nm0191: try and run the course is by i'll give you at the there'll be a handout 
each week which will more or less summarize the information content that i'm 
trying to get across and most weeks there will be exercises er in the sense of 
data handling and er er written exercises for you er to try and consolidate the 
material in er this spoken session what i say in the spoken session should 
correspond almost exactly although we will take longer with what is written in 
the handout and but no sorry but nonetheless since there is only one of you 
whose native language is English if i am going too fast please ask me to slow 
down if i say something that you don't understand give yourself ten seconds to 
understand it and then ask me because it is much better if i can keep you with 
me i would some of the material the logic is quite complicated and if i lose 
you on the second step and i carry on to the end we've wasted a lot of time and 
you will feel depressed whereas [laughter] 
if i sort it out as we go alone so don't hesitate to interrupt me er the more 
we can do it as er a question and answer session the better if you read through 
the handouts before you come again i hope that will be helpful er i ought to 
say something about the general pattern of the course because it's been taken 
out of the handbook so er i'll do that on the board hope we can rub out 
kilodalton yes good oh and they've got pens here too right great okay er should 
have given you a handout for this sorry roughly speaking i'm going to talk 
about the population dynamics weeks one and two i'm going to talk about yield 
er disease and pathogen relations in week three i'm going to talk about the 
genetic basis or the the use of genetic resistance in both as to both how it 
works how it can be used in populations how pathogens respond what happens in 
the wild so that's four five six i'm going to talk er about that may even be 
four 
five six seven no i think it's four five six er sorry it's late in the term er 
i'm then going to move on to er chemistry which i shall be spending a couple of 
sessions on oh it is seven as well genetic resistance and that moves in by a 
curious piece of logic to talking about space chemistry eight nine and then a 
sort of consolidation session in week ten the assessment for the course is er 
usually an exam er which i think you two will take are the rest of you here in 
the Summer term 
sm0192: no 
sm0193: 
nm0191: er okay well if you're here in the Summer term er there will be an exam 
and an in course assessment which takes place over these three weeks in which i 
ask you to manage an imaginary crop i'll explain more about how that works but 
basically you have to research what you would actually do in terms of planting 
a variety of wheat er when and what chemicals you would apply and why and i 
keep feeding you information about what's happening to the season and you keep 
telling me what's going 
on as if we were running a whole year over a couple of weeks so that will 
happen at the end of term for those of you not taking the exam there will 
probably also be an essay to do over the following vacation which you can send 
back okay 
sm0194: er so this er module is going to be carried out er through the Summer 
term 
nm0191: no 
sm0194: 
nm0191: but the exam is timetabled in the first week of the Summer term er so 
if you are here in the Summer term 
sm0194: yes 
nm0191: it will be easiest and most consistent for me if you take the exam but 
for those who are actually not going to be here i can't insist you come back to 
do that obviously so i will set an essay type assessment instead okay am i 
talking clearly enough for you to understand so far 
sm0193: [cough] [cough] does not has to be hand in at week ten or 
nm0191: er no i well i can arrange that if you prefer but i would i feel that 
the cour-, you will gain more from the course if you reflect on it a bit 
afterwards so i would prefer to set you an essay with a deadline three four 
weeks after the end of the course you wi-, mi-, may wish to complete it after 
you go back to Germany and then send it by post it depends if you need to take 
do you need to take marks with you when you go or can we send the marks on 
afterwards 
sm0193: i think you can send the marks afterwards 
nm0191: yes 
sm0193: because even if i hand it in at week ten 
nm0191: yeah i'm not going to mark it immediately yeah well probably not 
sm0193: 
nm0191: yes [laughter] okay so that's the course structure er it's not a 
practical course er in the sense of hands on er but i hope it will engage with 
reality you may need to be a little bit patient about that engagement with 
reality because i am going to try and build up the subject systematically so 
i'm going to er develop things from a fairly basic point of view i'm not 
immediately going to say in fact i'm almost never going to say if you're 
growing this crop you spray this thing at such and such a time and you plant 
this variety i'm always going to be talking about underlying principles or 
almost always okay can i wipe this off now thank you so some of you have 
already picked 
up that the course is entitled Management of Disease and that is a deliberate 
form of words i think that the best management of plant disease arises if you 
