by
RoY R. SILEN
EDWARD J. DIMOCK II
ABSTRACT. Data on deer and hare preference for Douglas-fir genotypes in eight pen and two field trials were compared to data generated from a mathematical model. The model predicted sequential preference changes from the products of two probabilities that accounted for a changing availability (P.) and an assumed constant palatability (P,) for each of several, simultaneously tested plant types. In all 10 experiments, data were closely mimicked by the model. In only one experiment did the predicted feeding sequence deviate significantly from actual data. High correlations were achieved among P, values calculated independently for duplicate tests of identical genotypes. Since P, is a mathematical estimate of palatability-itself a qualitative phenomenon-the concept may prove useful for aiding interpretations of other studies expressing animal preference as an integration of plant availability and palatability. FoREST Sci. 24:57-64.
ADDITIONAL KEY WORDS. Availability, clone, cross, Lepus americanus, Odocoileus hemi­ onus columbianus, palatability, Pseudotsuga menziesii.
PROVING PRACTICAL genetic resistance in Douglas-fir (Pseudotsuga menziesii) to damage by snowshoe hare (Lepus americanus) and black-tailed deer (Odocoileus
hemionus columbianus) required testing feeding preference by captive and free­ ranging wild animals for candidate genotypes (Dimock and others 1976). Various measures were used to compare test results, but all had limitations. In seeking better means to quantify animal preference, we derived a simple, mathematical model.
Preference by herbivores for specific plants is usually thought to be a net function of both plant availability and palatability. Though availability can be measured, palatability is not readily quantifiable. For lack of a quantitative expression of palatability, most workers employ a concept of animal preference which lumps availability and palatability into one expression that integrates both variables (Leo­ pold 1933). More specifically, preference is commonly inferred from amounts of forage consumed or frequencies of forage occurrence in animal diets composed of many plant species available in widely varying abundance (Brown 1961, Poelker and Hartwell 1973).
Damage to Douglas-fir seedlings, and particularly to terminal shoots, was the focal point of our preference studies. Hence, first evidence of animal feeding on each test plant was the primary statistic. Though alternative plant choices were equal for each genotype at test beginning, they immediately became unequal as selection by animals proceeded. As there was no plant replacement, abundance of more palatable plants declined during early portions of each trial. Thus ranges of discrimination among genotypes, as reported only by preference measures, may mask wider differences in actual palatability.
The authors are, respectively, principal plant geneticist and principal silviculturist, Pacific
Northwest Forest and Range Experiment Station, Corvallis, Oregon. Manuscript received Sep­ tember 4, 1975, and in revised form November 2, 1977.
VoLuME 24, NuMBER 1, 1978 I 57

Our approach to a model involved quantifying availability and palatability.
Changes in availability can be conveniently quantified by count of uneaten plants of each candidate type for each exposure period of a study. Quantifying palatability could be complex for a plant type because of high genetic or physiological variabil­ ity. As a simplification, we assumed that palatability for a plant type remained constant and in the same relation to other plant types within a given test. Logic for the assumption was based on the use of genetically identical clonal cuttings for six of the tests. Would some assigned palatability value and a measure of changing availability explain a significant portion of the feeding pattern we found in our tests? More fundamentally, could palatability itself be quantified with any degree of confidence? If so, such model principles could well apply to other studies of animal-plant relationships in which plant abundance is measured but not con­ trolled. We feel that our model helps answer these questions. This report shows that a single probability estimate for each genotype could, indeed, be used to quan­ tify its palatability in a rough mathematical sense.
PROCEDURES
In early preference trials, we individually randomized Douglas-fir cuttings from dis­ crete clones or full-sib crosses to simulate seedlings exposed in preference trials to small, mixed-sex groups of either captive deer or hare. In later tests, we randomly exposed seedlings from full-sib crosses by planting on forest sites containing high populations of free-ranging hare. For convenience in presentation, we refer to both cutting and seedling test materials as "plants."
