Lecture - 28
Population viability analysis
[FL] In today’s class we will have a look at Population Viability Analysis or an analysis of the viability of a population.
(Refer Slide Time: 00:22)
Now, population has we have seen before is a collection of individuals of the same species that are residing in the same area, that are interbreeding amongst each other, and that are separated from any other such similar group of species.
(Refer Slide Time: 00:39)
So, let us begin with population viability. So, when you say population viability, what do we mean? Population viability is the ability of a population to persist or to avoid extinction. Now, what we are asking here is that, suppose you have see around 10 tigers in Panna tiger reserve. So, if we have these 10 tigers, will these 10 tigers be able to persist for a long period of time, will they be able to avoid extension, or will they will go extent in short while? So, population viability analysis is an analysis of the viability of the population. So an analysis of whether or not this population will be able to persist or not. (Refer Slide Time: 01:09)
(Refer Slide Time: 01:23)
Now, why do you need to perform such an analysis? So, we have seen before that populations can become extinct because there are two factors operating at all times that could lead to their extinction. These are deterministic factors and stochastic factors; deterministic factors, that act at large population sizes and stochastic factors, that are chance factors acting at smaller population sizes.
(Refer Slide Time: 01:43)
Now, to recap, we have these 3 deterministic factors birth rate, death rate, and the population structure. So, if your death rate is greater than birth rate then the population might become extent or if the population has comprising only of very old individuals then also it may be moving towards an extinction.
(Refer Slide Time: 02:03)
Whereas, in the case of stochastic factors or chance factors, we saw that we have demographic stochasticity factors including the occurrence probabilistic events such as reproduction, litter size, sex determination and death. So, this means that probably that even if you have a very small death rate, you could have a situation in which all the adults died off in certain time period or probably all the breeding individuals at a very small litter size or probably all the off springs that were born happened to be males. So, these are as stochastic factors that would be working in the population sizes or smaller otherwise they would get averaged out and so, we would not be able to see this stochasticity.
The second are environmental variations and fluctuations so, things such as temperatures of a droughts. The third is catastrophes such as forest fires and diseases. Then genetic processes including loss of heterogeneity and inbreeding depression that could also be acting at very small population sizes because all the individuals are now genetically related to each other.
(Refer Slide Time: 03:11)
Or we could have some deterministic processes such as density dependent mortality on exceeding the carrying capacity of the habitat. So, if you have a habitat in which we have very small carrying capacity. So, carrying capacity will tell us the number of individuals that this habitat would be able to sustain. So, for instance, if you have a tiger reserve and this tiger reserve is all full of say, trees and only full of say, wetlands but it does not have any grasses. So, there would be a very less number of herbivores that this tiger reserve would be able to sustain and a less number of herbivores would mean less prey population. We should also tell us that this tiger reserve would be able to sustain a very less number of tigers.
On the other hand, if he tried to increase the carrying capacity of the habitat probably by say, cutting of a few trees and converting some areas into grasslands, maybe also by draining of some amount of the wetlands and converting those also in to grasslands, in those cases the carrying capacity of the habitat would increase. So, it would be able to sustain more number of a herbivores and also more number of carnivores such as the tigers. And the last is migration amongst population, so if there is a very small population and there are a few individuals that migrate out, then whatever remains might not be able to sustain the population in its own place.
(Refer Slide Time: 04:33)
Another definition of population viability analysis is that, it is a process by which the extinction probability of a certain species or population is assessed by integrating data on the life history, demography, genetics of the species with information on the variability of environment, diseases, stochasticity, etc. by utilizing mathematical modules and computer simulations in order to predict whether the population will remain viable or go extinct in a decided time frame under various management options.
Essentially what this is trying to say is, that we know what is the demography of the population, how many males and females are there, what is their age classification? We also know the life history of the population i.e. how long does an individual survive, at what age do the individuals become productive, what is the little size you also know the genetics of the species, what is the level of homogeneity or heterozygosity that is present in that species.
We can also make some guess about the variability in the environment by looking at past data. So, for instance, if we say that every 3rd year we get a draught, so we can make use of this information, we can also look at the diseases that are prevalent there and how frequent do we get an outbreak of diseases, we can look at some other stochasticities.
And when we have all these information we can put these information into a mathematical model or a computer simulation. So, when all of these data are being fit into a computer simulation then we can use the simulation to predict, whether this population will remain viable or go extinct in a decided time frame. So, essentially we could say that we have looking at population viability for say, the next 100 years or say, for the next 1000 years and with all these initial conditions will our population able to survive or not under various management options.