think of it as a management problem and not a control problem control implies 
right that isn't going to lead you to the most economic environmentally 
friendly and effective solutions the most effective solutions are ones which 
work with what's going on based on an understanding of what's going on and only 
limit disease to the extent that is necessary and in order to do this the two 
things that you need to know are how do you find out at any given moment in 
growing a crop what is the best decision and the second thing is what decisions 
could i possibly make okay you need to know the spectrum of things you might do 
and then you need to know how to choose among them and i'm going to begin with 
an example which will probably take me about twenty minutes or so to set out 
and then we'll have a short break for 
you to get your brains back er and ask any questions and maybe stretch your 
legs and so on and then i'm going to talk you through some theory of er which 
will explain and provide a foundation for what i've said and for the general 
population dynamics of disease and that will take us to all about half past 
twelve okay so what i want to do as an e-, with an example is look at why it is 
that wheat growers in Australia do not use fungicides on their wheat but wheat 
growers in England or the U-K or indeed Germany apply two or three fungicides 
to their crops so i'll try and develop this as a contrast U-K Germany i'm 
getting obsessed Australia i say U-K that will apply to most of northern Europe 
welcome 
sf0195: sorry so sorry 
nm0191: abo-, 
sf0195: about late er 
nm0191: that's okay you are can i just 
pass you this so that we have a record of everyone who's here you are 
sf0195: namex 
nm0191: namex from 
sf0195: i'm a from er doing M-S-C horticulture 
nm0191: M-S-C horticulture okay thank you okay the first difference and perhaps 
this is probably the key one is that in the U-K we are growing our wheat with 
cool summer conditions the average temperature in June is fourteen degrees the 
average in July is eighteen whereas in Australia you're growing under a hot 
summer conditions temperatures up to thirty even more because the s-, summers 
are hot the wheat ripens rapidly because the development of the crop depends on 
the temperature okay it develops very slowly at low temperatures very fast at 
high temperatures development in the sense of going from stage to stage in the 
ripening process and the days are relatively short they're quite close to the 
Equator we're talking twelve or thirteen hour days whereas in the middle of the 
summer we're talking long days and it's no accident that the world 
record wheat yield actually comes from Scotland the further north you go with a 
sufficiently mild climate the better the summer yields you'll get because with 
a cool summer the crop develops slowly because it develops slowly and the long 
days there is a lot of time for so-, photosynthesis so these two together mean 
a low potential yield the crop has to make all the sugars it can to fill the 
grain with an if if you find it i'm going to use this board it may be helpful 
to sit further forward if you're having having trouble seeing 
sm0196: oh i can see but the 
nm0191: but is the light bad shall i adjust the lighting er 
sm0197: i think it's the reflects the 
sm0198: yes that's it's some kind of reflection 
nm0191: yes that's er hang on 
sf0199: the pen is red so can't see that 
nm0191: okay the red doesn't show so i'll change that then er oh no i want that 
don't i sliders which is reflecting is that better worse 
sf0199: same 
nm0191: same it's just that it's red 
sm0200: 
sm0201: yep change pens 
nm0191: okay change pens i like playing with the lights that's better 
[laughter] okay change pens aye [sigh] let's try b-, green so this just says 
cool summer and this says long days and they are anyway remember that this is 
all written down already in the handout but the consequence of that is that you 
have a high potential yield not only that but generally speaking water is not 
an important limiting factor it rains it rains all the year round whereas in 
Australia with hot summers short days and therefore low potential yields 
there's also generally speaking a shortage of water Australia is the sort of 
place where wheat evolved it's quite good at surviving on relatively low 
amounts of 
water but it doesn't encourage it to make high yields and because the water is 
limited that means that fertilization and nutrient supply is not a limiting 
factor therefore there is no point in adding fertilizer whereas water is not 
limiting in the U-K so the crop is responsive to nitrogen nitrogen generally is 
a limiting factor and so it pays farmers to add nitrogen and f-, frequently 
that would be in the region of one-hundred-and-fifty to two-hundred-and-fifty 
kilos per hectare really quite a lot unresponsive to N so this yie-, gives us 
average yields i'm just abbreviating average to A-V-G-E average yields in the 
region of seven to eight tons per hectare whereas the with a good yield being 
ten tons or more per hectare whereas in Australia you're talking one to two 
tons per hectare with three tons being good 
sm0193: i've got a question 
nm0191: have it 
sm0193: er the plant density in Australia 
nm0191: it's much lower 