Eight pen and two field experiments described in our previous work served to develop and test the descriptive model:
Test designation, duration, and year
A. 18 days (1967)
B. 7 days ( 1967) c.
15 days ( 1967)
D. 10 days (1967)
E. 7 days ( 1968)
F. 9 days ( 1968)
G. 26 days ( 1970)
H. 15 days ( 1970)
I. 14 weeks (1970-71)
J. 16 weeks (1972-73)
Species and number Number and kind of animals of treatments
Captive deer (5)
Captive hare (8)
Captive deer (6)
Captive hare (7)
Captive deer (8)
Captive hare (12)
Captive deer (6)
Captive hare (10)
Free hare (unltd.)
Free hare (unltd.)
5 clones
5 clones
5 clones
5 clones
5 clones
5 clones
1 clone
+
4 crosses
1 clone
+
4 crosses
4 crosses
4 crosses
Number of plants per treatment
100
100
100
100
144
100
100
100
100
100
Full details of original test designs, layouts, results, and analyses are not germane to development or interpretation of the model, but may be consulted elsewhere
(Dimock and others 1976).
The model is based upon two probabilities arising from simple proportions. The first probability cPa) accounts for periodic (daily or weekly) changes in plant avail­ ability; the second probability (Pp) is an assumed proportional index of plant pal­ atability. Pa for all plant types in any trial is equal at test beginning, but changes periodically for each plant type as the test proceeds. P p, on the other hand, differs for each plant type at test beginning, but remains constant as the trial progresses.
Both Pa and PP values range between 0.00 and 1.00. Also, at any point during a test, sums of Pa values for all plant types-and similarly sums of PP values-must equal 1.00. Starting P a values are fixed by the number of plant types in a given
58 I
FOREST SCIENCE

TABLE 1. A hypothetical damage pattern to illustrate computation method (see text).
Day and plant type
Day 1:
A
B c
D
Total
Day 2:
A
B c
D
Total
Day 3:
A
B c
D
Total
Day 4
Number undamaged at start of day
90
80
70
60
300
100
100
100
100
400
Pa
0.25
0.25
0.25
0.25
1.00
0.30
0.27
0.23
0.20
1.00
Probabilities
P. PaX P.
0.10
0.20
0.30
0.40
1.00
0.10
0.20
0.30
0.40
1.00
0.025
0.050
0.075
0.100
0.250
0.030
0.054
0.069
0.080
0.233
77
57
40
26
200
0.38
0.29
0.20
0.13
1.00
0.10
0.20
0.30
0.40
1.00
All remaining plants damaged.
0.038
0.058
0.060
0.052
0.208
Proportion of day's damage
0.100
0.200
0.300
0.400
1.000
0.129
0.232
0.296
0.343
1.000
0.183
0.279
0.288
0.250
1.000
Cumulative number damaged
Number undamaged at end of day
10
20
30
40
100
41
71
89
99
300
23
43
60
74
200
59
29
11
1
100
77
57
40
26
200
90
80
70
60
300 test-i.e., equal amounts of 3 plant types would each start with Pa's of 0.33, 4 with
0.25, 5 with 0.20, etc. Though assumed PP values remain constant throughout any given test, they are expected to vary from trial to trial. Palatability of a plant type is only relative to palatability of other plant types with which it is associated.
The strategy, then, in modeling requires that the products of Pa and PP values associated with each plant type at any point in time be used to predict animal preference for a succeeding period. The expected number of plants damaged within a given period (E) for the ith plant type is predicted by the product of its two probabilities, divided by the sum of these products for all tested plant types, then multiplied by the total number of plants (N) actually damaged during the period:
., =
(P p).
,. a p l
N
~PaPp t=l
A sample computation in Table 1 illustrates the changing proportions of rela­ tively palatable and unpalatable plant types. The calculation assumes: a test with
100 individually randomized plants in each of 4 plant types (A-D); damage occur­ rence to 100 plantsjday with all plants damaged at end of the 4th day; and Pp values of 0.10, 0.20, 0.30, and 0.40 for plant types A, B, C, and D, respectively.
We derived sets of PP values for different tests by iterative minimal chi-square fits of predicted and actual data according to goodness-of-fit principles outlined by
VoLUME 24, NuMBER 1, 1978 1 59

100
80
60
40
PERCENT DAMAGE
100
80
60
5 CLONES o----o 8
,______.., 13
Y-----111'
15
4 6 8 10 12 14 16 18
DAYS OF EXPOSURE
100
80
60
5 CLONES o----o 8
•·-········• 10
.,... ___..,.