So, various management options could include harvest of some individuals or say, supplementation of some individuals. Harvest means that we are culling off some individuals and then removing them from the population so that our population does not go very close to the carrying capacity. Supplementation is a process in which we are bringing in individuals from some other area into our population so as to bring about a genetic rescue or to increase the population size. So, given all of these conditions we can use a mathematical model or computer simulation to predict what is going to happen, and this prediction will be very important for our management interventions. (Refer Slide Time: 07:12)
The third definition says that population viability analysis may be defined as any methodology that is used to determine a minimum viable population or the size at which the population has a 99 percent probability of persistence for 1000 years. Now, in this case, we are turning our earlier definition upside down; we are saying that we will not start by saying that we have this much size of the population.
But, we are going to back calculate, that if we have a time frame of 1000 years, if we have are the survival probability of 99 percent and given all of our other inputs i.e. the life history, the stochasticity, the rates at which the environment fluctuates and so on, we will use all of this information to back calculate the minimum viable population that needs to be there in an area. So, essentially we could go or with this and both the ways.
So, in our previous definition, so in this definition what we could do is that, we can start with say, 4 individuals and with 4 individuals for the next 1000 years what is the extinction probability? If the extension probability is less than one percent or the survival probabilities more than 99 percent then we would say that that 4 individuals are enough.
But, then if the probability of survival for the next 1000 years is say, 80 percent then in place of 4 individual we will go for 5 individuals, then this 6 individuals and so on so as to determine the minimum viable population that is needed to get to are decided outputs of 99 probability for 1000 years. And we look at it in more details when we going to the computer simulation in a short while.
(Refer Slide Time: 08:58)
Now, population viability analysis also goes by a number of other terms such as extinction risk assessment. So, in this case, we are trying to emphasize that we want to know, what is the probability of the population getting extinct in a decided time frame? So, it is an extinction risk assessment. It is also a population vulnerability analysis. Why that a vulnerability analysis?
Because we can tinker with our stochastic variables to see, whether our population is more vulnerable to extinction because of poaching or our population is more vulnerable to extinction because it is reaching the carrying capacity or say, our population is more vulnerable to extinction because of say, inbreeding depression. So, we can play with all of our parameters to understand which parameter is making our population most vulnerable to extinction. So, this is also another way in which this analysis can be used.
Next is predictive simulation modeling. So in this case we are doing a simulation and modeling to predict the future of the population. And next is the stochastic population modeling because we are using stochastic phenomena to model our population to understand how this population will behave in the next few years.
(Refer Slide Time: 10:18)
And there are 3 ways of doing population viability analysis; the first one is to use empirical observation. The empirical observation means that, we are referring to the field observation. So, field observation of the stability and long term fates of a number of population of various sizes; an example is this study of viability of various population sizes of the bighorn sheep. So, what we are saying here in the case of empirical observations is that, we have a number of case studies from the field and in these case studies we are looking at a number of populations.
(Refer Slide Time: 10:45)
So, the first population is started with 10 individuals. There was some of the population that started with 12 individuals, 14, 16 and so on. See n is equal to 50, n is equal to 100, n is equal to 500. Now, we have all of these case studies that we have been observing out there in the field.
Now, what were the results of these cases? So, in this instance, there was a population of 12 individuals that was say, residing in one mountain top and this mountain top population was separated from all of the other populations. So, we started observing these populations and we saw that after say, 4 generation this population went into an extinction, because of say, inbreeding. Then we also looked at some other populations we look at a population at 40 sizes.
So, we had 40 individuals on top of a mountain and this population was also separated from all the other surrounding population and say, this population in able to survive for say, 20 generations and even after up to 20 generation this population surviving and same with the case of the 50 individual population or 500 individual population. So, we would say, in the case of 38 individual population, this population survive for say, 20 generations and after that this population became extinct.
So, by using all of these empirical observations we would say that 10, 12, 14, 16 anything up to 38 dies off in 20 generations, but anything that is 40 or more it is survives. So, this survives, this survives, this survives, this survives and all of these survive.
So, in this case we would say that are minimum viable population is 40, because if we have 40 individuals then our population will survive for a very long period, more than 20 generation or say more than 100 years more than or 1000 years. So, this is one way in which we are just making use of field information or empirical information to understand the viability of different populations sizes; so, this is the 1st approach. (Refer Slide Time: 13:02)
The 2nd approach is the development of analytical models of the extinction process that permit calculation of the probability of extinction from measurements of a small number of measurable parameters. So, an example is Goodman’s model of the demography of chance extinction.