sm0193: and how much er are they sowing per hectare how much kilogram 
nm0191: er i couldn't give you an actual figure for the seed rate but if we're 
sowing two-hundred-and-fifty here i would guess they were sowing actually no i 
would guess they were sowing a more or less similar seed rate but the tillering 
will be much less effective here you would expect each seed to produce two to 
three tillers so you would aim for a final plant density of eight to nine-
hundred stems per square metre whereas in Australia you'll be you may well be 
sowing the same number of plants or more or less the same number of plants but 
you might well get only one one-and-a-half stems per plant so you might have a 
density perhaps four-hundred stems per square metre in a good crop and it could 
be lower depending on when it runs out of water the essential point is that the 
limiting factors are different in Australia starting right from the top a whole 
sequence of things mean that the potential yields are much lower that's what i 
need for now now consider the question 
a farmer faces when asking shall i apply a fungicide which may cost me thirty 
pounds per hectare er i'm afraid i haven't revised the wheat cost on your 
handout but it doesn't actually alter the answers i've said that the wheat was 
costing a hundred pounds a ton i think the current figure is probably nearer 
eighty pounds if you're lucky so with wheat at at eighty pounds per ton that 
fungicide cost er fungicide costs about four-hundred kilos nought-point-four of 
a ton per hectare okay what i'm doing is translating the price of the fungicide 
into an equivalent weight of wheat okay you can still see it yes yeah 
sm0202: 
nm0191: okay now that is around let's say roughly a five per cent of the crop 
value so if applying a fungicide will increase the yield by five per cent it's 
worth doing so a relatively minor disease problem which reduces yield by five 
per cent will still be worth spraying against and in the days 
before fungicides were added before fungicides were used we have survey data 
showing that an average wheat crop was losing about three to ten per cent of 
its yield due to disease the figure could be much higher occasionally and it 
could be lower but on average it was a figure larger than five per cent 
therefore it is profitable to apply fungicides and of course once you've 
applied a fungicide your yield increases slightly so it is favourable to apply 
more nitrogen you make good use of your high water retention soils and it goes 
around in Australia by contrast fungicide costs er if we're talking let's take 
this er two t-, ah well let's take i took the high figure there i'll take the 
high figure here er you e-, we're getting a yield of two-hundred-and-forty 
pounds a hectare sorry costs fifteen to twenty per cent of the crop value okay 
so 
sf0203: er is the price of wheat in Australia the same 
nm0191: yes 
sf0203: 
nm0191: this is more or less the world price 
sf0203: it is 
nm0191: 
it is now yes the calculation would have been different and even more dramatic 
when er at current present day prices wheat in the U-K was a hundred-and-sixty 
pounds a ton and wheat in Australia was a hundred pounds a ton but the E-U 
price the E-U support is much reduced the price of the wheat is more or less 
the world price so here the fungicide on average you'd have to get about twenty 
per cent extra yield and on average you don't so the routine management of 
crops in Australia does not include the use of fungicide er whereas in the U-K 
it's logical from this analysis that fungicide will usually be used and indeed 
it is er by now something like ninety-five to ninety-eight per cent of all 
wheat crops in the U-K except organic ones are have a fungicide applied and 
about two-thirds of those cases the fungicide will be profitable er there's a 
little footnote here for those who are actually interested in wheat management 
that's the general 
principle okay so this is little footnote the little footnote is that the 
Strobilurin group of fungicides so i'll come back to this in lecture eight 
Strobil urin which are a novel group of fungicides introduced in the last three 
or four years er give a substantial yield increase of the order of ten per cent 
in the absence of any detectable disease problem and therefore [cough] it is 
almost always profitable to apply one of those so the actual er profitability 
of fungicide treatment has increased recently as has the profitability of the 
manufacturers of Strobilurin fungicides the A-S-F and Zeneca so people have 
shares in okay 
sf0203: does that mean the Australians have started using this Strobilurin 
nm0191: well 
sf0203: so does that one give them 
nm0191: no it wouldn't because their crop is water-limited effectively what the 
Strobilurin is doing is enabling you to use nitrogen better because it's 
keeping the crop green for longer a crop which is green for longer in Australia 
may actually yield less because it'll be pumping water out into the atmosphere 
and it 
will get shrivelled and die it won't get the won't be able to translocate any 
photosynthesis it does do into the grain er and again er one can come back to 
that there are actually cases in Mediterranean climates where a small amount of 