~-~ 17
2 3 4. 5
DAYS OF EXPOSURE
6 7
........··
~····
5 CLONES o--o I
---····• 13
.,.._..., 22 c----a
23
4 6 8 10 12 14
DAYS OF EXPOSURE
100
80
60
PERCENT DAMAGE
100
[j
80
1967
DEER
(penned)
60­
80
1967
HARE
(penned) 40
100
(5
80
1967
DEER
(penned)
60
40
100
~
80
1967
HARE
(penned)
60
2 4 6 8 10 12 14 16 18
DAYS OF EXPOSURE
2 3 4 5 6
DAYS OF EXPOSURE
4 6 8 10 12
DAYS OF EXPOSURE
7
14
,
...
2 4 6 8
DAYS OF EXPOSURE
10 2 4 6 8
DAYS OF EXPOSURE ro
100
80
60
5 CLONES o---o I
............ 13
100
[3
80
1968
DEER
(penned)
60
2 3 4 5 6 7
DAYS OF EXPOSURE
2 3 4 5 6 7
DAYS OF EXPOSURE
FIGURE 1. Cumulative plots of actual (left) and modeled (right) damage sequences from 10 tests of Douglas-fir clones and crosses exposed to deer and hare. Goodness of fit is shown by probability (P) of larger chi-square.
Freese ( 1960). We made preliminary estimates of P v by using mid-test selection index values, defined in previous work as the proportion of each plant type dam­ aged when half the plants in a particular trial had been browsed or clipped. These
Pv's were then repeatedly adjusted until correspondence between predicted and
60 I
FOREST SCIENCE

PERCENT DAMAGE
100
80
60
2
5 CLONES o---<::J I
.......
~ ... 13
6------619
~-•22
D---1:1
23
_,_
3 4 5 6 7 8 9
DAYS OF EXPOSURE
PERCENT DAMAGE
100
IJ
80
1968
60
HARE
40
(penned)
20
P=.41
2 3 4 5 6 7 8 9
DAYS OF EXPOSURE
I CLONE
+
4 CROSSES
C>---<:)
13
............ 10
X
I b:----r:l
19
X]
~-~ 13x2
6 8 ~ Q ~ ~ ~ ~22~
DAYS OF EXPOSURE
~
1970
DEER
(penned)
4o
100
80
60
100
80
60
40
100
80
60
1 CLONE
+
4 CROSSES o---o 22
•·· ....... 19 X 8
~IOxB
Y----..,. 13
X
22 o---a
22
X
I
4 6 8 10 12 14
DAYS OF EXPOSURE
1970
60
HARE
(penned)
4o
............ ·•
4 CROSSES
......... Bx 10 lxB
I X 22
2 4
I
6 8 10 12 14 16 18
WEEKS OF EXPOSURE
100
~
80
1970-71
60
HARE
(field)
100
J)
80
1972-73
60
HARE
40
(field)
40
20
..······ ...·············
__
...
;~:>------~ k~~j'2
4 CROSSES
4 6 8 10 12 14
WEEKS OF EXPOSURE
Continued.
FIGURE
1.
P=.22
6 8 10 12 14 16 18 20 22 24
DAYS OF EXPOSURE
8 10 12 14
EXPOSURE
.......
··
..
2 4 6 8 10 12 14 16 18
WEEKS OF EXPOSURE
4 6 8 10 12 14
WEEKS OF EXPOSURE actual data approached the least pooled chi-square. All analyses of predicted versus actual values were based on periodic, not cumulative, changes. Goodness of fit was indicated by a single chi-square probability value with degrees of freedom equal to total observations less number of plant types and observation periods. Deviations of predicted from actual feeding sequences were considered significant at P < 0.05.
Finally, we compared Pp's in duplicate tests by linear correlation analysis.
VOLUME
24,
NUMBER
1, 1978 I 61

TABLE 2. PP, chi-square, and probability values from 10 tests of Douglas-fir clones and crosses exposed to deer and hare.
Test
A.
B.
1967 Deer (Captive)
1967 Hare (Captive) c.
D.
1967 Deer (Captive)
1967 Hare (Captive)
E.
F.