So, what you doing in this method of population viability analysis is that we are developing an extinction model, an analytical model or a mathematical model of the extinction process. So, we are doing some amounts of computations to develop a model which is a mathematical model and once you have this model. So, this model will be using a number of inputs. So, this is our model and in this model we are providing a number of inputs. (Refer Slide Time: 13:44)
These inputs could be say, population size or the stochasticity or this stochasticity would include environmental variation or say, diseases. Then we could also include things such as the life history of the population which tells us the area at which individuals become reproductive, the litter size and so on or we could also include things such as the amount of inbreeding that is there in the population so, all of these are different inputs.
Now, we put all these inputs in a mathematical model and we understand the population viability for this population size of ‘n’ for ‘n’ number of years or ‘t’ number of years which could be 100 years of 1000 years. So, in this second method we have development of analytical models of the extinction process that permits the calculation of population viability of the extinction possibility.
Refer Slide Time: 15:02)
But these days, because we have quite a good amount of computing power, this is our 3rd method that we use most often. So, this is utilization of computers simulations and modeling to project the probability distribution of possible fates of a population, an example is the software ‘Vortex’. So, what we are doing here is that we are using a computer to do a brute force analysis.
(Refer Slide Time: 15:34)
So, in this case what we are doing is that, suppose we have the probability of drought is say, 1 in every 3 years and the probability of a disease is say, 1 in every 5 years. So, what we are doing here is that we are asking our computer to start with our population size say, 20 individuals and then it will go with the number of simulations so it will go with a number of simulations.
Now, there would be one simulation that would say that in the Ist year we have a draught and a disease, then there is another simulation that says that we begin only with a disease, there is a IIIrd simulation that says we begin only with a draught. Now, in this simulation a draught and a disease here is followed by only a disease here or we could have another year both draught and disease or we could have a third year that has only a draught or we can have a fourth here that does not have any of these; so, it is a blank year.
And then each of these would then again be forked up. So, once we are using such a method, we have a computer simulation and modeling to project the probability distribution of possible fates. So, probability distribution of possible fates would mean that, once we have done all of these simulations we would say that we have say, done 10,000 simulations and out of these 10,000 simulations, we observed that in 300, the population went to an extinction. So, then we would say that the probability of extinction is given by 300 by 10,000 into 100 which is 3 percent.
So, there is a 3 percent possibility of extinction under these circumstances, of every third year being a drought or probability of disease being 1 in 5. So, here we are doing a probability distribution of the possible fates of a population and an example is a software vortex, that we will look into any short while. But before we do that, what does this model require?
Refer Slide Time: 17:32)
So, population viability analysis through this method has two defining prerequisite characteristics, one is an explicit model of the extinction process. So, basically earlier when we saw that we used a mathematical model or an analytical model such an explicit model of extinction process is also required for the computer simulation to begin with. And also it requires a quantification of the threats to extinction, i.e. we require a quantification of all of these probabilities.
So, the probability of draught, probability of a diseases or say probability of a flood or probability of extinct of temperatures all of these we will also need to be quantified. So, quantified means that we cannot just say that we will have a draught some time we will have to put a figure regarding how many years will we get a draught.
(Refer Slide Time: 18:28)
So, now we will go into a demonstration of the vortex software. So, let us now, have a look at a demonstration of the vortex software and here we are using the eddy software which is an educational lite version of the same software.
(Refer Slide Time: 18:35)
Refer Slide Time: 18:45)
So, we open our project. Now, we have name this as a project tiger, and here we are required to give all different sorts of input that we just discussed. So essentially, we are putting number of iterations. So, basically how many number of cases do we want to see; do we want to see a 100 cases, do we want to see 100 cases or 10,000 cases or so on. And then how many years do we require the simulation to run. So, do we want to see the extinction probability in the next 100 years or say, the next 1000 years and so on? In this case, we are only dealing with one population, so we are not dealing with any migration immigration and emigration.
(Refer Slide Time: 19:25)
Then, we could also include things like inbreeding depression and the lethal equivalents, but for simplicity we will ignored this for the time being.
