, now recovering from near extinction, are very large birds that will be the subject of some sample calculations a little later. For now, the question is why condors don’t have type II survivorship?To persist with a reasonable pre-reproductive survivorship (> 0.5), they have to maintain an annual adult survivorship of > 0.7. That is more like type I than type II.Can we understand why many larger birds don’t have a type II survivorship?There are two types of development in birds. Some birds are altricial. They are born without feathers and require initial parental care. At hatching they are basically weak and helpless, and typically have relatively high mortality as hatchlings, nestlings and immediately after fledging, but a constant mortality rate thereafter.
27Precocial birds, (hatched more completely developed, with feathers, and capable of independent existence from hatching) like ducks and geese, delay reproduction for a longer period. Many of these species form long-term pair bonds at their first mating; learning processes enhancing successful reproduction must be completed before their first serious reproductive effort. Higher mortality extends through the pre-reproductive period, and the lower rate characteristic of adult life (the diagonal curve) begins at . This is the condor pattern.However, the condor is altricial!
28Here are the theoretical survivorship patterns you’ve seen before: Next time we’ll begin using a life table and begin calculations…