1968 Deer (Captive)
1968 Hare (Captive)
G. 1970 Deer (Captive)
H. 1970 Hare (Captive)
I. 1970-71 Hare (Free)
J. 1972-73 Hare (Free)
Clone or cross (light face) and P, value (bold face)
8
0.22
.22
1
.22
.18
10
0.23
.24
13
0.14
.16
13
.13
.23
19
.25
.31
.22
.18
13
.14
.20
19
.26
.31
15
0.20
.22
17
0.21
.16
22
.18
.11
23
.22
.17
22
.18
.15
23
.20
.16
13
.61 lOX 1
.14
19Xl
.11
8xl 13X22
.08 .06
22
.so
19X8
.08
10X8 13X22 22X 1
.06 .03 .03
8X10
.40
1X8
.29
1X22 22X 1
.16 .15
19X8
.33
10X8 13 X22 22X 1
.29 .23 .15 x."
26.19
12.93
24.55
23.91
12.60
18.82
26.86
41.21
22.01
9.92
Chi-square df probability
31
10
29
20
10
18
22
20
17
7
0.67
.26
.70
.27
.41
.41
.22
.01
.19
.19
RESULTS AND DISCUSSION
Cumulative plots of data generated from Pa and Pv probabilities strikingly resemble plots of actual data (Fig. 1). Both general trends and minor variations in cumula­ tive damage were quite faithfully portrayed by the model. Nine out of 10 plots of predicted data did not differ significantly from the actual feeding sequences upon which they were based. Typically, the majority of predicted plot sequences closely followed their actual counterparts, and the few that did not varied for only a portion of the actual sequence. The few examples of crossing observed in the cumulative curves is apparently due to experimental error. Fortunately no more than five types were tested together, so that Pv differences were proportionately larger than experi­ mental error. This would obviously become a problem if more types were tested together.
As expected, the model best accommodated results from six tests of clonal parent materials (A-F). Chi-square probabilities ranged from 0.26 to 0.70 (with 10-31 df), and all obviously were fitted by the model (Table 2). Somewhat poorer fits resulted with four tests of full-sib progeny from six of the above clones (tests G-J).
However, only one of these (H) deviated significantly from actual data. In this case (a 1970 hare test), a single clone was included in a test of four crosses. Due to differences in plant ages, fertilizer regimes, and other variables associated with material sources, the clone (by Pv index) was 16 times more palatable than the mean of the four crosses compared against it. Nevertheless, visual correspondence between modeled and actual data is still obvious (Fig. 1). Most deviation in this test was due to variation in short segments of the feeding sequence. Moreover, in a similar trial (G 1970 Deer) in which one clone was six times more palatable than the mean of four associated crosses, the model fit was excellent-both by ocular inspection and goodness-of-fit analysis.
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FoREST SciENCE

Consistency of P v values was found for the same five clones tested against differ­ ent animals of the same species in two different years (tests C and E with deer; tests
D and F with hare) (Table 2). A Pv correlation with r
=
0.96** (3 df) was highly significant for 1967 and 1968 deer tests. This value compared favorably to corre­ sponding correlations 1 with r
=
0.98** and r
=
0.91 * for mean exposure prefer­ ence index (MEPI) and mid-test selection index (MTSI), respectively-measures of preference used in previous analyses (Dimock and others 1976). Likewise, for
1967 and 1968 hare tests, a Pv correlation with r
=
0.94* (3 df) again compared well to correlations with r
=
0.92* and r
=
0.90* for MEPI and MTSI, respectively.
A like comparison was made between the four crosses employed in the 1970 test with captive hare (H) and the same crosses exposed to free-ranging hare in
1972-73 (J). A nonsignificant Pv correlation was obtained in this case (r
=
0.76 with 2 df), which compared to a correlation by MTSI (r
=
0.90) that was also nonsignificant.
As in prior work with preference indices, we found generally poor Pv correlations between deer and hare acting on the same clones tested separately in 1967 and 1968
-even though we had intentionally selected clones for maximum preference agree­ ment between species of test animal. Use of P v values in such correlations did not improve them, and all were nonsignificant at 3 df:
Tests
1967 (C vs. D)
1968 (E vs. F)
Pv
0.30
Correlation coefficients (r)
MEPI
0.31
MTSI
0.23
0.62 0.58 0.50
Though above correlations were poor, Pv values and preference indices gave results that were much alike.