(Refer Slide Time: 19:37)
Now, in the case of reproductive system, we are saying that a tiger is a polygynous individual. So, essentially one male tiger can made with any number of females. Then we are putting in all the life history. So, for the females the age of first off spring is the age of sexual maturity that is 3 years, for the males the sexual maturity is 4 years, the maximum lifespan.
Now, in the zoo conditions we have seen tigers growing living for as many as 26 years, but in the forest areas in the national scenarios we will put it as 20 years. Now, maximum number of broods per year is 1, maximum number of progeny per brood is how many individuals are born in a later let us call it 3; sex ratio of birth let us see that 50 percent of the individuals that are born a brood or males; maximum is a female reproduction and male reproduction we keep it at 14.
Refer Slide Time: 20:34)
Next we go to the reproductive rates; now, this is asking us, percentage of adult females that are breeding. So, if we have 10 adult females, do all of them breed at the same time? Now, it is observed that in the case of tigers, if there is female that has given one litter, the cub remains with the mother for around 3 years. So, in that case let us put this as 40 percent and then distribution of broods per year. So, we will say that let 0 broods 0, 1 broods is 100 so, these are things that we can play with.
(Refer Slide Time: 21:07)
Next we are putting it in the mortality rates. So, in the case of females and in the case of males as well, so we are saying that mortality from age 0 to 1 is 50 percent. So, here we are talking about the infant mortality rate. Let us put it 50 percent and then if there is a tigress of age 1, then in the next one year there is only 10 percent mortality and so on, so we can put all of these figures.
(Refer Slide Time: 21:34)
Next we are putting in catastrophes and we are saying here that we are going to have 2 number of catastrophes; 2 types of catastrophes and then we can also put in their frequencies.
Refer Slide Time: 21:43)
The next talks about the population size so, let us begin with a population size of 30 and here we are having a female distribution and the male distribution, when we are having 30 individuals. So, we can either use a stable age distribution in which the software computes it automatically or we can calculate any of these values by ourselves. So, we can say, in place of two individuals here we have 3 individuals and in case of say, at age 7 we do not have any individual so, we can play with all these parameters.
(Refer Slide Time: 22:18)
Next we have the carrying capacity so this has more to deal with our density dependent mortality. So, let us say that the carrying capacity of the environment is 100 individuals; so, it can support 100 tigers.
(Refer Slide Time: 22:32)
Harvest is talking about the number of tigers that has been removed say, by poaching or by culling. So, poaching could be say, illegal poaching and which is hunters are getting insides and killing tigers for their skin or say, for their bones or we could even go for culling of tigers. So, if there is a huge amount of inbreeding depression then we could go for a departmental culling. Now, departmental culling is not done in India, so we will we will ignore this.
Refer Slide Time: 22:57)
And supplementation is talking about how many individuals you are bringing in, from some other population to supplement this population. So, we will ignore this for the time being. So, let us see that if you have 30 individual population how does the simulation look like? So, let us run the simulation.
(Refer Slide Time: 23:15)
So, what we saw is that, up till the age of up till this 100 years and we have run 100 number of simulations. Now, in these 100 number of simulation we are seeing that the probability of extinction is 0 percent because there was no scenario in which any of these populations came to a decline. But in the case of this particular simulation, we see that the population size decreased from 20 to say, close to around 6. But then it was able to recover after this, but then it is also possible that it could have gone down. Next let us begin with an initial population size of say 4.
(Refer Slide Time: 24:04)
So, we have or let us take the extreme case, we are starting only with 2 individuals. (Refer Slide Time: 24:09)
Now, in these 2 individuals we are having the female of age 5 and we are having a male of age 5. So, now, let us run the simulation again, with only two individuals. Now, what
we are observing here is that, there is an 82 percent probability of extinction, because of all the 100 simulations that we run 82 were touching this line of 0. So, one it has raised to a population size of 0, so the population become extinct. Let us now, increase the population size so, in place of having 2 individuals, let us begin with 4 individuals. (Refer Slide Time: 24:20)
Now, with 4 individuals; now, we are automatically saying that we have an individual of age 2 and age 8 both for males and females, but then we can also change this. (Refer Slide Time: 24:50)
So, let us say that in place of having age 2 individual, let us have a female of age 4 and a female of age 8. Now, let us run the simulation again.
(Refer Slide Time: 25:12)
Now, from an 82 percent probability of extinction now the probability of extinction has come down to 55 percent. So, it tells us that only 55, out of these 100 simulations touch 0 rest were able to reach the carrying capacity or somewhere in between. Now, let us increase our population size, let us begin with 6 individuals.