disease is causes a yield increase because it improves the overall efficiency 
of water use by destroying leaf tissue okay so it it gets very complicated but 
once you're into water-limited situations there's no point in retaining a green 
crop for a long time 
okay so this is the first half here i'm showing you that Australians won't 
apply fungicides for very good reasons there's a positive feedback you've got a 
high-yielding crop which therefore justifies expensive management which makes 
it even more high-yielding which means that it's justified to put in even more 
inputs we've got a potentially yo-, low-yielding crop which is low-yielding so 
it isn't justified to do anything difficult so it stays low-yielding so there's 
a a a positive feedback in there but this analysis doesn't apply if we're 
talking about genetically based resistance to disease if we're talking about 
the choice the management decision to plant a variety which has good disease 
resistance as against a variety which has worse disease resistance but is 
higher yielding in the absence of disease so i'm going to wipe this off now 
okay and i'm going to make the point that the yield if you're breeding a crop 
it's difficult to breed for 
several things at once that means that if you've got a resistant crop and a 
susceptible crop you will often find that you have the situation where without 
or let's put disease without disease in the absence of the disease the 
susceptible crop is the best it outyields the resistant crop whereas the 
situation is reversed for the case where you do have where you have disease the 
cost of changing a cultivar isn't usually very expensive there's small 
differences in seed prices but seed prices are er a percentage of the 
production costs the example i've written down is that if seed costs if seed 
was as much as twenty per cent of the input or production costs if it was as 
much as that then a ten per cent difference in seed cost would be only two per 
cent of your input costs so the cost of changing variety is not normally very 
large and therefore the continental system which we've already seen is 
not able to use fungicide sensibly will therefore use a resistant variety when 
it's available even if there is a small premium on the seed price whereas the 
farmer in the high input system who's applying fungicide anyway and who only 
requires a small yield response from the application of fungicide will be 
tempted to say the fungicide's dealing with the disease i will continue to grow 
my susceptible variety and the example i would give of that is the wheat 
variety Riband in this country which is still grown i think on seventy per cent 
of the Scottish acreage and a substantial fraction of the English acreage sorry 
acreage means the same as area [laugh] the acre is an old unit of agricultural 
area so and i will slip into saying it i'm sorry so seventy per cent of the agr-
, of the Scottish area is sown to Riband which is appallingly susceptible to 
the commonest wheat disease in this country which is septoria tritici similarly 
er well no i'll i'll but i can 
multiply examples but i i won't i won't bother er now the only caveat i want to 
add to that so i want to qualify this statement somewhat by saying that 
obviously if there is no great disadvantage to the resistance then a farmer 
will adopt the resistant crop as well if you can have the resistance without 
much yield penalty then obviously you'll take it and the phrases resistant and 
susceptible are always relative all of our crop protection all of our disease 
management is based on er crops which have very good resistance to almost all 
diseases chemistry chemicals can help you a bit but the closer you get to a non-
resistant to a completely susceptible variety or cultivar the less effective 
the chemicals and other protection measures can be and if there is one message 
that i want to gev-, gi-, get across in this course it is that everything helps 
everything else if you start from a resistant crop everything else is easy if 
you start with a disease-susceptible 
crop everything else is difficult there is no such thing as a solution a 
protection measure management of disease always comes in a package and comes 
with feedback loops like those i've described one thing leads to another thing 
which leads to another thing which causes you to make particular decisions if 
you're interested in arable crops and wheat then that example and analysis is 
fine but you might like to consider in particular if you're a horticulturalist 
[laugh] you might like to try and run through a similar analysis for apples 
where the information is fairly easily available or some other er culinary crop 
and there are quite interesting differences if we're talking about a bulk 
arable crop or if we're talking about something that is consumed as a vegetable 
as a culinary crop where quality considerations become more important but i 
will come back to that in lecture three so i've given you an example i don't 
want you to learn the example i 
want you to pull out the general ideas by reflecting on the example 
sf0203: can i just ask a question 
nm0191: do yeah 
sf0203: you haven't mentioned it's like you mentioned Riband but that's 
nm0191: but i didn't say it was because it could be sold for biscuit in Spain 