Similar correlations obtained with Pv values and preference indices suggest that probability estimates of plant palatability can be realistic in controlled experiments involving clones or full-sib families. For comparing actual quality differences such estimates may be superior to preference measures confounded by availability changes. We encountered both narrow and wide ranges of animal preference in our
10 tests. The model was sufficiently sensitive to accommodate both, and left little unexplained variation beyond random experimental error. Duplicate tests in suc­ cessive years fitted the model especially well, and palatability values proved to be highly correlated. Tests using clonal materials of identical genotype optimized model fit. However, added genetic variation within full-sib families caused unex­ pectedly little reduction in model reliability applied to either captive animals in short tests or free-ranging animals in long ones. No tests were conducted with open­ pollinated families.
Among closely related plants, such as those compared in our tests, palatability changes that do occur probably parallel one another and affect model fit only slightly. Among more diverse forage complexes, palatability changes within seasonal plants-particularly over long time periods-would almost certainly violate the constant palatability assumed in modeling. However a more complex model may also accommodate such changes.
CONCLUSIONS
Principles underlying the model could prove useful to others studying animal feed­
'*=P<0.05; **=P<O.Ol.
VOLUME 24, NUMBER 1, 1978 I 63

ing preference as a function of forage quality and abundance. Best potential for application lies in improving quantification of palatability differences among known amounts of similar forage plants. Our studies dealing with tree resistance to animal damage as a result of discriminant feeding were well suited to modeling. The simple model accommodated a relatively wide range of differences in animal preference, and limits to model application appear broader than those encountered. We can only speculate how generally an assumption of constant palatability will apply. That it applied as well as it did to examples described in our work is notable.
LITERATURE CITED
BROWN, ELLSWORTH READE. 1961. The black-tailed deer of Washington. Wash State Game
Dep, Bioi Bull 13, 124 p.
DIMOCK, EDWARD J. II, RoY R. SILEN, and VIRGIL E. ALLEN. 1976. Genetic resistance in
Douglas-fir to damage by snowshoe hare and black-tailed deer. Forest Sci 22:106-121.
FREESE, FRANK. 1960. Testing accuracy. Forest Sci 6:139-145.
LEOPOLD, ALoo. 1933. Game management. Charles Scribner's Sons, New York. 481 p.
POELKER, RICHARD J., and HARRY D. HARTWELL. 1973. Black bear of Washington. Wash
State Game Dep, Bioi Bull 14, 180 p.
Physiological Plant Pathology
Encyclopedia of Plant Physiology, New Series Volume 4
Edited by R. Heitefuss and P. H. Williams. 1976. Springer-Verlag, Berlin, Heidel­ berg, New York. 890 p. $79.60.
Reviewed by Louis Shain
Department of Plant Pathology, University of Kentucky, Lexington, Kentucky
40506
The physiology and biochemistry of the disease process are receiving increased attention by plant and forest scientists. This reflects the attitude that an understanding of the com­ plex relationship between host and pathogen at the tissue, cell, and molecular level will increase the chances of reducing disease losses to tolerable levels by means that are economically feasible and ecologically acceptable.
Several textbooks and recently published symposia are available on many aspects of this subject. Many of the journal articles now appearing in phytopathological literature could be considered under the general heading of "physiological plant pathology." Indeed this title has already been used for a textbook (Wood 1967) and a quarterly journal now in its seventh year.
This volume, consequently, does not fill an obvious void. Several of the authors have contributed similar chapters to other volumes published within the past 2-3 years. The present volume, however, provides good balance and a more comprehensive coverage than most texts and symposia proceedings published in the recent past.
The volume is divided into eight sections. Section 1, entitled "General," consists of chapters by Fuchs on history and by Daly on general aspects of host-pathogen inter­ actions. Daly's advocacy and evidence for the concept of "induced susceptibility" in con­ trast to the widely held concept of "induced resistance" is of particular interest in these introductory chapters.
Spore germination and its regulation are considered in Section 2. Allen's chapter is on self inhibition and stimulation as well as formation of infection structures, particularly in rust fungi. Staples and Yaniv have a chapter on nucleic acid metabolism during germina­ tion. Mitchell's chapter on the effect of roots on the activity of soil-borne pathogens should be of interest to forest scientists who are working on root diseases.
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FoREST SciENCE