(Refer Slide Time: 25:42)
Now, when we begin with 6 individuals, here again we are seeing extinctions.
Refer Slide Time: 25:46)
So now, the probability of extinction has come down to 36 percent. Now, we can just go on playing with these figures. So, let us begin with our population size of 8. (Refer Slide Time: 26:04)
Now, more and more population or more and more simulation are able to avoid extinction.
So, from 36 percent it has come down to 27 percent.
Refer Slide Time: 26:06)
So, what we are trying to do here is that, we are trying to understand the minimum viable population size.
(Refer Slide Time: 26:19)
Refer Slide Time: 26:22)
Here also we are seeing extinction so, we will see that this is also not a viable population, but then the extinction probability is now only 19 percent.
(Refer Slide Time: 26:40)
Now, with 12 individuals as our starting we have an extinction probability of 17 percent, let us increase it even further, we have brought it down to 12 percent.
Refer Slide Time: 26:49)
(Refer Slide Time: 27:01)
Let us, talk about a cut off, let us say that if it is less than 5 percent then we will say that our population will be say, minimum viable population.
Refer Slide Time: 27:08)
Because, even if you have a very low probability of extinction even if it is 1 percent, it is possible that our population will go extinct after sometime so here we are very close to our cut off of 5 percent, so we are at 6 percent.
(Refer Slide Time: 27:35)
Let us put at 18 individuals, run it again. Here we have reached 5 percent.
Refer Slide Time: 27:38)
So, in this case, once we have decided on our cutoff, so we said that if our probability of extinction is less than 5 percent less than or equal to 5 percent then we will say that this will be a minimum viable population. So, by this way, we have come to the conclusion that 18 individuals is something that will provide us the minimum viable population. And then we can also include thinks like harvest. So, in the case of harvest we can say how many individuals are getting poached out? So, let us say that let us use our default values and run the simulation again.
(Refer Slide Time: 28:23)
So, we are harvesting some individuals, but not to a very large extent and our probability of extinction has gone up, it has gone to 9 percent. So, we would say that our population cease to be a minimum viable population.
(Refer Slide Time: 28:45)
Or let us say that we increase it further, 1 and number of females of each age is to be harvested; let us say 1 here and number of males here is let us say 2. So, now, we are intensifying the level of poaching that is there in the population. So, it is still 9 percent. (Refer Slide Time: 29:01)
So, basically we can play with such parameters and once we go on running these simulation we will get an idea of how all of these things, whether our poaching or also supplementation are going to help us or are going to lead this population to extinction. So, this is the demonstration of the vertex software.
(Refer Slide Time: 29:21)
(Refer Slide Time: 29:39)
Now, apart from just using softwares and simulations for understanding of just the population viability, these days population viability analysis is also being used for other things besides extinction, such as the measure of the health of the population, such as the mean and variance in the population growth, changes in the range distribution, inhabited occupancy, and losses of genetic variability. So, when we look in our simulation we saw that our last column was the amount of genetic heterozygocity that was present in the population. So, things such as these can also be understood by using methods that are very similar to our population viability analysis.
(Refer Slide Time: 30:18)
Now, the utility of such an exercise is that, it is an important management tool for conservation, because we can compute a number of parameters and we can answer a number of questions. Such as calculation of the probability of persistence of a population under current conditions. So, for instance, if you have a tiger reserve and if you want to say that only this small size tiger reserve is not going to be sufficient for the population because the carrying capacity is less. So, you can use these simulations to come out with a minimum area that would be required for your tiger reserve.
Similarly, calculation of the probability of persistence of a population under altered management intervention conditions. So, altered management intervention conditions would include say, increase of the size of the tiger reserve. So, you can also include in an increased carrying capacity and then redo the calculation to see if it increases the probability of persistence of the population.
Also, calculation of the most likely average population conditions including population size, range of population sizes across years and of loss of genetic variation. So, when we are doing the simulations, we can ask the computer that at every iteration it should give us the population size, the range of population sizes, and also the rate of loss of genetic variation. We can even look at things such as the numbers of males and the number of females, that would be there under different conditions.
(Refer Slide Time: 31:46)
So, that for example, if there is a poaching and poaching is mostly done for males because they are offer larger size and also because they come out of the reserve area when they are dispersing. So, in those situations males are preferentially removed from the system. So, we can use such an analysis to ask this question that how would the sex ratio change with time.
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