[laughter] 
sf0203: well yeah and because the millers like Riband as well 
nm0191: yes 
sf0203: it is though there's also an 
nm0191: well our millers don't like Riband but 
sf0203: mm but but it's grown because they 
nm0191: it you can se-, you can sell it for export markets 
sf0203: m-, 
nm0191: no i haven't and that's the extra factor which comes in if you start to 
analyse apples you can no longer leave that out wheat is simpler to consider 
it's easier to see the underlying principles because it is a bulk crop and 
although increasingly it's that that that is breaking down but you can say you 
just want to buy some Canadian hard red wheat and nobody worries what the 
variety is actually called and it makes it easier to see what's going on yeah 
so what were the what are the overall er what's been going on there what is a 
farmer doing we've got we've had a number of things that i've supplied you with 
a-, 
answers to so one question is how much disease is likely okay i put that in by 
saying that losses were around five per cent and there's a subsidiary question 
of is there a serious risk of a lot of disease in other words is there a 
serious risk of losing the crop which you may want to in which case people may 
take measures which on average costs them money it's known as an insurance 
premium okay insurance companies make a profit therefore on average it must 
cost more to insure something than to just pay for the loss when it c-, occurs 
the problem is that if it's your car or your house we don't have the capital to 
buy a new one so we opt for the option which is more expensive on average which 
is to pay a small amount to an insurance company they take a slice and then 
they pool the slices and people whose houses burn down get a large sum of money 
so i talked in the wheat because it's an 
example where crop destruction is relatively unlikely but this kind of serious 
risk could modify decisions there so we need to know about both and we need to 
know what will the disease do to yield the reason i put yield in quotation 
marks is because some diseases will mean that you don't get much off the land 
other diseases will mean that you get the same amount as you would have had but 
you can't sell it there are lots of examples in horticulture of diseases which 
are completely the plant doesn't care about in the slightest but the customer 
won't buy it that's equivalent to a complete yield loss so when i say yield i 
suppose i'm meaning something like marketable yield and then you've got what 
management actions will alter disease amounts 
how much do they cost and how reliable are they now this is where this course i 
hope where the emphasis of this course differs most from what you may have had 
in introductory pathology course where people tend to say oh well you can 
control this disease by and then there's a sort of list of things rotation 
chemistry whatever some of those will be completely ineffective for certain 
diseases or in certain settings so the question is always what things can you 
do which will alter disease if you take great care to plant a clean crop but 
the disease comes from elsewhere then you won't alter the amount of disease 
there's no point in spending huge amounts of money on crop hygiene on not 
planting infected seed if the disease is going to come from somewhere else 
anyway and once you know something that will work you need to know how much it 
will cost and you also need to know will it always work will it sometimes fail 
and 
the answers to those questions are put in the context of managing a a growing 
business a a farming business or a horticultural business which has two 
objectives first is to stay in business which is mainly about minimizing the 
risks of things going wrong and then provided you can stay in business most 
organizations attempt to maximize their profit consistent with certain social 
societal pressures so that all gets a bit big what does a disease specialist 
need to do a disease specialist needs to know the answers to these questions in 
the context of their client er it mean they need to know what management 
options are possible what they will do how they will interact how they will 
interact in the system that they're looking at and you've seen the example of 
wheat identical crop different places completely different decisions are 
appropriate and the rest of the course is really concerned with setting up a 
situation in which we understand the answers to these questions 
i'd like to give you a short break now er i am going to start talking at twelve 
gives you time to go to the loo and okay i'm going to start talking at twelve 
and i'll run for about another half hour okay i suggest 
nm0191: okay so now i'm going to try and answer the questions which i set out 
earlier and the first one i'm going to tackle er which is going to take me 
basically er this lecture the rest of this lecture and the next one is what 
determines how much disease there is in a crop okay and in particular how does 
it change and increase in time what i'm not going to do yet is to talk about 
how we actually measure disease i'm just going to assume for now that we can 
measure disease that we can get a number which corresponds to some notion of 
how much disease there is in the crop and that that measurement of how much 
disease there is in the crop is in some way related to how much pathogen there 
is in the crop and how fast it and and its capacity 
to multiply so i'm going to begin by showing you some examples of how er 
disease builds up in time so i'm going to show you er actually a slightly more 
limited number than is on the back er of disease increase curves if you turn to 
the extreme back of the handout okay the first one i'm going to show you er i'm 
sorry i had s-, we have some problems er which meant that i didn't have as long 
to look for the overhead which turned out not to be in the place where i 
thought it was this morning as i should have had so i haven't got the first 
overhead the basic point here i'm talking about a disease called Dutch elm 
disease elms are large forest trees which used to be one of the commonest trees 
in the U-K and across northern Europe in the nineteen-seventies an epidemic of 
a disease called Dutch elm disease caused by a fungus ophiostoma novae- ulmi 
fungus disease and this increased on two different varieties of elm two 
different species of elm 
roughly like that small-leaved elm carpinifolia and what's known as the English 
elm ulmus procera okay an increasing curve now i do have some overheads here's 
a curve of can you see this this thing is always a 
sm0204: closer 
nm0191: a great nuisance and for the less pompous among us er this is 
sf0205: can you just lift it a bit higher 
nm0191: yes i can 
sm0206: 
nm0191: it's all right it's got something on the bottom which i'll explain i'll 
explain this bit later okay so it's an S- shaped curve very little disease very 
little disease very little disease very little disease and then a very sharp 
and sudden increase this is a rust disease yellow rust of barley er so i take 
it you're all familiar with rust diseases with what a rust is puccinia yep yep 
sf0207: yep 
nm0191: yep good okay er so it increases like that then a very different one er 
so this is a disease of cocoa in West Africa i should have drawn your attention 
to the time scale on this one which is running over forty days from day one-
sixty of the year so 
that's mid-June to the end of July whereas this is running from nineteen-forty-
four to nineteen-fifty-two so that's an eight year run of data and you'll see 
that there's a general S- shaped curve with most rapid increase in the mid-
nineteen-forties here's one from even earlier this is cotton i should have said 
that P- omnivorum on cotton between nineteen-thirty-seven and nineteen-forty-
one 
so this is repeated crops of cotton planted each year but planted in the same 
general area whereas the cocoa swollen shoot is a tree crop those trees were 
all there at the beginning and they're all there at the end and you see again 
this low level to begin with and then a period of very rapid increase and the 
final example is P-I- two where's P-I-one where indeed is P-I had it this 
morning sorry this is classic which i should not be doing at this stage the 
final example then appears on your handout over the page at the bottom and is 
potato blight phytophthora infestans on potato showing an increasing curve over 
a time scale of around fifty days reaching about fifty per cent or nought-point-
five severity oh here it is sorry put it out ready and then took the board away 
there you go so that is a hundred per cent severity that is 
fifty per cent severity that's none okay so we have an increasing curve going 
up fastest at the end now what i want to do is ask is that what we expect and 
not only is that what we expect but how can we describe these different curves 
so the arg-, the the method of of reasoning i'm going to use is one that you 
may not have come across too much in biology it's to start from some 
assumptions use those assumptions to argue for what we would expect to happen 
in a crop and then compare our expectation with reality in order to find out 
how things are different and as it happens this reasoning process will also 
allow us to describe all of these different situations disease which increases 
over ten years disease which increases over twenty days by one number okay so 
imagine a pathogen individual in an otherwise healthy crop so er i think i'll 
do this on the board so i'm 
going to draw a little imaginary crop on the board in green here are my plants 
okay and one of them becomes diseased for some reason now this disease this 
pathogen must have some way of propagating itself either spores or vectors if 
it's a virus and let's suppose so i'm talking an imaginary situation at the 
moment imagine that a week later its spores have infected two other individuals 
so in the week one in week one we had one individual in week two we've got 
three and i'll just put in the new ones which is two one new one in week one 
two new ones in week two now all of these if nothing changes okay i'm 
specifically trying to argue if nothing changes in week three these two will 
each infect two more plants on average because if this one infected two plants 
over a period of week and nothing else changes there's no reason why these 
won't infect two more plants in another week so in 
week three we're going to have er if we assume it's probably simplest to make 
them die after the first week though the sums come out the same we'll have four 
new diseased individuals okay so what will happen in week four each of the new 
diseased ones becomes infectious is producing spores so what number should i 
write here 
sm0208: can you repeat that please 
sf0209: yes 
nm0191: okay in week four each of the four new infections that occurred in week 
three will become infectious will start producing spores 
sf0209: will contaminate another two 
nm0191: so they will each contaminate another two so what number goes here 
sm0194: two-, twelve 
sf0209: eight 
nm0191: eight 
ss: 
nm0191: exactly yeah 
sm0194: 
sf0209: 
nm0191: population sorry 
sf0210: 
sm0194: the infection 
nm0191: and then it says new er okay so what we have here is an exponential 
progression so what we'd expect is that if nothing else changed disease would 
grow exponentially it would go 
on whatever time scale was appropriate it would go something like one it would 
go one ah that's two that's where i've gone wrong [laughter] knew there was 
something funny about this two four eight sixteen okay an exponential increase 
sf0209: quite the imaginary though isn't it
nm0191: i-, 
sf0209: even the if you don't use like er er if you don't like use fungicide i 
mean then 
nm0191: even if you use fungicide 
sf0209: 
nm0191: the effect will be that instead of each diseased individual succeeding 
in infecting two more each diseased individual may only infect 
sf0209: one more
nm0191: half or one that does not alter the argument that it should be an 
exponential but bear with me because i have pointed out that i'm trying to 
argue what we would expect to happen if we didn't change anything 
sf0209: 
nm0191: and it's worth arguing that through because otherwise when you look at 
a i maybe i should have done it like this if i put this up the farmer's field 
in 
mid-June was free of disease two weeks later it was nearly free of disease 
three weeks later it was completely devastated the natural question to ask is 
what happened here and if you go out into the field and start looking for funny 
weather conditions in that you're going to find them if you look for an eclipse 
of the moon you may find it if you look for er somebody who wal-, a black cat 
walked in front of me you'll find it you will be able to find something strange 
about that period but the question is did anything funny happen there and 
that's why i'm trying to work out not because the argument that something funny 
happens there is actually based on an implicit assumption if somebody thinks 
something funny happened here they're saying well what i would have expected is 
that i am saying well let's just think about that what would we expect and so 
far i've established that we would expect exponential growth initially 
yeah 
sm0194: sorry er so we have to determine which factors er er has er an effect 
er to the rapid development of the disease that case 
nm0191: well but what i'm arguing is that no let let me finish constructing the 
sm0194: 
nm0191: no no no it's all right sorry you're getting the point but the point 
that's what you would you would tend to say okay what factors cause the rapid 
increase i'm saying i don't yet know whether there is a rapid increase i don't 
yet know whether anything changed because i don't know what to expect from a 
disease what would i expect disease progression in a field where nothing 
changed to be like okay we are very used to the idea that if nothing happens 
things stay as they are but when you learned physics in school and we're also 
used to the idea that if you drop something it'll fall but when you learned 
physics in school you did a lot of thought experiments in which the teacher 
said contrary to all everything you knew that if no 
force acted on an object it would stay where it was yeah and they said so if 
you were out in space and not on Earth and you let go of the pencil it would 
just stay where it is it doesn't stay whether it is therefore okay so there's a 
whole lot of thought experiments going on in the background if you were out in 
space and let the pencil go what would happen to it the answer is nothing 
therefore there must be something acting to make it fall i want to do the same 
kind of thing i want to construct a rational expectation of what would happen 
in a field which we can then use to compare against what we actually see 
okay and so far i've shown that i've got what i would expect is that the log of 
the population will increase in a straight line initially because i have 
exponential growth but of course once disease is really common lots of these 
spores will start to fall on tissue which is already infected yeah is that and 
one way to see what effect we would expect that to have is to say okay imagine 
a field which is half infected half diseased the diseased material produces 
spores or vectors which fall randomly all over the field half of those will 
therefore fall on infected material and won't produce any new disease so the 
rate of increase of the disease will decrease in proportion to the diseased 
fraction of the field as disease becomes if it's increasing exponentially as it 
becomes commoner the rate of that exponential will fall off until when almost 
the whole field is infected almost no spores will be able to cause any new 
disease because they can't find a host so the shape we expect is something 
that starts off exponential and then turns over and a little mathematics which 
might be a dangerous thing but a little mathematics shows that the logarithm of 
the healthy fraction of the diseased fraction over the healthy fraction 
increases smoothly with time that's equation one on your handout so if nothing 
changes in the host- pathogen relation and if spores or vectors are evenly 
distributed over the whole area we expect the logarithm of the diseased 
fraction over the healthy fraction to increase steadily with time okay and 
that's written out in mathematical symbols as equation one and this thing here 
has a name because we use it quite commonly it's called the logit not the log 
but the logit of the diseased fraction okay now what i've done there is just 
argue informally and then if you wish you can see what the formal mathematical 
argument is what should happen if certain conditions hold now 
here is the yellow rust case here's the original data and here it is replotted 
on a new scale in which this is logit of disease okay it doesn't matter what 
the actual numbers work out at to er work out at the important point is that 
it's a straight line 
sm0193: and where course there is er half of the field filled with disease 
nm0191: no no no no sorry that was a that was the easiest case to see here 
there is a very small proportion of the field filled with the disease here 
ninety per cent of it is filled with the disease and just there [laugh] only on 
that one occasion is half filled with disease 
sm0193: yeah i thought about er the log of disease fraction of 
nm0191: divided by the healthy 
sm0193: yes then it's one to one and
nm0191: no if the diseased fraction is let's do some examples if the diseased 
fraction is nought-point-one then this thing is log of nought-point-one divided 
by nought-point-nine 
sm0193: no i thought about er if half of the field is 
nm0191: yes 
sm0193: diseased
nm0191: yes 
sm0193: then we have O-point-five 
nm0191: yes 
sm0193: diseased fraction 
nm0191: yes 
sm0193: and O-point-f O-point-five healthy fraction 
nm0191: yes yes 
sm0193: then we get a log of one 
nm0191: then we get the 
logarithm of one 
sm0193: yes 
nm0191: which is zero 
sm0193: yes and i ask if there is 
nm0191: there it is 
sm0193: yes 
nm0191: so that corresponds to that 
sm0193: yes 
nm0191: yes sorry i i thought you were asking a different question i beg your 
pardon okay so this is this data replotted and we see a straight line okay it 
works for winter barley if you look at the er pictures at the back you'll see 
that it works for Dutch elm disease and if i take the cocoa swollen shoot 
example show it in a slightly different way there's our curve running over a 
period of eight years if we replot on a logit scale but the same time scale 
here's the blue line corresponding to the blue axis a logit scale this bendy 
curve is more or less a straight line not that point is a little bit off at the 
end but basically over this period it runs as a straight line 
sm0194: sorry at the logit er axis er zero is the point that the half of the 
nm0191: yes 
sm0194: plants are infected 
nm0191: yes that's right 
sm0194: okay 
nm0191: and it even works for the phymatotrichum case er if i can get the 
axes to overlap again the time scale stays the same but the disease has been 
replotted on a logit scale and we have a straight line for the first four 
points and then this one at the end which is decreasing here is quite obviously 
not on the curve that actually corresponds then here is where something has 
happened not the sharp increase but at the end something has happened and what 
happened here of course was that when they reached the situation with eighty 
per cent of the cotton infected they did something about it wasn't a terribly 
effective action but it was perhaps even more effective than they realized in 
that without that they'd have probably gone to ninety-five per cent okay so by 
replotting the data you begin to see what's happening cocoa swollen shoot and 
the final one is phytophthora that's puccinia striiformis i th-, this i seem to 
want to lose this one don't i here it is yep potato blight the great classic 
plant disease here we are very different scale of 
epidemic but replotted on a logit scale it's a straight line and not only this 
but we've also now got a way of describing these very diverse diseases in a way 
which makes it possible to compare what is different about them here's 
phytophthora infestans the logit rate of increase i'm sorry this isn't terribly 
distinct owing to having got and that says nought-point-six okay if we go from 
there to there a span of fifty days the change in the logit amount of disease 
is minus-two-point-five to nought-point-six which is three-point-one over fifty 
days so the slope is point-o-six-two per day if we compare that with the 
phymatotrichum the slope on this one is an increase of five logits over four 
years sorry i was blocking that an increase of five logits over four years so 
the rate of increase is one-point-two-five per year far far far slower than the 
potato blight but just the same pattern if we look at the cocoa swollen shoot